resources/fib... · subject to priorities defined by the technical council and the presidium, the...

This document is the intellectual property of the fib – International Federation for Structural Concrete. All rights reserved. This PDF of fib Bulletin 58 is intended for use and/or distribution solely within fib National Member Groups.

Design of anchorages

in concrete

Guide to good practice prepared by

fib Special Activity Group 4

July 2011


Subject to priorities defined by the Technical Council and the Presidium, the results of fib’s work in

Commissions and Task Groups are published in a continuously numbered series of technical publications

called 'Bulletins'. The following categories are used:

category minimum approval procedure required prior to publication

Technical Report approved by a Task Group and the Chairpersons of the Commission

State-of-Art Report approved by a Commission

Manual, Guide (to good practice)

or Recommendation approved by the Technical Council of fib

Model Code approved by the General Assembly of fib

Any publication not having met the above requirements will be clearly identified as preliminary draft.

This Bulletin N° 58 was approved as a “Guide to good practice” by the Technical Council of fib in June 2011.

This Guide was drafted by Special Activity Group 4, Fastenings to structural concrete and masonry

structures.

Rolf Eligehausen (Convener)

Akiyama (Tokyo Soil Research, Japan), Asmus (IEA, Germany), Barthomeuf (SPIT, France),

Bergmeister (Universität für Bodenkultur, Austria), Cook (Univ. of Florida, USA), Elfgren (Luleå Univ. of

Technology, Sweden), Fletcher (Australia), Genesio (Univ. Stuttgart, Germany), Grosser (Univ. Stuttgart,

Germany), Hoehler (Hilti, Liechtenstein), Hofmann (Univ. Stuttgart, Germany), Klingner (Univ. of Texas,

Hordjik (Adviesbureau, The Netherlands), USA), Hosokawa (Univ. of Tokyo, Japan), Kuhn (Adolf Würth,

Germany), Lange (DIBt, Germany), Li (fischerwerke, Germany), Lotze (MPA Stuttgart, Germany), Mallée

(Germany), Matsuzaki (Science Univ. of Tokyo, Japan), Mattis (CEL Consulting, USA), Mesureur (CSTB,

France), Michler (Techn. Univ. Dresden, Germany), Nakano (Tokyo Univ., Japan), Olsen (Powers, USA),

Rieder (BBT, Austria), Roik (Halfen, Germany), Rutz (MKT, Germany), Silva (Hilti, USA), Sippel

(VBBF, Germany), Spieth (fischerwerke, Germany), Stochlia (ICC-ES, USA), Turley (Simpson Strong Tie,

USA), Vintzileou (National Technical Univ. Athens, Greece), Wall (Hilti, Liechtenstein), Wollmershauser

(USA), Yamamoto (Shibaura Institute of Technology, Japan), Ziegler (Powers, USA)

The complete list of members and corresponding members who have contributed to this Design Guide over the

years is given on pages iv-v.

Left cover photo: Anchorage of the column of a timber bridge (Courtesy of Institute of Construction Materials,

University of Stuttgart)

Right cover photo: Anchorage of a pipe (Courtesy of Hilti North America)

© fédération internationale du béton (fib), 2011

Although the International Federation for Structural Concrete fib – fédération internationale du béton – does its

best to ensure that any information given is accurate, no liability or responsibility of any kind (including liability

for negligence) is accepted in this respect by the organisation, its members, servants or agents. All rights reserved. No part of this publication may be reproduced, modified, translated, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without prior written permission. First published in 2011 by the International Federation for Structural Concrete (fib) Postal address: Case Postale 88, CH-1015 Lausanne, Switzerland Street address: Federal Institute of Technology Lausanne – EPFL, Section Génie Civil Tel +41 21 693 2747 • Fax +41 21 693 6245 [email protected] • www.fib-international.org

ISSN 1562-3610

ISBN 978-2-88394-098-7

Printed by DCC Document Competence Center Siegmar Kästl e.K., Germany


fib Bulletin 58: Design of anchorages in concrete iii

Preface

Modern fastening technique is employed extensively for the transfer of concentrated loads into

concrete and masonry structures. Cast-in-place anchors, placed in the formwork before casting of the

concrete, and post-installed systems, which are installed in hardened structural concrete or masonry,

are equally common. Loads are transferred into the concrete or masonry by mechanical interlock,

friction, bond or a combination of these mechanisms. However, independent of the load-transfer

mechanism, all anchorages rely on the tensile strength of the concrete or masonry, a fact which must

be taken into account in both assessment and design.

Despite the widespread use of cast-in-place and post-installed anchors in construction, the overall level

of understanding in the engineering community regarding their behaviour remains quite limited.

In order to improve the general state of knowledge in this field, Task Group III/5: “Fastenings to

reinforced concrete and masonry structures” was formed within the Comité Euro-International du

Béton (CEB) in 1987.

In 1996 the group published the CEB design guide “Design of Fastenings in Concrete”. It covered

expansion, undercut and headed anchors in concrete under predominately static loading, and has been

a widely-referenced resource document for code development in this area.

Following the transformation of the CEB into the International Federation for Structural Concrete (fib)

in 1998, the group was re-named as Special Activity Group (SAG) 4 “Fastenings to Structural

Concrete and Masonry Structures”.

Since the publication of the original CEB guide ongoing research and additional application

experience has led to an improved understanding and deepened knowledge in various areas of

fastening technology.

This publication “Design of Anchorages in Concrete” represents a substantial revision of the original

1996 design guide. It addresses a variety of loading types and failure modes and takes into account the

current state of the art for anchorages in new construction as well as for their use in the repair and

strengthening of existing concrete structures. The following significant additions and revisions are

incorporated in this document:

a new section on the design of bonded anchors and connections with post-installed

reinforcing bars;

a new section addressing the design of anchor channels;

a new section on the design of anchorages for fire;

a new section on the design of anchorages under earthquake loading;

inclusion of detailed design provisions for anchorages subjected to fatigue loading;

significantly improved design provisions for the critical case of shear-loaded anchorages

close to edges; and

improved design provisions for combined tension and shear loading.

Among other topics, the group continues to investigate design provisions for shear lugs; this work will

be included in a future edition.

Rolf Eligehausen

Chairman, SAG 4

“Fastenings to Structural Concrete

and Masonry Structures”

Stuttgart, November 2010


iv fib Bulletin 58: Design of anchorages in concrete

Acknowledgments

This document was drafted by the fib Special Activity Group 4 “Fastenings to Structural Concrete

and Masonry Structures”.

Convenor: Rolf Eligehausen Germany

Technical Secretary: John Silva USA

Members: Tomoaki Akiyama Japan

Jörg Asmus (since 2007) Germany

Jean-Paul Barthomeuf (since 2005) France

Konrad Bergmeister Austria

Didier Bourette (from 1987 to 2004) France

Ronald Cook USA

Vicky Covert (from 1987 to 2005) USA

Lennart Elfgren Sweden

Georg Feistel (from 2006 to 2008) Germany

Giovacchino Genesio (since 2006) Germany

Philipp Grosser (since 2007) Germany

Matthew Hoehler (since 2006) USA

Jan Hofmann (since 2009) Germany

Paul Hollenbach (from 1987 to 2000) USA

Dick Hordijk (from 1987 to 2000) The Netherlands

Hiroshi Kimura (from 1987 to 2001) (deceased) Japan

Richard Klingner (from 1987 to 2002) USA

Gerhart Lange (since 2008) Germany

Klaus Laternser (from 1987 to 2006) Germany

Longfei Li (since 2001) Germany

Dieter Lotze (since 1996) Germany

Rainer Mallée (since 2000) Germany

Yasuhiro Matsuzaki Japan

Lee Mattis USA

Bruno Mesureur France

Yoshiaki Nakano (from 1987 to 2001) Japan

Peter Pusill-Wachtsmuth (from 1987 to 2007) Liechtenstein

Matthias Roik (since 2007) Germany

Isabelle Simons (from 2007 to 2009) Germany

Hannes Spieth (since 2001) Germany

Kurt Stochlia (since 2001) USA

Johann Tschositsch (from 1987 to 1999) Germany

J. Bret Turley (from 1998 to 2007) USA

Elizabeth Vintzileou Greece

Friedrich Wall (since 2007) Liechtenstein

Harry Wiewel (from 1987 to 2002) USA

Richard Wollmershauser USA

Yasutoshi Yamamoto (since 2001) Japan

Corresponding Members: Jörg Appl (from 2004 to 2007) Germany

Emmanuel David (from 2005 to 2008) France

Geoff Fletcher (since 2006) Australia

Brian Gerber (since 2003) USA

Thierry Guillet (since 2009) France

Yuriko Hattori (from 2001 to 2008) Japan

Jan Hofmann (from 2003 to 2004) Germany


fib Bulletin 58: Design of anchorages in concrete v

Andra Hörmann-Gast (since 2007) Germany/USA

Youji Hosokawa (since 1999) Japan

Kiyoshi Imai (from 2001 to 2005) Japan

Taichi Katagiri (from 1998 to 2001) Japan

Kimihito Kimura (from 1987 to 2004) Japan

Joseph Kraus (from 1999 to 2001) Germany

Bernhard Lehr (from 2001 to 2002) Germany

Harald Michler (since 2001) Germany

Katsuhiko Nakano (since 2005) Japan

Eichi Nishizono (from 1987 to 2004) Japan

Jake Olsen (since 2008) USA

Goran Periškić (from 2007 to 2009) Germany

Anton Rieder (since 2007) Austria

Thomas Sippel (since 2010) Germany

Reiji Tanaka (from 1987 to 2007) Japan

Xuekang Tao (from 1999 to 2002) China

Rüdiger Tewes Switzerland

Mark Ziegler (since 2009) USA

The final draft of this document was prepared in Stuttgart by an Editorial Board:

Convenor: Rolf Eligehausen Germany

Members: Giovacchino Genesio Germany

Philipp Grosser (since 2007) Germany

Rainer Mallée Germany

Peter Pusill-Wachtsmuth (until 2007) Liechtenstein

John Silva USA

Elizabeth Vintzileou (until 2007) Greece

Friedrich Wall (since 2007) Liechtenstein


vi fib Bulletin 58: Design of anchorages in concrete

Contents

Preface iii

0 Introduction x

Part I - General provisions

1 Scope 1

1.1 General 1

1.2 Permissible anchor type and anchorage configurations 1

1.3 Prequalification and quality control requirements for products 9

1.4 Permissible anchor dimensions and materials 10

1.5 Permissible anchor loading 11

1.6 Permissible concrete strength 15

1.7 Permissible loading of the concrete members 15

1.8 Reliability classes 16

2 Terminology 21

2.1 Definitions 21

2.2 Indices (subscripts/superscripts) 26

2.3 Actions and resistances 28

2.4 Concrete and steel 31

2.5 Notation – dimensional 32

2.6 Greek symbols 35

2.7 Units 35

3 Basis of design 36

3.1 General 36

3.2 Required verifications 37

3.3 Design format 42

3.4 Partial factors 44

3.4.1 Partial factors for actions 44

3.4.2 Partial factors for resistance 45

3.5 Project specifications and anchor installation 48

3.5.1 Project specification 48

3.5.2 Installation 49

4 Determination of action effects 52

4.1 General 52

4.2 Effect of friction 52

4.3 Ultimate limit state 55

4.3.1 Elastic analysis 55

4.3.2 Plastic analysis 96

4.4 Serviceability limit state and fatigue 102

4.5 Seismic loading 102

5 Determination of concrete condition 102

6 Verification of limit states 103

6.1 Ultimate limit state 103

6.2 Serviceability limit state 104

6.3 Fatigue 105

6.4 Verification for load combinations including seismic actions 111

6.5 Fire 116

6.5.1 General 116

6.5.2 Partial factors 116

6.5.3 Resistance under fire exposure 117


fib Bulletin 58: Design of anchorages in concrete vii

7 Durability 122

8 Provisions for ensuring the characteristic resistance of the concrete

member 124

8.1 General 124

8.2 Shear resistance of concrete member 124

8.3 Resistance to splitting forces 128

Part II - Characteristic resistance of anchorages with post-installed expansion anchors,

undercut anchors, screw anchors and torque-controlled bonded expansion anchors

9 Scope 130

10 Ultimate limit state – elastic design approach 136

10.1 Resistance to tension load 136

10.1.1 Required verifications 136

10.1.2 Steel failure 137

10.1.3 Pullout failure 137

10.1.4 Concrete cone failure 137

10.1.5 Splitting failure 143

10.2 Resistance to shear load 145




10.2.4 Concrete pryout failure 148

10.2.5 Concrete edge failure 149

10.3 Resistance to combined tension and shear load 163

10.3.1 Anchorages far from edges, anchorages close to edges with shear resisted

by front anchors 163

10.3.2 Anchorages close to edges with shear resisted by the back anchors 165

10.3.3 Anchorages loaded by a tension load and a shear load with lever arm 167

11 Ultimate limit state – plastic design approach 168

11.1 Field of application 168

11.2 Resistance to tension load 168



11.2.3 Concrete cone failure 169

11.2.4 Splitting failure 169

11.3 Resistance to shear load 169



11.3.3 Concrete pryout failure 170

11.3.4 Concrete edge failure 171

11.4 Resistance to combined tension and shear load 171

12 Serviceability limit state 171

13 Fatigue loading 172

14 Seismic loading 172


viii fib Bulletin 58: Design of anchorages in concrete

Part III - Characteristic resistance of anchorages with bonded anchors and connections with

post-installed reinforcing bars

15 General 173

16 Anchorages with bonded anchors 176

16.1 Scope 176

16.2 Ultimate limit state – elastic design approach 181

16.2.1 Resistance to tension load 181

16.2.2 Resistance to shear load 187

16.2.3 Resistance to combined tension and shear load 188

16.3 Ultimate limit state – plastic design approach 188

16.4 Serviceability limit state 189

16.5 Fatigue 189

16.6 Seismic loading 189

17 Connections with post-installed reinforcing bars 189

17.1 Scope 189

17.2 Prequalification testing 190

17.3 Design 192

17.3.1 General 192

17.3.2 Dimensioning of the connection 193

17.4 Design for fire 194

17.5 Installation and job site quality control 195

Part IV - Characteristic resistance of anchorages with cast-in headed anchors

18 Scope 196

19 Ultimate limit state - elastic design approach 202

19.1 Anchorages without anchor reinforcement 202


19.1.2 Resistance to shear load 208

19.2 Anchorages with anchor reinforcement 209


19.2.2 Resistance to shear loads 214

19.2.3 Resistance to combined tension and shear loads 220

20 Ultimate limit state - plastic design approach 221




Part V - Characteristic resistance of anchorages with cast-in anchor channels

24 Scope 225

25 Determination of action effects 230

25.1 Derivation of forces acting on anchors of anchor channels 230

25.1.1 General 230

25.1.2 Tension loads 230

25.1.3 Shear loads 232

26 Ultimate limit state - elastic design approach 232

26.1 Anchor channels without anchor reinforcement 232

26.1.1 Resistance to tension loads 232

26.1.2 Resistance to shear loads 241

26.1.3 Resistance to combined tension and shear load 248


fib Bulletin 58: Design of anchorages in concrete ix

26.2 Anchor channels with anchor reinforcement 250


26.2.2 Resistance to shear failure 252

26.2.3 Resistance to combined tension and shear loads 254




References 257


0 Introduction x

0. Introduction Anchorages are commonly used to transfer loads into concrete

structures or to connect concrete elements.

As illustrated in Figure 0-1, in general a connection (anchorage) to

concrete is composed of the following basic components:

– a fixture that in connection with the attachment distributes loads to

the anchors;

– the anchors which attach the fixture to the concrete; and

– the base material, consisting of the concrete surrounding each

anchor.

In some special cases the attachment may be anchored directly to the

concrete, i.e., without a common fixture.

Figure 0-1: Basic anchorage nomenclature

This Design Guide covers anchorages to concrete. The concrete may be

assumed to crack during the service life of the anchorage or remain uncracked.

The structure that is anchored may be either statically determinate or statically

indeterminate. An anchorage (support) may consist of one anchor or a group of

anchors.

This Design Guide provides a method for the design of the anchorage and

additional rules for the design of the concrete member to which the load is

transferred. The provisions are based on the available research. The design of

the fixture must be performed according to the relevant code of practice for the

fixture material.

The design methods provide an adequate level of safety for the given

application conditions. The legal aspects of how these design rules are

implemented in codes is beyond the scope of this document. However,

throughout the Design Guide it is made clear where for proprietary products

specific design resistances/parameters are required, the values given in the

relevant Approval are decisive. There is an inherent assumption in this directive

that Approval guidelines provide conservative recommendations. Although

manufacturer recommendations may also be valid, no judgment regarding the

adequacy of manufacturer recommendations for design is provided.

This Design Guide is applicable provided that the following conditions are met:

– the anchorages are designed by qualified and experienced personnel;

– the installation is performed by personnel having the required skill and

experience;

– the structure is adequately maintained during its intended service life; and

– the specified use of the anchorage is not changed in a manner that

imposes more severe requirements on the anchors during their intended

service life, unless redesign is carried out to verify their suitability for the

new use.

The anchorages should be fully described in the construction documents.

The minimum required information that should be provided is described in

Section 3.5.1.


fib Bulletin 58: Design of anchorages in concrete xi

This Design Guide is subdivided into five parts:

Part I : General provisions

Part II : Characteristic resistance of anchorages with post-installed

expansion anchors, undercut anchors, screw anchors and

torque-controlled bonded expansion anchors

Part III : Characteristic resistance of anchorages with bonded anchors

and connections with post-installed reinforcing bars

Part IV : Characteristic resistance of anchorages with cast-in headed

anchors

Part V : Characteristic resistance of anchorages with cast-in anchor

channels

The design method given in this Design Guide is based on the safety

concept adopted by the CEB-FIP Model Code 1990 (CEB, 1993). This

safety concept is suitable for statically determinate systems, i.e., where

failure of a single anchorage will result in failure of the entire system. It is

also valid for statically indeterminate systems, e.g., continuous beam

elements, distributed piping systems and ceiling support structures. It takes

into account the current state of knowledge.

The attachment usually consists of a structural steel element, and often

includes a fixture (baseplate). However, attachments may also be made of

timber, structural concrete or other structural materials.

While Part I gives rules that are valid for all types of anchors, Parts II to V

contain provisions that are valid for specific types of anchors. A flowchart for

the design of anchorages is given in Figure 0-3. Flowcharts for calculating the

resistance of specific types of anchorages are given in the respective part of this

Design Guide.

The right side of each page contains design provisions. The left side provides

commentary to these provisions.

This Design Guide replaces the CEB document “Design of Fastenings in

Concrete” published in 1997 (CEB, 1997).

a1) a2) b)

Figure 0-2: Examples of anchored components: a1) and

a2) statically determinate; b) statically indeterminate


0 Introduction xii

Start

Calculate design

actions on anchors

NSd, VSd

Elastic design

see flowchart B

in respective Part

Sd Rd

Fastener prequalification

demonstrate suitability in cracked and/or

uncracked concrete (Section 1.3)

Characteristic actions

on fixture (Section 4)

Plastic design

see flowchart C

in respective Part

Design actions

on fixture (Section 4)

Calculate design actions

on anchors (Section 4)

Elastic analysis

(Section 4.3.1)

Plastic analysis

(Section 4.3.2)

Calculate design

actions on anchors

NSd, VSd

Calculate design

resistance

NRd, VRd

Serviceability

limit state

NSd NRd

Calculate design

resistance

NRd, VRd

Fatigue

Seismic

End

Evaluate state of concrete

(cracked or uncracked) (Section 5)

Fire

(Section 6.5)

Ensuring char. resistance of

concrete member (Section 8)

VSd VRd

Interaction equation

Sd Rd

Durability

(Section 7)

Figure 0-3: Flowchart A for the design of anchorages


fib Bulletin 58: Design of anchorages in concrete 1

PART I: GENERAL PROVISIONS

1 Scope 1.1 General

The provisions of the Design Guide are addressed to connections

involving the transmission of loads within the primary load-resisting frame

of a structure. They are equally applicable, however, to the attachment of

elements such as façades, piping, etc., often referred to as non-structural

components, and to temporary anchorages, e.g., for lifting precast elements

or securing site equipment such as scaffolding and barriers.

The limiting criteria given here (collapse prevention, health and life

preservation, economic protection) should be used as a guideline in

determining the scope of application. In all cases, it is assumed that the

anchorage design will be carried out by a design professional competent in

the field of reinforced concrete.

This Design Guide provides requirements for the design of anchorages

used to transmit loads to concrete. It is intended for applications in which the

failure of the anchorage could:

– result in collapse or partial collapse of the structure, or

– cause injury or risk to human life, or

– have significant economic, social or environmental consequences.

The applications may be structural or non-structural in nature; that is, the

connected elements may be part of the primary structural system or may

consist of appurtenances such as guardrails, façade elements or mechanical

components.

This Design Guide is applicable to permanent anchorages in both new and

existing structures. It may, however, also be applied to the design of

temporary anchorages.

The design of the attachment (component, fixture, baseplate) is not

addressed by the Design Guide, except where it may affect the distribution of

loads to the anchors.

This Design Guide does not cover the design of the fixture (baseplate) or

attached component (see Figure 0-1). The design of these elements should be

carried out in accordance with applicable Standards. Requirements on the

stiffness and ductility of the baseplate and/or attachment to ensure that the

relevant assumptions for load distribution are met are given in Sections 4.3.1,

4.3.2 and 6.4.

1.2 Permissible anchor type and anchorage

configurations

Examples of anchor types covered by this Design Guide are given in

Figure 1.2-1 to Figure 1.2-7. In these figures the predominant load transfer

mechanism of the different anchor types is indicated.

This Design Guide addresses the following anchor types: post-installed

anchors (expansion anchors, undercut anchors, screw anchors, bonded

anchors, torque-controlled bonded expansion anchors) and cast-in anchors

(headed anchors and anchor channels). Furthermore, guidance is provided for

the design of post-installed reinforcing bars.


Part I: 1 Scope 2

The installation, load-transfer mechanisms and behaviour in cracked and

uncracked concrete of the different types of anchors are described in detail in

CEB (1994) and Eligehausen et al. (2006-2).

a) b)

Figure 1.2-1: Typical torque-controlled expansion anchors:

a) single-cone sleeve type; b) bolt or wedge type

Figure 1.2-2: Typical deformation-controlled expansion anchor:

‘drop-in anchor’



a) b)

c) d)

e)

Figure 1.2-3: Typical undercut anchors: a) reversed undercut; b) to

d) forward undercut; e) other interlocking system. a),

b) and e): undercut formed before anchor installation;

c) and d): undercut formed during anchor installation


Part I: 1 Scope 4

Figure 1.2-4: Typical screw anchor

a) b)

Figure 1.2-5: Typical bonded anchors: a) bonded anchor with all-

thread rod; b) torque-controlled bonded expansion

anchor



a) b) c) d)

Figure 1.2-6: Typical headed anchors: a) headed bolt; b) embed

plate with welded headed stud (embed plate placed in

formwork); c) cast-in headed anchor with internal

thread; d) anchor rod with bearing plate

a) b)

Figure 1.2-7: Typical anchor channels: a) anchor welded to channel

bar; b) components of an anchor channel

The description of the behaviour of anchor groups in the Design Guide is

predicated on the assumption that all anchors in the group exhibit roughly the

same stiffness. This is most easily verified if the anchors are all of the same

type, diameter and embedment. Note, that the characteristic spacings for the

various failure modes may be different (see Parts II to V).

This Design Guide covers the design of single anchors and anchor groups.

For the purpose of this Design Guide, anchor groups are assumed to be joined

by a common structural element capable of distributing loads to the individual

anchors of the group and the anchors spacing does not exceed the

characteristic spacing for the failure mode under investigation. In addition, all

anchors in a group are assumed to be of the same type, size and embedment.


Part I: 1 Scope 6

Because the Design Guide makes certain assumptions with regards to load

distribution and the behaviour of anchor groups, it does not directly address

cases where interaction could occur between individual anchors not

connected by a common attachment and/or fixture (Figure 1.2-8) and

between anchor groups (Figure 1.2-9 and Figure 1.2-10). It may be assumed

that interaction between individual anchors loaded in tension and tension-

loaded anchor groups is precluded if the spacing between the outer anchors

of adjoining tension-loaded groups or the distance between adjacent single

anchors loaded in tension is not less than the minimum of the following:

– the characteristic spacing for concrete cone failure (combined pullout

and concrete cone failure for bonded anchors) and splitting failure;

– the characteristic spacing for concrete cone failure (combined pullout

and concrete cone failure for bonded anchors) and splitting failure

based on a reduced embedment required to resist the applied tension

(Figure 1.2-9b).

These requirements are also valid for single anchors or anchor groups

loaded in shear with sufficient edge distance to preclude concrete edge

failure.

In the case of single anchors and anchor groups close to the edge loaded

in shear it may be assumed that interaction is precluded if the spacing

between the outer anchors of adjoining groups or between adjacent single

anchors is not less than three times the minimum of the following:

– the actual edge distance (Figure 1.2-10a);

– the edge distance corresponding to full utilization of the anchor steel

capacity; and

– the reduced edge distance required to resist the applied shear (Figure

1.2-10b).

When evaluating the reduced embedment depth and/or reduced edge

distance of adjacent single anchor groups loaded by combined tension and

shear loads, interaction of tension and shear loads should be taken into

account.

Where interaction between individual anchors or neighbouring anchors

groups not connected by a common fixture may occur (Figure 1.2-8, Figure

The methods described in this Design Guide assume that single anchors not

connected by a common structural element and anchor groups are spaced

sufficiently to preclude interaction.



1.2-9 and Figure 1.2-10a), engineering judgement is required to adapt the

rules given in this Design Guide to the specific geometry and loading in

question.

Figure 1.2-8: Example of an anchor configuration not directly

addressed by this Design Guide – closely spaced

single anchors with unequal loads (it is assumed that

the critical distance is controlled by concrete cone

failure)


Part I: 1 Scope 8

a)

b)

Figure 1.2-9: a) Example of an anchor configuration not directly

addressed by this Design Guide – adjacent anchor

groups loaded in tension; b) method of assessment to

avoid interaction of neighboring anchor groups. This

approach is valid if the anchorages with the reduced

embedment depth '

efh can safely transfer the design

tension loads into the concrete member (it is assumed

that the critical distance is controlled by concrete cone

failure)



a) b)

Figure 1.2-10: Example for the assessment of adjacent shear-loaded

anchor groups for applicability of the Design Guide:

a) actual anchorage configuration; b) anchorages

with reduced edge distance '

1c to avoid interaction.

This approach is valid if the anchorages with the

reduced edge distance '

1c can safely transfer the

design shear loads into the concrete member (it is

assumed that the critical distance is controlled by

concrete edge failure)

1.3 Prequalification and quality control

requirements for products

Prequalification procedures may differ from country to country. At

present, prequalification procedures that produce design data compatible with

this Design Guide are included in:

– European Technical Approval Guideline ETAG 001 (EOTA, 1997),

associated Technical Reports (EOTA, 2003-1) and Common

Understanding of Assessment Procedures (CUAP) (EOTA, 2003-2 and

EOTA, 2004-1) issued by the European Organisation for Technical

Approvals (EOTA);

– Acceptance Criteria AC193 (ICC-ES, 2010-1 and AC308 (ICC-ES,

2009) issued by the ICC Evaluation Service (ICC-ES);

– ACI Standard 355.2 (ACI 355.2, 2007) issued by the American

Concrete Institute (ACI).

This Design Guide is valid only for anchor products prequalified for the

intended use whereby the manufacturer of the product is subject to a quality

control system. The prequalification procedure should yield design data

applicable to the design method provided in this document.


Part I: 1 Scope 10

Reports on prequalified anchors issued under ETAG 001 are referred to as

European Technical Approvals (ETAs). Similarly, reports issued under

AC193 or AC308 are referred to as Evaluation Service Reports (ESRs). In

the following text these and other such documents are generically referred to

as Approvals. Note, however, that ESRs are actually recommendations used

by the authority having jurisdiction to help verify code compliance.

Other nationally-based prequalification procedures may be established.

When products are prequalified in accordance with alternative criteria,

verification of the conformance of such criteria with the requirements set by

this Design Guide should be performed on a case by case basis.

The required quality control system for the manufacture of the product is

typically linked to the Approval and may vary regionally.

1.4 Permissible anchor dimensions and

materials

The minimum embedment depth of 40 mm is based on the following

considerations:

– in general, anchors should not be placed so that transfer of tension

loads takes place within the cover layer of concrete. The quality of the

cover concrete may vary considerably, depending on the reinforcement

density, casting direction and method of consolidation. Cover concrete

may also be subjected to spalling under adverse conditions (corrosion

of reinforcing, structure overload, etc.);

– consider the flexural member shown in Figure 1.4-1. To reduce the

degree of superposition of anchorage and bond stresses in the concrete,

it is preferable that the load-transfer zone of the tension-loaded

anchors be positioned beyond the innermost flexural reinforcement

layer as shown. As a minimum the load-transfer zone should extend

beyond the outermost layer of principal reinforcement.

Consideration of typical cover requirements and reinforcement

configurations leads to a minimum embedment depth of 40 mm. Approvals

may define embedment depths less than 40 mm on the basis of product-

specific testing and restrictions on use. Lesser embedment depths may also

be appropriate if increased factors of safety are applied.

This Design Guide applies to anchors with a minimum thread size of 6 mm

(M6) or an equivalent cross-section. In general, the minimum embedment

depth is taken as 40 mm.

This Design Guide covers metal anchors made of carbon steel (ISO 898-2

(ISO, 1992)) or stainless steel (ISO 3506-1 (ISO, 2009-2) and ISO 3506-2,

ISO, 2009-3)). The surface of the steel may be coated or uncoated. The

anchors may include non-load bearing material, e.g., plastic parts. This

Design Guide is valid for anchors with a nominal steel tensile strength,

fuk ≤ 1000 MPa.

The bonding material of bonded anchors may be made primarily of resin,

cement or a combination of the two. In addition, fillers and additives may be

used. The grout used for bonded anchors may consist of organic or inorganic

compounds used separately or in combination.

The viscosity of the flowable bonding material or grout should be adequate

to ensure correct placement (i.e., minimization of voids) considering:

– drilled hole diameter and depth;

– ratio of anchor element diameter to hole diameter (annular gap); and

– installation conditions (ambient and concrete temperatures and

installation direction (downwards, horizontal or upwards)).



Figure 1.4-1: Example of an anchorage where the load-transfer

area is beyond the innermost layer of reinforcement

Anchors may be produced from other materials than mentioned in Section

1.4, if these materials are shown to perform adequately. The limit on nominal

tensile strength is intended to avoid the use of less ductile materials. Steel

with strength fuk > 1000 MPa or hardened steel may be sensitive to stress

corrosion or hydrogen embrittlement. The suitability of these steels for the

intended application should be assessed by prequalification tests (see Section

1.3). Concrete screws may include locally hardened steel (e.g., in the threads)

that exceeds 1000 MPa. The potential for hydrogen embrittlement or

corrosion is checked in the appropriate suitability tests for the Approval (see

EOTA, 1997; ICC-ES, 2010-1).

The suitability of bonding materials and grouts used for bonded anchors is

assessed via the prequalification test program. The degree to which grout

shrinkage can be tolerated will depend on the thickness of the bond line

(annular gap) associated with the anchor system. The use of highly expansive

(as opposed to shrinkage compensating) grouts should be avoided in order to

reduce the potential for premature splitting. Consideration should also be

given to the ability of the grout to protect the anchor element from corrosion.

1.5 Permissible anchor loading

The actions on the anchor resulting from the actions on the fixture

(tension, shear, bending or torsional moments or any combination thereof)

will generally be axial tension and/or shear. When the shear force is applied

with a lever arm, the anchor will be subjected to a bending moment as well.

This Design Guide applies to anchors subjected to predominately static

loading. Certain types of anchors, however, may also be subjected to fatigue

and/or seismic loads as stated in the respective Part of this Design Guide.


Part I: 1 Scope 12

Examples of loadings on anchorages are shown in Figure 1.5-1. Compression loads on a fixture are allowed provided that (i) they are

transferred from the fixture to the concrete without loading the anchors or

alternatively, (ii) the anchors are suitable to transfer compression loads

(Figure 1.5-3).

a) b)

c) d)

Figure 1.5-1: Loading on anchorages and on anchors: a) tension

load; b) shear load; c) combined tension and shear

load; d) shear load with lever arm

Figure 1.5-2 represents conditions where compression forces are resisted

by bearing at the concrete surface. Care should be exercised in cases where

the compression forces are taken directly into the anchors, e.g., where

levelling nuts are provided without bearing nut and washer as shown in

Figure 1.5-3. There are two considerations in this case:

– expansion anchors and some undercut anchors placed in direct

compression may become dislodged and lose the ability to resist

tension forces (Figure 1.5-4a);

– where the member thickness is limited, resisting the compression loads

through the anchor may result in concrete breakout failure at the

backside of the member (Figure 1.5-4b).



a)

b)

Figure 1.5-2: Examples of anchors where the anchors are not

loaded by a compression force: a) anchorage loaded

by a bending moment and/or a compression force;

b) stand-off installation with bearing nut and washer


Part I: 1 Scope 14

Figure 1.5-3: Anchorage with anchors loaded by a compression

force (base plate grout omitted)

a) b)

Figure 1.5-4: Possible failure modes for a compression-loaded

anchor when the compression load is not transferred

at the concrete surface: a) anchor becomes dislodged

(loss of expansion force); b) concrete breakout failure

at backside of member



1.6 Permissible concrete strength

Structural normal weight concrete of strength class C20 to C50

corresponds roughly to the range of 2500 psi to 7500 psi concrete.

Insufficient data for anchors installed in lightweight concrete exist to

provide general guidance for their design. Product-specific data may be

developed for these cases in accordance with prequalification procedures.

Concrete having a compressive strength less than 20 MPa may exhibit

local variations in concrete density and quality that could lead to

unacceptable scatter of anchor load-displacement behaviour and strength.

The upper limit of concrete strength is derived from the following

considerations:

– the equations included in this Design Guide for the calculation of the

resistance associated with pullout may be unconservative for high

strength concrete;

– experience regarding the response of post-installed anchors to tension

loading in high strength concrete (e.g., follow-up expansion and bond

strength of bonded anchors) is limited.

The Design Guide is organised around anchorages in concrete that is

expected to remain uncracked over the service life of the anchorage based on

the calculated stress state (uncracked concrete) and those in concrete that

may be expected to crack in the anchorage vicinity over the anchorage

service life (cracked concrete).

In general, this Design Guide applies to anchorages in structural normal

weight concrete (concrete produced with normal weight aggregates) of

strength class C20 to C50 in accordance with CEB-FIP Model Code 1990

(CEB, 1993). For particular anchor types the permissible range of concrete

strength classes may be less restrictive than given above (see Part IV and Part

V).

This Design Guide addresses anchorages in both uncracked and cracked

concrete.

The bond between non-structural layers (screeds and toppings, plaster)

and concrete can be highly variable. As such these layers may not be able to

transfer loads induced by the anchorage to the underlying structural concrete.

This Guide does not address anchorages in thin non-structural layers such

as screeds and toppings. For the case where anchors project through screeds

or toppings, this Design Guide considers the screed or topping to be incapable

of transferring loads.

1.7 Permissible loading of the concrete member

Cyclic loading of structural concrete members may imply cycles of

opening and closing of cracks that may cause deterioration of anchor

performance. Knowledge regarding the behaviour of the various anchor types

under these conditions is limited.

This Design Guide addresses anchorages in concrete members subjected

predominantly to static loading. Where certain anchor types are deemed

permissible for use in concrete members subjected to fatigue or seismic

loading, this is stated in the relevant parts of the Design Guide.


Part I: 1 Scope 16

1.8 Reliability classes

The establishment of factors of safety for structures is typically based on a

concept of the consequences of failure. The Consequences Classes as defined

in EN 1990 (CEN, 2002-1) are given in Table 1.8-1. The Consequences

Classes CC1, CC2, and CC3 correspond to Reliability Classes RC1, RC2 and

RC3 according to EN 1990 (CEN, 2002-1).

The safety factor concept used in this document is predicated on the

approach according to CEB-FIP Model Code 1990 (CEB, 1993) as adopted

by EN 1990 (CEN, 2002-1). The basic requirements of EN 1990 are deemed

to be satisfied for anchorages, when the following requirements are satisfied:

– limit state design is carried out according to the partial factor method in

conformity with EN 1990 (See Section 3) and

– resistances, durability and serviceability are calculated on the basis of

the models of this Design Guide.

For the application of these procedures with other Reliability Classes, it is

recommended to use the relevant provisions of EN 1990.

Table 1.8-1: Definition of Consequences Classes according to EN

1990 (CEN, 2002-1)

Consequences Class Description Examples of buildings

and civil engineering

works

CC1

Low consequence for

loss of human life and

economic, social or

environmental

consequences

small or negligible

Agricultural buildings

where people do not

normally enter (e.g.,

storage buildings),

greenhouses

CC2

Medium consequence

for loss of human life,

economic, social or

environmental

consequences

considerable

Residential and office

buildings, public

buildings where

consequences of failure

are medium (e.g., an

office building)

CC3

High consequence for

loss of human life, or

economic, social or

environmental

consequences very great

Grandstands, public

buildings where

consequences of failure

are high (e.g., a concert

hall)

In general, a design using the partial factors given in this Design Guide

and the partial factors given for loads in EN 1990 Annex A is considered to

lead to a structure in compliance with Reliability Class RC2 according to EN

1990 (CEN, 2002-1). Use of the loads and safety factors given in ASCE/SEI

7-05 (ASCE, 2006) and the strength reduction factors given in ACI 318

(2008) is also admissible. See Section 3.

Use of other safety factor concepts is admissible if appropriately adjusted

to ensure a similar probability of failure.



For other reliability classes than RC2, the actions should be adjusted in

accordance with Table 1.8-2. For example, for the same design, supervision

and execution inspection levels, a multiplication factor KFI may be applied to

the partial factors f.

Table 1.8-2: Adjustment of action for reliability classes RC1 to RC3

according to EN 1990 (CEN, 2002-1)

KFI factor for actions Reliability class

RC1 RC2 RC3

KFI 0.9 1.0 1.1

Note: In particular, for Class RC3, other measures such as increased jobsite

inspection requirements are preferred to using KFI . KFI should be applied only to

unfavourable actions

In other countries different classifications for Consequences Classes may be

used, e.g., in the U.S. the classification shown in Table 1.8-3 applies.


Part I: 1 Scope 18

Table 1.8-3: Occupancy categories of buildings and other

structures for floor, wind, snow, earthquake and ice

loads taken from ASCE/SEI 7-05 (ASCE, 2006)

Nature of occupancy Occupancy

category

Buildings and other structures that represent a low hazard to

human life in the event of failure, including, but not limited to:

Agricultural facilities

Certain temporary facilities

Minor storage facilities

I

All buildings and other structures except those listed in

Occupancy Categories I, III, and IV II

Buildings and other structures that represent a substantial hazard

to human life in the event of failure, including, but not limited to:

Buildings and other structures where no more than 300

people congregate in one area

Buildings and other structures with day-care facilities with

a capacity greater than 150

Buildings and other structures with elementary school or

secondary school facilities with a capacity greater than

250

Buildings and other structures with a capacity greater than

500 for colleges or adult education facilities

Health care facilities with a capacity of 50 or more

resident patients, but not having surgery or emergency

treatment facilities

Jails and detention facilities

Buildings and other structures, not included in Occupancy

Category IV, with potential to cause a substantial economic

impact and/or mass disruption of day-to-day civilian life in the

event of failure, including, but not limited to:

Power generating stationsa)

Water treatment facilities

Sewage treatment facilities

Telecommunication centres

III



Buildings and other structures not included in Occupancy

Category IV (including, but not limited to facilities that

manufacture, process, handle, store, use, or dispose of such

substances as hazardous fuels, hazardous chemicals, hazardous

waste, or explosives) containing sufficient quantities of toxic or

explosive substances to be dangerous to the public if released.

Buildings and other structures containing toxic or explosive

substances shall be eligible for classification as Occupancy

Category II structures if it can be demonstrated to the satisfaction

of the authority having jurisdiction by a hazard assessment as

described in Section 1.5.2 that a release of the toxic or explosive

substances does not pose a threat to the public.

Buildings and other structures designated as essential facilities,

including, but not limited to:

Hospitals and other health care facilities having surgery or

emergency treatment facilities

Fire, rescue, ambulance, and police stations and

emergency vehicle garages

Designated earthquake, hurricane, or other emergency

shelters

Designated emergency preparedness, communication, and

operation centres and other facilities required for

emergency response

Power generating stations and other public utility facilities

required in an emergency

Ancillary structures (including, but not limited to commu-

nication towers, fuel storage tanks, cooling towers, elec-

trical substation structures, fire water storage tanks or other

structures housing or supporting water, or other fire-

suppression material or equipment) required for operation

of Occupancy Category IV structures during an emergency

Aviation control towers, air traffic control centers, and

emergency aircraft hangars

Water storage facilities and pump structures required to

maintain water pressure for fire suppression

Buildings and other structures having critical national

defense functions

IV


Part I: 1 Scope 20

Buildings and other structures (including, but not limited to

facilities that manufacture, process, handle, store, use, or dispose

of such substances as hazardous fuels, hazardous chemicals, or

hazardous waste) containing highly toxic substances where the

quantity of the material exceeds a threshold quantity established

by the authority having jurisdiction.

Buildings and other structures containing highly toxic substances

shall be eligible for classification as Occupancy Category II

structures if it can be demonstrated to the satisfaction of the

authority having jurisdiction by a hazard assessment as described

in Section 1.5.2 that a release of the highly toxic substances does

not pose a threat to the public. This reduced classification shall

not be permitted if the buildings or other structures as function as

essential facilities. a)

Cogeneration power plants that do not supply power on the national grid shall be

designated Occupancy Category II

The classification according to Table 1.8-3 corresponds approximately

with the classes given in Table 1.8-1 as shown in Table 1.8-4.

Table 1.8-4: Comparison of Consequences Classes in Europe and

U.S.

Consequences Class according

Table 1.8-1

Occupancy categories according

Table 1.8-3

CC1 I

CC2 II

CC3 III + IV

Use of the safety factors given in ASCE/SEI 7-05 (ASCE, 2006) and the

strength reduction factors given in ACI 318 (2008) leads to a reliability level

in line with that associated with Reliability Class 2 (RC2).



2 Terminology

The definitions, notations and symbols frequently used in this Design

Guide are listed below. Further notation is given in the appropriate sections of

the Design Guide.

2.1 Definitions

Anchor = Steel element either cast into concrete or post-

installed into hardened concrete and used to

transmit applied loads (see Figure 1.2-1 to

Figure 1.2-7). In the case of anchor channels, a

steel anchor is rigidly connected to the back of

the channel and embedded in concrete.

Anchor channel = Steel profile (called channel) with rigidly

connected anchors (see Figure 1.2-7) (also

called channel bar) installed prior to

concreting.

Anchor channel

loading: Tension

= Load applied perpendicular to the surface of

the base material.

Anchor channel

loading: Bending

= Bending effect induced in the channel by a

tension load applied perpendicular to the

longitudinal axis of the channel.

Anchor channel

loading: Combined

= Axial and shear load applied simultaneously

(oblique loading).

Anchor channel

loading: Shear

= Shear acting parallel to the concrete surface

and perpendicular to the axis of the channel.

Anchor group = A number of anchors with identical charac-

teristics acting together to support a common

attachment where the spacing of the anchors

does not exceed the characteristic spacing.

Anchor loading:

Bending

= Bending effect induced by a shear load applied

with a lever arm with respect to the surface of

the base material (see Figure 1.5-1d).


Part I: 2 Terminology 22

Anchor loading:

Combined tension and

shear

= Axial and shear load applied simultaneously

(oblique loading) (see Figure 1.5-1c).

Anchor loading: Shear = Load applied perpendicular to the longitudinal

axis of the anchor (see Figure 1.5-1b).

Anchor loading:

Tension

= Load applied perpendicular to the surface of

the base material and parallel to the anchor

longitudinal axis (see Figure 1.5-1a).

Anchor reinforcement = Reinforcement used to transfer the design load

from the anchors into the structural member.

Anchor spacing = Distance between the centre lines of the

anchors.

Attachment = Metal assembly that transmits loads to the

anchor. In this Design Guide 'attachment',

'baseplate' and 'fixture' are used synonymously.

Baseplate = See 'Attachment'.

Blowout failure = Spalling of the concrete on the side of the

anchorage component at the level of the

embedded head with no major breakout at the

top concrete surface. This is usually associated

with anchors with small side cover and deep

embedment.

Bonded anchor

= Anchor placed into a hole in hardened concrete

which derives its resistance from a bonding

material placed between the wall of the hole in

the concrete and the embedded portion of the

anchorage (see Figure 1.2-5a). Bonded anchors

are also referred to as adhesive, chemical or

resin anchors.

Bond failure = Failure that occurs at the interface between the

bonding material and the base material or

between the bonding material and the steel part

(anchor element) of a bonded anchor.



Cast-in anchor = Headed bolt, headed stud or anchor channel

installed before placing the concrete (see

Figure 1.2-6 and Figure 1.2-7).

Channel bolt = T-bolt which connects the element to be fixed

to the anchor channel (see Figure 1.2-7b).

Characteristic

resistance

= The 5% fractile of the resistance (value with a

95% probability of being exceeded, with a

confidence level of 90%).

Characteristic spacing = Spacing required to ensure the characteristic

concrete resistance of a single anchor.

Clamping force = Prestressing force resulting from tightening of

the anchor against the fixture.

Concrete breakout

failure

= Corresponds to a volume or cone of concrete

surrounding the anchor or group of anchors

separating from the base material (see Figure

3.2-1b and Figure 3.2-2b). In tension and shear

loading this failure mode is denoted as

„concrete cone failure‟ and „concrete edge

failure‟, respectively.

Concrete member = Structural or non-structural member in which

the anchorage is placed or installed.

Concrete pryout

failure

= Corresponds to the formation of a concrete

spall opposite to the loading direction under

shear loading (see Figure 3.2-2c).

Concrete screw = Threaded anchor screwed into a predrilled hole

where threads create a mechanical interlock

with the concrete (see Figure 1.2-4). In this

Design Guide 'concrete screw' and 'screw

anchor' are used synonymously.

Concrete strength = Concrete compressive strength from uniaxial

compression tests on cylinders with diameter

150 mm and height 300 mm.



Displacement = Movement of the anchor at the concrete

surface relative to the surface of the concrete

member into which it is installed. In tension

tests displacement is measured parallel to the

anchor axis. In shear tests, displacement is

measured perpendicular to the anchor axis.

Deformation-

controlled expansion

anchor

= A post-installed anchor that derives its tensile

resistance by expansion against the side of the

drilled hole through movement of an internal

plug in the sleeve or through movement of the

sleeve over an expansion element (plug). Once

set, no further expansion can occur (see Figure

1.2-2).

Ductile steel element = A steel element with sufficient ductility. The

ductility conditions are given in the relevant

sections of this Design Guide.

Edge distance = Distance from the edge of the concrete

member to the centre of the anchor.

Effective embedment

depth

= Distance between the concrete surface and the

deepest point of effective load transfer. The

definition of the effective embedment depth for

the different types of anchors is given in Figure

2.5-1 to Figure 2.5-4. The effective

embedment depth for post-installed anchors is

provided in the Approval.

Fixture = See „Attachment‟.

Headed anchor = Steel anchor that derives its tensile resistance

from mechanical interlock at the anchor head

and which is cast in place (see Figure 1.2-6).

Hole clearance = Annular gap between anchor and fixture (see

Figure 4.3-12).

Installation safety

factor

= Partial factor that accounts for the sensitivity

of an anchor to installation inaccuracies (see

Section 3.4.2.1.2).



Mechanical interlock = Load transfer to a concrete member via

interlocking surfaces.

Minimum edge

distance

= Minimum distance from the centre of the

anchor to the concrete edge to allow adequate

placing and compaction of concrete (cast-in

anchors) and to avoid damage to the concrete

during installation (post-installed anchors);


Minimum member

thickness

= Minimum thickness of the concrete member in

which an anchor is allowed to be installed;


Minimum spacing = Minimum centre to centre spacing of anchors

to allow adequate placing and compaction of

concrete (cast-in anchors) and to avoid damage

to the concrete during installation (post-

installed anchors), provided in the Approval.

Post-installed anchor = An anchor installed in hardened concrete (see

Figure 1.2-1 to Figure 1.2-5).

Pullout failure = Failure mode in which the anchor pulls out of

the concrete without development of the full

concrete resistance.

Pull-through failure = Failure mode in which the anchor body pulls

through the expansion sleeve without

development of the full concrete resistance.

Spacing = Distance between anchors measured centreline

to centreline.

Splitting failure = Concrete failure mode in which the concrete

fractures along a plane passing through the

axis of the anchor or anchors (see Figure

3.2-1c).

Steel failure of anchor = Failure mode characterized by fracture of the

steel anchor parts (see Figure 3.2-1d and

Figure 3.2-2a).



Torque-controlled

bonded anchor

= Bonded anchor designed such that the anchor

bolt can move relative to the hardened bonding

material (see Figure 1.2-5b) resulting in

follow-up expansion.

Torque-controlled

expansion anchor

= Post-installed expansion anchor that derives its

tensile resistance from the expansion of one or

more sleeves or other components against the

sides of the drilled hole through the application

of torque, which pulls the cone(s) into the

expansion sleeve(s) during installation (see

Figure 1.2-1). After setting, tensile loading can

cause additional expansion (follow-up

expansion).

Undercut anchor = A post-installed anchor that develops its tensile

resistance from the mechanical interlock

provided by undercutting of the concrete at the

embedded end of the anchor (see Figure 1.2-3).

The undercutting is achieved with a special

drill before installing the anchor or

alternatively, by the anchor itself during its

installation.

2.2 Indices (subscripts/superscripts)

F = load

G = permanent action

M = material

N = axial force

Q = variable action

R = resistance; restraint

S = action effects

V = shear force

b = bond



c = concrete

cb = concrete blowout

cl = clearance hole

cp = concrete pryout

cr = cracked

d = design value

el = elastic

eq = earthquake (seismic)

f = action in general, friction, fixture

fat = fatigue

fi = fire

fix = fixture

flex = bending

g = group of anchors in context of load or resistance

h = highest loaded anchor in a group

ind = induced deformation

inst = installation

k = characteristic value

l = local

max = maximum

min = minimum

nom = nominal

p = pullout or pull-through

pl = plastic

re = reinforcement

s = steel



sp = splitting

u = ultimate

uncr = uncracked

y = yield

0 = reference value

= perpendicular to the edge

= parallel to the edge

2.3 Actions and resistances

C = compression force

G = permanent action

F = force

M = bending moment on anchor

M1 = bending moment on fixture around axis in direction 1

M2 = bending moment on fixture around axis in direction 2

Mflex = bending moment on channel of an anchor channel

N = axial force (positive denotes tension force, negative denotes

compression force)

Q = variable action

R = resistance

S = action

T = torsional moment on fixture, tension force on anchor

V = shear force

( ; )Rk Rk RkF N V = Characteristic value of resistance of a single

anchor or an anchor group (normal force,

shear force). Only those anchors susceptible

to the particular failure mode under

investigation shall be included in the group.



( ; )Rd Rd RdF N V = Design value of resistance of a single

anchor or an anchor group respectively

(normal force; shear force). Only those

anchors susceptible to the particular failure

mode under investigation shall be included

in the group.

( ; ; ; )Sk Sk Sk Sk SkF N V M T = Characteristic value of actions acting on a

single anchor or the fixture of an anchor

group (normal load, shear load, bending

moment and torsional moment). In the case

of anchor channels characteristic values of

actions acting on the channel bolts.

( ; ; ; )Sd Sd Sd Sd SdF N V M T = Design value of actions acting on a single

anchor or the fixture of an anchor group

(normal load, shear load, bending moment,

and torsional moment); in the case of

anchor channels, design values of actions

acting on the channel bolts.

( ; )a a a

Sd Sd SdF N V = Design value of action on one anchor of an

anchor channel.

, , ,( ; )a a a

Sd i Sd i Sd iF N V = Design value of action on anchor i of an

anchor channel.

( )h h

Sd SdN V = Design value of tensile load (shear load)

acting on the most stressed anchor of a

group.

( )g g

Sd SdN V = Design value of the resultant tensile (shear)

load acting on an anchor group effective in

taking up tension (shear) loads.

NSd,re

= Design value of tension load acting on an

anchor reinforcement (see Figure 23.2-1c

and Figure 23.2-2).

NRk,s,a = Characteristic steel tension resistance of

one anchor of an anchor channel.



NRk,s,c = Characteristic tension resistance of

connection between anchor and channel

(anchor channel).

NRk,s,l = Characteristic tension resistance for local

failure of channel lips (anchor channel).

NRk,s,flex = Characteristic tension resistance for flexural

failure of channel (anchor channel).

NRd,s,a = Design steel tension resistance of one

anchor of an anchor channel.

NRd,s,c = Design tension resistance of connection

between anchor and channel (anchor

channel).

NRd,s,l = Design tension resistance for local failure

of channel lips (anchor channel).

NRd,s,flex = Design tension resistance for flexural

failure of channel (anchor channel).

NRd,s,ch = Design steel tension resistance of channel

of an anchor channel (minimum value of

NRd,s,a, NRd,s,c and NRd,s,l).

VRk,s,a = Characteristic steel shear resistance of one

anchor of an anchor channel.

VRk,s,c = Characteristic shear resistance of

connection between anchor and channel

(anchor channel).

VRk,s,l = Characteristic shear resistance for local

failure of channel lips (anchor channel).

VRd,s,a = Design steel shear resistance of one anchor

of an anchor channel.

VRd,s,c = Design shear resistance of connection

between anchor and channel (anchor

channel).



VRd,s,l = Design shear resistance for local failure of

channel lips (anchor channel).

VRd,s,ch = Design steel shear resistance of the channel

of an anchor channel (minimum value of

VRd,s,a, VRd,s,c and VRd,s,l.

2.4 Concrete and steel

As = stressed cross section of steel

Cx = concrete strength class where x is given as the characteristic

concrete compression cylinder strength in MPa

fck = characteristic compressive strength of concrete (strength

class) measured on cylinders 150 mm x 300 mm, according

to CEB-FIP Model Code 1990 (CEB, 1993)

fck,cube = characteristic compressive strength of concrete (strength

class) measured on cubes with a side length 150 mm

(usually the word “cube” is substituted by the side length

measured in mm)

fyk = characteristic steel yield strength or steel proof strength

respectively (nominal value)

fuk = characteristic steel ultimate tensile strength (nominal value)

Iy = moment of inertia of the channel [mm4] relative to the y-

axis (Figure 2.5-4)

Wel = elastic section modulus of anchor calculated from the

stressed cross section of steel



2.5 Notation - dimensional

Note: For torque-controlled expansion anchors, hef is measured to the

end of the expansion element(s) in the untorqued condition.

Figure 2.5-1: Effective embedment depth hef for post-installed

anchors

Figure 2.5-2: Effective embedment depth for screw anchors

a1 (a2) = spacing between outer anchors in adjoining anchorages in

direction 1 (direction 2) (Figure 2.5-5)

a3 = distance between concrete surface and point of assumed

restraint of an anchor loaded by a shear force with lever arm

(see Section 4.3.1.5)

acl = hole clearance according to Figure 4.3-12

acl,1 = normal hole clearance according to Table 4.3-1

b = width of concrete member

bch = width of channel (Figure 2.5-4)

bfix = width of fixture

c = edge distance of an anchor (Figure 2.5-5) or an anchor

channel

c1 (c2) = edge distance in direction 1 (direction 2) (Figure 2.5-5)

ccr = characteristic edge distance for ensuring the transmission of

the characteristic resistance of a single anchor

cmin = minimum allowed edge distance

d = diameter of anchor bolt or thread diameter (Figure 2.5-1

and Figure 2.5-2), diameter of the stud or shank of headed

anchors (Figure 2.5-3)

d0 = nominal diameter of drilled hole

df = diameter of clearance hole in fixture

df,1 = normal diameter of clearance hole in fixture according to

Table 4.3-1

dh = diameter of anchor head (headed anchor) (Figure 2.5-3)

dnom = outside diameter of anchor (Figure 2.5-1)

= d for anchors without sleeve

ds = diameter of reinforcing bar



a) b) c)

Figure 2.5-3: Definition of effective embedment depth hef for cast-in

headed anchors: a) without baseplate; b) with a large

baseplate with b1 > 0.5hef or tfix > 0.2hef in any

direction; c) with a small baseplate b1 ≤ 0.5hef or

tfix ≤ 0.2hef in each direction

Figure 2.5-4: Definitions for anchor channels

e1 = distance between shear load and concrete surface (Figure

4.3-36)

eN = eccentricity of resultant tension force of tensioned anchors

in respect to the centre of gravity of tensioned anchors

eV = eccentricity of resultant shear force of sheared anchors in

respect to the centre of gravity of sheared anchors

h = thickness of concrete member in which the anchor is

installed (Figure 2.5-5)

hch = height of channel (Figure 2.5-4)

hef = effective embedment depth (Figure 2.5-1 to Figure 2.5-4)

hmin = minimum allowed thickness of concrete member

hnom = nominal anchor length (Figure 2.5-2 and Figure 2.5-3)

hs = distance between tip of screw anchor and beginning of the

thread

ht = thread pitch

l = lever arm of the shear force acting on an anchor (Figure

4.3-36)

lin = influence length of an external load NSd along an anchor

channel (Figure 25.1-1)

lv = embedment depth of post installed reinforcing bars

n1 (n2) = number of anchors in a group in direction 1 (direction 2)

s = spacing of anchors in a group (Figure 2.5-5) or spacing of

reinforcing bars

s1 (s2) = spacing of anchors in a group in direction 1 (direction 2)

(Figure 2.5-5)

scr = characteristic spacing for ensuring the transmission of the

characteristic resistance of a single anchor

si = distance between anchor under consideration and

neighbouring anchors in anchor channels



a) Definition of c, s, a and h for tension loaded anchorages

b) Definition of c and s for shear loaded anchorages

Figure 2.5-5: Definitions related to concrete member dimensions,

anchor spacing and edge distance: a) anchorages

subjected to tension load; b) anchorages near to an

edge subjected to shear load; indices 1 and 2 depend

on the edge for which the verification for concrete

breakout is made: index 1 denotes the direction

perpendicular to the edge for which the verification

for concrete breakout is made; index 2 denotes the

direction perpendicular to direction 1

smin = minimum allowed anchor spacing

tfix = thickness of fixture (Figure 4.3-34 and Figure 4.3-35)

tgrout = thickness of grout layer (Figure 4.3-34)

th = thickness of anchor head (Figure 2.5-3)

x = depth of the compression zone below the fixture (Figure

4.3-2)



2.6 Greek symbols

= factor for interaction equation

ch,N = factor taking into account the influence of the channel on

the concrete cone failure load of anchor channels

ch,V = factor taking into account the influence of the channel on

the concrete edge failure load of anchor channels

V = angle between resultant shear load on anchors and a line

perpendicular to the edge for which the verification for

concrete edge failure is made

'V = angle between resultant shear load on fixture and a line

perpendicular to the edge for which the verification for

concrete edge failure is made

eq = seismic reduction factor

= displacement

= partial factor

= strain

= coefficient of friction

= bond stress

Rk = characteristic bond strength of bonded anchors

= factor to account for various influences in the calculation

of concrete failure modes

2.7 Units

Conversions:

SI unit inch-pound equivalent

1 millimetre = 0.03937 inches

1 mm2 = 0.001550 square inches

1 mm3 = 0.00006102 cubic inches

In this document SI units are used. Unless stated otherwise in the

equations, the following units are used: dimensions are given in mm, cross

sections in mm2, section modulus in mm

3, forces and loads in N, moments in

Nmm and stresses in MPa (N/mm2). Equations containing the concrete

compression strength assume the use of cylinder strength (fck). Cube strength

may be converted to cylinder strength using the conversion according to EN

206-1 (CEN, 2000) and CEB-FIP Model Code 1990 (CEB, 1993):


Part I: 3 Basis of design 36

1 newton (N) = 0.2248 pound force

1 MPa = 145.0 pounds per square inch

1 Nm = 8.850 inch pounds

C20 fck = fck,150 / 1.25

C50 fck = fck,150 / 1.20

If cubes with a side length larger or smaller than 150 mm are used, the

followings conversion factors may be used:

fck,150 = 0.95 fck,100

fck,150 = 1.05 fck,200

3 Basis of design

3.1 General

In this Design Guide a nominal service life of at least 50 years is assumed

for the anchorage. Further details on service life may be given in the relevant

product Approvals.

The serviceability limit state is defined in CEB-FIP Model Code 1990

(CEB, 1993) as:

– limited local structural damage such as excessive cracking or

excessive compressive stress, producing irreversible strains and micro

cracks;

– deformations which produce unacceptable damage in non-structural

elements or excessively affect the use or appearance of structural or

non-structural elements;

– vibrations resulting in discomfort, alarm or loss of utility.

Anchors under service loads may produce microcracking in the load

transfer area. In as much as this microcracking is implicitly included in the

calculation of the anchorage capacity, it may be neglected from a

serviceability standpoint.

Anchors should sustain all actions (forces and deformations) and

environmental influences likely to occur during execution and use with an

appropriate degree of reliability (ultimate limit state). At service loads they

should conform to the serviceability requirements of CEB-FIP Model Code

1990 (CEB, 1993) (serviceability limit state). Additionally, they should

remain fit for the use for which they are required over the service life of the

anchorage (durability).

Anchorages should be designed according to the same principles and

requirements applicable to structures designed according to relevant design

codes. The design service life of the anchors should not be less than that of

the fixture.

Actions on the anchorage should be obtained from the relevant design

codes.

In many cases, anchorage design is limited to considerations for the local

transfer of load from the attachment to the concrete. It may be necessary,

however, to explicitly verify the continuous load path in the supporting structure

accounting for the local loads originating from the anchorage. Such verification

should be conducted to the extent that such forces significantly influence the

design of the supporting structural elements or their connections.

The local transmission of the anchor loads to the concrete is checked in

accordance with this Design Guide. It is assumed that under the design action

of the anchorage the supporting structure is still at the serviceability limit

state. The further transfer of loads originating in the anchorage to the

remainder of the supporting structure should be considered in the design of

the structure. Requirements for the concrete member are given in Section 8.



Quality requirements valid for design and execution of the RC structure

and of the attachment are applicable to the design and execution of

anchorages.

3.2 Required verifications

The following failure modes can be distinguished for cast-in-place and

post-installed anchors:

Tension loading (Figure 3.2-1):

– steel failure (Figure 3.2-1d)

– pullout or pull-through failure (Figure 3.2-1a1-2), combined pullout and

concrete cone failure for bonded anchors (Figure 3.2-1a3)

– concrete cone failure (Figure 3.2-1b1-3)

– blowout failure (Figure 3.2-1b4)

– splitting failure (Figure 3.2-1c)

Pullout failure occurs when the entire anchor is pulled out of the drilled

hole.

The definition of pull-through failure depends on the type of anchor as

follows: In torque-controlled expansion anchors, the expansion cone is pulled

through the expansion elements. In torque-controlled bonded expansion

anchors, the anchor bolt is pulled through the hardened mortar. Pull-through

failure is allowed for torque-controlled expansion anchors and for torque-

controlled bonded expansion anchors, since pulling the cone(s) into the

expansion elements (torque-controlled expansion anchor) or into the mortar

(torque-controlled bonded-expansion anchors) constitutes the working

mechanism of these anchor types.

The assessment of these failure modes is performed in the relevant

approval process and one characteristic value is given, which is termed

“pullout” resistance.

The concrete cone breakout failure mode is characterised by the formation

of a cone-shaped fracture surface originating in the load-transfer zone of the

anchor and radiating towards the concrete surface.

Blowout failure is a result of high bearing pressure generated in the load-

Anchorages should be designed for the following limit states:

– ultimate limit state;

– serviceability limit state.

Design for fatigue, seismic and fire exposure should be performed if

applicable. Furthermore, adequate durability of the anchors for the intended

use should be ensured.

In the ultimate limit state verifications are required for all appropriate

loading directions and for all relevant failure modes. In the serviceability limit

state, the requirements given in Section 6.2 should be fulfilled.

The material of the anchor and the appropriate measures for corrosion

protection should be selected taking into account:

– the intended working life;

– the environmental conditions at the place of installation;

– the conditions of inspection, maintenance or possible replacement of

the anchors.

Guidance for ensuring durability is given in Section 7.

Where applicable, the anchorage should have an adequate fire resistance

(see Section 6.5). For the purpose of this Design Guide it is assumed that the

fire resistance of the fixture conforms to the applicable fire design regulations.



transfer area of the anchor. These high bearing stresses cause bursting forces

transverse to the load direction which create a concrete breakout on the side

face of the member.

Splitting failure is caused by the hoop stresses around the anchor. The

hoop stresses originate from local load transfer and expansion forces.

a1) Pullout failure a2) Pull-through failure a3) Combined pullout and concrete cone failure of bonded anchor

b1) Concrete cone failure



b2) Group breakout; b3) Edge breakout; b4) Blowout

c1) Splitting failure

c2) Splitting failure of a group; c3) Near-edge splitting failure

d) Steel failure

Figure 3.2-1: Failure modes associated with tension loading



Shear loading (Figure 3.2-2):

– steel failure (Figure 3.2-2a)

– pryout (Figure 3.2-2c) or pullout failure (Figure 3.2-2d)

– concrete edge failure (Figure 3.2-2b)

Steel failure is often accompanied by crushing and spalling of the

concrete ahead of the anchor. The effect of the resulting secondary tensile

and flexural stresses in the anchor bolt is accounted for in the design model

for steel resistance.

Pryout failure is caused by rotation of the anchor and the catenary tension

force generated in the anchor bolt as a result of lateral deformation and the

eccentricity between the acting shear force and the resultant resisting force in

the concrete. Pullout under shear load is generated by the catenary tension

force when the pullout resistance of the anchor is insufficient to generate

concrete breakout.

Concrete edge failure mode is characterised by the formation of a cone-

shaped fracture surface originating at the anchor shaft and radiating towards

the concrete edge.

The failure modes of anchor channels are explained in Section 24.

a) Steel failure b1) Edge breakout; b2) Group edge breakout; b3) Corner edge breakout



b4) Thin member edge breakout

b5) Narrow member edge breakout

c1) Pryout c2) Group pryout

c3) Pryout at an edge d) Pullout (catenary action)

Figure 3.2-2: Failure modes associated with shear loading



3.3 Design format

For the design of anchorages, the safety concept of partial factors

according to the CEB-FIP Model Code 1990 (CEB, 1993) is applied.

According to this concept, in the ultimate limit state and for all relevant

combinations of actions (including fatigue and seismic, where applicable) the

value of the design actions Sd should not exceed the value of the design

resistance Rd.

d dS R (3.3-1)

where:

In Load and Resistance Factor Design (LRFD), design actions are

denoted as factored loads.

Sd = value of design actions on anchors

Rd = value of design resistance of anchors

In the serviceability limit state Equation (3.3-1) applies as well. In this

case, the design action Sd as well as the design resistance Rd are generally

expressed in terms of displacement or rotation (see Section 6.2).

The design actions on anchors may also be calculated according to

corresponding standards, e.g., CEN (2002-2).

The design actions on the anchorage should be calculated according to

CEB-FIP Model Code 1990 (CEB, 1993).

In the simplest case (permanent load and one variable load acting in the

same direction as the permanent load) the following equation applies:

d G k Q kS G Q (3.3-2)

where:

Gk(Qk) = characteristic value of permanent (variable) actions

G(Q) = partial factor of permanent (variable) actions

For more complex loading situations refer to CEB (1993).

If deformations imposed on the anchored element, e.g., due to

temperature variations, are restrained by the anchorage, then the

corresponding actions on the anchorage (Qind) multiplied by an appropriate

safety factor (γind) should be added in Equation (3.3-2).



If LRFD or strength design is used e.g., in ACI 318 (ACI 318, 2008) the

basic requirement is expressed as follows:

Design strength ≥ required strength (3.3-4)

In the ultimate limit state, the value of the design resistance is obtained

from the characteristic resistance of the anchor or anchor group as follows:

kd

M

RR

(3.3-3)

The required strength is derived from the design actions and is expressed

in terms of actions (loads) multiplied by load factors (usually greater than 1)

corresponding to specific load combinations specified in the applicable

building code. The design strength (or design resistance) is obtained by

multiplying the nominal strength (characteristic resistance) by a strength

reduction factor (with ≤ 1) instead of dividing it by a partial factor γM

(with γM ≥ 1). Hence the basic requirement can be expressed as:

· (nominal strength) ≥ required strength (3.3-4a)

The strength reduction factors are given in the corresponding design

Standard and in the Approval.

Theoretically, the conversion of γM–factors given in this Design Guide into

factors can be accomplished as follows using as an example the basic load

combination of ASCE/SEI 7-05 (ASCE, 2006) and EN 1990 (CEN, 2002-1):

1.2 1.6 d d kD L S R R (3.3-5a)

1.35 1.5k k d d k MG Q S R R (3.3-5b)

with:

D, Gk = dead load, permanent load

L, Qk = live load, variable load

For example, resolving Equations (3.3-5a,b) with respect to for the case

Sd = Rd yields:

1.2 1.6

1.35 1.5M k k

D L

G Q

(3.3-5c)

where:

Rk = characteristic resistance of single anchor or anchor group to the

examined action effect (e.g., NRk or VRk)

γM = partial factor for material

For various ratios of variable to permanent action the following

equivalent strength reduction factors are obtained assuming M = 1.5:



L/D = Qk/Gk for M = 1.5

0.4 0.63

1.0 0.67

10.0 0.70

Equation (3.3-5c) is valid for the simplest case (permanent load and one

variable load acting in the same direction as the permanent load). For more

complicated loadings, Equation (3.3-5c) should be modified accordingly.

Note that the partial factors M may address different safety aspects than

the strength reduction factors .

3.4 Partial factors

3.4.1 Partial factors for actions

The partial factors for actions are independent of the materials used. In

the absence of a generally accepted code for actions, they should be taken

from CEB-FIP Model Code 1990 (CEB, 1993). Default values for the

ultimate limit state are given in Table 3.4-1.

The partial factors for actions depend on the type of loading and should be

taken from CEB-FIP Model Code 1990 (CEB, 1993).

Table 3.4-1: Partial factors for actions (ultimate limit state)

Actions Unfavourable effect Favourable effect

Permanent, G 1.35 1.0

Variable, Q 1.5 Usually neglected

Accidental, A c)

1.0 Usually neglected

Induced deformations,

ind

1.0 a)

1.3 b)

Usually neglected

a) Suggested value if the characteristic resistance is governed by ductile steel

failure b)

Suggested value if the characteristic resistance is governed by any other failure

mode c)

E.g., impact caused by vehicles



In case of accidental loading safety is normally ensured by the design

values of the accidental action or by other parameters describing the

accidental situation. Therefore, A = 1.0 is recommended.

For serviceability limit state, as well as for fatigue actions, all partial

factors for actions may be assumed to be 1.0. For seismic actions refer to the

relevant design code, e.g., EN 1990 (CEN, 2002-1), Section 6.4.3.4.

3.4.2 Partial factors for resistance

The partial factor for materials given here are valid for Reliability Class

RC2 according to EN 1990 (CEN, 2002-1) (see Section 1.8). Partial factors

for Reliability Classes RC1 and RC3 should be determined depending on the

guidelines in each country.

3.4.2.1 Ultimate limit state

3.4.2.1.1 Partial factors for steel failure

In the absence of more accurate information, the values for γMs given in

Equations (3.4-1) through (3.4-7) are recommended. Equations (3.4-1)

through (3.4-5) were derived taking into account that the ultimate strength of

steel fuk is used for the calculation of the characteristic resistance of an anchor

(including an anchor that is part of an anchor channel, see Figure 2.5-4) or of

an anchor group. Equations (3.4-6) and (3.4-7) take into account that fyk

should be used for calculating the characteristic bending resistance of the

channel of anchor channels and the characteristic resistance for steel failure

of anchor reinforcement.

Tension load on anchors and channel bolts of anchor channels:

1.2 1.4ukMs

yk

f

f (3.4-1)

Shear loading on anchors and channel bolts of anchor channels with and

without a lever arm:

1.25ukMs

yk

f

f ( 800 MPa and 0.8 )uk yk ukf f f (3.4-2)

The partial factors for steel Ms, Ms,c, Ms,l, Ms,flex and Ms,re

should be taken

from the relevant Approval.



1.5Ms ( 800 MPa or 0.8 )uk yk ukf f f (3.4-3)

Connection between anchor and channel of anchor channels assuming

current channel fabrication steels and methods:

, 1.8Ms c (3.4-4)

Local failure of the anchor channel by bending of the lips in tension and

shear:

, 1.8Ms l (3.4-5)

Bending of the channel of anchor channels:

, 1.15Ms flex (3.4-6)

Steel failure of anchor reinforcement:

, 1.15Ms re (3.4-7)

3.4.2.1.2 Partial factors for concrete failure

In order to provide uniformity in the recommended values for the partial

factors γMc, γMsp and γMp, the partial factor γMc takes into account not only the

concrete quality, but also the sensitivity of the anchor to installation

conditions and the coefficient of variation of the failure loads.

The value for γMc is therefore determined as follows:

Mc c inst COV (3.4-8)

with:

γc = Partial factor for concrete under compression. The

recommended value is γc = 1.5.

γinst = Partial factor taking into account installation safety of the

anchorage system. It is given in the Approval and represents

a characteristic of the anchor.

For information the following values γinst for post-installed

anchors are given:

The partial factor γMc covers concrete breakout failure modes (cone failure,

blowout failure, pryout failure and edge failure). The partial factor γMsp covers

splitting failure. These partial factors should be taken from the relevant

Approval.



Tension loading:

γinst = 1.0 for systems with high installation safety

= 1.2 for systems with normal installation safety

= 1.4 for systems with low but still acceptable

installation safety

Shear loading:

γinst = 1.0

For cast-in anchors and anchors channels a partial factor

γinst = 1.0 may be taken if the conditions of Section 3.5 are

fulfilled.

The factors given above or in the relevant Approval are valid

only if after installation the actual values of the effective

embedment depth, spacing and edge distance are not less than

the values used in the design (only positive tolerances are

allowed on site).

γCOV = Partial factor taking into account the coefficient of variation

of the failure loads in the service condition tests of the

prequalification procedure

= 1.0 (COV ≤ 15%)

> 1.0 (15% < COV ≤ 20%)

It is typically calculated according to Equation (3.4-9):

1.0 [%] 15 0.03COV COV (3.4-9)

In any case, the coefficient of variation of the failure loads in the service

condition tests should be COV ≤ 20%.

For the partial factor of γMsp the value for γMc is recommended.

The partial factor for friction between fixture and concrete may be taken

as γMf = 1.5.



3.4.2.1.3 Partial factor for pullout/pull-through failure

In the absence of specific information, the partial factor γMp should not be

taken less than the value for γMc. This assumes that the effect of the concrete

properties on the pullout/pull-through failure mode is similar to that

associated with concrete cone breakout failure.

The partial factor for pullout/pull-through failure γMp should be taken from

the relevant Approval.

3.4.2.2 Serviceability limit state

The partial factors for resistance should be taken as

γMs = γMc = γMp = γMf = γMsp = 1.0.

3.4.2.3 Fatigue loading

It is recommended to take the partial factor for material as γMs,fat = 1.35

(steel failure) and γMc,fat = γMsp,fat = γMp,fat (concrete cone failure, splitting

failure and pullout failure) according to Equation (3.4-8). For the partial

factor for friction between the fixture and concrete a value γMf,fat = 1.5 is

recommended.

Partial factors for fatigue loading should be taken from the relevant

Approval.

3.4.2.4 Seismic actions

For seismic strengthening and repair of existing structures the partial

factor for concrete γc in Equation (3.4-8) may be modified according to the

relevant Standards.

Partial factors for the calculation of resistances, when seismic actions are

considered, are assumed to be the same as for the ultimate limit state under

static actions (see Section 3.4.2.1), unless otherwise stated in the relevant

Approval.

3.5 Project specifications and anchor

installation

3.5.1 Project specification

The description of the anchors should include the manufacturer (if

applicable), make, model, dimensional and material characteristics and the

embedment depth.

Adherence to the specified edge distances, spacing and anchor

embedment depth can be critical for the performance of an anchorage.

Project specification should typically include the following information

with regard to anchorages:

– strength class of the concrete used in the design;

– environmental exposure assumed in the design;



Specification of tolerances is useful in this regard. Where tolerances are

specified, only positive tolerances should be used (exception: for the annular

gap negative tolerances should be used). In general, tolerances should be

specified for anchorages close to edges.

Where stand-off installations are specified, the project specification for

mechanical anchors should include provision of a nut and washer at the

concrete surface.

– construction drawings that include:

– location of the anchors in the structure

– number and detailed description of anchors including the grade and

the type of steel, e.g., galvanized or corrosion resistant steel

– spacing and edge distances of the anchors

– thickness of fixture and diameter of holes in the fixture (as

applicable)

– all relevant dimensional characteristics of the attachment

– maximum thickness of grout pads (if applicable) and maximum

stand-off dimension (if applicable)

– (special) installation instructions (if applicable)

– reference to the manufacturer's installation instructions;

– a note indicating that the anchor specification should not be changed

without checking the original design.

3.5.2 Installation

The resistance and reliability of anchorages are significantly influenced by

the manner in which the anchors are installed. The partial factors given in

Section 3.4 are valid only when the following conditions are fulfilled:

Often the anchor installation instructions are referenced in the Approval.

These should be checked against the installation instructions provided with

the product. Instructions should be explicit and direct. Performance

specifications (e.g., “Holes shall be free of all dust and debris” or “Air

bubbles in the bonding material should be avoided”) are generally not

acceptable if not accompanied by clear instructions for achievement of the

required condition.

Gross errors are variations from the manufacturer instructions that result

from carelessness or deliberate disregard and can significantly influence the

performance of the anchor. This varies depending on the anchor type. Some

examples of gross errors may be:

– the manufacturer‟s published instructions for installation of the anchor

are followed. The installation instructions and all necessary information

for correct installation should be available where the installation takes

place;

– gross errors on site are avoided;

– inspection and verification of the correct installation of the anchors is

carried out by appropriately qualified personnel.

The provisions of this Design Guide are based on assumptions as given in

this section with respect to installation of the various anchor types.

Installation instructions provided with specific proprietary products should be

in conformity with these assumptions.



– use of an anchor diameter or embedment depth other than specified;

– use of a drill bit with the incorrect diameter, especially for mechanical

expansion anchors, undercut anchors or screw anchors; incorrect

placement of cast-in anchors or channel anchors in the formwork;

omission of installation torque, especially for torque-controlled

anchors;

– omission or incorrect placement of anchor reinforcement where

required;

– improper cleaning of the hole, in particular for bonded anchors.

To avoid gross installation errors, anchors should be installed by trained

personnel under adequate supervision.

Job-site proof loading, whereby a specified number of installed anchors

are loaded to some percentage beyond the design tension resistance to verify

their correct installation, is one method to improve anchor installation

quality. Because proof loading typically involves loads that are significantly

below the expected anchor failure load, it may not detect minor defects in

installation. Proof loading may be useful, however, to detect gross

installation errors and to encourage quality control procedures on the job site.

3.5.2.1 Post-installed mechanical and chemical anchors

The following provisions apply to the installation of post-installed

mechanical and chemical anchors.

– The concrete should be adequately consolidated in the region of the

anchorage. This should be checked prior and during installation via a

visual inspection.

– Requirements for drilling operation and drilled hole:

– holes should be drilled perpendicular to the surface of the concrete

unless otherwise required by the manufacturer‟s installation

instructions or in the project specification

– drilling should be carried out by the method specified in the

manufacturer‟s installation instructions and in the project

specification



Many drill bits exhibit a mark indicating that they are in accordance with

a national Standard. If the drill bits do not bear a conformity mark,

conformity with the Approval should be provided.

Carbide drill bits should comply with the relevant product Standards or

specification, e.g., ANSI B212.15 (ANSI, 1994) and DIBt (2002).

– Core bit diameter should comply with the prescribed diameter.

Where holes are drilled in reinforced concrete or in concrete containing

embedded items (electrical conduit, etc.), care should be exercised at the

planning phase to reduce the degree of interference. While it may be

permissible to interrupt existing reinforcing (e.g. by core drilling) in specific

cases, damage to flexural or shear reinforcing should in general be avoided.

Due to the potentially extreme consequences associated with damage to

prestressing tendons, it is advisable to specify in the project specifications a

minimum clearance, e.g., 50 mm, between the drilled hole and the

prestressing tendon location.

– Reinforcement should not be damaged during drilling of holes for

anchors unless specifically permitted in the project specifications.

Special care should be exercised when drilling in the vicinity of

prestressing tendons. A suitable device, such as a pacometer or other

non-destructive reinforcement detector should be used to determine

the position of the reinforcement in the structure prior to drilling.

– Holes should be cleaned according to the instructions given in the

relevant Approval or manufacturer‟s installation instructions.

In the process of installing post-installed anchors it may be necessary to

relocate the anchor, e.g., if reinforcement is encountered. In general,

abandoned holes filled with high strength non-shrinking mortar do not

adversely influence the anchorage resistance. Where damage to the concrete

is excessive, other measures may be required.

– Abandoned drilled holes close to the final anchor location should be

filled with high-strength non-shrink mortar.

3.5.2.2 Cast-in headed anchors and anchor channels

The following provisions apply to the installation of cast-in headed

anchors and anchor channels:

– the anchor or anchorage assembly should be secured in the formwork

such that the anchor will remain in the specified location during

placement and compacting of the concrete;

Adjustment of anchor or anchorage position after placement of the

concrete but prior to curing should be avoided as it may lead to voids and

localised weakness in the concrete.

It may be advisable, depending on anchorage geometry and orientation, to

provide vent openings in base plates larger than 400 mm x 400 mm to

prevent air pockets from forming under the base plate during concrete

placement.

– the correct position of the anchorage or anchor should be verified prior

to concrete placement in accordance with codes of practice for the

control of reinforcement;

– the concrete should be adequately consolidated in the area of the

anchorage, particularly around the head of the stud or anchor and under

the fixture;

– in general, placement of anchors or anchorages subsequent to concrete

placement is not permitted unless tested procedures that ensure correct


Part I: 4 Determination of action effects 52

Placement of baseplates with welded anchors and anchor channels with

vibration following concrete placement may be acceptable under the

following conditions:

– the size of the baseplate (length of the anchor channel) is small enough

that proper consolidation of the concrete can be assured, that air voids

can be avoided and that correct placement of the fixture is assured;

– the installation should be performed according to a quality control

system and the anchorages should not be moved after vibrating.

In particular, the positioning of anchor reinforcement for shear loading

may be particularly critical for the performance of the anchorage.

anchorage position and concrete consolidation in the anchorage vicinity

are provided in the project specifications;

– welding of headed studs to an embed plate to create a group should be

performed in accordance with the provisions given in the relevant

Standard;

– welding of attachments to the anchorage should be performed in

accordance with relevant Standards. In specific cases, measures to

avoid transmission of excessive heat to the base plate or anchors may

be required;

– size and positioning of anchor reinforcement should be performed in

accordance with the project specifications.

4 Determination of action effects

4.1 General

In general, when calculating the actions on the fixture, the displacement

of the anchors is neglected. However, when anchoring statically

indeterminate components, the effect of anchor displacements (support

settlements) on the support reactions and bending moments of the anchored

component may be significant and should be considered in the design.

This section provides guidance for the determination of the design actions

on the anchors from the design actions on the fixture.

Deformations imposed on the anchored element, e.g., due to temperature

variations, may be restrained by the anchors.

When calculating the design actions on the fixture, actions due to restraint

of deformations should be taken into account.

4.2 Effect of friction

An example where friction resistance is developed is shown in Figure

4.2-1.

When a bending moment and/or a compression force acts on an anchorage

that is in direct contact with the concrete or baseplate grout, friction forces

between the baseplate and the concrete or grout will develop. In general, it is

conservative to neglect this friction in the design of the anchorage, although it

may in some cases lead to an underestimation of concrete cracking at the

serviceability level.



Figure 4.2-1: Friction force due to a resulting compression reaction

on the fixture

For anchorages located near a free edge, friction forces should not be

considered to act in the design when they occur within the assumed fracture

body. Consider an anchorage located close to an edge and loaded with a

moment and compression force as shown in Figure 4.2-2. For the case shown

in Figure 4.2-2a, the frictional resistance can mainly be developed in the

edge breakout and should not have any appreciable effect on the shear

resistance of the anchorage. Theoretically, if the moment is reversed, as

shown in Figure 4.2-2b-c, and the edge failure is assumed to originate at the

lead anchors, the resistance of the anchorage is increased by the friction force

acting outside of the concrete failure cone (Figure 4.2-2b). However, if the

fracture is assumed to originate at the back-most anchors (Figure 4.2-2c), the

frictional resistance cannot be added to the resistance associated with edge

breakout, because it is located within the fracture body. For these reasons,

and since in general shear and moment generally act in combination as

shown in Figure 4.2-2a (and not as shown in Figure 4.2-2b,c), the friction

between concrete and fixture should be neglected.

Note also, however, that the existence of frictional resistance may reduce

the load at which cracking initiates at the front anchors, even if the strength

of the anchorage is based on the capacity associated with fracture from the

back-most anchors. This may have consequences for the serviceability check

of the anchorage design.

As a rule, frictional resistance should be neglected if:

– the thickness of the grout layer exceeds one-half the anchor diameter d;

– the anchorage capacity is governed by a near-edge condition; or

– the anchorage is intended to resist earthquake loads.

Where frictional resistance is taken into account, the design value of shear

resistance corresponding to friction may be estimated as follows:

,

,

Rk f

Rd f Sd

Mf Mf

VV C

(4.2-1)

with:

μ = coefficient of friction

CSd = compression force under the fixture

γMf = partial factor for friction = 1.5 (see Section 3.4.2)



In general, the coefficient of friction between a flat steel element (base

plate, etc.) and the concrete may be taken as μ = 0.4.

a) b)

c)

Figure 4.2-2: Actions and resulting shear failure patterns for a near

edge anchorage a),c) friction force should not be

considered in the design; b) for this combination of

forces and failure pattern, friction force may be

considered in the design

When the friction force calculated according to Equation (4.2-1) is taken

into account in the design, it is treated as follows: In the elastic design

approach the frictional force is usually subtracted from the shear force acting

on the fixture; in the plastic design approach, it is added to the design shear

resistance of the anchorage. Note that both of these approaches assume that

the frictional resistance remains constant for all levels of anchorage

displacement.



4.3 Ultimate limit state

The degree of load redistribution assumed in the analysis should be in

conformity with the available ductility of the anchors. For example, in a

plastic analysis, anchor ductility shall be sufficient to ensure that all anchors

on the tension side can achieve their full design resistance.

In addition to verifications for acting forces and moments, it may also be

necessary to check the rotation of the connection for conformity with the

analysis of the attached structure. For example, if the analysis assumes fixity

at the connection, it should be verified that the calculated rotation of the

connection due to the design actions is sufficiently small to support this

assumption. This may be particularly relevant if the design of the anchorage

is based on plastic analysis. Similarly, an assumption of zero fixity (hinging)

at the connection may be unconservative for the anchorage design if the

detailing of the connection is inappropriate to ensure this condition.

In general, the distribution of design actions to the anchors in an anchor

group is predicated on linear elastic material behaviour. Under certain

conditions (see Section 4.3.2.1), however, distribution of actions may be

based on assumptions of plastic material behaviour.

4.3.1 Elastic analysis

Brittle failure modes include concrete fracture (breakout, splitting) and

fracture of brittle steel elements.

The elastic design approach is conservative for ductile failure modes.

The action effects on an anchor at the concrete surface may be derived from

the action effects on the fixture using an elastic analysis. The use of this method is

compulsory when the expected mode of failure of the anchorage is brittle.

In this section, anchorages with post-installed anchors and cast-in headed

anchors are considered. For the determination of action effects on anchor

channels Part V of this Design Guide applies.

4.3.1.1 Scope of the design method

Tests have shown that the design method given in this Design Guide

yields satisfactory strength predictions for large (6 x 6) anchor groups

subjected to concentric tension loading that exhibited concrete cone failure.

In these tests, the fixture was sufficiently stiff to ensure equal distribution of

the tension force to all anchors.

For anchors loaded in tension, the design concept described in this Design

Guide applies to any number of anchors in a group provided that the fixture is

sufficiently stiff to ensure that the distribution of loads to the anchors is in

conformity with the theory of elasticity (e.g., equal axial tension to all anchors,

when a concentric tension load is applied to the anchorage).

For the design of anchors loaded in shear, the number of anchors in a

group that may be considered as effective in resisting the shear load should

be limited depending on considerations of hole clearance and edge distance.

Anchor configurations as shown in Figure 4.3-1 and loaded in tension,

shear or in combined tension and shear are covered by this Design Guide.



A distinction is made between anchors installed in fixtures with and

without hole clearance. Hole clearances need not be considered in the

design in the following cases:

– bolts that are welded to or threaded into the fixture, or

– assemblies in which the annular gap between the anchor and the

fixture is filled with a mortar of appropriate flowability and

compression strength or eliminated by other suitable means.

For shear loading, the permissible anchor configurations given in Figure

4.3-1a are intended to prevent excessive shear lag (non-uniform shear

distribution in the direction of the shear load over the length of the

connection).

The limitations regarding configurations of anchors with hole clearance

close to an edge (Figure 4.3-1b) are based on the following considerations: at

the onset of concrete failure, the displacement of each individual anchor

within a group may be equal to or smaller than its hole clearance. This

situation may lead to high uncertainties in the load distribution in groups

with more than one anchor row perpendicular to the edge and more than two

anchors per row located close to a free edge. Such configurations with more

than two anchors in a row close to an edge or more than two anchor rows

perpendicular to the edge have not been sufficiently investigated.

Thus, in case of anchor groups exceeding the limits indicated in Figure

4.3-1, the provisions of this Design Guide should be applied with engineering

judgement.

a)

b)

Figure 4.3-1: Anchor configurations under tension, shear or combined

tension and shear loading covered by this Design Guide:

a) anchorages without hole clearance for all edge distances and anchorages

with normal hole clearance (acl ≤ acl,1 with acl,1 according to Table 4.3-1))

situated far from edges (c1 ≥ max(10hef, 60dnom)) (configurations valid also for

c1 ≥ cmin if only tension loads are acting); b) anchorages with normal hole

clearance (according to Table 4.3-1) having an edge distance

c1 < max(10hef, 60dnom)



4.3.1.2 Tension loads on anchors

The assumption of a linear distribution of strains across the fixture

(Figure 4.3-2a) is analogous to the Bernoulli hypothesis of plane sections

used in the analysis of reinforced concrete members. This assumption is valid

only if the flexural rigidity of the fixture is large compared to the axial

stiffness of the anchors so that at the design load the deformation of the

fixture in the vicinity of the tension-loaded anchors is small compared to the

anchor axial displacement. This requires, among other considerations, that

the fixture remains elastic under design actions.

In general, the approach described above calls for an iterative solution

procedure to calculate the position of the neutral axis and the tension forces

on the anchors. To avoid this iterative solution procedure it might be

assumed that the resultant compression force is located at the toe of the

attachment (see Figure 4.3-2b). For further discussion see Cook, Klingner

(1992).

The design value of tension loads on each anchor can be calculated from

the design values of normal forces and bending moments acting on the fixture

based on the assumption that the distribution of tensile strains across the

fixture is linear. Furthermore, a linear relationship between strains and

stresses is assumed.

If the fixture bears on the concrete (directly or through a grout layer), the

compression forces are transmitted to the concrete by the fixture. The

distribution of tension loads to the anchors may be calculated by applying the

method of reinforced concrete sections using the following assumptions:

– The axial stiffness Es·As of all anchors is equal. The cross-sectional

area of the anchor, As, may, in general, be calculated using the nominal

diameter of the anchor, dnom. Es is the modulus of elasticity of the

anchor material. For threaded anchors the stressed cross section

according to ISO 898-1 (ISO, 2009-1) should be taken.

As a simplification, the modulus of elasticity of concrete may be assumed

as Ec = 30,000 MPa.

– The modulus of elasticity of the concrete may be taken from relevant

Standards.

– In general, anchors do not resist compressive forces.



a) b)

Figure 4.3-2: Examples of elastic load distribution for an

anchorage with a rigid fixture loaded by a bending

moment and a normal force: a) distribution according

to theory of elasticity; b) simplifying assumption of

compression reaction at toe of column

Fixtures that exhibit large deformations under the design load may also be

used, provided that the resultant non-linear load distribution (Figure 4.3-3a)

and associated potential prying forces are taken into account

(Figure 4.3-3a, b). In this Design Guide no guidance is given regarding the

determination of the design actions on anchors in these applications.



a) b)

Figure 4.3-3: Examples of anchorages with flexible attachment:

a) column baseplate subjected to a moment; b) hanger

connection

For anchor groups loaded in tension and/or a bending moment, only the

anchors loaded in tension are included in the group resistance. In the example

in Figure 4.3-4b, only the anchors to the right of the neutral axis are

considered. The anchors located in the zone of compression are neglected.

An eccentricity due to non-equal tension forces in the individual anchors

affects the concrete cone resistance of the anchor group.

If the tension-loaded anchors do not form a rectangular pattern (example

see Figure 4.3-4c) the group of tensioned anchors may be reorganised into a

rectangular group to calculate the centre of gravity, which is point 'A' in

Figure 4.3-4c. This simplification will lead to a larger eccentricity and a

reduced concrete resistance.

For anchor groups with different levels of tension forces NSd,i acting on the

individual anchors of a group, the eccentricity eN of the tension force g

SdN of

the group of tensioned anchors with respect to their centre of gravity should

be calculated.



a)

b)

c)

Figure 4.3-4: Examples of anchorages subjected to an eccentric

tensile load: a) eccentricity along one axis – all

anchors in tension; b) eccentricity along one axis –

only some of the anchors of the group are in tension;

c) eccentricity along two axes – unsymmetrical tension

loading of the anchors



4.3.1.3 Shear loads on anchors

4.3.1.3.1 Distribution of shear loads – general method

Figure 4.3-5: Examples of distribution of applied shear load and

torsional moment acting on the fixture to anchors of a

group if hole clearances have not been provided in the

fixture or if the hole clearance is small (acl ≤ acl,1 with

acl,1 according to Table 4.3-1), and the resistance to

edge failure need not to be verified (because the edge

distance is large)

(1) General Determine the shear forces on the anchors of the group from the shear

forces and/or torsional moments acting on the fixture in accordance

with the theory of elasticity assuming equal stiffness for all anchors of

a group that participate in the resistance of shear forces. When

distributing the shear forces to anchors, equilibrium should be satisfied

(examples see Figure 4.3-5). Where the assumption of participating

anchors results in an eccentricity of the shear component relative to the

centre of gravity of the participating anchors, include the corresponding

eccentric torsional moment in the distribution of loads (examples see

Figure 4.3-16a and Figure 4.3-25).

Figure 4.3-6: Resolution of a shear force on the fixture acting

inclined to the edge and with an eccentricity in respect

of the centre of gravity of the anchor into orthogonal

shear loads and a torsional moment

If the shear load acting on the fixture is inclined to the edge and/or with

an eccentricity in respect to the centre of gravity of the anchors, in

general the determination of the distribution of the shear loads to the

anchors of a group is done for each of the orthogonal shear components

acting centrically on the fixture, i.e., perpendicular ( ,SdV ) and parallel

(VSd,) to the edge, and a torsional moment (TSd) (where applicable) (see

Figure 4.3-6). Subsequently, the calculated anchor shear forces are

added vectorially.

The anchors participating in the shear resistance in a group will depend on

a number of factors such as hole clearance, edge distance of the anchors,

orientation of the applied forces and the assumed location of concrete

fracture pattern in relation to anchor positions (i.e., when the anchors are

located within the volume of the concrete that is assumed to have failed).

For determination of the anchors that participate in resisting shear

forces the provisions (2) to (5) are valid. Furthermore, for the

verification of steel failure, pryout failure and concrete edge failure the

provisions in Section 4.3.1.3.2 should be observed.



For anchorages without hole clearance close to an edge (Figure 4.3-7) the

shear force is initially distributed to all anchors. When the distance between the front and back anchor is large (s1 > 1.0c1,1), a crack occurs first at the

front anchor closest to the edge (see Figure 4.3-7a). Often in the ultimate

limit state this crack is taken as the failure crack. This assumption leads to a

conservative estimation of the resistance with respect to concrete edge

failure, but is conversely associated with the maximum resistance with

respect to steel and pryout failure (greatest number of anchors active).

(2) Determination of anchors participating in shear for anchorages

without hole clearance

All anchors located in the line of the assumed failure plane and further

away from the edge are assumed to resist shear forces. Examples are

shown in Figure 4.3-5 for anchorages, where resistance to edge failure

need not to be evaluated (because the edge distance is large) and in

Figure 4.3-7 for a shear force acting perpendicular to the edge.

The maximum resistance in the ultimate limit state with respect to

concrete edge failure is reached after a redistribution of the shear loads from

the front anchors to the back anchors and the formation of a failure crack

originating at the back anchors (Figure 4.3-7b). However, in general the front

anchors do not take up a significant part of the shear load acting on the

fixture due to the prior formation of the failure crack and in this case the

resistance with respect to steel and pryout failure should be calculated with

the back anchors only.

The failure of the front anchor may have consequences for the structural

member from either a strength or serviceability standpoint. Therefore, in

general, the shear resistance associated with the concrete edge breakout

strength of the back anchors in a near-edge anchor group should be

accompanied by a serviceability check for front anchor edge breakout (see

Section 6.2).

For cases where combined tension and shear loading is present and where

the shear resistance is assumed to be provided entirely by the back anchors,

see Section 10.3.2.



a) b)

Figure 4.3-7: Example of distribution of applied shear VSd to

anchors in a group for verification of steel, pryout and

edge breakout failure, anchorage without hole

clearance: a) edge breakout failure assumed to initiate

at front anchor; b) edge breakout failure assumed to

initiate at back anchor (front anchor assumed to have

failed)

The described anchor shear load redistribution is shown in the examples

in Figure 4.3-8 to Figure 4.3-10, in which it is assumed that only the diameter

of the anchor is varied. In this case, the steel resistance varies significantly

whereby the concrete edge breakout and pryout resistances are nearly

constant. In Figure 4.3-8 it is assumed that the steel and pryout resistance of

the back anchor is higher than the concrete edge resistance of this anchor. In

Figure 4.3-9 failure is caused by steel failure of the back anchor because of

the assumed higher concrete edge resistance. In Figure 4.3-10 the assumed

low steel resistance could theoretically lead to progressive steel failure after

the formation of an edge breakout at the front anchor without additional load

resistance.



Figure 4.3-8: Example of an anchor group loaded in shear near a

free edge, transition of failure states from concrete

edge breakout at front anchor to concrete edge

breakout at back anchor



Figure 4.3-9: Example of an anchor group loaded in shear near a

free edge, transition of failure states from concrete

edge breakout at front anchor to steel failure of back

anchor



Figure 4.3-10: Example of an anchor group loaded in shear near a free

edge, progressive failure of concrete edge breakout at

front anchor followed by steel failure of back anchor

However, in the case of anchorages with an anchor spacing in the

direction perpendicular to the edge that is small relative to the edge distance

of the front anchors (s1 / c1,1 < 1.0), the formation of a crack originating from

the front anchors is suppressed by the compression stress field originating

from the back anchors (Anderson, Meinheit, 2005, 2007; Hofmann, 2005;

Periškić, 2006 and Grosser, Cook, 2009) and, at failure, the front anchors still

resist a fraction of the total shear force. Note that the behaviour of groups

under shear load inclined in respect to the edge has not been investigated.

Therefore, for reasons of simplicity this behaviour as it applies to the steel

and pryout capacity is neglected in this Design Guide.

Figure 4.3-11 shows an anchorage close to a corner for which both edges

should be verified. When calculating the resistance for concrete failure of the

bottom edge (shear load perpendicular to the edge) and of the right edge

(shear load parallel to the edge), the same number of anchors for transmitting

the shear load should be assumed for each considered case.



a)

b)

c)

Figure 4.3-11: Anchorage without hole clearance in a corner for

which verification of both edges is required: a) Shear

load is assumed to be transferred by all anchors; b)

front anchor is assumed to have failed; c) shear load is

assumed to be transferred by back anchor only

For anchor groups loaded in shear it is generally preferable to ensure that

no annular gap exists between the anchors and the fixture in order to promote

a uniform load distribution to the anchors. This may be accomplished as

described in Section 4.3.1.1. In many cases, however, it is not practical or

possible to provide for zero hole clearance.


with normal hole clearance

a) In this Design Guide normal hole clearances are defined in Table

4.3-1.



acl = df - d

acl = df - dnom

a) b)

Figure 4.3-12: Definition of hole clearance, acl, of anchors: a) bolt

projects through fixture; b) sleeve and bolt project

through fixture

For hole clearances acl ≤ acl,1 (with acl,1 = df,1 – d or acl,1 = df,1 – dnom) the

requirement for “normal hole clearance” as defined in Table 4.3-1 is met.

Table 4.3-1: Normal hole clearance acl,1 (see definition of hole

clearance, acl, in Figure 4.3-12)

1

Anchor

diameter da)

or

dnomb)

[mm] 6 8 10 12 14 16 18 20 22 24 27 30 > 30

2

Diameter df,1 of

clearance hole

in fixture [mm] 7 9 12 14 16 18 20 22 24 26 30 33

1.1da)

or

1.1dnom b)

3 Clearance acl,1

[mm] 1 1 2 2 2 2 2 2 2 2 3 3

0.1da)

or

0.1dnom b)

a) Bolt projects through fixture (Figure 4.3-12a)

b) Bolt and sleeve project through fixture (Figure 4.3-12b)

The basis for determining the distribution of shear loads in anchor groups

provided with normal hole clearance is the degree of anchor displacement

associated with concrete edge failure relative to the hole clearance in the

fixture. Test results show that with a large edge distance c ≥ 10hef and

c ≥ 60d (if bolt projects through the fixture) or c ≥ 60dnom (if sleeve projects

through the fixture) shear displacements at failure are much larger than the

normal hole clearances according to Table 4.3-1. Therefore, all anchors take

up shear loads.

b) Anchorages with a large edge distance in all directions: c ≥ 10hef and

c ≥ 60d (if bolt projects through the fixture) or c ≥ 60dnom (if sleeve

projects through the fixture).

All anchors are assumed to resist shear loads. Examples are shown

in Figure 4.3-5.

For cases involving small edge distances, the displacements associated

with concrete edge failure resulting from loading perpendicular to the edge

may be smaller than the normal hole clearances according to Table 4.3-1 (see

Figure 4.3-13a).

Therefore, for anchor groups in fixtures provided with normal hole

clearances and loaded by a shear force perpendicular to an edge, often only

the anchors closest to the edge are assumed to carry shear loads, when

checking the resistance against concrete edge failure (Figure 4.3-14a). This

c) Anchorages close to an edge: c1 < max(10hef , 60d) (if bolt projects

through the fixture) or c1 < max(10hef , 60dnom) (if sleeve projects

through the fixture) loaded by a shear force perpendicular to the

edge.

The determination of the anchors that resist shear loads depends on

the failure mode:



approach is conservative in cases, where the anchor displacement may be

estimated to be much larger than the provided hole clearance. When

checking the resistance against steel and pryout failure, anchor shear

displacements may be expected to be much larger than the allowable hole

clearances according to Table 4.3-1. Therefore, all anchors may be assumed

to resist shear forces (Figure 4.3-14b). Steel or pryout failure will govern the

design for relatively large edge distances only.

As with anchorages without hole clearances, the maximum resistance in

respect to concrete edge failure is reached when the load is redistributed to

the back anchor and the failure crack is generated from this anchor (crack 2

in Figure 4.3-14c). Because the front anchor has lost its resistance, only the

back anchor should be taken into account, when calculating the resistance

against concrete edge-, steel- and pryout failure. However, according to

results of tests described in Grosser, Cook (2009) for anchorages with a small

edge distance and a ratio s1 / c1,1 ≤ 1 the concrete edge failure load of the

back anchor(s) may be negatively influenced (up to 20%) by the crack

generated at the front anchor(s).

Concrete edge failure: only the anchors generating the assumed

failure plane should be assumed to take up shear forces (see

Figure 4.3-14a,c).

Steel and pryout failure: the anchors located in the assumed failure

plane and further away from the edge may be assumed to take up

shear loads (Figure 4.3-14b,c).

a) b)

Figure 4.3-13: Relative anchor displacements associated with shear

loading perpendicular and parallel to the edge



a) b)

c)

Figure 4.3-14: Example of distribution of applied shear load VSd to

anchors in a group with normal hole clearance

(acl ≤ acl,1): a) verification for edge breakout failure

when edge breakout is assumed to initiate at the front

anchor; b) verification for steel and pryout failure

when edge breakout is assumed to initiate at the front

anchor; c) verification for steel, pryout and edge

breakout failure when edge breakout is assumed to

initiate at the back anchor

Under otherwise constant conditions, the concrete edge failure load of

anchorages loaded in shear parallel to the edge is about two to three times the

value valid for anchorages loaded in shear perpendicular to the edge. As a

consequence, the displacements at failure are significantly larger compared

to loading perpendicular to the edge (increased resistance = increased

displacement at failure). In general, the displacements at failure are larger

than the allowable hole clearance according to Table 4.3-1 (see Figure

4.3-13b). For this reason it is assumed that all anchors resist shear forces.

The influence of the possible uneven distribution of the shear load acting on

the fixture to the anchors is taken into account in the resistance model.

d) Anchorages close to an edge: c1 < max(10hef , 60d) (if bolt projects

through the fixture) or c1 < max(10hef , 60dnom) (if sleeve projects

through the fixture) loaded in shear parallel to the edge or by a

torsional moment:

All anchors located in the line of the assumed failure plane and

further away from the edge are assumed to resist shear forces (see

examples in Figure 4.3-15). Figure 4.3-16 shows cases, where the

failure crack is assumed to occur at the back anchors.



a) b)

c)

,2 2

1 22

SdSd anchor

TV

s s

d)

Figure 4.3-15: Distribution of shear forces for anchorages with no

hole clearance or normal hole clearance (acl ≤ acl,1):

a) shear load parallel to the edge, concrete edge

failure assumed to originate at the front anchors;

b) torsional moment on a group of two anchors;

c) torsional moment on a group of four anchors, edge

failure assumed to originate at the front anchors;

d) torsional moment on a group of four anchors, edge

failure assumed to originate at the back anchors and

no torsional restraint



When a shear load acting on the fixture parallel or inclined to the edge is

distributed to the back anchors, a torsional secondary moment is generated. If

the fixture is not restrained (e.g., in case of a cantilever without connection to

another sufficiently stiff structural element) this torsional moment must be

resisted by the back anchors (see Figure 4.3-16a). In the case of an anchorage

with two anchors oriented perpendicular to the edge, the loss of the front

anchor leads to the failure of the anchorage. However, with a group of four

anchors the shear resistance might be increased due to redistribution of the

shear forces to the back anchors.

If the torsional secondary moment is taken up by another structural

element (e.g., by a floor or a cross beam) the back anchors are loaded by the

shear load only (Figure 4.3-16b). When designing the element that is

attached to the fixture and the element(s) that takes up the torsion moment,

the torsional secondary moment must be taken into account.



Rotation unrestrainedRotation unrestrained

a)

Rotation restrained by deckingRotation restrained by decking

b)

Figure 4.3-16: Anchor group close to an edge loaded by a shear load

parallel to the edge (after failure of the front anchors):

a) without torsional restraint; torsional moment

TSd = VSd·s1/2 is taken up by the back anchors;

b) with torsional restraint, torsional moment is taken

up by the beam attached to the fixture in connection

with another structural element(s) restraining the

beam (e.g., floor) (in a) and b) the bending moment on

the anchorage resulting from the load shown in the

3D-sketches is disregarded)



When a torsional moment acts on the fixture of a group of four anchors,

in the extreme case only the two front anchors may resist shear forces (see

Figure 4.3-17). However, in practice the position of the anchor as shown in

Figure 4.3-17 is considered as highly unlikely. Therefore, in general it may

be assumed that all anchors contribute to resist the torsional moment (see

Figure 4.3-15c).

Figure 4.3-17: Possible distribution of torsional moment to a group of

four anchors with unfavourable anchor positions

relative to holes in baseplate for evaluation of concrete

edge breakout (normal hole clearances (acl ≤ acl,1)

exaggerated for clarity)

a) b) c)

Figure 4.3-18: Examples of distribution of shear load and torsional

moment to anchors of a group (where concrete edge

failure need not to be verified because the edge

distance is large) in fixtures provided with large hole

clearance (acl > acl,1 according to Table 4.3-1)


with a large hole clearance (acl > acl,1 according to Table 4.3-1)

Only the most unfavourable anchors (having the highest ratio between

design actions and design resistance due to combined loading and/or

positioning) should be assumed to carry shear loads. Examples are

shown in Figure 4.3-18 and Figure 4.3-19.



Figure 4.3-19 shows an anchorage with four anchors with large hole

clearance close to an edge loaded by a bending moment and a shear load

towards the edge. The bending moment causes tension forces in the back

anchors. For the verification of steel and pryout resistance it should be

assumed that the shear force is taken up by the back anchors (unfavourable

anchor loading), while for the verification of concrete edge failure the front

anchors should be assumed to take up the shear force (unfavourable anchor

positioning).

a)

b)

c)

Figure 4.3-19: Example of an anchorage close to an edge with large

hole clearance (acl > acl,1 according to Table 4.3-1):

a) loading pattern (the two back anchors are loaded

by a tension force); b) distribution of shear forces for

verification of steel failure; c) distribution of shear

forces for verification of concrete edge failure



Figure 4.3-20: Example for the use of oversized or slotted holes to

prevent participation of near edge anchors in resisting

shear forces

(5) Determination of anchors that resist shear forces for anchorages

with slotted holes in the fixture oriented parallel to the direction of

the shear load

The anchors not located in slotted holes are assumed to take up shear

loads. Slotted holes can be used to relieve anchors close to an edge

which may otherwise cause a premature edge failure (Figure 4.3-20). In

this case no check in the serviceability limit state is necessary.

In Table 4.3-2 through Table 4.3-4 examples are given for the distribution

of concentrically applied shear loads to a far- and near-edge orthogonal six-

anchor array (anchorage with no hole clearance) or orthogonal four-anchor

array (anchorage with normal hole clearance (acl ≤ acl,1) close to an edge).

Table 4.3-2 addresses shear loads acting perpendicular to the edge, Table

4.3-3 shear loads acting parallel to the edge on an anchor group without

torsional restraint, and Table 4.3-4 handles torsional moments. Note that for

checking concrete edge failure the provisions in Section 4.3.1.3.2b) should

additionally be taken into account in Table 4.3-3 and Table 4.3-4.



Table 4.3-2: Anchors resisting shear forces in the case of an

applied shear load acting perpendicular to the

edge. Note, that for anchors with normal hole

clearance only anchorages with two anchor rows

perpendicular to the edge are covered by this

Design Guide (see Figure 4.3-1)

Edge

distance

Considered failure

plane

Steel and pryout failure.

No and normal hole clearance (acl ≤ acl,1)

Concrete edge

failure. No hole clearance

Concrete edge failure. Normal

hole clearance

(acl ≤ acl,1)

Sufficient

to not

require verification

of concrete

edge breakout

resistance

Not applicable

Not applicable Not applicable

Concrete edge

break ut

resistance applicable

Not covered

Unloaded anchor

Loaded anchor

Unloaded anchor

Loaded anchor



Table 4.3-3: Anchor resisting shear forces in the case of an applied

shear load acting parallel to the edge (figure valid for

case without rotational restraint). Note, that for

anchors with normal hole clearance only anchorages

with two anchor rows perpendicular to the edge are

covered by this Design Guide (see Figure 4.3-1)

Edge distance Considered failure plane

Steel and pryout failure. No

and normal hole clearance

(acl ≤ acl,1)

Concrete edge failure.

No or normal hole

clearance (acl ≤ acl,1)

Sufficient to

not require

verification of concrete edge breakout

resistance

Not applicable

Not applicable

Concrete

edge breakout


Shear due to torsion: 2 2

1,2 1,2 22 2SdV s s s

Shear due to torsion: 1,2 2SdV s s

Unloaded anchor

Loaded anchor

Unloaded anchor

Loaded anchor



Table 4.3-4: Anchors resisting shear forces in the case of an

applied torsional moment. Note, that for anchors

with normal hole clearance only anchorages with

two anchor rows perpendicular to the edge are

covered by this Design Guide (see Figure 4.3-1)

Edge

distance Considered failure plane

Steel and pryout failure. No

and normal hole clearance

(acl ≤ acl,1)

Concrete edge failure.

No or normal hole

clearance (acl ≤ acl,1)

Sufficient to

not require verification

of concrete

edge breakout

resistan e

Not applicable

Not applicable

Concrete edge

breakout


1)

1)

Unloaded anchor

Loaded anchor

Unloaded anchor

Loaded anchor

1)

For concrete edge failure further distribution of shear loads according to Figure

4.3-27



4.3.1.3.2 General aspects for verification of failure modes

a) b) c)

Figure 4.3-21: Example of the resolution of unequal shear forces on

anchors in the group into an eccentric shear force:

a) forces acting on fixture; b) determination of shear

forces on anchors; c) resolution of anchor shear

forces into an eccentric shear force

(1) Verification of steel failure

Determine the highest loaded anchor in the group of anchors that are

assumed to resist shear.

(2) Verification of pryout failure

Determine the resultant shear load acting on the anchors that are

assumed to resist shear. Where applicable, determine the eccentricity of

the resultant shear force with respect to the centre of gravity of the

anchors resisting shear. An example is shown in Figure 4.3-21.

If an anchorage is loaded by a combination of a shear force perpendicular

and/or parallel to the edge and a torsion moment, the shear loads on the

anchors are calculated for each individual load case as explained in Section

4.3.1.3.1 (1) to (5) and then superimposed. This approach has been chosen

for reason of simplicity even if it may not be considered as fully consistent in

all cases.

(3) Verification of concrete edge failure

a) Determine the resultant shear load of the anchors located in the

assumed line of failure plane according to Section 4.3.1.3.1 (1) to

(5) and taking into account b) and c) below. Examples are shown in

Figure 4.3-22 to Figure 4.3-27.



a)

b)

c)

Figure 4.3-22: Examples of distribution of shear forces on anchors of

a group with normal hole clearance (acl ≤ acl,1, with

acl,1 according to Table 4.3-1) for verification of

concrete edge failure assumed to be generated at the

front anchors: a) shear load perpendicular to the

edge; b) shear load parallel to the edge; c) shear load

acting inclined to the edge



Various investigations (Mallée, 2001, 2002 and Hofmann, 2005) have

shown that in general shear components acting perpendicular and away from

an edge do not significantly influence the concrete edge breakout resistance

of the group. Therefore, these components may be neglected in the

assessment of the concrete breakout resistance. If in the case of shear loads

with opposed directions (see Figure 4.3-23c), the ratio between spacing and

edge distance of the anchors resisting the shear force is small and the ratio

between the characteristic resistances for pryout and concrete edge failure is

high, the above approach may be unconservative up to 20% as reported in

Grosser (2008). Further research is required to provide specific guidance for

these cases.

Note that the verification of steel and pryout failure should be performed

with all loads acting on the anchors (omission of shear component acting

perpendicular and away from the edge is not permitted).

b) Components of the resultant shear forces on anchors acting

perpendicular away from the edge may be neglected. Examples are

shown in Figure 4.3-23 through Figure 4.3-25.

c) Where applicable, determine the eccentricity of the resultant shear

force with respect to the centre of gravity of the anchors resisting

shear and the angle αV (the angle between the resultant shear force

on the anchors and a line perpendicular to the edge). Examples are

given in Figure 4.3-21, Figure 4.3-22c and Figure 4.3-24 through

Figure 4.3-27.

a)



b)

c)

Figure 4.3-23: Examples of anchor groups at the edge loaded by a

shear force or torsional moment for verification of

concrete edge failure: a) group of two anchors at an

edge loaded by VSd directed away from the edge; b)

group of two anchors at an edge loaded by VSd with an

angle 90° < 'v < 180°; c) group of two anchors at

the edge loaded by a torsional moment



a)



b)

Figure 4.3-24: Examples of anchor groups at the edge loaded by a

shear force and a torsional moment for verification of

concrete edge failure: a) shear component due to

torsional moment larger than component of shear

force; b) shear component due to torsional moment

smaller than component of shear force



a) b) c)

d1)

d2)

Figure 4.3-25: Distribution of an inclined shear load to a group of

four anchors with no or normal hole clearance

(acl ≤ acl,1) without torsional restraint for verification

of concrete edge breakout failure assumed to be

generated at the back anchors: a) inclined shear load

acting at centroid of anchor group; b) shear load



resolved in a centric shear load and a torsional

moment on back anchors; c) resulting shear

components applied to back anchors; d1) combination

of shear components resulting in both anchors loaded

in shear towards the edge and resultant shear load on

group; d2) combination of shear components resulting

in only one anchor loaded in shear towards the edge

and resultant shear load on group

a) b) c)

Figure 4.3-26: Example of distribution of shear load to the back

anchors of a group with four anchors with no or

normal hole clearance (acl ≤ acl,1) with torsional

restraint. Shear load inclined with respect to the edge:

a) resolution of load into orthogonal components;

b) distribution of load to back anchors assuming edge

breakout failure originating at the back anchors;

c) resultant shear load on back anchors



,2 2

1 22

SdSd anchor

TV

s s

a) b)

c) d)

Figure 4.3-27: Distribution of shear load and torsional moment to a

group of four anchors with normal hole clearance

(acl ≤ acl,1), failure is assumed to be initiated at front

anchors: a) shear resisted by front anchors, torsional

moment by all anchors; b) loads on back anchors

neglected; c) load components on front anchors

combined; d) orthogonal loads resolved into an

inclined load with eccentricity and angle V for

assessment of concrete edge breakout resistance

With regard to the distribution of a shear load and a torsional moment to the

anchors of a group with four anchors with s2 >> s1 (see Figure 4.3-28a) it

should be noted, that the shear loads resulting from the torsional moment,

VSd,anchor act almost perpendicular to the concrete edge. In such a situation one



may consider a different distribution of the shear loads resulting from the

torsional moment than shown in Figure 4.3-27 by assuming that the back

anchors do not contribute to take up the torsional moment. This results in the

distribution of shear forces shown in Figure 4.3-28b. Since no research is

available regarding this aspect, a specific value for the ratio s2 / s1, which

requires a distribution of shear loads according to Figure 4.3-28b cannot be

provided and engineering judgement is necessary. Note, that the assumption

according to Figure 4.3-28b is conservative.

a)

b)

Figure 4.3-28: Distribution of shear load and torsional moment to a

group of four anchors with normal hole clearance

(acl ≤ acl,1) and s2 >> s1, failure is assumed to be

initiated at front anchors: a) shear resisted by front

anchors, torsional moment by all anchors; b) shear

and torsional moment resisted by front anchors only



4.3.1.3.3 Distribution of shear loads – alternative approach

(1) For the verification of steel and pryout failure Section 4.3.1.3.1 applies

without modifications.

When an anchor is loaded in shear parallel to the edge, concrete edge

failure is initiated by the splitting forces perpendicular to the edge. The

failure surface is rather similar to the failure surface when the shear load acts

perpendicular to the edge (compare Figure 4.3-29a with Figure 4.3-29b).

In an alternative approach (Mallée, Pusill-Wachtsmuth, 2007) a shear

load acting parallel to an edge (Figure 4.3-30a) is substituted by a virtual

shear load perpendicular to the edge (Figure 4.3-30b). This virtual shear load

is equal to the splitting force shown in (Figure 4.3-29b). If the load acts

under an angle towards the edge (Figure 4.3-31a), the component of the shear

load acting parallel to the edge is substituted by a virtual shear load, which is

added to the component of the shear load acting perpendicular to the edge

(Figure 4.3-31b). Mallée, Pusill-Wachtsmuth (2007) propose the factor

according to Equation (4.3-1b):

10.4 1 2d c (4.3-1b)

In this Design Guide the factor 90 ,1 V , with 90°,V according to

Section 10.2.5.1.1f), is assumed as:

0.4 anchorage with 3 anchors in the considered failure plane, see

Figure 10.2-5

0.5 anchorage with 2 anchors in the considered failure plane, see

Figure 10.2-5

0.67 single anchor

(2) For the verification of concrete edge failure, the shear forces on the

shear carrying anchors are calculated according to Section 4.3.1.3.1 (2)

to (4). Components of the resultant shear forces on anchors acting

perpendicular away from the edge may be neglected (see 4.3.1.3.2(3)b).

Components of the shear force acting parallel to the edge are

substituted by a shear force acting perpendicular to the edge according

to Equation (4.3-1)

VSd, = VSd, (4.3-1)

with:

,SdV = virtual design shear force on anchor acting perpendicular to

the edge

VSd, = design value of shear force on anchor acting parallel to the

edge

=

90 ,1 V (4.3-1a)

90°,V = factor according to Equation (10.2-5f) or Equation

(10.2-5f1)

When using the approach with virtual shear loads acting perpendicular to

the edge, the same assumptions for the distribution of shear loads to the

anchor of a group should be used as given in Section 4.3.1.3.1. In addition

general aspects for verification of failure modes as given in Section 4.3.1.3.2

should be taken into account.

The real and virtual shear forces on anchors acting perpendicular to the

edge are superimposed.

The calculation of the virtual shear loads is exemplified in Figure 4.3-32

using the example of Figure 4.3-25 as well as in Figure 4.3-33 using the

example of Figure 4.3-26.



a) b)

Figure 4.3-29: Single anchor at an edge loaded in shear

a) b)

Figure 4.3-30: Substitution of a shear load acting parallel to the edge

(a) by a virtual shear load acting perpendicular to the

edge (b).

a) b)

Figure 4.3-31: Substitution of a shear load acting with an angle V to

the edge (a) by a superimposition of a real and a

virtual shear load acting perpendicular to the edge (b)



a)

b1)

b2)


anchors of a group with four anchors without

torsional restraint with no or normal hole clearance

(acl ≤ acl,1) loaded by a shear load inclined with

respect to the edge using the virtual load method:



a) resolution of load into orthogonal components

(compare with Figure 4.3-25a,b,c); b1) resultant shear

forces on both back anchors act toward the edge;

b2) resultant shear force on one back anchor acts

away from the edge

a) b)

c) d)


anchor of a group with four anchors with torsional

restraint with no or normal hole clearance (acl ≤ acl,1)

using the virtual load method. Shear load inclined

with respect to the edge: a) resolution of load into

orthogonal components (compare Figure 4.3-26a); b)

redistribution of shear load to back anchors; c) sub-

stitution of shear load components acting parallel to

the edge by a virtual shear load acting perpendicular

to the edge; d) resultant shear load on back anchors



4.3.1.4 Shear loads without lever arm

Figure 4.3-34: Anchorage with baseplate and grout

In general, static shear loads acting on anchors may be assumed to act

without a lever arm if all of the following conditions are fulfilled:

a) the fixture is made of metal and in the area of the anchorage is fixed

directly to the concrete without an intermediate layer or with a

levelling layer of mortar with a compressive strength ≥ 30 MPa and a

thickness tgrout ≤ d/2 (Figure 4.3-34);

b) after anchor installation and prestressing the fixture is in contact with

the anchor over a length of at least 0.5tfix (relevant for sleeve anchors,

see Figure 4.3-35) and the bearing pressure between sleeve and fixture

is smaller than the value allowed by the code for steel design (e.g., EN

1993-1-8:2005 (CEN, 2005)).

Figure 4.3-35: Bearing length of a sleeve anchor in fixture

With load cases including fatigue and seismic loads it should only be

assumed that shear loads act without a lever arm, when the fixture bears

directly against the concrete (no levelling mortar is present or if the thickness

of the grout is not larger than approximately 3 mm).



4.3.1.5 Shear loads with lever arm

a) b)

Figure 4.3-36: Anchorage with lever arm

a) b)

Figure 4.3-37: Examples of anchorages a) without and b) with full

rotational restraint of the anchorage at the end of the

fixture

If one of the conditions a) and b) of Section 4.3.1.4 is not fulfilled, it should

be assumed that the shear force acts on the anchor with a lever arm. The lever

arm l is calculated according to Equation (4.3-2):

3 1l a e (4.3-2)

with:

e1 = distance between shear load and concrete surface

a3 = 0.5d for post-installed and cast-in-place anchors (see Figure 4.3-36a)

= 0 if a washer and a nut are directly clamped to the concrete surface

(see Figure 4.3-36b)

The design moment acting on the anchor is calculated according to

Equation (4.3-3):

Sd Sd

M

lM V

(4.3-3)

The value M depends on the degree of restraint of the anchor at the side

of the fixture of the application in question and should be determined

according to good engineering practice.

No restraint (M = 1.0) should be assumed, if the fixture can rotate freely

(see Figure 4.3-37a). This assumption always is on the safe side. M = 1.0

should always be assumed, if the diameter of the hole in the fixture is greater

than the value df,1 according to Table 4.3-1 or if the hole clearance is acl ≤ acl,1

and the fixture is not clamped to the anchor by nut and washer.

In general full restraint (M = 2.0) may be assumed only if the fixture

cannot rotate (see Figure 4.3-37b) and either:

(1) the anchor is welded to, or threaded into the fixture, or

(2) is clamped to the anchor by nut and washer (see Figure 4.3-36b) and

the hole clearance in the fixture is acl ≤ acl,1 with acl,1 according to

Table 4.3-1.

If restraint of the anchor is assumed, the fixture and/or the anchored

element should be able to take up the restraining moment.



4.3.2 Plastic analysis

The plastic design approach may enable the use of anchors with a smaller

cross sectional area compared to the elastic design approach. However, the

required embedment depth and edge distance may be larger than for the

elastic design approach to preclude a concrete failure.

4.3.2.1 Field of application

Currently there is only limited information regarding the plastic behaviour

of anchor groups loaded by moments acting in two directions and/or by

torsional moments. Therefore, these cases are not covered by this Design

Guide.

In a plastic analysis it is assumed that significant redistribution of anchor

tension and shear forces will occur in a group. Therefore, this analysis is

acceptable only when the failure is governed by ductile steel failure of the

anchor.

The attachment shown in Figure 4.3-38 is for illustration purposes. Other

forms of the attachment are permissible.

Anchor configurations covered by this Design Guide are shown in Figure

4.3-38. The number of anchors parallel to the axis of bending may be larger

than two.

Figure 4.3-38: Examples of anchor configurations covered by this

Design Guide for plastic design.



The use of bonded anchors in cases where plastic design is to be used

presents special problems. It is necessary to ensure that the unbonded length

is adequate to guarantee the necessary elongation associated with plastic

design. This may be accomplished by de-bonding a length of the anchor, or

by providing sufficient rod length between the surface of the concrete and the

fixture (e.g., as in an anchor chair). The use of screw anchors and other

anchor types where sufficient stretch length cannot be provided is not

recommended for plastic design.

Pullout failure may occur at large displacements allowing for some

redistribution of tension forces. However, redistribution of shear forces may

not be significant. Due to the lack of relevant information, plastic analysis

should not be applied for this type of failure.

Anchorages loaded by normal and shear forces and by a bending moment

around one axis may be assumed to exhibit ductile steel failure if the

following conditions are met:

(1) The number of anchors in the plane of the moment is limited to 3.

The Equation (4.3-4) is based on evaluations of Hoehler (2006) (Section 8

– Probability of Brittle Failure During an Earthquake) whereby the

probability that concrete failure occurs prior to steel failure is taken as 10-2

.

Plastic analysis is also allowed for anchorages with anchor reinforcement

to take up tension or shear forces acting on the fixture. When anchor

reinforcement is provided, this reinforcement should be dimensioned such

that it is able to carry the tension forces in the concrete associated with

concrete cone or a concrete edge failure.

(2) The strength of the anchorage is governed by ductile steel failure of

the anchors. To ensure ductile steel failure of the anchorage Equation

(4.3-4) should be satisfied:

,

, 0.6k c

k s

inst

RR

(4.3-4)

with:

Rk,s = characteristic resistance of the anchors against steel failure

Rk,c = minimum characteristic resistance against relevant concrete

failure modes. For anchorages without anchor

reinforcement: pullout, concrete cone, splitting, blowout

failure (tension loading), concrete pryout or edge failure

(shear loading). In case of anchor reinforcement, the value

Rk,c corresponding to concrete cone failure (tension loading)

or concrete edge failure (shear loading) should be replaced

by the characteristic resistance of the anchor reinforcement.

γinst = partial factor for installation safety according to Section

3.4.2.1

(3) Equation (4.3-4)) should be checked for tension, shear and combined

tension and shear forces on the anchors.



Sufficient ductility of the anchor may be assumed if the following

conditions are fulfilled (Cook, Klingner, 1992):

(1) The nominal anchor steel strength should not exceed

fuk = 800 MPa, the ratio of nominal steel yield strength to nominal

ultimate strength should not exceed fyk / fuk = 0.8, and the rupture

elongation (measured over a length equal to 5d) should be at least

12%. ASTM A193 (ASTM, 2009) B7 steel may be assumed to fulfil

these requirements.

(2) Anchors that incorporate a reduced section (e.g., bolt with partial

thread) should satisfy the following conditions:

a) For anchors loaded in tension, the strength Nuk of the reduced

section should be adequate to permit yielding over the balance of

the anchor length and sufficient stretch length should be provided.

In cases where the steel at the reduced section meets the minimum

requirements outlined in (1) above, the plastic steel elongation

should be roughly the same as for an anchor without a reduced

section. For cases involving multiple reduced sections (e.g.,

threads as well as deformations in the expansion zone), it may be

necessary to conduct an analysis for the critical anchor segment,

and to establish that the strength of this critical element is

sufficient to induce yielding in the other, non-critical sections.

Note that many steels used in anchor fabrication do not exhibit a

clear yield point, and that the yield strength is determined by

convention based typically on the 0.2% offset method. For this

reason, it may be necessary to develop some multiple of the yield

strength at the critical section. This is product and material-

dependent.

b) For anchors which are assumed to redistribute shear forces, the

reduced section should begin at a distance ≥ 5d below the concrete

surface. In the case of threaded anchors, the threaded part should

extend for a length ≥ 2d into the concrete.

c) For anchors loaded in combined tension and shear, the conditions

a) and b) above should be met.

(4) The ductility of the anchor should be adequate to allow the assumed

redistribution of forces.



(5) The steel fixture should be embedded in the concrete or fastened to

the concrete without an intermediate layer or with a layer of mortar

with a thickness ≤ d/2 (d = anchor diameter) and a compressive

strength, fck ≥ 30 MPa. In case of seismic or fatigue loading, the

thickness of the mortar should be not larger than approximately 3 mm.

(6) The diameter of the clearance hole in the fixture should be

df ≤ df,1 with df,1 as given in Table 4.3-1.

4.3.2.2 Loads on anchors

It may be assumed that all anchors are stressed up to their design

resistance without taking into account compatibility conditions. However, the

following conditions should be met:

(1) Tension and shear acting on each anchor should lie within the

tension-shear interaction diagram for that anchor (see Parts II to

IV of this Design Guide).

cd = 6fck / Mc is 50% larger than the maximum value according to CEB

FIP Model Code 1990 (CEB, 1993) for partial loading. This increase is based

on the results of tests by Cook, Klingner (1992). The assumed stress

distribution is indicated in Figure 4.3-39 and Figure 4.3-40.

For both rigid and flexible baseplate behaviour, the distribution of

compressive stress between the baseplate and concrete is non-linear. It is

assumed that the stress distributions shown in Figure 4.3-39 and

Figure 4.3-40 are conservative.

(2) For design purposes, a rectangular compressive stress block

between fixture and concrete may be assumed; the compressive

stress can be taken as cd ≤ 6fck / Mc.

(3) The location of the resultant compressive force CSd should be

determined based on rigid or flexible baseplate behaviour in

accordance with (a) or (b) below.



Figure 4.3-39: Rigid baseplate behaviour

(a) Rigid baseplate behaviour:

For rigid baseplate behaviour, the compressive force is assumed to

act at the extreme edge of the baseplate (see Figure 4.3-39). To

ensure this behaviour, the baseplate should be of sufficient

thickness to prevent yielding of the fixture at the edge of the

attached member on the compression side of the fixture. The

minimum baseplate thickness may be determined on the basis of

Equation (4.3-5)

4yd SdM C a (4.3-5)

with:

Myd = design moment that causes yielding of the fixture

calculated with fyd = fyk / Ms (Ms may be taken as 1.1)

CSd = design resultant compressive force

a4 = distance from the edge of the attached member to the

resultant compressive force

Figure 4.3-40: Flexible baseplate behaviour

(b) Flexible baseplate behaviour:

If the baseplate is not stiff enough to obtain rigid baseplate

behaviour, a hinge will form on the compression side of the

baseplate at the edge of the attached member. This will cause the

compressive reaction to move inward toward the attached

member. The distance a4 between the edge of the attached

member and the resultant of the compressive reaction may be

calculated according to Equation (4.3-6) (compare Figure 4.3-40).

5

yd

Sd

Ma

C (4.3-6)

with Myd and CSd defined in Equation (4.3-5).



Equations (4.3-5) and (4.3-6) can only be used if the thickness of the

baseplate is known. If this is not the case, designers may assume that the

compressive reaction is located at either the edge (a4 = 0) or centroid of the

compression element of the attached member. This conservative assumption

simplifies design calculation.

Equation (4.3-7) is valid for one row of tensioned welded member.

Figure 4.3-41: Prevention of prying action

(4) Both for rigid and flexible baseplate behaviour, the formation of a

hinge in the baseplate on the tension side of the connection should

be prevented. This is necessary to ensure that prying action

between the baseplate and the concrete (see Section 4.3.1.2) does

not develop. Prying action may be prevented by satisfying

Equation (4.3-7).

6yd SdM N a (4.3-7)

with Myd as defined in Equation (4.3-5) and

NSd = sum of the design tension forces of the outermost row of

anchors

a6 = distance between outermost tension anchors and edge of

the attached member (see Figure 4.3-41)

Figure 4.3-42: Condition for anchors transferring a tension force

equal to the design yield resistance

(5) Only those anchors which satisfy Equation (4.3-8) should be

assumed to transfer a tension force.

7 80.4a a (4.3-8)

with:

7 8( )a a = distance between the resultant compression force

and the innermost (outermost) tensioned anchor

(see Figure 4.3-42)

(6) It may be assumed that all anchors or only part of the anchors

carry shear loads. The shear load acting on the individual anchors

of a group may not be equal.


Part I: 5 Determination of concrete condition 102

4.4 Serviceability limit state and fatigue

In the serviceability limit state and for fatigue loading the forces on

anchors should be determined according to Section 4.3.1 (elastic analysis)

with γG = γQ = γind = 1.0.

4.5 Seismic loading

The assumption of elastic distribution of loads is generally conservative

for the case of seismic loads. The use of the plastic analysis methods

described in Section 4.3.2 should be applied with caution, since the low-cycle

fatigue behaviour of anchors yielding in tension and subject to cyclic shear is

poorly understood.

Note that in general this Design Guide limits the size of anchor groups

loaded in shear due to the concern for excessive shear lag. In practice, much

larger groups are typically used (e.g., for collectors, perimeter anchorage of

braced frame elements, etc.). In these cases, there may be some justification

for the assumption of uniform load distribution (i.e., due to progressive

softening of the anchor response under cyclic shear) however, these cases are

not addressed further in this Design Guide.

When considering seismic loading, load distributions in accordance with

either the elastic or plastic analysis procedures described in this document are

admissible provided that the specific conditions of Sections 4.3.1 and 4.3.2

are fulfilled.

5 Determination of concrete condition (1) The designer should check whether the concrete in the region of

the anchorage is cracked or uncracked. The check on the condition

of the concrete can be avoided by assuming that the concrete is

cracked.

(2) For seismic design situations the concrete should always be

assumed to be cracked in the region of the anchorage.

(3) For non-seismic design situations uncracked concrete may be

assumed in the design of anchorages, if for each anchor it is

proven that under service conditions of the concrete member the

anchor with its entire embedment depth is located in uncracked

concrete. The concrete may be assumed to be uncracked, if

Equation (5-1) is observed:



0L R (5-1)

with:

L = stresses in the concrete induced by external loads

including anchor loads

If no detailed analysis is conducted, then R should be assumed to be

equal to 3.0 MPa. This value is used in EN 1992-1-1:2004 (CEN, 2004-1)

when calculating the minimum reinforcement to limit crack widths.

R = stresses in the concrete due to restraint of intrinsic

imposed deformations (e.g., shrinkage of concrete) or

extrinsic imposed deformations (e.g., due to

displacement of support or temperature variations)

The stresses L and R should be calculated assuming that the

concrete is uncracked.

(4) For anchorages in slabs, walls and shells, Equation (5-1) should be

checked for both mutually perpendicular directions in the plane of

the structure.

6 Verification of limit states

6.1 Ultimate limit state

The characteristic resistance is defined as the 5%-fractile of the strength of

the total population for a confidence level of 90%.

Often in codes, the nominal steel yield strength and nominal steel ultimate

strength are given. These nominal values may be assumed as characteristic

values for tension and shear, respectively.

The characteristic concrete breakout resistance under tension and shear for

any anchor should be based on design models which result in prediction of

strength in good agreement with results of comprehensive tests, accounting

for size effects as well. The models should take into account factors which

affect anchor strength, such as embedment depth, spacing and edge distance,

depth of the structural member, and the presence or the absence of concrete

cracking. Limits on edge distance and anchor spacing in the design model

For each anchorage the characteristic resistance to all possible failure

modes should be calculated. Specifically, the following characteristic

resistances should be calculated: steel failure under tension and shear,

concrete cone, blowout, concrete splitting and pullout failure under tension

loading, concrete edge and concrete pryout failure under shear loading of the

anchors. Where anchor reinforcement is provided, the calculation of the

characteristic resistances associated with the concrete cone and concrete edge

failure modes is replaced by a check of the characteristic resistance associated

with the anchor reinforcement (steel and bond resistance). The minimum of

the above mentioned resistances divided by the appropriate partial factor for

resistance (see Section 3.4.2) should be taken as the design resistance of the

anchorage.


Part I: 6 Verification of limit states 104

should be consistent with the tests that have verified the model. Interaction of

tensile and shear loads should be considered in the design using an interaction

expression which results in prediction of strength in substantial agreement

with results of comprehensive tests.

The above requirements are satisfied by the Concrete Capacity Method

(CC-Method) described in the following parts of this Design Guide.

For combined tension and shear forces, the effect of their interaction on

the resistance should be taken into account.

The design models adopted in this Design Guide for the determination of

the characteristic resistances for the different concrete failure models are

valid under the assumption that the structural element that takes up the loads

transferred by the anchorage is at or below the serviceability limit state, when

the anchorage reaches the ultimate limit state.

Possible failure modes for anchorages are shown in Figure 3.2-1 (tension)

and Figure 3.2-2 (shear).

6.2 Serviceability limit state

It may also be necessary to limit the rotation of the fixture, if excessive

rotations could lead to aesthetic or non-structural damage. If the design is

done according to the elastic design approach, this condition is satisfied when

the partial factors in the ultimate limit state proposed in this Design Guide

both for actions and for the resistance to steel failure are applied. If the design

is performed according to the plastic design approach, then a check that this

condition is satisfied may be necessary.

In the serviceability limit state it should be shown that the displacements

occurring under the design actions do not exceed the admissible displacement

and that no excessive cracking occurs.

It should be demonstrated that Equation (3.3-1) is fulfilled for all loading

directions (tension, shear, combined tension and shear), assuming design

action and resistance are expressed in terms of displacements. The admissible

displacement, d, depends on the application in question and should be

evaluated by the designer.

For the determination of displacements, S, resulting from loads acting on

the anchorage, a linear function between loads and displacements may be

assumed. In the case of combined tension and shear loads, the displacements

for the shear and tension components of the resultant load should be added

vectorially.

The characteristic displacements under tension and shear loads of the

anchor are given in this Design Guide (for headed anchors and anchor

channels) or in the Approval.

Using the partial factors for steel failure given in this Design Guide (see

Section 3.4.2.1.1) will prevent yielding under service loads.

In the case of anchor groups near a free edge and loaded towards or

parallel to the edge, particular consideration should be given to the potential

for premature cracking of the concrete originating from the near-edge anchors

leading to excessive crack widths under service loads. Such premature

The resultant stress in the most loaded anchor under the design tension or

shear actions should not exceed yield.

If it is assumed in the verification of the concrete edge resistance in the

ultimate limit state that the failure crack does not start from the front

anchor(s) of a group (those anchors nearest the edge), it should be verified

that in the serviceability limit state the crack widths do not exceed the



cracking may occur if it is assumed in the design that the failure crack does

not start from the front anchor(s). The likelihood of premature failure of the

near-edge anchors is influenced by the hole clearance, the ratio of edge

distance to anchor spacing in the direction orthogonal to the edge and the

absence or presence of anchor reinforcement. In general, welded headed studs

with close spacing (s1 ≤ c1,1) are not susceptible to such premature edge

failure. Where hole clearances are present, the check according to Equation

(6.2-1) should be done independent of the ratio s1 / c1,1.

Theoretically, the first crack can occur at a row beyond that nearest to the

edge. However, the occurrence of an initial crack at a row beyond the near

edge row has so far not been experimentally verified. Therefore, it is assumed

that an SLS check for the anchors nearest to the edge is sufficient. If anchor

reinforcement designed according to Section 19.2.2 is provided to take up

shear loads, it may be assumed that the width of cracks starting from the front

anchors is limited to acceptable values. Therefore, the check according to

Equation (6.2-1) may be omitted.

serviceability crack width limits. This is accomplished by checking for

concrete breakout starting from the near edge anchors (see Equation (6.2-1)).

1,1Sd RdV V c (6.2-1)

with:

VSd = design shear force acting on the front anchor(s) calculated

according to Section 4.3.1.3 with G = Q = 1.0

1,1RdV c = design concrete edge resistance of the front anchor(s) with

an edge distance c1,1 calculated with Mc = 1.0

Furthermore, for cases where combined tension and shear loading is

present and where the shear resistance is assumed to be provided entirely by

the back anchor(s), a reduction in the calculated resistance of the front

anchor(s) in tension due to the formation of a shear crack at the near-edge

anchor(s) must be taken into account (see Section 10.3.2).

For anchor groups loaded in both tension and shear, additional

considerations apply (see Section 10.3.2).

6.3 Fatigue

Figure 6.3-1 illustrates a pulsating action. Figure 6.3-2 illustrates an

alternating shear action.

This Design Guide covers applications with anchors subjected to pulsating

tension load, alternating shear load and combinations thereof. For load

combinations including seismic loading see Section 6.4.



Figure 6.3-1: Definition of pulsating actions

Figure 6.3-2: Definition of alternating shear actions

Alternating axial loads on the anchor are not addressed for fatigue loading,

because in general compression loads are transferred directly from the fixture

to the base material (Figure 1.5-2).

Loosening of the nut or bolt under fatigue loading may be prevented by

the use of lock nuts, counter nuts or other suitable means. Elimination of hole

clearance in the connection can be accomplished through the use of e.g.,

welded anchors, weld washers or by filling the annular gaps with suitable

grout. It is advisable to maintain some level of prestress in the connection in

order to avoid secondary effects associated with anchor displacements.

Fatigue verification should be carried out, when anchors are subjected to

regular load cycles (e.g., anchorage of cranes, reciprocating machinery, guide

rails of elevators). Fatigue loading may also arise due to restraint of members

subjected to temperature variations, e.g., façades.

Anchors used to resist fatigue loading should be prequalified by

appropriate tests.

Anchorages subjected to fatigue shear loading should be constructed such

that there is no annular gap between the anchors and the baseplate. Loosening

of the nut or bolt should be avoided.



In general, fatigue verification is not required when:

Fewer than 1000 load cycles are expected for pulsating loads on

the anchor with a load range NSk = NSk,max – NSk,min less than or

equal to NRd / Q where NRd is the design resistance for steel failure

and Q = 1.5.

Fewer than 10 load cycles of alternating shear are expected with a

load range VSk = VSk,max – VSk,min less than or equal to VRd / Q

where VRd is the design resistance for steel failure and

Q = 1.5. For smaller amplitudes of the shear load the number of

load cycles where no verification is required may be increased.

Load cycles are imposed by climatic variations and the stress

range caused by the restraint forces in the most stressed anchor is

limited to Sk = Sk,max – Sk,min ≤ 100 MPa or, in the case of

shear loading, if the maximum stress range of the most stressed

anchor is limited to Sk = Sk,max – Sk,min ≤ 60 MPa (τ = shear

stress in the anchor). These values have historically been used for

the design of façade anchorages.

The values of NRk,s, NRk,p, VRk,s and VRk,sm should be established for 62 10 load cycles.

The verification under fatigue loading consists of both the verification

under static and fatigue loading. Under static loading, the anchorage design

should be based on the design methods given in the relevant Sections of this

Design Guide. The verifications under fatigue loading are given below.

The required verifications for all load directions are summarised in Table

6.3-1 and Table 6.3-2

Table 6.3-1: Required verifications - tension loading

Failure

mode Single anchor Anchor group

a)

1 Steel

failure

,

,

,

Rk s

F fat Sk

Ms fat

NN

,

,

,

RN Rk sh

F fat Sk

Ms fat

NN

2 Pullout

failure

,

,

,

Rk p

F fat Sk

Mp fat

NN

,

,

,

RN Rk ph

F fat Sk

Mp fat

NN

3

Concrete

cone

failure

,

,

,

Rk c

F fat Sk

Mc fat

NN

,

,

,

Rk cg

F fat Sk

Mc fat

NN

4

Concrete

splitting

failure

,

,

,

Rk sp

F fat Sk

Mc fat

NN

,

,

,

Rk spg

F fat Sk

Mc fat

NN

5

Concrete

blowout

failure

,

,

,

Rk cb

F fat Sk

Mc fat

NN

,

,

,

Rk cbg

F fat Sk

Mc fat

NN

a) For steel and pullout failure modes, check critical anchor (anchor that

experiences the largest stress range)

with:

F,fat = partial factor for action (see Section 3.4.1)

= 1.0

Ms,fat = partial factor for steel failure (see Section 3.4.2.3)



Mp,fat = partial factor for pullout failure (see Section 3.4.2.3)

Mc,fat = partial factor for concrete failure (see Section 3.4.2.3)

RN = factor for anchor groups; taken from relevant Approval or

determined from the results of suitable prequalification tests

< 1.0

NSk = NSk,max – NSk,min; twice the amplitude of the fatigue tensile

action, see Figure 6.3-1

NRk,s = characteristic fatigue resistance in tension to steel failure;

taken from the relevant Approval or determined from the

results of suitable prequalification tests

NRk,p = characteristic fatigue resistance in tension to pullout failure;



NRk,c = characteristic fatigue resistance in tension to concrete cone

failure

Tests by Lotze (1993) indicate that the fatigue resistance corresponding to

concrete cone failure is roughly 60% of the static resistance. It is assumed

that this ratio is also valid for other concrete failure modes.

~ 60% of the characteristic resistance corresponding to

concrete cone failure under static loading, i.e., NRk,c

NRk,sp = characteristic fatigue resistance in tension to concrete

splitting failure


splitting failure under static loading, i.e., NRk,sp

NRk,cb = characteristic fatigue resistance in tension to blowout failure


blowout failure under static loading, i.e., NRk,cb

The values NRk,c, NRk,sp and NRk,cb should be evaluated according to the

corresponding parts of this Design Guide.



To account for the potential non-uniform loading of anchors in a group

arising from differences in anchor stiffness, the fatigue resistance of the most

loaded anchor is reduced by RN for tensile loading or by RV for shear

loading. The factors RN and RV should be evaluated from prequalification

tests. For the special case of groups of two anchors subjected to shear loading

perpendicular to the axis of the anchorage when the fixture is able to rotate,

the value of RV may be taken as 1.0. In many applications

0.70 ≤ RN (RV) ≤ 0.85 may be used.

Table 6.3-2: Required verifications - shear loading

Failure

mode Single anchor Anchor group

a)

1

Steel failure

without

lever arm

,

,

,

Rk s

F fat Sk

Ms fat

VV

,

,

,

RV Rk sh

F fat Sk

Ms fat

VV

2

Steel failure

with lever

arm

,

,

,

Rk sm

F fat Sk

Ms fat

VV

,

,

,

RV Rk smh

F fat Sk

Ms fat

VV

3

Concrete

pryout

failure

,

,

,

Rk cp

F fat Sk

Mc fat

VV

,

,

,

Rk cpg

F fat Sk

Mc fat

VV

4 Concrete

edge failure

,

,

,

Rk c

F fat Sk

Mc fat

VV

,

,

,

Rk cg

F fat Sk

Mc fat

VV

a) For steel failure modes, check critical anchor (anchor that experiences the largest

stress range)

with:

Ms,fat = partial factor for steel failure (see Section 3.4.2.3)

Mc,fat = partial factor for concrete failure (see Section 3.4.2.3)

RV < 1.0; for anchor groups; taken from relevant Approval or

determined from the results of suitable prequalification tests

VSk = VSk,max – VSk,min; twice the amplitude of the fatigue shear

action, see Figure 6.3-2

VRk,s = characteristic fatigue resistance in shear to steel failure;



VRk,sm = characteristic fatigue resistance in shear to steel failure with

anchor bending (see relevant sections in the following

Parts)

The values VRk,cp and VRk,c should be evaluated according to the

corresponding parts of this Design Guide.

VRk,cp = characteristic fatigue resistance in shear to concrete pryout

failure


concrete pryout failure under static loading, i.e., VRk,cp



It should be noted that limited testing indicates that anchors subjected to

alternating shear near free edges may exhibit a reduced fatigue capacity

associated with concrete edge failure as compared to anchors loaded in

pulsating shear. In these cases, it may be appropriate to limit the load

amplitude VRk = VSk,max – Vsk,min to 0.3VRk,c.

VRk,c = characteristic fatigue resistance in shear to concrete edge

failure


concrete edge failure under static loading, i.e., VRk,c

For combined tension and shear loading the Equation (6.3-1) should be

satisfied:

, , 1.0N fat V fat

(6.3-1)

with:

N,fat = ,

,

1.0F fat Sk

Rk M fat

N

N

single anchors (6.3-1a1)

= ,

,

1.0

h

F fat Sk

RN Rk M fat

N

N

steel and pullout

failure of anchor

groups

(6.3-1a2)

= ,

,

1.0

g

F fat Sk

Rk M fat

N

N

concrete failure of

anchor groups

(concrete cone,

splitting and

blowout failure)

(6.3-1a3)

V,fat = ,

,

1.0F fat Sk

Rk M fat

V

V

single anchors (6.3-1b1)

= ,

,

1.0

h

F fat Sk

RV Rk M fat

V

V

steel failure of

anchor groups (6.3-1b2)

= ,

,

1.0

g

F fat Sk

Rk M fat

V

V

concrete pryout

and concrete edge

failure of anchor

groups

(6.3-1b3)

= factor taken from the relevant Approval or determined from

the results of suitable prequalification tests (see Section

1.3). In general = 1.0 should be taken.



Alternatively, the interaction Equation (6.3-1) may be checked separately

for steel failure modes and concrete failure modes (including pullout failure)

under tension and shear loads. The corresponding factors should be

evaluated from appropriate prequalification tests. In general = 1.0 may be

taken.

The largest value of N,fat and V,fat calculated according to Equations

(6.3-1a1) to (6.3-1b3) for the different failure modes should be inserted in

Equation (6.3-1).

6.4 Verification for load combinations

including seismic actions

The proper design of anchorages for seismic conditions involves many

considerations apart from the specific resistances assigned to the anchors.

These may include the effects of large displacements, degradation of the

supporting member, secondary forces associated with eccentricities and

requirements for ductile behaviour.

This section provides additional requirements for anchorages used to resist

seismic actions. It is applicable to connections between structural elements or

between non-structural attachments and structural elements.

The simulation of seismic loading in prequalification tests should properly

include consideration of crack width, number and amplitude of load cycles on

the anchorage and the member resulting in opening and closing of cracks,

strain rate and loading direction. Other factors may be relevant for specific

cases.

Anchors used to resist seismic actions should be prequalified for cracked

concrete. In addition, they should be prequalified by suitable tests simulating

seismic conditions.

When performing anchorage design for seismic applications, the concrete

in the region of the anchorage should always be assumed to be cracked.

Critical regions include, but are not limited to zones where plastic hinges

in a beam or column may form and regions in shear walls or coupling beams

where large diagonal cracks may occur.

The question of anchor displacements in the case of seismic loading

should be considered from two perspectives:

– the anchor displacements in response to the imposed loading may be

large and may have negative consequences for the performance of the

attachment;

– the displacements imposed by the response of the structure on the

anchorage may be large and may exceed the anchor displacement

capacity.

Each of these considerations requires careful assessment of the anchorage

detailing and the expectations for the anchorage performance.

The provisions in this section do not apply to the design of anchorages in

critical regions of concrete elements where concrete spalling or excessive

cracking may occur.

Anchor displacements in the case of seismic loading should be assessed

using engineering judgement.



When distributing forces to the individual anchors of a group, the designer

should take into account the stiffness of the fixture and its ability to

redistribute loads to other anchors in the group beyond yield of the fixture.

Yielding of the fixture is not excluded by the design.

Annular gaps should be avoided to prevent movement of the fixture

relative to the anchor during cyclic shear. Such movement may result in an

increase of the shear load on the anchorage due to impact (Rieder,

Bergmeister, 2010). Furthermore, under cyclic shear, gaps will lead to

unequal distribution of shear loads to the anchors of a group, thus resulting in

a reduced group resistance.

Engineering judgement is necessary to determine whether the restriction

on annular gaps applies in every case.

In general, annular gaps between an anchor and its fixture should be

avoided for anchorages to be subjected to seismic actions. Loosening of the

nut or screw should be prevented by appropriate measures. For less critical

applications, a small annular gap (df ≤ df,1 with df,1 as defined in Table 4.3-1)

may be allowed if the effect of this gap on the magnitude of the shear load

acting on the anchorage, on the distribution of the shear load to the anchors of

a group and on their resistance is taken into account.

Design values of the effect of seismic actions on the fixture should be

determined according to structural design codes using the partial factors

given in Section 3.4.1. Vertical seismic actions acting on elements should

also be considered where appropriate.

In general, the loads acting on the fixture should be distributed to the

anchors of a group according to Section 4.3.1 (see also Section 4.5).

For steel and pullout failure under tension and shear load of single

anchors, the characteristic resistances to seismic actions, Rk,eq

(NRk,s,eq; VRk,s,eq; MRk,s,eq; NRk,p,eq), should be determined on the basis of the

results of appropriate qualification tests. For the calculation of concrete cone,

blowout or splitting failure under tension loading and pryout or concrete edge

failure under shear loading, the characteristic resistance to seismic actions is

assumed to be equal to the resistance under static loading multiplied with the

seismic reduction factor eq.

Uncertainty exists on both the resistance and actions side with respect to

the design of anchorages to resist seismic forces.

In Equation (6.4-1b,c), the term eq is primarily intended to address

uncertainty associated with anchorage resistance. In Equation (6.4-1b) it

accounts for the potential non-uniform loading of anchors in a group arising

from differences in anchor stiffness (compare factors RN and RV in Section

6.3). A value eq = 0.75 is proposed in CEN-TS (CEN, 2009) and eq = 1.0

in ACI 318-08 App. D (ACI 318, 2008). These values are valid for the anchor

The design resistance of an anchorage to seismic actions for tension and

shear loads Rd,eq should be calculated as follows:

– characteristic resistance determined in appropriate prequalification

tests (steel failure under tension and shear load and pullout failure

under tension load):

,

,

k eq

d eq

M

RR

(single anchors) (6.4-1a)

,

,

k eq

d eq eq

M

RR

(anchor groups) (6.4-1b)

– characteristic resistance not determined in appropriate prequalification

tests (concrete cone, blowout or splitting failure under tension loading

and pryout or concrete edge failure under shear loading):



configurations covered in this Design Guide. For larger anchor configurations

(e.g., collector elements) a more detailed analysis to account for the load

distribution to the anchors should be performed. In Equation

(6.4-1c) the value eq accounts for crack widths under seismic conditions

that may be larger than those in non-seismic conditions and the general

damage state of the concrete. A value of eq = 0.75 is suggested based on

current experience (ACI 318-08 App. D (ACI 318, 2008), CEN-TS (CEN,

2009)). Further research is needed to determine the value eq for the different

failure modes.

,k

d eq eq

M

RR

(6.4-1c)

with:

Rk,eq = characteristic seismic resistance for a given failure mode

determined in appropriate prequalification tests

Rk = characteristic resistance for a given failure mode under static

loading

eq = seismic reduction factor

γM = partial factor for resistance according to Section 3.4.2.4.

The principle objective of the seismic design of anchorages is to prevent

brittle failure. In the case of structural connections (e.g., beam to column) the

connection should not fail (i.e., suffer loss of load-carrying capacity) prior to

the development of the yield capacity of the connected members (see Figure

6.4-1a). It may also be permissible to develop the yield capacity of the fixture

or baseplate (Silva, 2002), thus affording sufficient displacement capacity to

avoid brittle failure (Figure 6.4-1b). Of course, these two options are not

mutually exclusive and a connection may permit the development of several

points of yielding. Where the attached member has a specific ultimate

capacity that can be reliably predicted, it is acceptable to proportion the

connection for this strength (Figure 6.4-1c).

a) b) c)

Figure 6.4-1: Seismic design for protection of the anchorage:

a) yielding of the attached element; b) yielding of the

fixture; c) design for capacity of the attached element

The design of anchorages to resist seismic actions should be based on at

least one of the following approaches:

(1) The anchorage is designed for the minimum of the following:

– the force corresponding to yielding of the attached ductile steel

element taking into account over-strength;

– the maximum force that can be transferred to the connection by the

attached element or structural system.



Equation (6.4-2) should be required for tension (shear) only, if only

tension (shear) loads act on the anchorage, or the Equation (6.4-2) should be

observed for tension and shear, if combined loading acts on the anchorage.

Under specific circumstances it may be desirable to design for yielding of

the anchors (Figure 6.4-2). A requirement for ductile anchor yielding in

tension requires consideration of the gauge length over which yielding can

occur in order to provide a meaningful degree of elongation. This may be

linked to the performance expectations for the structure.

Figure 6.4-2: Seismic design for ductile anchor yield

Equation (6.4-2) is based on a statistical assessment of various prescribed

margins of safety between concrete and steel failure. The factor 0.6 is

intended to give a 1% probability of concrete failure prior to the intended

anchor steel failure for typical anchor and material parameters (Hoehler,

2006).

Pseudo-ductile failure modes such as anchor pull-through or pullout may

be acceptable. However, sufficient knowledge is not currently available to

provide design guidelines for these cases.

Note also that the use of anchor yielding or other pseudo-ductile anchor

response modes for energy dissipation in system response should be

approached with caution. Furthermore, anchor displacements corresponding

to yielding, pullout, etc. may result in amplified tension demands as a result

of impact.

(2) The strength of the anchorage is governed by the strength of ductile

steel anchor. To ensure ductile steel failure of the anchorage, the

following relation should be satisfied:

, ,

, , 0.6k other eq

k s eq

inst

RR

(6.4-2)

with:

Rk,s,eq = characteristic seismic resistance for steel failure

Rk,other,eq = characteristic seismic resistance for all non-steel failure

modes

inst = partial factor for installation safety according to

Section 3.4.2.1

Simultaneously, condition (4) of Section 4.3.2.1 should be observed.

Where ductile behaviour of the anchorage is precluded either due to

geometrical limitations (e.g., member thickness, edge distance, anchor

spacing) or for strength reasons, brittle failure of the anchorage is avoided by

designing for a multiple of the calculated seismic force (Figure 6.4-3).

For non-structural elements, it may be permissible to satisfy Equation

(6.4-3) in lieu of (1) and (2) above.



The value 2.5 corresponds to the usual assumption for the ratio between

elastic and inelastic response and it is commonly referred to as response

modification factor. The following relationship between the response

modification factor, R, and the system ductility, μ is assumed: 2 1R .

The implied value of μ is approximately 3.5 (Newmark, Hall, 1982).

This approach is primarily intended for non-structural elements and

should in general be avoided for the connection of primary structural

elements. Implicit in this design option are the following assumptions:

– brittle failure is associated with a higher probability of failure because

the uncertainties in the earthquake induced actions influence directly

the forces on the anchorage;

– failure of non-structural elements is less likely to result in catastrophic

consequences than failure of structural connections.

Figure 6.4-3: Seismic design for a multiple of the calculated seismic

force

, ,2.5 d eq d eqS R (6.4-3)

with:

Rd,eq according to Equation (6.4-1a,b,c).

Minimum edge distance and minimum spacing between anchors should be

determined as for static design situations.

Different product specific values for seismic design situations may be

evaluated from suitable seismic prequalification tests.

The interaction between tension and shear forces should be determined

assuming a linear interaction relation as given in Equation (6.4-4).

, ,

, ,

1.0Sd eq Sd eq

Rd eq Rd eq

N V

N V

(6.4-4)

In Equation (6.4-4) the largest ratios NSd,eq / NRd,eq and VSd,eq / VRd,eq, for the

different failure modes should be inserted.



6.5 Fire

6.5.1 General

For bonded anchors and bonded-expansion anchors the fire resistance

associated with bond failure is product dependent, therefore no general rules

can be given. Product specific rules may be given in the relevant Approval.

However, currently no acceptance criteria for bonded anchors under fire

exposure are available. Anchor channels are not covered because sufficient

experience is not available.

Anchorages close to an edge with fire exposure from two or more sides

(see Figure 6.5-1) are not covered due to lack of experience. Some results

based on numerical simulations are given in Periškić (2010).

Figure 6.5-1: Anchorage subjected to fire exposure from multiple

directions

The design method is valid for cast-in-place headed anchors, expansion

anchors, undercut anchors and concrete screws only. The design method

covers anchors with fire exposure from one side or from more than one side if

the edge distance of the anchor is c ≥ 300 mm and c ≥ 2hef.

The fire resistance is classified according to EN 13501-2 (CEN, 2007)

using the Standard ISO time-temperature curve according to ISO 834

(ISO, 1999).

The design under fire exposure is carried out according to the design

method for ambient temperature given in this Design Guide with the

modifications given below.

When performing anchorage design under fire exposure, the concrete in

the region of the anchorage should always be assumed to be cracked. As a

consequence, it is likewise assumed that the concrete is reinforced.

It is assumed that fire does not occur concurrently with wind and seismic

loading. Therefore, the verification for fire resistance is not required for

anchors designed exclusively for wind or seismic loading.

Where anchors resist only wind or seismic forces, verification for fire

resistance is not required.

6.5.2 Partial factors

In general, the values for the partial factors are F,fi = 1.0 and M,fi = 1.0.

Partial factors for actions F,fi and for materials M,fi should be taken from

CEB (1991) or CEN (2004-2).



6.5.3 Resistance under fire exposure

The characteristic values given in this Design Guide are superseded by

data given in the relevant Approval.

In the absence of test data for a specific anchor the following

characteristic resistances in the ultimate limit state under fire exposure may

be taken. They are valid for anchors installed in concrete strength classes C20

to C50. These values are conservative.

6.5.3.1 Tension load

6.5.3.1.1 Steel failure

The characteristic resistance of an anchor associated with steel failure

under fire exposure (NRk,s,fi) is given by Equation (6.5-1)

, , , ,Rk s fi Rk s fi sN A (6.5-1)

with:

Rk,s,fi = taken from Table 6.5-1 and Table 6.5-2. These values are also

valid for the unprotected steel part of the anchor outside the

concrete

As = minimum cross section along the stressed anchor length

Table 6.5-1: Characteristic tension strength of a carbon steel

anchor under fire exposure

Anchor

bolt/thread diameter, d

Effective

embed-ment

depth

hef

Characteristic tension strength Rk,s,fi of an unprotected anchor made of carbon

steel according to ISO 898 (ISO, 2009-1) in case of fire exposure in the time up

to: Rk,s,fi [MPa]

[mm] [mm] 30 min

(R 15 to R30)

60 min

(R45 and R60)

90 min

(R90)

120 min

(R120)

6 30 10 9 7 5

8 30 10 9 7 5

10 40 15 13 10 8

≥ 12 50 20 15 13 10



Table 6.5-2: Characteristic tension strength of a stainless steel

anchor (steel according to Table 7-1, lines 8 to 11)

under fire exposure

Anchor

bolt/thread diameter, d

Effective

embedment depth

hef

Characteristic tension strength Rk,s,fi of an unprotected anchor of stainless

steel according to ISO 3506 (ISO, 2009-2) in case of fire exposure in the time up to:

Rk,s,fi [MPa]

[mm] [mm] 30 min

(R 15 to R30)

60 min

(R45 and R60)

90 min

(R90)

120 min

( R120)

6 30 10 9 7 5

8 30 20 16 12 10

10 40 25 20 16 14

≥ 12 50 30 25 20 16

6.5.3.1.2 Pullout failure

The characteristic resistance of anchors associated with pullout failure

under fire exposure (NRk,p,fi) may be obtained from Equation (6.5-2).

, , , , ,Rk p fi p N fi Rk pN N (6.5-2)

with:

Based on limited test experience (Reick, 2001) the following values of

p,N,fi may conservatively be used:

p,N,fi = 0.25 for fire exposure up to 90 minutes

p,N,fi = 0.20 for fire exposure exceeding 90 minutes and up to 120

minutes

p,N,fi = reduction factor

NRk,p = characteristic resistance in cracked concrete C20 under

ambient temperature given in the relevant Approval

6.5.3.1.3 Concrete cone failure

The characteristic resistance of an anchorage associated with concrete

cone failure under fire exposure (NRk,c,fi) may be calculated according to the

relevant parts of this Design Guide valid for ambient temperature with the

following modifications:

Based on studies in Reick (2001) and Periškić (2010) the following values

of c,N,fi may conservatively be used:

– replace 0

,Rk cN by 0

, ,Rk c fiN according to Equation (6.5-3).



, , 1.0200

ef

c N fi

h for fire exposure up to 90 minutes

, , 0.8 1.0200

ef

c N fi

h for fire exposure exceeding 90 minutes and up to

120 minutes

hef = effective embedment depth in mm

Note that according to Reick (2001) and EOTA TR 020 (EOTA, 2004-2)

the value 0

,Rk cN is limited to C20. However, based on the Periškić (2010) this

limitation has been neglected here.

0 0

, , , , ,Rk c fi c N fi Rk cN N (6.5-3)

with:

c,N,fi = reduction factor

0

,Rk cN

= characteristic resistance of a single anchor in cracked

concrete under ambient temperature according to the

relevant product specific part of this Design Guide

A limited number of test results indicate that the critical spacing should be

increased to account for the reduction in concrete strength associated with

fire exposure (Reick, 2001).

– replace scr,N = 2ccr,N = 3hef by scr,N,fi according to Equation

(6.5-4):

, , , ,2 4cr N fi cr N fi efs c h (6.5-4)

6.5.3.1.4 Splitting failure

The assessment for splitting is predicated on the assumption that the

concrete member in which the anchor is located is reinforced.

The assessment of splitting failure due to loading under fire exposure is

not required because the splitting forces are assumed to be taken up by the

reinforcement.

6.5.3.2 Shear load

6.5.3.2.1 Steel failure

6.5.3.2.1.1 Shear load without lever arm


under fire exposure (VRk,s,fi) is given by Equation

(6.5-5):

, , 2 , ,Rk s fi Rk s fi sV k A (6.5-5)

with:

Under normal temperature the ratio between the characteristic shear and

tensile strength is assumed as 0.5 (see Equation 10.2-1). A limited number of

tests indicate that this ratio increases under fire conditions. It is assumed here

as k2 = 1.0.

k2 = ratio between shear and tensile strength

= 1.0

Rk,s,fi = taken from Table 6.5-1 or Table 6.5-2

As = stressed cross section of the anchor in the shear plane



6.5.3.2.1.2 Shear load with lever arm

The approach for anchors loaded in shear with a lever arm is based on

theoretical considerations only.


loaded in shear with a lever arm under fire exposure (VRk,sm,fi) is given by

Equation (6.5-6):

0

, ,

, , , ,

M Rk s fi

Rk sm fi Rk s fi

MV V

l

(6.5-6)

with:

M = factor discussed in Section 4.3.1.5

l = length of the lever arm according to Equation (4.3-2)

0

, ,Rk s fiM = characteristic bending resistance of an individual anchor

Equation (6.5-6a) is taken from EOTA Technical Report TR 020 (EOTA,

2004-2).

= , ,1.2 el Rk s fiW [Nm] (6.5-6a)

Wel = elastic section modulus of an individual anchor at the sheared

cross-section

Rk,s,fi = according to Table 6.5-1 or Table 6.5-2

VRk,s,fi = characteristic shear resistance for a lever arm equal to zero

calculated according to Equation (6.5-5)

6.5.3.2.2 Concrete pryout failure

The characteristic resistance of an anchor associated with pryout failure

under fire exposure (VRk,cp,fi) may be obtained using Equation (6.5-7):

, , 4 , ,Rk cp fi Rk c fiV k N (6.5-7)

with:

According to current experience:

k4 = 1.0 hef < 60 mm

k4 = 2.0 hef ≥ 60 mm

k4 = factor valid for ambient temperature. It is given in the

Approval.

NRk,c,fi = calculated according to Section 6.5.3.1.3



6.5.3.2.3 Concrete edge failure

The characteristic resistance of an anchorage associated with concrete

edge failure under fire exposure (VRk,c,fi) may be calculated according to the

relevant product specific part of this Design Guide valid for ambient

temperature by replacing 0

,Rk cV with 0

, ,Rk c fiV according to Equation (6.5-8):

0 0

, , , , ,Rk c fi c V fi Rk cV V (6.5-8)

with:

The concrete edge resistance under fire exposure is influenced by several

parameters including member thickness, edge distance, etc. The following

values for c,V,fi , taken from EOTA Technical Report TR 020

(EOTA, 2004-2), are believed to be conservative:

c,V,fi = 0.25 for fire exposure up to 90 minutes

c,V,fi = 0.20 for fire exposure exceeding 90 minutes and up to 120

minutes

Note, that according to Reick (2001) and EOTA TR 020 (EOTA, 2004-2)

the value 0

,Rk cV is limited to C20. However, based on the Periškić (2010) this

limitation has been neglected here.

c,V,fi = reduction factor

0

,Rk cV

= characteristic concrete edge resistance of a single anchor in

cracked concrete under ambient temperature according to the

relevant product specific part of this Design Guide

6.5.3.3 Combined tension and shear load

Due to a lack of available data for combined loading under fire exposure

conditions, the combined loading condition is evaluated based on experience

with ambient temperature conditions.

The interaction equations given for ambient temperature are assumed to be

valid for fire loading; however, the resistances for ambient temperature

should be replaced with those for fire.


Part I: 7 Durability 122

7 Durability This section provides general guidance on corrosion protection. The

required method of corrosion protection should be evaluated by the design

professional on a case by case basis. The following considerations are

relevant:

In general, moisture is necessary for corrosion to occur. Therefore, for

anchorages for use in structures subject to dry conditions no special corrosion

protection is necessary for steel parts. However, care should be taken that

anchors in interior conditions will not be exposed to moisture resulting from,

e.g., condensation or the application of wet finish materials such as plaster,

over the life of the anchorage.

The coatings on post-installed anchors and anchor channels, e.g., a zinc

coating with a minimum thickness of 5 μm, are provided only to prevent

corrosion during storage and shipping prior to use.

For anchorages for use in structures subject to normal atmospheric

exposure or exposure in damp internal conditions, the metal parts should be

protected in an appropriate manner. One such type of protection is the use of

an appropriate type of corrosion resistant steel. The type of corrosion resistant

steel used for the various service environments should be in accordance with

Standard Codes of Practice. In general, austenitic steels meeting the

requirements of corrosion protection Class III as given in Table 7-1 have

shown good performance in exterior environmental conditions. The use of

other corrosion protection methods such as hot-dip galvanizing, sheradizing,

etc. may also be appropriate in some cases.

In particularly aggressive environments such as permanently alternating

immersion in seawater or the splash zone of seawater, chloride atmosphere of

indoor swimming pools or atmosphere with extreme chemical pollution, e.g.,

in desulphurisation plants or road tunnels especially when de-icing materials

are used, special consideration should be given to corrosion resistance. The

metal parts of the anchor (bolt, screw, nut and washer) should be made of

corrosion resistant steel suitable for the high corrosion exposure. In general,

steel types according to corrosion Class IV in Table 7-1 have shown good

performance. Another alternative to ensure corrosion resistance is to provide

non-alloyed steel with double corrosion protection (e.g., hot-dip galvanizing

with a coating thickness of 70 µm to 100 µm plus a plastic coating).

The durability of an anchorage should not be less than the intended period

of use of the part of the structure for which the anchorage is required. For this

period of use, the mechanical properties as well as the load bearing behaviour

of the anchorage should not be adversely affected by environmental

influences such as corrosion, oxidation, aging or alkalinity of the concrete.

The anchorage and its protection should be selected in accordance with

the environmental conditions at the location of the anchorage. It should be

borne in mind that there may be an adverse change in the environmental

conditions over the period of use, e.g., corrosion as a result of increased

industrialization and that in general, anchorages cannot be inspected and

maintained.

The use of anchors in the context of durability requirements is regulated

by the Approval. In general, the requirements correspond to an assumed

intended working life of the anchorage of 50 years.



Table 7-1: Examples of corrosion resistant steels and their

applications (DIBt, 2009)

European

Material

Number

Common

abbreviation

Corrosion

protection class Typical applications

1 1.4003 I / Low Interiors

2 1.4016

3 1.4301 A2

II / Moderate Accessible constructions without significant

chloride or sulphur dioxide loads

4 1.4307 A2L

5 1.4567 A2L

6 1.4541 A3

7 1.4318 A2

8 1.4401 A4

III / Medium Inaccessible constructions 1) with moderate

chloride or sulphur dioxide loads

9 1.4404 A4L

10 1.4578 A4L

11 1.4571 A5

12 1.4439 4)

13 1.4362 4)

14 1.4462 4)

IV / Severe

Installations with high corrosion potential

due to exposure to chlorides or sulphur

dioxide (or due to chemical concentrations,

e.g., as found in seawater and road tunnel

atmosphere); for indoor pools see footnotes 2) 3).

15 1.4539 4)

16 1.4565 4)

17 1.4529 4)

18 1.4547 4)

1) Inaccessible means constructions whose condition cannot be inspected or can only be

inspected with difficulty and can only be repaired, if necessary, at very great expense 2) Steel with material No. 1.4539 for components in indoor pool atmospheres without regular

cleaning of the steel and water complying with German‟s Drinking Water Statute 3) Steel with material Nos. 1.4565, 1.4529 and 1.4547 for components in indoor pool

atmospheres without regular cleaning of the steel and water rich in chloride salt (e.g., brine

water) 4) No common abbreviation has been decided yet

Electrolytic corrosion may occur between dissimilar metals, e.g. carbon

steel in contact with corrosion resistant steel. Other forms of corrosion may

occur, e.g. pitting corrosion, crevice corrosion and stress corrosion. These may

be particularly relevant for corrosion resistant steels or high strength steel.

If an anchor is coated to ensure its proper functioning, e.g. the expansion

cone of a torque-controlled expansion anchor, the durability of the coating

should be checked in the prequalification tests for the intended conditions of

use.


Part I: 8 Provisions for ensuring the characteristic resistance of the concrete member 124

8 Provisions for ensuring the

characteristic resistance of the

concrete member

8.1 General

Forces originating from anchored components should be accommodated in

the design of the structure as required to prevent local overstress of the

immediate structural elements. One approach is to check the capacity of the

first structural element in the load path (for example, the floor beam directly

under an anchored component) for all loads, including the anchorage load.

This procedure is repeated for each successive structural element or

connection in the load path until the load case including the anchorage loads

no longer governs the design of the element. This will occur when the

anchorage loads become small relative to the other actions on the structural

element.

The local transmission of the anchor loads to the concrete is checked

according to Equation (3.3-1). The characteristic resistance of the anchorage

for various types of anchors and for various possible failure modes is given in

the following Parts of this Design Guide.

The transmission of the anchor loads to the remainder of the structure

should be checked for the ultimate limit state and the serviceability limit state

according to the usual verifications with due consideration of the anchor

loads. For these verifications the additional provisions given in Sections 8.2

and 8.3 should be taken into account.

8.2 Shear resistance of concrete member

The reasoning for the provisions according to Section 8.2 are given in

Lieberum et al. (1987) and Reuter, Eligehausen (1992).

Where a strut and tie model is used for the determination of shear

resistance (Figure 8.2-1), the influence of the anchor-induced stresses on the

design shear resistance associated with concrete struts, VRd,c, and tension ties

(shear reinforcement), VRd,s, may be taken into account in lieu of using

Equation (8.2-1b).

(1) In general, the shear forces VSd,a induced in the concrete member at the

support by anchor loads should not exceed the value

, ,10.4Sd a RdV V (8.2-1a)

(member without shear reinforcement)

, , ,0.4 min( ; )Sd a Rd s Rd cV V V (8.2-1b)

(member with shear reinforcement)

with:

VRd,1 = design shear resistance of member without shear

reinforcement according to CEB-FIB Model Code

1990 (CEB, 1993), Equation (6.4-8)

VRd,s = design shear resistance of member with shear

reinforcement as governed by strength of web

reinforcement according to CEB-FIB Model Code



, ,min ,Rd Rd c Rd sV V V

VRd,c = design shear resistance of concrete compression strut of member

with shear reinforcement

VRd,s = design shear resistance of web reinforcement of member with shear

reinforcement

Figure 8.2-1: Strut and tie model for the determination of shear

resistance of a reinforced concrete member

1990 (CEB, 1993), Equations (6.3-12) and (6.3-13)

VRd,c = design shear resistance of member with shear

reinforcement as governed by strength of concrete

compression strut according to CEB-FIB Model Code

1990 (CEB, 1993), Equations (6.3-10) and (6.3-11)

When calculating VSd,a the anchor loads should be assumed as point

loads with a width of load application t1 = st1 + 2hef and

t2 = st2 + 2hef where st1 and st2 are the distances between the outermost

anchors of a group in direction 1 and direction 2, respectively.

Aids for calculating the active width are given in textbooks, e.g., in

DAfStb (1991).

The width over which the shear force is transmitted should be

calculated according to the theory of elasticity.

(2) Equation (8.2-1) may be neglected if one of the following conditions

a) to d) is met.

a) The embedment depth of the anchor is

0.8efh h (8.2-2)

b) The shear force VSd,a at the support of the concrete member caused

by the design actions including the anchor loads is

, ,10.8Sd a RdV V (8.2-3a)

(member without shear reinforcement)

, , ,0.8 min ;Sd a Rd s Rd cV V V (8.2-3b)

(member with shear reinforcement)

with VRd,1, VRd,s and VRd,c as defined in Equation (8.2-1).

c) Under the characteristic actions, the tension force NSk of a single

anchor or the resultant tension force g

SkN of the tensioned anchors

of an anchor group is ≤ 30 kN and the spacing, a, between the



outer anchors of adjacent groups or between the outer anchors of a

group and single anchors or between single anchors satisfies

Equation (8.2-4).

In Equation (8.2-4a) and Equation (8.2-4.b) the constant carries the

dimension [mm / kN0.5

]

200 Ska N for single anchors (8.2-4a)

200 g

Ska N for anchor groups (8.2-4b)

with a in [mm] and NSk in [kN].

Shear stirrups may be provided in order to accommodate transmission of

the anchorage loads to the compression zone of the concrete member.

Provision of appropriate stirrups is assumed to prevent any negative influence

of the anchorage on the shear capacity of the concrete member. The stirrups

may also be used to increase the capacity of the anchorage (see Part IV and

Part V).

d) The anchor loads are taken up by stirrups that enclose the tension

reinforcement of the concrete member and are anchored at the

opposite side of the concrete member. The distance from any

anchor to the stirrups should not be larger than hef (see Figure

8.2-2). At least two stirrups should be provided.

Figure 8.2-2: Stirrups to transfer the loads to the compression zone

of the concrete member

(3) If under the characteristic actions, the tension force NSk of a single

anchor or the resultant tension force g

SkN of the tensioned anchors of

an anchor group is larger than 60 kN, then either the embedment depth

of the anchors should be hef ≥ 0.8h or supplementary stirrups

according to paragraph (2)d) above should be provided.



The shear resistance of slabs and beams made of prefabricated concrete

and added cast-in-place concrete depends on the amount of shear

reinforcement crossing the joint area. If the shear reinforcement takes up all

the shear forces (Figure 8.2-3a), then the anchor loads may be transmitted

into the precast concrete. However, if the shear reinforcement takes up only a

part of the shear forces or if precast and cast-in-place concrete are not

connected by a shear reinforcement (Figure 8.2-3b,c), then the shear capacity

of the structural member may be significantly reduced by anchor loads

transmitted into the precast concrete, because they increase the tensile

stresses in the joint area. In these applications, the anchor loads should be

transmitted into the cast-in-place concrete only (Figure 8.2-3c). Therefore,

only the embedment depth of the anchor in the cast-in-place concrete should

be assumed as effective. An exception is the anchorage of suspended ceilings

or similar construction with a weight up to 1.0 kN/m2 (Figure 8.2-3b),

because the tensile stresses in the joint area caused by this load are

insignificant.

a) b) c)

Figure 8.2-3: Anchorages in beams and slabs made of prefabricated

concrete and added cast-in-place concrete

(4) The above conditions also apply to slabs and beams made of

prefabricated units and added cast-in-place concrete. However, anchor

loads may be transmitted into the prefabricated concrete only if the

safe transmission of the loads into the cast-in-place concrete can be

shown. This condition may be assumed as satisfied, if the precast

concrete is connected with the cast-in-place concrete by shear

reinforcement (e.g., stirrups) according to CEB-FIP Model Code 1990

(CEB, 1993), Equation (6.10-1) with β = 0.0 (Figure 8.2-3a). If this

shear reinforcement between precast and cast-in-place concrete is not

present, only the loads of suspended ceilings or similar construction

with a weight up to 1.0 kN/m2 may be anchored in the precast

concrete (Figure 8.2-3b). Alternatively, the anchor should extend into

the cast-in-place concrete and the embedment depth in the precast

concrete is disregarded, when calculating the anchor resistance

(Figure 8.2-3c).



8.3 Resistance to splitting forces

Anchor splitting forces are induced in a concrete member by two actions:

(1) transfer of a concentrated load into the concrete member (compare

Figure 8.3-1a with Figure 8.3-1b);

(2) the wedging action of undercut anchors (a wedging action will occur

also for headed anchors after the formation of a concrete wedge under

the head at a high bearing pressure), by bond stresses caused by

bonded anchors or by expanding torque-controlled or deformation-

controlled anchors.

a) b)

Figure 8.3-1: Splitting forces due to concentrated loads and

simplified strut-and-tie models: a) Load applied at the

concrete surface (compression); b) load transmitted by

anchor (tension)

The splitting forces may be taken up by reinforcement or by compression

forces if the load transfer area is located in the compression zone of the

concrete member.

In general, the splitting forces caused by anchors should be considered in

the design of the concrete member.

The splitting forces may be neglected if one of the following conditions is

met:

(1) The load transfer area is in the compression zone of the concrete

member. For anchorage in slabs, walls and shells the compression

zone should be present in both directions.



For normal reinforced slabs of typical thickness the splitting forces

induced by the anchor may be neglected for anchor loads less than 10 kN.

If anchors are located in the tension zone of a concrete member, in general

the splitting forces will increase the tension force in the reinforcement (see

Figure 8.3-2). This should be taken into account in the design, if the

conditions (2) or (3) of Section 8.3 are not observed. The ratio between

splitting force FSp and anchor tension force N should be given in the relevant

Approval or should be evaluated in the prequalification procedure (see

Section 1.3). If not, the following values should be considered as a first

indication:

FSp = 0.5NSd for bonded anchors, headed anchors and anchor channels

1.0NSd for undercut anchors

1.5NSd for torque-controlled expansion anchors

2.0NRd for deformation-controlled expansion anchors

(2) Under the characteristic actions, the tension force NSk of single

anchors, or the resultant tension force g


an anchor group, is small in respect to the tension resistance of the

member longitudinal reinforcement.

(3) Under the characteristic actions, the tension force NSk of a single

anchor, or the resultant tension force g


an anchor group is not larger than 30 kN. In addition, for anchorages

in slabs and walls an appropriate reinforcement for concentrated loads

is provided in both directions in the region of the anchorage. The area

of the transverse reinforcement should be at least 60% of the

longitudinal reinforcement required for the actions due to anchor

loads.

Figure 8.3-2: Increase of tension force in reinforcement due to

anchor splitting forces

The limiting value of 30 kN in condition (3) is valid for a reinforcement

ratio = As / (b·h) ≈ 0.5%. For a larger reinforcement ratio this value may be

increased.


Part II: 9 Scope 130

PART II: CHARACTERISTIC RESISTANCE OF ANCHORAGES WITH POST-

INSTALLED EXPANSION ANCHORS, UNDERCUT ANCHORS, SCREW ANCHORS

AND TORQUE-CONTROLLED BONDED EXPANSION ANCHORS

9 Scope Structural concrete is defined as all concrete used for structural purposes

including plain, reinforced and prestressed concrete. In general, the strength

classes, for which the design method is valid, is C20 to C50 according to


Part I applies unless otherwise noted. Part II applies to anchorages with

post-installed expansion anchors, undercut anchors, screw anchors, and

torque-controlled bonded expansion anchors (see Figure 1.2-1 to Figure 1.2-4

and Figure 1.2-5b) loaded by tension, shear, combined tension and shear

forces as well as bending and torsional moments. It applies to members made

of structural concrete with normal weight aggregates. The range of concrete

strength classes, for which the design method is valid, is given in the

corresponding Approval.

In general, for screw anchors having an embedment depth up to

approximately hef = 10d0, the pullout resistance exceeds 85% of the concrete

cone resistance. The value of 85% is derived from theoretical considerations,

which indicate that screw anchors with a characteristic pullout resistance less

than 85% of the characteristic concrete cone resistance will exhibit combined

pullout and concrete cone failure similar to bonded anchors. This failure

mode has not been studied in detail to date.

Additional rules for anchors with larger embedment depths may be given

in the relevant Approval.

For screw anchors the design method given in this Part is valid only if the

characteristic resistance for pullout failure, NRk,p, given in the Approval is

larger than 85% of the characteristic concrete cone resistance of a single

screw anchor, 0

,Rk cN , according to Equation (10.1-2a).

To ensure suitability and durability of these anchors for use in structural

concrete, prequalification testing should be performed (see Section 1.3).

In general, this Part is valid for concrete members and anchorages

subjected to predominantly static loading. Exceptions to this rule are

addressed in Sections 13 and 14.

According to the safety concept of partial factors (see Equation (3.3-1)), it

should be shown that the design value of the actions does not exceed the

design value of the resistance. Equation (3.3-1) should be applied for all types

of actions on the anchors (tension, shear, combined tension and shear), as

well as for all possible failure modes (steel failure, pullout failure, concrete



cone failure and splitting failure under tension loading and steel failure,

pullout failure, pryout failure and concrete edge failure under shear loading).

Flowcharts for the calculation of the characteristic resistances for the

elastic and plastic design approach are given in Figure 9-1 and Figure 9-2,

respectively.

In the following sections, equations for calculating the characteristic

resistance of anchorages without anchorage reinforcement for the elastic

design approach (Section 10) and plastic design approach (Section 11) are

given for all types of actions and for all failure modes. Requirements for the

serviceability and fatigue limit states and for seismic actions are given in

Sections 12 to 14. The provisions are valid, when the spacing between the

outer anchor of adjoining anchor groups or to single anchors or the distance

between single anchors are a > scr,N (concrete failure in tension or pryout

failure in shear), a > scr,sp (splitting failure) and a > 3c1 (concrete edge failure

in shear) (see Figure 1.2-8 to Figure 1.2-10).

The effect of abandoned drilled holes can be neglected in the design,

provided that those holes are filled with high strength non-shrink mortar.

In general, for the majority of structures the positioning and size of

existing reinforcement in the concrete member in which post-installed

anchors are placed is not known. However, in the following situations

detailed information may be available:

– during design of new construction, anchor reinforcement for post-

installed anchorages is specified;

– drawings and construction protocols of existing structures are

available;

– detection tools based on scanning techniques are used to provide

information on existing reinforcement.

Provided the location as well as the size of the existing reinforcement is

known and the existing reinforcement fulfils the requirements to act as

anchor reinforcement, then this reinforcement may be taken into account in

the design of post-installed anchorages. The design should be carried out

following the approach for headed anchors given in Section 19.2 for the

verification of failure modes affected by anchor reinforcement (concrete cone

failure under tension loading and concrete edge failure under shear loading).

Where the existence of anchor reinforcement can be verified with respect

to size and positioning, this reinforcement may be taken into account for the

calculation of the characteristic resistance of the anchorage following the

approach for headed anchors given in Section 19.2. Tolerances on the

position of the post-installed anchors in respect to the location of the anchor

reinforcement should be taken into account in an unfavourable way such to

reduce the calculated resistance.



Note that for the typical range of embedment depth of post-installed

mechanical anchors the consideration of anchor reinforcement may rather be

applicable for the calculation of the resistance to shear loading than for the

resistance to tension loads.

Because the exact location of the anchors with respect to the position of

anchor reinforcement may not be known, the corresponding tolerances need

to be taken into account in an unfavourable way, when designing post-

installed anchors including anchor reinforcement.

For anchorages close to an edge with an anchor reinforcement to take up

shear loads, cracks caused by the shear load will occur in the concrete well

before reaching the ultimate load. The width of these cracks is limited to

about 0.3 mm in the serviceability limit state. To avoid failure of the

tensioned anchors, the design should be performed using anchors suitable for

cracked concrete. Design for cracked concrete is not necessarily required

where the exponent in the interaction Equation (10.3-1d) (simplified

approach) or Equation (10.3-3) (alternative approach) is conservatively taken

as = 2/3 (see Section 19.2.3).

In case of combined tension and shear loads where the shear load is taken

up by anchor reinforcement, premature failure of the tension loaded anchors

due to excessive cracking caused by the shear load should be avoided. It is

therefore mandatory in such cases to use anchors suitable for cracked

concrete.

To use this Design Guide the following values should be available either

from an Approval or they should be evaluated from the results of

prequalification tests (see Section 1.3).

- NRk,s (or As, fuk) See Section 10.1.2

- NRk,p See Section 10.1.3

- kcr, kuncr See Section 10.1.4

- hef See Section 10.1.4 and Figure 2.5-1

- scr,N, ccr,N See Section 10.1.4

- ccr,sp , scr,sp See Section 10.1.5

- cmin, smin, hmin See Section 10.1.5

- VRk,s (or As, fuk and k2) See Section 10.2.2.1

- 0

,Rk sM See Section 10.2.2.2

- VRk,p (or k3) See Section 10.2.3



- k4 See Section 10.2.4

- d, dnom, See Section 10.2.5.1 and Figure 2.5-1

- lf See Section 10.2.5.1

- Type of steel (ductile, brittle) See Sections 10.2.2.1, 11.1 and

4.3.2.1(4)

- Mi for different failure

modes

See Section 3.4.2

- Ratio between splitting force

and anchor tension force

See Section 8.3

- Limitation on concrete strength classes of base material

The minimum values for member thickness and reinforcement as well as

for edge distance and spacing of anchors given in the relevant Approval

should be respected.



Start

Application criteria

(Sections 4.3.1 and 9)

Steel resistance Concrete resistance Steel resistance Concrete resistance

Pullout

(Sect. 10.1.3)

Without

lever arm

(Sect. 10.2.2.1)

Concrete

pryout

(Sect. 10.2.4)

Concrete

edge

(Sect. 10.2.5)

Find appropriate

partial factors (Section 3.4.2)

Find smallest

design resistance NRd

Find appropriate


Find smallest

design reisstance VRd

NSd NRd VSd VRd

If combined

tension and shear

(Section 10.3)

Fatigue

(Section 13)

Seismic

(Section 14)

Concrete

cone

(Sect. 10.1.4)

Splitting

(Sect. 10.1.5)

With

lever arm

(Sect. 10.2.2.2)

Fire

(Section 6.5)

Pullout

(Sect. 10.2.3)

Serviceability limit state

(Section 12)

Durability

(Section 7)

Section

10.1.2

Tension

(Section 10.1)

Shear

(Section 10.2)

End

Ensuring characteristic

resistance of concrete

member (Section 8)

Figure 9-1: Flowchart B for the calculation of the resistance of

anchorages with post-installed expansion anchors,

undercut anchors, concrete screws or torque-

controlled bonded expansion anchors (elastic design

approach)



Shear

(Section 11.3)

Steel resistance Concrete resistance

Equation

(11.3-2)

Equation

(11.3-3)

Seismic

(Section 14)

Fire

(Section 6.5)



member (Section 8)

Concrete

pryout

(Sect. 11.3.3)

Concrete

edge

(Sect. 11.3.4)

Durability

(Section 7)

If combined

tension and shear

(Section 11.4)

Section

11.2.1

NSd NRd,s VSd VRd,s

Start


(Sections 4.3.2.1 and 11.1)

Tension

(Section 11.2)

Concrete resistanceSteel resistance

Pullout

(Sect.11.2.2)

Concrete

cone

(Sect. 11.2.3)

Splitting

(Sect. 11.2.4)

Without

lever arm

(Sect.11.3.2)

Equation

(11.2-2)

Equation

(11.2-3)

End

Seviceability limit state

(Section 12)

Fatigue

(Section 13)

Figure 9-2: Flowchart C for the calculation of the resistance of

post-installed expansion anchors, undercut anchors,

concrete screws or torque-controlled bonded

expansion anchors (plastic design approach)


Part II: 10 Ultimate limit state – elastic design approach 136

10 Ultimate limit state – elastic design

approach According to the elastic design approach, loads are distributed to the

anchors of an anchor group following the theory of elasticity (see Section

4.3.1).

The field of application is given in Section 4.3.1.1. For screw anchors see

also Section 9.

10.1 Resistance to tension load

10.1.1 Required verifications

The most loaded anchor of a group is the anchor with the highest design

tension load ( h

SdN ).

The required verifications are summarized in Table 10.1-1.

Table 10.1-1: Required verifications for tension loading (elastic

design approach)

Failure

mode Single Anchor

Anchor group a)

Most loaded anchor Anchor group a)

1 Steel

failure ,

,

Rk s

Sd Rd s

Ms

NN N

,

,

Rk sh

Sd Rd s

Ms

NN N

2 Pullout

failure ,

,

Rk p

Sd Rd p

Mp

NN N

,

,

Rk ph

Sd Rd p

Mp

NN N

3

Concrete

cone

failure

,

,

Rk c

Sd Rd c

Mc

NN N

,

,

Rk cg

Sd Rd c

Mc

NN N

4 Splitting

failure ,

,

Rk sp

Sd Rd sp

Msp

NN N

,

,

Rk spg

Sd Rd sp

Msp

NN N

a) Verification is performed for those anchors of a group loaded in tension.



10.1.2 Steel failure

The characteristic resistance NRk,s of an anchor in the case of steel failure

given in the Approval is obtained from Equation (10.1-1).

,Rk s s ukN A f (10.1-1)

For anchors having a variable cross section over the anchor length,

Equation (10.1-1) should be verified for the various cross sectional areas and

corresponding steel strengths.

The characteristic resistance NRk,s of an anchor in case of steel failure

should be taken from the relevant Approval.

10.1.3 Pullout failure

Reliable design models for calculation of the characteristic resistance for

pullout failure modes are not available. Therefore, the resistance for pullout

failure is evaluated from the result of Approval tests (see Section 1.3).

The characteristic resistance NRk,p of an anchor in case of pullout failure


10.1.4 Concrete cone failure

The characteristic resistance against the formation of a concrete cone may

be increased by a compressive force acting on the concrete surface close to

the tensioned anchors, e.g., when a bending moment is acting on the fixture

and the anchor spacing is s ≤ 1.5hef (see Figure 10.1-1). This influence is

neglected in Equation (10.1-2), since no generally accepted design model is

yet available. Design equations are discussed in Bruckner et al. (2001) and

Fichtner, Eligehausen (2007).

Figure 10.1-1: Example of an anchorage where the compression force

caused by a bending moment acting on the fixture may

increase the concrete cone capacity of the tensioned

anchor

The characteristic resistance NRk,c of an anchor or an anchor group in the

case of concrete cone failure is obtained from Equation (10.1-2):

0

, , , , , ,Rk c Rk c A N s N ec N re NN N (10.1-2)

with:

0

,Rk cN

= characteristic resistance of a single anchor without edge and

spacing effects

A,N = 0

, ,/c N c NA A

= factor accounting for the geometric effects of spacing and edge

distance

s,N = factor accounting for the influence of edges of the concrete

member on the distribution of stresses in the concrete

ec,N = factor accounting for the group effect when different tension

loads are imposed to the individual anchors of a group (e.g.,

eccentric loading)

re,N = factor accounting for the negative effect of closely spaced

reinforcement in the concrete member on the strength of

anchors with an embedment depth hef < 100 mm



The definition of the embedment depth hef as used in the following

equations is shown in Fig. 2.5-1 and Fig. 2.5-2 for the various anchor types.

The different quantities in Equation (10.1-2) are explained below.

The reduced concrete cone capacity in cracked concrete relative to the

value in uncracked concrete is due to the disturbance of the distribution of

stresses in the concrete.

Certain types of torque-controlled expansion anchors (see Figure 1.2-1)

and deformation controlled expansion anchors (see Figure 1.2-2) may not be

suitable for transferring tension loads into cracked concrete. Therefore, these

anchors may only be used in concrete that remains uncracked in the

proximity of the anchor during the service life of the anchorage.

According to Equation (10.1-2a), the concrete cone resistance increases

with 1.5

efh . This is in conformity with experimental and analytical results based

on fracture mechanics (Eligehausen et al., 2006-2).

a) The characteristic resistance of a single anchor without edge and

spacing effects, 0

,Rk cN , is obtained from Equation (10.1-2a):

0 1.5

, 1Rk c ck efN k f h (10.1-2a)

1 7.7crk k [N0.5

/ mm0.5

] cracked concrete

1 11.0uncrk k [N0.5

/ mm0.5

] uncracked concrete

On the basis of a large experimental database the mean concrete cone

failure load (mean resistance) of a single anchor in uncracked concrete can be

approximated by (Eligehausen et al., 2006-2):

0 1.5

, ,200Rm c cc efN k f h (10.1-3a)

where fcc,200 represents the concrete strength measured on cubes with a

side length of 200 mm and k has been identified as 13.5 for mechanical

anchors.

The values of k1 used in Equation (10.1-2a) are derived based on the

Equations (10.1-3a,b,c):

,2000.84ck ckf f (10.1-3b)

Note that Equation (10.1-3b) is valid for concrete C20. However, this

factor may be conservatively taken as constant for all concrete strength

classes.

, ,0.75Rk c Rm cN N assuming a COV = 15% (10.1-3c)



Comparison of experimental data has shown that the mean concrete cone

capacity of cracked concrete may reasonably be assumed as about 70% of the

capacity in uncracked concrete (Eligehausen et al., 2006-2).

k1-values depend on anchor type and dimensions. k1-values other than

given in Equation (10.1-2a) but not larger than the values valid for headed

bolts (see Section 19.1.1.4) kcr = 8.9 and kuncr = 12.7 may be taken if proven

by suitable prequalification tests. For undercut anchors with a bearing area

fulfilling the requirements given in Section 19.1.1.3, values kcr = 8.9 and

kuncr = 12.7 may be assumed.

Figure 10.1-2: Idealised concrete cone and area 0

,c NA of an individual

anchor loaded in tension

b) The factor A,N = 0

, ,/c N c NA A takes into account the geometric effects of

spacing and edge distance, where:

0

,c NA = reference area of the concrete cone of an individual anchor

with large spacing and edge distance projected on the

concrete surface; the concrete cone is idealised as a pyramid

with a height equal to hef and a base length equal to scr,N (see

Figure 10.1-2)

= 2

,cr Ns (10.1-2b)

Ac,N = actual projected area of concrete cone of the anchorage at

the concrete surface, limited by overlapping concrete cones

of adjacent anchors (s < scr,N), as well as by edges of the

concrete member (c < ccr,N). It may be deduced from the

idealised failure cones of single anchors. Examples for the

calculation of Ac,N are given in Figure 10.1-3 and

Figure 10.1-4. In general the values scr,N and ccr,N may be

taken according to Equation (10.1-2b1,2)

, 3cr N efs h (10.1-2b1)

, ,0.5 1.5cr N cr N efc s h (10.1-2b2)



a) b)

c)

Figure 10.1-3: Examples of idealised concrete cones and areas Ac,N in

the case of tension loading: a) anchor group (s1 < scr,N,

s2 < scr,N) far from edges; b) single anchor at an edge

(c1 < ccr,N); c) anchorage with s1 > scr,N, s2 < scr,N far

from edges



For anchorages with s1 > scr,N (example see Figure 10.1-3c) a common

failure cone of all anchors is not expected to occur. Therefore, the

characteristic concrete cone resistance should be calculated taking into

account the subgroups.

a) b)

Figure 10.1-4: Examples of areas Ac,N in the case of tension load:

a) group of two anchors at the edge of a concrete

member; b) group of four anchors at the corner of a

concrete member

Anchorages with a large edge distance show a rotationally symmetric

distribution of stresses in the concrete. This distribution is disturbed if the

anchor is located close to an edge, which causes a reduction of the concrete

cone failure load.

c) The factor s,N accounts for the disturbance of the distribution of

stresses in the concrete by edges of the concrete member. For

anchorages affected by more than one edge, e.g., anchorages in the

corner of a concrete member or in a narrow member, the smallest edge

distance, c, should be inserted in Equation (10.1-2c).

,

,

0.7 0.3 1.0s N

cr N

c

c (10.1-2c)

For reason of simplicity, the eccentricity factor may be taken as ec,N = 1.0

if the most stressed anchor is verified ( ,

h h

Sd Rk c McN N ) and the

characteristic resistance of this anchor is taken as , ,

h

Rk c Rk cN N n with NRk,c

according to Equation (10.1-2) with ec,N = 1.0 and n = number of anchors

loaded in tension.

d) The factor ec,N accounts for the reduction of the group capacity when

the tension loads acting on the individual anchors of a group are not

uniform.

,

,

11.0

1 2ec N

N cr Ne s

(10.1-2d)



with:

For the example shown in Figure 4.3-4c, ec,N to be inserted in Equation

(10.1-2) is:

,

,1 , ,2 ,

1 1

1 2 1 2ec N

N cr N N cr Ne s e s

eN = eccentricity of the resulting tensile force acting on the

tensioned anchors with respect to the centre of gravity of the

tensioned anchors (see Section 4.3.1.2). Where there is an

eccentricity in two directions (see Figure 4.3-4c), ec,N should

be determined separately for each direction according to

Equation (10.1-2d) and the product of both factors should be

inserted in Equation (10.1-2).

For anchorages in the vicinity of reinforcement, the tensile stresses in

concrete induced by the anchorage and by the bond action of reinforcement

are superimposed. This effect is especially pronounced for small bar spacing

and large bar diameters. Furthermore, the concrete strength in the region of

closely spaced reinforcement may be smaller than in the core of the member.

Both effects are taken into account by the factor re,N.

For anchorages with an embedment depth hef ≥ 100 mm surface

reinforcement may have positive effects. The concrete cone capacity may

increase due to confinement of the concrete and the ductility may increase

due to dowel action of the reinforcement (Nilsson, Elfgren, 2009). Further

investigations are needed in order to clarify and quantify these effects.

e) The factor re,N accounts for the reduced strength of anchors with an

embedment depth hef < 100 mm, inserted in a concrete element with

closely spaced reinforcement.

, 0.5200

ef

re N

h

for s < 150 mm (for any diameter ds)

or s < 100 mm (for ds ≤ 10 mm) (10.1-2e1)

re,N = 1.0 for s ≥ 150 mm (for any diameter ds)

or s ≥ 100 mm (for ds ≤ 10 mm)

(10.1-2e2)

where s denotes the spacing of reinforcement within the concrete

element.

a) b)

Figure 10.1-5: Examples of anchorages in concrete members where '

efh , '

,cr Ns and '

,cr Nc may be used: a) anchorage with

three edges; b) anchorage with four edges

f) Special cases

In applications where three or more edge distances are smaller than

ccr,N (see Figure 10.1-5), Equation (10.1-2) leads to conservative

results. In case of a single anchor, more precise results are obtained if

the value hef is substituted by:

' max

,

ef ef

cr N

ch h

c (10.1-2f1)

For groups of anchors hef should be substituted by the larger of the

following values:

' max

,

ef ef

cr N

ch h

c and ' max

,

ef ef

cr N

sh h

s (10.1-2f2)

with:



Figure 10.1-6: Illustration of the calculation of '

efh for an anchorage

with two anchors influenced by four edges. When

calculating '

efh , scr,N = 2ccr,N = 3hef is assumed.

cmax = maximum distance from the centre of an anchor to the edge of

concrete member ≤ ccr,N

smax = maximum centre to centre spacing of anchors ≤ scr,N

The value '

efh is inserted in Equation (10.1-2a) for hef. Furthermore, for

the determination of 0

,c NA and Ac,N according to Figure 10.1-2 to Figure

10.1-4 and in Equations (10.1-2c) and (10.1-2d) the values scr,N and

ccr,N are replaced by '

,cr Ns and '

,cr Nc , determined according to Equation

(10.1-2f3), respectively:

'

' '

, , ,2ef

cr N cr N cr N

ef

hs c s

h (10.1-2f3)

An example for the calculation of '

efh is illustrated in Figure 10.1-6.

10.1.5 Splitting failure

Splitting failure may occur either during installation of anchors or due to

loading. In any case, splitting failure should be avoided. The design model

for splitting failure in uncracked concrete does not take into account the

influence of edge reinforcement. Because at edges the concrete tensile

strength may be partly used up by tensile stresses due to shrinkage, edge

reinforcement should be provided to compensate for this effect.

A general design model allowing for the calculation of the characteristic

splitting resistance is not yet available. In absence of more accurate

information, adequate conservative rules should be adopted.

If the edge distance of an anchor is smaller than the value ccr,sp (ccr,sp see

Section 10.1.5.2), then adequate reinforcement should be provided parallel to

the edge of the member.



10.1.5.1 Splitting failure due to anchor installation

Splitting failure is avoided during anchor installation provided that

sufficient edge distance, spacing of anchors, member thickness and

reinforcement are ensured. Minimum values for those parameters are

included in the relevant Approval or, alternatively, they should be evaluated

on the basis of results obtained from appropriate tests in the prequalification

procedure (see Section 1.3).

10.1.5.2 Splitting failure due to anchor loading

a) Verification of splitting failure is not required provided that one of the

following conditions is fulfilled:

The characteristic edge distance, ccr,sp, (= 0.5scr,sp) is normally evaluated

by testing single anchors at the corner. Since higher splitting forces are

generated in the concrete by a group of anchors, larger edge distances

(c ≥ 1.2ccr,sp) are required for anchor groups to preclude a splitting failure.

As a first indication the following values may be taken, which are valid

for a member thickness h = 2hef :

ccr,sp = 2hef for undercut anchors, screw anchors and

torque-controlled bonded expansion anchors

(10.1-4a)

= 3hef for expansion anchors (10.1-4b)

(1) The depth of the concrete member is h ≥ hmin and the edge

distance in any direction is c ≥ 1.0ccr,sp for single anchors and

c ≥ 1.2ccr,sp for anchor groups. The characteristic edge distance

ccr,sp and the characteristic spacing scr,sp should be taken from the

relevant Approval.

The splitting forces generated by the anchor may cause splitting cracks in

the concrete. However, if the concrete member is adequately reinforced and

the crack width due to quasi-permanent actions including the splitting forces

induced by the anchors is limited to wk ~ 0.3 mm, it may be assumed that the

concrete cone resistance and the pullout resistance valid for anchors in

cracked concrete will be reached. Naturally, the anchor should be qualified

for application in cracked concrete.

(2) Anchors suitable for application in cracked concrete are used. The

characteristic resistance for pullout failure and concrete cone

failure is calculated for cracked concrete and adequate

reinforcement is arranged in the concrete element able to resist the

splitting forces and to limit the crack width.

Equation (10.1-5) is an approximation, because the splitting failure load

depends partly on other parameters than the concrete cone failure load.

However, it is believed that Equation (10.1-5) is conservative for anchors

exhibiting concrete cone failure. Adequate values for ccr,sp and scr,sp should be

given in the relevant Approval or be evaluated from the results of appropriate

tests during the prequalification procedure (see Section 1.3). The

b) If condition a) above is not fulfilled, then the characteristic resistance

of a single anchor or an anchor group for splitting failure should be

calculated according to Equation (10.1-5):

0

, , , , , , ,Rk sp Rk c A N s N ec N re N h spN N (10.1-5)



characteristic edge distance, ccr,sp, ensures that single anchors with c ≥ ccr,sp

will reach the concrete cone failure load according to Equation (10.1-2a).

For anchors that exhibit pullout failure in single anchor tests at large edge

distance, the value ccr,sp is evaluated for the characteristic pullout resistance

NRk,p. Hence, Equation (10.1-5) yields unconservative results because the

outset value is taken as concrete cone resistance for a single anchor instead of

the pullout resistance. In this case, the value of NRk,p should be substituted for 0

Rk ,cN in Equation (10.1-5). This adjustment is unnecessary if the pullout and

concrete cone resistances are nearly equal.

The special case of anchorages with three or more edge distances c < ccr,sp

is addressed by including Equation (10.1-2f) in Equation (10.1-5).

If ccr,sp as determined in the prequalification tests is not larger than ccr,N,

then splitting failure is assumed not to occur and Equation (10.1-5) may be

neglected for all applications.

The member thickness influences the splitting failure load up to a limiting

value. The value hef + 1.5c1 is based on experimental investigations by Asmus

(2007). The factor ψh,sp is limited to 2.0 because in tests a larger increase of

the splitting failure load due to an increase of the member depth has not been

observed.

with 0

Rk ,cN , s,N, ec,N and re,N according to Equations

(10.1-2a) to (10.1-2f) and 0

, , ,/A N c N c NA A as defined in Section

10.1.4b. When applying the relevant equations, the values scr,N and ccr,N

should be replaced by the values scr,sp and ccr,sp, defined on the basis of

a member thickness equal to hmin, respectively.

h,sp = factor to account for the influence of the actual

member thickness on the characteristic splitting

resistance

2 / 32 / 3 1

, minmin

1.52.0

1.0

ef

h sp

h ch

hh

(10.1-5a)

For anchorages affected by more than one edge, e.g., anchorages in the


distance should be inserted for c1 in Equation (10.1-5a).

10.2 Resistance to shear load

For consideration of friction forces in the design, see Section 4.2. In general, the contribution of friction between fixture and concrete

surface to the shear resistance of anchorages is neglected.

The shear resistance of an anchorage should be calculated for all possible

failure modes.


The most loaded anchor of a group is the anchor with the highest design

shear load ( h

SdV )

The required verifications are summarised in Table 10.2-1.



Table 10.2-1: Required verifications for shear loading (elastic design

approach)

Failure

mode Single Anchor

Anchor groupa)

Most loaded anchor Anchor group

1

Steel

failure

without

lever arm

,

,

Rk s

Sd Rd s

Ms

VV V

,

,

Rk sh

Sd Rd s

Ms

VV V

2

Steel

failure

with

lever arm

,

,

Rk sm

Sd Rd sm

Ms

VV V

,

,

Rk smh

Sd Rd sm

Ms

VV V

3 Pullout

failure

,

,

Rk p

Sd Rd p

Mp

VV V

,

,

Rk ph

Sd Rd p

Mp

VV V

4

Concrete

pryout

failure

,

,

Rk cp

Sd Rd cp

Mc

VV V

,

,

Rk cpg

Sd Rd cp

Mc

VV V

a)

5

Concrete

edge

failure

,

,

Rk c

Sd Rd c

Mc

VV V

,

,

Rk cg

Sd Rd c

Mc

VV V

b)

a) Verification is performed for those anchors of a group loaded in shear

b) Verification is performed for the anchors assumed to generate concrete edge

failure; see Section 4.3.1.3


10.2.2.1 Shear load without lever arm

In general the value VRk,s given in the Approval is obtained from Equation

(10.2-1):

, 2Rk s s ukV k A f (10.2-1)

with:

k2 = 0.5

The characteristic resistance VRk,s of an anchor in the case of steel failure




For anchors with a reduced section along the length of the bolt, e.g., bolt

type expansion anchors, the characteristic resistance for steel failure VRk,s may

be smaller than the value given by Equation (10.2-1) if failure is caused by

shear in the reduced section.

In a case where the sleeve of a sleeve-type anchor extends through the

fixture, the shear resistance VRk,s of the anchor is increased beyond the

capacity of the bolt, depending on the ductility and relative stiffness of the

anchor sleeve and bolt. The degree to which the shear resistance is increased

is highly dependent on the anchor design.

In both cases, the characteristic resistance should be taken from the

relevant Approval or evaluated from the results of appropriate


When the shear load is acting in the direction of a row of anchors with

hole clearance (acl ≤ acl,1 according to Table 4.3-1) and all anchors are

assumed to resist the imposed shear load, the strength of the anchors made of

brittle steel (rupture elongation measured over a length of five bolt diameter

< 8%) is negatively affected by the limited anchor deformability. To account

for this effect, an adequate reduction factor (~ 0.8) should be used (Fuchs,

1992). This effect can be neglected if the anchor steel is ductile (rupture

elongation measured over a length of five bolt diameter ≥ 8%). For

anchorages with acl > acl,1, the influence of the hole clearance with respect to

the anchor diameter on the anchorage behaviour is taken into account by

assuming that only some of the anchors resist the imposed shear load

(examples see Figure 4.3-18 and Figure 4.3-19).

A reduction factor equal to 0.8 should be applied to the shear resistance of

the most loaded anchor of a group of anchors, calculated according to

Equation (10.2-1), when the hole clearance is acl ≤ acl,1 (acl,1 see Table 4.3-1),

the anchors are made of steel with low ductility, the shear load is acting in the

direction of the row of anchors and all anchors are assumed to resist the

applied shear load (for examples see Figure 4.3-5).

When shear loads of alternating sign are imposed to the anchorage,

appropriate measures should be taken to avoid a fatigue failure of the anchor

steel (see Section 6.3).

10.2.2.2 Shear load with lever arm

For anchors with a significantly reduced section along the anchor length,

the characteristic bending resistance should be calculated for the reduced

section or evaluated by appropriate tests.

The characteristic resistance of an anchor is obtained from Equation

(10.2-2).

0

,

, ,

M Rk s

Rk sm Rk s

MV V

l

(10.2-2)

where:

M = a factor discussed in Section 4.3.1.5

l = length of the lever arm according to Equation (4.3-2)



In general the characteristic bending resistance of an anchor is calculated

according to Equation (10.2-2a):

0

, 1.5Rk s el ykM W f (10.2-2a)

Equation (10.2-2a) is based on Scheer et al. (1987).

0

,Rk sM = characteristic bending resistance of an individual anchor taken

from the relevant Approval

Wel = section modulus of an individual anchor at the sheared cross-

section

VRk,s = characteristic shear resistance for lever arm equal to zero taken

from the relevant Approval (see Section 10.2.2.1)


Anchors with a low pullout resistance, NRk,p, compared to concrete cone

resistance, 0

,Rk cN , may fail by pullout failure under shear load. The

corresponding characteristic resistance should be evaluated from test results.

As a first indication Equation (10.2-3) can be used (compare Section 3.2

and Equation (10.2-4)):

, 3 ,Rk p Rk pV k N (10.2-3)

with:

k3 = 2.0

NRk,p = characteristic resistance according to Section 10.1.3

The characteristic resistance VRk,p of an anchor in case of pullout failure


The factor k3 in Equation (10.2-3) should be considered as approximation.

More exact values of k3 should be given in the Approval or may be evaluated

from the results of prequalification tests (see Section 1.3).

10.2.4 Concrete pryout failure

The characteristic resistance VRk,cp of an anchorage in case of pryout

failure is obtained from Equation (10.2-4):

The effect of the eccentricity in creating an uneven shear load distribution

needs to be accounted for. A reasonable assumption is to set eN = eV.

As a first indication the following values may be taken for k4:

, 4 ,Rk cp Rk cV k N (10.2-4)

with

NRk,c = characteristic resistance according to Section 10.1.4,

determined for the anchors loaded in shear assuming eN = eV

k4 = 1.0 for hef < 60 mm

= 2.0 for hef ≥ 60 mm

k4 = factor to be taken from the relevant Approval.



s1 ≤ scr,N and s2 ≤ scr,N

a)

(c1;c2) ≤ ccr,N and s1 ≤ scr,N

b)

Figure 10.2-1: Calculation of area Ac,N for pryout failure for group

anchorages with shear load (or components thereof)

on anchors acting in opposing directions: a) group of

four anchors away from edges; b) group of two

anchors located in a corner.

For anchor groups with shear forces (or components thereof) on the

individual anchors in opposing directions (e.g., anchorages loaded

predominantly by a torsion moment), the most unfavourable anchor should be

verified. When calculating the area Ac,N it should conservatively be assumed

that there is a virtual edge (c = 0.5s) in the direction of the neighbouring

anchor(s) (see Figure 10.2-1).

10.2.5 Concrete edge failure

In general, for anchor groups with 4 or less anchors and an edge distance

c ≥ max(60dnom, 10hef) in all directions, it may be assumed that no concrete

edge failure will occur. For anchor groups with more than 4 anchors the

verification of concrete edge failure should be performed.

According to Section 4.3.1.3, in case of anchors close to an edge loaded

by shear forces or torsional moments, it may be assumed that the failure crack

originates either from the front or from the back anchor(s). If it is assumed

that the failure crack originates from the front anchors and the required

verifications for tension, shear as well as combined tension and shear loads

are satisfied, no serviceability check is necessary. If it is assumed that the

failure crack does not originate from the front anchors, then an additional

check at the serviceability limit state is required (see Section 6.2).

In Section 4.3.1.3 a general method and an alternative approach are

presented to calculate the shear loads on anchors. The corresponding concrete

edge resistance should be calculated according to Section 10.2.5.1.1 or

10.2.5.1.2, respectively.



10.2.5.1 General method

10.2.5.1.1 Failure crack originating from the front anchors

The characteristic resistance VRk,c of a single anchor or the front anchors of

an anchor group without or with hole clearance close to an edge is obtained

from Equation (10.2-5):

0

, , , , , , , ,Rk c Rk c A V h V s V ec V V re VV V (10.2-5)

where:

0

,Rk cV

= characteristic resistance of an anchor loaded perpendicular to the

edge, where effects of spacing, further edges and member

thickness are not applicable

A,V = factor to take into account the geometric effects of spacing,

member thickness and further edges

= 0

, ,/c V c VA A

h,V = correction factor to take into account that the resistance does not

decrease linearly with the member thickness as assumed by the

ratio 0

, ,/c V c VA A

s,V = factor to take into account the influence of further edges on the

distribution of stresses in the concrete

ec,V = factor to take into account a group effect when different shear

loads are acting on the individual anchors of a group (e.g.,

eccentric shear loading)

,V = factor to take into account the angle between the shear load

applied and the direction perpendicular to the free edge of the

concrete member under consideration

re,V = factor to take into account the type of edge reinforcement



a)

b) c)

Figure 10.2-2: a) Example of a group of anchors with normal hole

clearance (acl ≤ acl,1) at a corner under shear loading;

b) resistance verified for the left edge; c) resistance

verified for the bottom edge

Care should be exercised in applying the correct angle of load direction,

edge distance and spacing for the calculation of the characteristic resistance

according to Equation (10.2-5). Because c1 is always defined as edge distance

in direction perpendicular to the edge for which the resistance is verified, the

indices of the spacing and edge distance in Figure 10.2-2c have been changed

compared to Figure 10.2-2b.

For anchorages placed at a corner, the characteristic resistance should be

checked for both edges, the smallest ratio ,

g

Sd Rd cV V is decisive (for an

example see Figure 10.2-2).

The different factors in Equation (10.2-5) are explained below.

According to Equation (10.2-5a) the concrete resistance increases with

c1.5

. This agrees with test results and can be explained by fracture mechanics.

The influence of the anchor stiffness on the concrete resistance is taken

into account by means of dnom and lf (see Equation (10.2-5a)), This effect

decreases with increasing edge distance.

a) The characteristic resistance of a single anchor with large values for

edge distance in direction 2 (see Figure 10.2-3) and member thickness

loaded in shear perpendicular to the edge corresponds to:

0 1.5

, 1Rk c v nom f ckV k d l f c (10.2-5a)

with:



Note that the given values for the parameter kv are determined based on SI

units.

The basic approach for calculating the characteristic concrete edge

breakout resistance as represented by Equation (10.2-5a) is based on

numerical simulations and numerous test results (Hofmann, 2005).

The concrete capacity design (CCD) approach for edge breakout (Fuchs et

al., 1995) as given in Equation (10.2-6a) is based on tests with anchors

having dnom ≤ 40 mm and lf ≤ 8dnom, the majority of tests having been

conducted with dnom ≤ 30 mm. 0.2

0 1.5

, ,200 11.0f

Rm c nom cc

nom

lV d f c

d

(10.2-6a)

where 0

,Rm cV is the mean concrete edge breakout resistance and fcc,200

represents the concrete strength measured with 200 mm cubes.

Hofmann (2005) proposed Equation (10.2-6b) and extended the ranges of

dnom and lf. 0 1.5

, ,200 13.0Rm c nom f ccV d l f c (10.2-6b)

where and are given by Equations (10.2-5a1) and (10.2-5a2),

respectively.

The majority of tests in the underlying database were carried out in the

range dnom ≤ 40 mm and lf ≤ 12.5dnom. In the associated numerical studies,

dnom was extended to 190 mm and lf to 16dnom. Hofmann (2005) noted that the

modified expression may be used for dnom ≤ 65 mm with a limit on lf of

16dnom.

Testing by Lee et al. (2010) with headed anchors of d between 60 mm and

90 mm indicates that Equation (10.2-6b) is unconservative for large

diameters, when lf is taken as equal to hef and the influence of lf on the

concrete edge breakout resistance is very limited for large diameters.

In Grosser (2011) bonded anchors with dnom ≤ 24 mm and lf ≤ 20dnom were

tested and the results were compared with Equation (10.2-6b). The

comparison indicates that for the tested anchors an upper limit for lf of 12dnom

yields reasonable results.

kv = kv,cr = 1.7 anchorages in cracked concrete

kv = kv,uncr = 2.4 anchorages in uncracked concrete

0.5

1

0.1fl

c

[-] (10.2-5a1)

0.2

1

0.1 nomd

c

[-]

(10.2-5a2)

dnom ≤ 60 mm

For anchors having dnom > 60 mm the limiting value of dnom = 60 mm

should be inserted in Equations (10.2-5a) and (10.2-5a2).

lf = influence length

= hef for anchors with constant diameter over the embedment depth

(e.g., threaded rods)

= for other cases, as given in the relevant Approval or as determined

from the results of prequalification tests (see Section 1.3)

The following limits on the influence length apply:

lf ≤ 12dnom for dnom ≤ 24 mm

≤ 8dnom for dnom > 24 mm

For anchors with constant diameter over the embedment depth (e.g.,

threaded rods) having an embedment depth hef larger than the limiting

values for lf, the limiting values are inserted in Equations (10.2-5a) and

(10.2-5a1).

Where the diameter is not constant over the embedment depth or where

the anchor is provided with a shear sleeve that does not extend

continuously over the entire embedment depth, the value of dnom and lf

are given in the relevant Approval or should be evaluated from the

results of prequalification tests (see Section 1.3).

For anchors without sleeves the term dnom is replaced by d in Equations

(10.2-5a) and (10.2-5a2).



Based on the sum of the previously discussed investigations, the following

limits on Equation (10.2-5a) have been developed:

dnom ≤ 60 mm

lf ≤ 12dnom for dnom ≤ 24 mm

≤ 8dnom for dnom > 24 mm

For anchors having dnom > 60 mm the limiting value of dnom = 60 mm

should be inserted in Equations (10.2-5a) and (10.2-5a2).

For anchors with constant diameter over the embedment depth, such as

e.g., bonded anchors using threaded rods, the influence length lf is equal to

the embedment depth hef. For this type of anchor with embedment depth hef

larger than the above given limiting values for lf, the limiting values are

inserted in Equations (10.2-5a) and (10.2-5a1). For anchors having

dnom ≤ 24 mm and hef > 12dnom, the limiting value of lf = 12dnom should be

inserted in Equations (10.2-5a) and (10.2-5a1). For anchors having

dnom > 24 mm and hef > 8dnom, the limiting value lf = 8dnom should be inserted

in Equations (10.2-5a) and (10.2-5a1).

Note that the investigations regarding the extension of the range for lf have

been carried out using bonded and headed anchors with a constant diameter

over the embedment depth. Where the diameter is not constant or where the

anchor is provided with a shear sleeve that does not extend continuously over

the entire embedment depth, the appropriate values for the diameter and

influence length should be taken from the relevant Approval or should be

determined from the results of prequalification tests, however, the limiting

values for dnom and lf given above should be respected.

The values of kv used in Equation ((10.2-5a) are derived using the

relationships given in Equations (10.1-3b,c).



Figure 10.2-3: Idealised concrete body and area

0

c,VA for a single

anchor loaded in shear

a)

b)

c)

d)

Figure 10.2-4: Examples of actual areas Ac,V for different anchor arrangements under shear load: a) single anchor at a corner; b) single anchor in a thin concrete member; c) group of anchors in a thin concrete member; d) group of anchors at a corner of a thin concrete member

b) The geometric effects of spacing, edge distances parallel to the

direction of load and thickness of the concrete member on the

characteristic resistance are taken into account by the factor:

,A V = 0

, ,/c V c VA A where:

0

,c VA

= area of concrete breakout body of a single

anchor at the lateral concrete surface not

affected by edges in direction 2, member

thickness or adjacent anchors, idealising the

shape of the fracture cone as a half-pyramid with

a height equal to c1 and base lengths of 1.5c1 and

3c1 (Figure 10.2-3)

= 2

14.5c (10.2-5b)

Ac,V = actual area of concrete breakout body of the

anchorage at the lateral concrete surface. It is

limited by overlapping concrete cones of

adjacent anchors (s < 3c1), by edges in direction

2 (c2 ≤ 1.5c1) and by member thickness

(h ≤ 1.5c1). It may be deduced from the idealised

half-pyramid of the individual anchors.

Examples for the calculation of Ac,V are given in

Figure 10.2-4

For the calculation of 0

,c VA and Ac,V it is assumed that the shear loads

are applied perpendicular to the edge of the concrete member.



The anchor resistance decreases with decreasing member thickness.

However, according to tests (Zhao et al., 1989; Eligehausen, Grosser, 2007)

and numerical simulations (Hofmann, 2005), the reduction of anchor

resistance is less pronounced than assumed by the factor 0

, ,/c V c VA A . This is

taken into account by the factor h,V according to Equation (10.2-5c).

Further experimental and numerical investigations (Eligehausen, Grosser,

2007) indicate that the adjustment for larger edge distances in thin members

(i.e., for values of c1 / h ≥ 1.5) should take the form: 1 3

1,

1.51.0h V

c

h

(10.2-5c1)

Note, however, that in such cases the presence of typical slab reinforcing

will serve to increase the shear resistance and the use of Equation (10.2-5c) is

still acceptable. Where larger shear forces must be resisted in thin members,

provision of dedicated anchor reinforcement is advisable.

c) The factor h,V takes into account that the resistance does not decrease

linearly with the member thickness as assumed by the ratio 0

, ,/c V c VA A .

1,

1.51.0h V

c

h (10.2-5c)

d) The factor s,V takes account of the disturbance of the distribution of

stresses in the concrete due to further edges of the concrete member on

the concrete edge resistance. For anchorages with two edges in

direction 2 (e.g., in a narrow concrete member) the smaller edge

distance c2 should be inserted in Equation (10.2-5d).

2,

1

0.7 0.3 1.01.5

s V

c

c (10.2-5d)

For reasons of simplicity the eccentricity factor may be taken as

ec,V = 1.0 if the most loaded anchor is verified ( , /h h

Sd Rk c McV V ) and the

characteristic resistance of this anchor is taken as , , /h

Rk c Rk cV V n with VRk,c

according to Equation (10.2-5) with ec,V = 1.0 and n = number of anchors

loaded in shear.

e) The factor ec,V takes into account a group effect when different shear

loads are acting on the individual anchors of a group.

,

1

11.0

1 2 3ec V

Ve c

(10.2-5e)

where:

eV = eccentricity of the resulting shear load acting on the anchors

relative to the centre of gravity of the anchors loaded in shear

(see Figure 4.3-21)



Where anchors are loaded in shear parallel to the concrete edge, failure is

initiated by splitting forces perpendicular to the edge. They are a fraction of

the applied shear load. In order to account for the fact that a higher shear load

acting parallel to the edge is required to cause edge failure as compared to a

shear load acting perpendicular to the edge, the factor 90°,V is introduced.

The ratio of the splitting force to the shear force applied parallel to the

edge depends on the pressure in front of the anchors in the direction of

loading compared to the concrete compression strength. This relation is

assumed to be a linear function. The pressure increases as a function of the

concrete resistance perpendicular to the edge, which is approximately

proportional to , ,Rk cV

, and decreases with the number of anchors in a group.

Therefore, the factor 90°,V increases with decreasing edge distance and with

increasing number of anchors (Hofmann, 2005; Grosser, Eligehausen, 2008).

The values 90°,V given in Equation (10.2-5f) are a simplification and are

valid for larger edge distances where the concrete edge resistance is equal to

the anchor steel resistance. At smaller edge distances the values 90°,V

increase. In such cases, the value 90°,V may be evaluated in accordance with

Equation (10.2-5f1). In ACI 318 Appendix D (ACI 318, 2008), the value of

2.0 is taken. In the CEN Technical Specification (CEN, 2009), a value of 2.5

is used.

0,5

2

2

90 . 4

, ,

4.0 4.0nom ck

V

Rk c

n d fk

V

(10.2-5f1)

with:

k4 = 1.0 [-] anchorages without hole clearance and single anchors

with hole clearance

= 0.8 [-] anchorages with normal hole clearance (acl ≤ acl,1)

n2 = number of anchors for which concrete edge failure is verified

(see Figure 10.2-5)

, ,Rk cV = concrete breakout resistance for loading perpendicular to an

edge according to Equation (10.2-5) without factor ,V

f) The factor ,V takes into account the angle V between the load

applied g

SdV and the direction perpendicular to the edge for which the

resistance is verified (see Figure 10.2-2b,c).

, 2

2

90 ,

11.0

sincos

V

vV

V

(10.2-5f)

with:

V = angle between design shear load g

SdV and a line

perpendicular to the edge for which the resistance is

verified (see Figure 10.2-2b,c)

90°,V = 1.5 for n2 = 1

= 2.0 for n2 = 2

= 2.5 for n2 = 3

n2 = number of anchors for which concrete edge failure is

verified (see Figure 10.2-5)



For a row of anchors arranged and loaded parallel to the edge it is

assumed that the shear load is distributed uniformly to all anchors of the

group (see Section 4.3.1.3). However, in the case of anchors with normal hole

clearance (acl ≤ acl,1) in the fixture and a small edge distance, the load may not

be distributed equally to the anchors. This is accounted for by the factor

k4 = 0.8 in Equation (10.2-5f1) (Hofmann, 2005). The values 90°,V given in

Equation (10.2-5f) are valid for anchorages with larger edge distances which

fail at displacements much larger than the hole clearance. Because of this, it

may be assumed that the shear force is equally distributed to all anchors.

Figure 10.2-5: Determination of n2 for the evaluation of 90°,V in

Equation (10.2-5f) based on the number of anchors for

which concrete edge failure is verified



Equation (10.2-5f) assumes a quadratic interaction between the shear

resistances for loading perpendicular and parallel to the edge. It is derived

from Equation (10.2-5f2).

2 2

, ,

, , , ,

cos sin1.0

Rk c V Rk c V

Rk c Rk c

V V

V V

(10.2-5f2)

with:

VRk,c = characteristic concrete edge resistance for a shear load acting

with an angle V to the edge

, ,Rk cV

= characteristic concrete edge resistance for a shear load acting

perpendicular to the edge calculated according to Equation

(10.2-5) with ,v = 1.0

VRk,c, = characteristic concrete edge resistance for a shear load acting

parallel to the edge

= 90 , , ,V Rk cV

V = angle as defined in Figure 10.2-2b,c

The value of re,V is based on experimental investigations by Fuchs and

Eligehausen (1989).

g) The factor re,V takes into account the type of edge reinforcement used.

re,V = 1.0, for anchorages without supplementary

reinforcement as defined in Figure 10.2-6

(10.2-5g1)

re,V = 1.4, for anchorages with edge reinforcement

(ds ≥ 12 mm) and closely spaced stirrups

(ds ≥ 12 mm, spacing ≤ 100 mm) and edge

distance ≥ 100 mm (see Figure 10.2-6)

(10.2-5g2)

VRk,c,



Figure 10.2-6: Anchorage at an edge loaded in shear with edge

reinforcement and closely spaced stirrups

Figure 10.2-7: Example for an anchorage in a thin, narrow member

where the value '

1c may be used

An example for the calculation of '

1c is illustrated in Figure 10.2-8.

h) Special cases

For anchorages in a narrow, thin member with c2,max < 1.5c1 and

h < 1.5c1 (see Figure 10.2-7) the calculation according to Equation

(10.2-5) leads to conservative results. More precise results are achieved

if c1 is limited in case of single anchors to the value of:

2,max'

1 max ;1.5 1.5

c hc

(10.2-5h1)

or in the case of groups, c1 is limited to the value of:

2,max 2,max'

1 max ; ;1.5 1.5 3

c shc

(10.2-5h2)

with:

c2,max = largest of the two edge distances in direction 2

s2,max = maximum spacing between anchors within the group in

direction 2 (≤ 3c1)



Figure 10.2-8: Example for the calculation of the value '

1c

The value '

1c is inserted in Equations (10.2-5a) to (10.2-5e) and it is used

to determine the areas A0

c,V and Ac,V according to Figure 10.2-3 and Figure

10.2-4 instead of c1.

For anchorages without hole clearance arrayed perpendicular to the edge

and having a small ratio s1 / c1, the verification assuming that only the part

VSd / n1 of the total load on the group is resisted by the front anchors may be

unconservative. This is explained in Figure 10.2-9 for a group of four anchors

without hole clearance loaded by a shear load oriented perpendicular to the

edge. It is assumed that a centric shear load acting toward the edge is

distributed equally to all anchors (see Section 4.3.1.3.1; subsection (2)). Tests

have shown, that the maximum concrete edge failure load of the group is

reached when the failure crack originates from the back anchors. This failure

load is not influenced significantly by the front anchors. In the case of a large

anchor spacing perpendicular to the edge, the resistance of the group is

greater than or equal to two times the resistance of the near edge (front)

anchors (Figure 10.2-9a). Therefore, the verification of the near edge anchors

according to Equation (3.3-1) is conservative. In the case of a very small

anchor spacing perpendicular to the edge (s1 << c1,1) (Figure 10.2-9b), the

resistance of the group is approximately equal to the resistance of the front

anchors. In this case the verification of only the front anchors - assuming an

equal distribution of the shear load to all anchors - is unconservative.

For anchor groups without hole clearance loaded by a shear load

perpendicular to the edge the characteristic concrete edge resistance should

be limited by Equation (10.2-6):

1, , 1, 1Rk c Rk c nV V c n (10.2-6)

with:

1, 1,Rk c nV c = characteristic edge resistance calculated for the back

anchor(s) according to Equation (10.2-5) inserting

11 1,nc c

n1 = number of anchors rows in the direction 1 perpendicular

to the edge



Therefore, since it has been assumed that the shear load is equally distributed

to all anchors, the concrete edge resistance of the front anchors is limited by

Equation (10.2-6). This equation gives the concrete edge resistance as the

concrete breakout calculated for the back anchors divided by the number, n1,

of anchor rows in the direction perpendicular to the edge (n1 = 2 in Figure

10.2-9). This limitation should assure that the whole group does not fail

before the assumed failure crack occurs at the front anchors.

a) b)

Figure 10.2-9: Example of a group of anchors without hole clearance

loaded in shear toward the edge: a) s1 large ;b) s1

small

For anchor groups with hole clearance loaded by a shear load

perpendicular to the edge it is assumed that the shear load is taken up by the

front anchors only (see Section 4.3.1.3.1, subsections (3) and (4)). Therefore,

the verification according to Equation (3.3-1) is conservative.

For anchor groups with no or normal hole clearance (acl ≤ acl,1) loaded in

shear parallel to the edge it is assumed that all anchors take up shear loads

(see Section 4.3.1.3.1, subsection (3)). Tests with anchor groups with

torsional restraint (compare Figure 4.3-16b) have shown that the failure load

of the group may be larger than twice the failure load calculated with the

edge distance of the front anchors.

Tests with anchor groups with a small spacing and small edge distance

without torsional restraint loaded in shear parallel to the edge have not been

performed. For these applications the characteristic concrete edge resistance



calculated for the front anchors according to Equation (10.2-5) should be

used with caution.

Equation (10.2-7) is conservative. Where the resistance , ,Rk cV for anchor groups without hole clearance is

limited by Equation (10.2-6), the characteristic concrete edge resistance for

an inclined shear load should be calculated as:

, , , ,Rk c Rk c VV V (10.2-7)

with:

, ,Rk cV = according to Equation (10.2-6)

,V = according to Equation (10.2-5f)

10.2.5.1.2 Cases where the failure crack originates from anchors

beyond the front anchor or front anchor row

The ultimate concrete edge failure load of anchor groups without or with

hole clearance arrayed perpendicular to the edge is reached, when a crack

originates from the back anchor or back anchor row. It is equal to the value

calculated using the edge distance corresponding to the back anchors or

anchor row. It is assumed that in this case the front anchor or front anchor

row do not significantly influence the concrete edge resistance of the group.

However, according to results of tests described in Grosser, Cook (2009) for

anchorages with normal hole clearance, a small edge distance and a ratio

s1 / c1,1 ≤ 1.0 the concrete edge failure load of the back anchor(s) may be

negatively influenced (up to 20%) by the crack generated at the front

anchor(s).

Note that for the verification of steel and pryout failure, it is assumed that

only those anchors located in the line of the considered failure plane and

further away from the edge resist shear forces (examples see Tables 4.3-2 to

4.3-4). Furthermore, serviceability limit state check according to Section 6.2

is required.

For anchorages with multiple anchors or anchors rows arrayed

perpendicular to the edge, the characteristic resistance corresponding to

concrete edge failure originating from the back anchor or anchor row

corresponds to:

0

, , , , , , , ,Rk c Rk c A V h V s V ec V V re VV V (10.2-8)

where 0

,Rk cV , A,V, h,V, s,V, ec,V, ,V and re,V are calculated in

accordance with Section 10.2.5.1.1 using the edge distance of the back

anchor or anchor row. The limitation given by Equation (10.2-6) does not

apply.

For anchorages without hole clearance, up to three anchors or anchor rows

are permitted perpendicular to the edge. In this case, the characteristic

concrete edge resistance corresponding to the middle anchor or anchor row

should be calculated in accordance with Equation (10.2-8) whereby the edge

distance of the middle anchor or anchor row is used. The limitation given by

Equation (10.2-6) applies in this case.

For combined tension and shear loading, additional restrictions apply; see

Section 10.3.2.



10.2.5.2 Alternative approach

– In the alternative approach, a shear force acting parallel to the edge is

substituted by a virtual shear force acting perpendicular to the edge (see

Section 4.3.1.3.3). When using this approach the characteristic resistance for

concrete edge failure should be calculated according to Equation (10.2-5) and

Equation (10.2-6) (failure crack is assumed to occur at the front anchors) or

Equation (10.2-8) (failure crack is assumed to occur at the back anchors),

however neglecting the factor ,V.

10.3 Resistance to combined tension and shear

load

10.3.1 Anchorages far from edges, anchorages close to

edges with shear resisted by front anchors

For the verification of anchorages under combined tension and shear loads

a simplified and an alternative, more accurate approach are distinguished:

Figure 10.3-1: Interaction diagram for combined tension and shear

loads

10.3.1.1 Simplified approach

For combined tension and shear loads the following conditions should be

satisfied:

1.0Sd

Rd

N

N (10.3-1a)

1.0Sd

Rd

V

V (10.3-1b)

1.2Sd Sd

Rd Rd

N V

N V (10.3-1c)

For the ratios NSd / NRd and VSd / VRd the largest value for the different

failure modes (see Table 10.1-1 and Table 10.2-1) should be inserted in

Equation (10.3-1a,b,c).



Equation (10.3-1a,b,c) may be replaced by Equation (10.3-1d):

1.0Sd Sd

Rd Rd

N V

N V

(10.3-1d)

where = 1.5 and NSd / NRd and VSd / VRd as given by Equation

(10.3-1a,b,c). = 1.0 may be taken as a conservative simplification.


An example for the interaction distinguishing between steel and concrete

failure modes is given in Figure 10.3-2, where the design resistance NRd under

tension load is plotted as a function of the design resistance VRd under shear

load. For comparison the interaction according to the Equation (10.3-1d) is

plotted as well.

Figure 10.3-2: Comparison of interaction approach according to

Equations (10.3-2), (10.3-3) and (10.3-1d)

Equations (10.3-1a,b,c) and (10.3-1d) may yield conservative results.

More accurate results are obtained by the following approach, which

distinguishes between steel and concrete failure modes.

For steel failure modes the interaction is verified according to Equation

(10.3-2):

, ,

1.0Sd Sd

Rd s Rd s

N V

N V

(10.3-2)

where = 2.0 and NRd,s and VRd,s are the characteristic steel resistances for

tension and shear loading, respectively. For anchor groups NSd and VSd are

replaced by h

SdN and h

SdV , respectively. If h

SdN and h

SdV are associated with

different anchors in a group, the interaction should be verified for all anchors.

For concrete failure modes the interaction is verified according to

Equation (10.3-3):

1.0Sd Sd

Rd Rd

N V

N V

(10.3-3)

where = 1.5 and NSd / NRd and VSd / VRd are taken as the maximum value

for applicable concrete failure modes under tension and shear loading,

respectively.

Equations (10.3-2) and (10.3-3) should both be satisfied.



10.3.2 Anchorages close to edges with shear resisted by

the back anchors

In cases where concrete failure governs, the initial concrete edge failure of

the front anchors will negatively influence the tension capacity of the group.

This case is handled in Eligehausen et al. (2006-2), Section 4.1.3.2. For this

reason, is taken as 1.0 for the verification of concrete failure modes.

In the simplified approach Equation (10.3-1d) should be satisfied,

however, the exponent should be taken as = 1.0.

Equation (10.3-1d) with = 1.0 may yield conservative results. More

accurate results are obtained by the alternative approach

In the alternative approach Equations (10.3-2) and (10.3-3) should be

satisfied; however, = 1.0 should be used in Equation (10.3-3).

Where the shear resistance is assumed to be provided entirely by the back

anchor(s), premature failure of the front anchors loaded in tension due to

excessive cracking associated with shear edge breakout should be avoided. It

is therefore necessary in such cases to provide reinforcement of appropriate

size and orientation to limit the crack width at the front anchors and perform

the design for cracked concrete using anchors suitable for this condition.

Regarding the optimal size and orientation of the reinforcement further

research is required.

For both, simplified and alternative, approaches the design (addressing the

ultimate as well as the serviceability limit state) should be performed for

cracked concrete using anchors suitable for this condition and reinforcement

of appropriate size and orientation should be provided to limit the crack width

at the front anchors.

If no suitable reinforcement is provided to limit the crack width, the front

anchor(s), i.e., anchor(s) located in the crack (see Figure 10.3-3b), do not

significantly and reliably contribute anymore to the transfer of the applied

tension and shear loads into the base material. Consequently, only the

remaining anchors (see Figure 10.3-3b,c) should be considered to resist

tension and shear forces in this case. It is assumed that the failure plane at the

front anchor(s) does not significantly influence the concrete resistance of the

remaining anchors subjected to shear loads acting towards the edge (see

Section 10.2.5.1.2). Therefore, the verification of shear resistance may be

performed for the subsystem shown in Figure 10.3-3b. On the other hand it

may be assumed that the failure plane at the front anchor(s) affect their

tension resistance associated with concrete failure. Therefore, it is reasonable

to conservatively assume a fictitious edge at the location of the front (failed)

anchor(s) for the verification of tension resistance of the remaining anchors

as shown in Figure 10.3-3c. In this case the exponent of the interaction

equation for the simplified approach (Equation (10.3-1d)) and the alternative

If the crack width at the front anchors is not limited, the anchors located in

the crack do not contribute to the tension resistance. Hence, the remaining

anchors must be able to transmit the tension load acting on the fastening to

the concrete base material, assuming a fictitious edge at the location of the

front anchors. In this case the exponent of the interaction equation for the

simplified approach (Equation (10.3-1d)) and the alternative approach

(Equation (10.3-3)) should not be taken greater than 1.5.



approach (Equation (10.3-3)) should not be taken greater than = 1.5. Note

that in the case of a group of two anchors perpendicular to the edge or a

group of four anchors subjected to combined tension and shear loading,

failure of the front anchors will likely lead to failure of the group due to the

resulting tension eccentricity (see Figure 10.3-4).

a) b) c)

Figure 10.3-3 Example of a group of anchors loaded in tension and

shear toward the edge: a) side view; b) subsystem for

verification of shear resistance; c) subsystem for

verification of tension resistance

a) b) c)

Figure 10.3-4 Example of a group of four anchors loaded in tension

and shear toward the edge where reinforcement to

limit crack width has not been provided: a) action and

resistance on group; b) failure of front anchors in

shear leading to loss of tension resistance;

c) premature failure of group due to unbalanced

tension



10.3.3 Anchorages loaded by a tension load and a shear

load with lever arm

The interaction Equation (10.3-4) is based on Scheer et al. (1987). For anchorages loaded by a tension load and a shear load with lever arm,

the following additional verification is required:

, ,

1.0Sd Sd

Rd s Rd sm

N V

N V (10.3-4)

with:

NSd = design tension force on anchor

NRd,s = design tension steel resistance

VSd = design shear force on anchor

VRd,sm = design shear steel resistance for an anchor loaded by a shear

force with lever arm (see Section 10.2.2.2)

11 Ultimate limit state – plastic design

approach In the plastic design approach the distribution of loads on the fixture to the

anchors of a group is performed according to the theory of plasticity (see

Section 4.3.2).

In general, the complete anchorage is checked according to Equation

(3.3-1). Therefore, in general the required verifications are written for the

group.

11.1 Field of application

The plastic design approach is allowed only if the conditions given in

Section 4.3.2.1 are satisfied.


Part II: 11 Ultimate limit state – plastic design approach 168

11.2 Resistance to tension load


Table 11.2-1: Required verifications for tension loading (plastic

design approach)

Failure mode Anchor groups

Steel failure , /g g

Sd Rk s MsN N

Pullout failure Equation (11.2-2)

Concrete cone failure Equation (11.2-3)

Splitting failure See Section 11.2.4

Only those anchors that satisfy Equation (4.3-8) of Section 4.3.2.2 should

be assumed to transfer a tension force.


In Equation (11.2-1) the same diameter and steel strength are assumed for

all tensioned anchors of a group.

The characteristic resistance of a group of tensioned anchors ,

g

Rk sN may be

taken as equal to the sum of the characteristic resistances of the anchors

loaded in tension (Equation (11.2-1)).

, ,

g

Rk s Rk sN n N (11.2-1)

with NRk,s obtained according to Section 10.1.2 and n = number of

tensioned anchors.


The factor 0.6 in Equation (11.2-2) is intended to give a 1% probability of

pullout failure prior to the intended anchor steel failure for typical anchor and

material parameters (Hoehler, 2006).

For the characteristic resistance NRk,p of one anchor in the case of pullout

or pull-through failure see Section 10.1.3. To satisfy Equation (4.3-4) of

Section 4.3.2.1, the pullout resistance of the most loaded tensioned anchor

should meet Equation (11.2-2):



, , 0.6Rk p Rk s instN N (11.2-2)

with NRk,p according to Section 10.1.3, NRk,s according to Section 10.1.2,

and γinst according to Section 3.4.2.1.2.

11.2.3 Concrete cone failure

If in the design a constant tension force is assumed for all tensioned

anchors, then the eccentricity factor is ec,N = 1.0.

In Equation (11.2-3) the same diameter, steel strength and embedment

depths are assumed for all anchors of a group.


concrete failure prior to the intended anchor steel failure for typical anchor

and material parameters (Hoehler, 2006).

For the calculation of the concrete cone resistance Section 10.1.4 applies.

To satisfy Equation (4.3-4) of Section 4.3.2.1, the anchorage depth should

be large enough for Equation (11.2-3) to be met:

, , 0.6g

Rk c Rk s instN N (11.2-3)

with NRk,c according to Equation (10.1-2) and ,

g

Rk sN according to Equation

(11.2-1) and γinst according to Section 3.4.2.1.2.

11.2.4 Splitting failure

A splitting failure is avoided by complying with Equation (11.2-3), where

NRk,c is replaced by NRk,sp according to Equation (10.1-5). The verification of

the splitting resistance may be omitted if one of the conditions in Section

10.1.5.2, subsection a) is met.

11.3 Resistance to shear load


The verification for pullout failure is not required, because anchorages

that meet Equation (11.2-2) will not fail due to pullout under shear loading.

Anchorages loaded in shear with lever arm (see Section 4.3.1.5) have not

been investigated and are not covered by this Design Guide.


Table 11.3-1: Required verifications for shear loading (plastic

design approach)

Failure mode Anchor groups

Steel failure, shear load without

lever arm , /g g

Sd Rk s MsV V

Concrete pryout failure Equation (11.3-2)

Concrete edge failure Equation (11.3-3)


Part II: 11 Ultimate limit state – plastic design approach 170


Because a plastic design approach is allowed only for ductile steel, the

factor 0.8 to account for the influence of hole clearance on the steel shear

resistance (see Section 10.2.2.1) may be increased up to 1.0. In Equation

(11.3-1) the same diameter and steel strength are assumed for all anchors of

the group loaded in shear.

The characteristic resistance of a group of anchors loaded in shear ,

g

Rk sV

may be taken as equal to the sum of the characteristic resistances of the

individual anchors loaded in shear (Equation (11.3-1)).

, ,

g

Rk s Rk sV n V (11.3-1)

with VRk,s obtained according to Section 10.2.2.1, and n = number of

anchors loaded in shear.

11.3.3 Concrete pryout failure

Equation (11.3-2) is satisfied if all anchors have an embedment depth that

meets Equation (11.2-3).


concrete pryout failure prior to the intended anchor steel failure for typical

anchor and material parameters (Hoehler, 2006).

To calculate the concrete pryout resistance Section 10.2.4 applies.

To satisfy Equation (4.3-4) of Section 4.3.2.1, Equation (11.3-2) should be

met:

, , 0.6g

Rk cp Rk sV V (11.3-2)

with VRk,cp according to Section 10.2.4 and ,

g

Rk sV according to Equation

(11.3-1).

11.3.4 Concrete edge failure

If in the design a constant shear force is assumed for all anchors loaded in

shear, then the eccentricity factor is ec,V = 1.0.

If in the design the friction resistance is neglected, then VRk,f may be

omitted in Equation (11.3-3).


concrete edge failure prior to the intended anchor steel failure for typical

anchor and material parameters (Hoehler, 2006).

To calculate the concrete edge resistance Section 10.2.5 applies.

To satisfy Equation (4.3-4) of Section 4.3.2.1, Equation (11.3-3) should be

met:

, , ,0.6g

Rk c Rk s Rk fV V V (11.3-3)

with:

VRk,c = characteristic edge resistance according to Equation

(10.2-5) and Equation (10.2-6) for the anchor(s) closest to the

edge

,

g

Rk sV = see equation (11.3-1)

,Rk fV = see Equation (4.2-1)



11.4 Resistance to combined tension and shear

load

Because in the plastic design approach the concrete design resistance is

required to be much higher than the steel design resistance, the interaction

Equations (10.3-2) should be applied for the most loaded anchor. Then NRd

and VRd are the design steel resistance in tension and shear, respectively, of

that anchor.

Section 10.3 applies.

12 Serviceability limit state In some Approvals the given characteristic displacements are valid for

short-duration loading only. They may increase because of sustained loads or

cracks with varying width caused by variable loads on the concrete structure.

The increase depends on the type of loading and the type of anchor and may

reach a factor of 1.5 to 2.0 for tension loading and 1.2 to 1.5 for shear

loading. Furthermore, the shear displacements may increase due to a gap

between fixture and anchor if the diameter of the clearance hole is larger than

the diameter of the anchor.

For the required verifications see Section 6.2.

The characteristic displacement of the anchor under given tension and

shear loads may be taken from the relevant Approval or from the results of


13 Fatigue loading Due to temperature variations, anchorages of façade elements experience

alternating shear loads. Therefore, either the façade elements are anchored so

that no significant shear forces due to the restraint of deformations imposed

on the façade element will occur in the anchorage, or, in a stand-off

installation, the bending stresses s = s,max – s,min in the most stressed

anchor, caused by temperature variations, should be limited to avoid a steel

fatigue failure. The characteristic fatigue bending resistance of anchors in a

stand-off installation to fasten façade elements may be taken as

Rk,fat = 100 MPa (Utescher, 1978). This value is valid for about 104 cycles

of temperature variations.

Fatigue loading on the member serving as the base material or on the

anchorage may be allowed, if this is stated in the relevant Approval or if it

has been shown in the prequalification procedure that the anchors are suitable

for these applications. In both cases the corresponding conditions (e.g.,

permanent prestressing force of sufficient magnitude) should be met.

In general the value MRk,s is calculated according to the Equation (13-1):

, ,Rk s Rk fat elM W (13-1)

The verification for fatigue loading on the anchorage should be performed

according to Section 6.3. The values NRk,s, NRk,p, VRk,s,VRk,sm, N and

RV should be taken from the relevant Approval or should be determined


Part II: 14 Seismic loading 172

where Rk,fat is the characteristic tension resistance under fatigue loading

given in the relevant Approval or determined from the results of suitable

prequalification tests.

from the results of suitable prequalification tests (see Section 1.3). The value

VRk,sm should be calculated according to Equation (10.2-2) replacing M0

Rk,s by

MRk,s and VRk,s by VRk,s. The value for MRk,s should be taken from the

relevant Approval.

14 Seismic loading Seismic loading on anchors may be allowed if this is stated in the relevant

Approval or it has been shown in the prequalification procedure (see Section

1.3) that the anchors are suitable to take up seismic loads.

The verification for seismic loading on the anchorage should be performed

according to Section 6.4.



PART III: CHARACTERISTIC RESISTANCE OF ANCHORAGES WITH BONDED

ANCHORS AND CONNECTIONS WITH POST-INSTALLED REINFORCING BARS

15 General It is necessary to distinguish between two types of connections: (see

Figure 15-1):

a) Connections with bonded anchors: The installed steel elements

(e.g., threaded rods) behave essentially like anchor bolts. They

may be stressed by tension, shear or combined tension and shear

loads. Anchor tension loads are introduced into the concrete by

bond and they cause tension stresses in the concrete in the region

of the anchorage (Figure 15-1a). The design of the connection is

performed in principle as for other types of anchors, however,

with some modifications to take account of the characteristics of

bonded anchors (see Section 16). The conditions of use of bonded

anchors are deduced under the assumption that the concrete

structure which takes up the load on the anchorage is essentially at

the serviceability limit state when the anchorage reaches its failure

load (see Section 6.1).

b) Connections with post-installed reinforcing bars: The bars are

essentially stressed by tension forces. These forces are introduced

into the concrete by bond and either transferred by compression

struts to the existing cast-in-place reinforcement (Figure 15-1b) or

they are balanced by a compression strut (e.g., at an end

anchorage, see Figure 15-1c). In both applications the behaviour

is mainly controlled by the splitting tensile resistance of the

concrete and the amount and detailing of transverse reinforcement

present. In cases with large confinement by concrete and/or

transverse reinforcement the behaviour is controlled by the pullout

strength of the post-installed or cast-in-place reinforcing bars.

Concrete cone failure or combined pullout and concrete cone

failure is prevented by the existing reinforcement (Figure 15-1b)

or by a compression strut (Figure 15-1c). The design of the

Part I applies unless otherwise noted. In general, Part III is applicable to

anchorages with bonded anchors (see Figure 1.2-5a) and post-installed

reinforcing bars. Anchorages with bonded anchors are addressed in Section

16. Connections with post-installed reinforcing bars are dealt with in

Section 17.


Part III: 15 General 174

connection is performed according to provisions for reinforced

concrete (see Section 17). They should ensure that yielding of the

reinforcement is reached before a bond failure occurs to reduce

the risk of brittle failure. The conditions of use are deduced under

the assumption that failure of the connection may cause failure of

the reinforced concrete structure.

While the force path shown in Figure 15-1b or Figure 15-1c is straight

forward and can be idealised in terms of bond stresses that develop in the

concrete surrounding the lap splice or the anchored bar, respectively, in many

cases the manner of force transfer is less obvious and may require a more

detailed analysis using strut and tie modelling.

It should be noted that with bonded anchors and post-installed reinforcing

bars, as with other types of anchors, the force path involves utilisation of the

tensile strength of the concrete.

a) b) c)

Figure 15-1: Application types: a) anchor application – bond/concrete

breakout may control tension resistance; b), c)

applications with reinforcing bars where embedment is

determined with development length theory – splitting /

pullout may control tension resistance

Additional characteristics for distinguishing between anchorages with

bonded anchors and connections with post-installed reinforcing bars are

given in Table 15-1.



Table 15-1: Characteristics for distinguishing between anchorages

with bonded anchors and connections with post-

installed reinforcing bars

Comparison Anchor applications Reinforcing bar

applications

Forces in the

bar

Tension, shear, combined tension

and shear

Tension only

Load transfer

mechanism

Tension stresses in concrete Splice with cast-in-place

rebar, anchoring in

compression strut

Failure modes

considered

Tension: steel, combined pullout

and concrete cone, concrete cone,

splitting.

Shear: steel, pullout, pryout,

concrete edge

Steel, bond (pullout,

splitting)

Supplemental

reinforcement

May be used to tie back the

concrete breakout body and to take

up splitting forces – In general not

considered in design concept

Generally used to take up

splitting forces –

considered in design

concept

Cracked

concrete

Different design resistances

assigned for:

- uncracked concrete

- cracked concrete

Implicit in the design

Ultimate limit

state

Limited by a variety of possible

failure modes including steel

failure; shallow embedment as

governed by concrete failure

accepted

Design for steel yield or

bond (pullout, splitting)

Design

method

fib Design Guide, CEN Technical

Specifications (CEN, 2009), EOTA

Technical Report 029 (EOTA,

2007), ETAG 001 Annex C

(EOTA, 1997), ACI 318 Appendix

D (ACI 318, 2008), AC 308 (ICC-

ES, 2009)

e.g., CEB-FIP Model Code

1990 (CEB, 1993),

Eurocode 2 (CEN, 2004-

1), ACI 318, Section 12

(ACI 318, 2008)


Part III: 16 Anchorages with bonded anchors 176

16 Anchorages with bonded anchors

16.1 Scope

Structural concrete is defined as all concrete used for structural purposes

including plain, reinforced and prestressed concrete. In general, the strength

classes, for which the design method is valid, are C20 to C50 according to


This section is applicable to bonded anchors installed in members made of

structural concrete with normal weight aggregates. The range of concrete

strength for which the design method is valid is given in the corresponding

Approval. The anchorages may be subjected to tension, shear, combined

tension and shear forces, as well as bending and torsion moments.

To ensure suitability and durability of bonded anchors for use in structural

concrete, prequalification testing should be performed (see Section 1.3).

In general, this Part is valid for concrete members and anchorages

subjected to predominantly static loading; for exceptions to this rule, see

Sections 16.5 and 16.6.

Discussion on the minimum embedment to avoid anchorage in

substandard cover concrete may include several considerations such as,

concrete type, compaction, reinforcing type, position, etc. Traditionally, a

limit of 40 mm has been used. However, larger values may be valid for

specific cases. It may also be desirable to avoid shallow anchorages, where

load redistribution and ductility are required.

A proposal for the minimum effective embedment depth as a function of

the anchor diameter that reflects the above considerations is given in Table

16.1-1.

Table 16.1-1: Recommended minimum embedment depths of bonded

anchors

Anchor diameter d [mm] ≤ 10 12 16 20 ≥ 25

Min hef [mm] 60 70 80 90 4d

Note: smaller minimum embedment depths may be valid for certain types of

bonded anchors if stated in the relevant Approval

The provisions are applicable to anchorages over a limited embedment

depth range. As a practical matter some limit on the minimum embedment is

necessary to avoid anchorage in cover concrete of lesser integrity. A

conservative minimum embedment that is consistent with the design models

in this Design Guide is given in Table 16.1-1. The limit on the maximum

embedment is given by hef = 20d. This reflects the limits of the existing

database.


resistance for the elastic and plastic design approach are given for all loading

directions and all failure modes.

Tension failure of bonded anchors may result from bond failure between

the bonding material and the concrete or between the anchor element and the

bonding material. Current research indicates that these two failure modes are

The upper limit on the drilled hole diameter is given by d0 ≤ 1.5d.



indistinguishable from the standpoint of resistance provided that the bond line

is kept relatively thin. This is accomplished with the limit of d0 ≤ 1.5d (Cook

et al., 1998).



design value of the resistance. Equation (3.3-1) should be applied for all types

of actions on the anchors (tension, shear, combined tension and shear), as

well as for all possible failure modes (steel failure, combined pullout and

concrete cone failure, concrete cone failure and splitting failure under tension

loading and steel failure, pryout failure and concrete edge failure under shear

loading).

Flowcharts for calculating the resistance for the elastic and plastic design

approach are given in Figure 16.1-1 and Figure 16.1-2.

In the following, equations for calculating the characteristic resistance for

the elastic design approach (Section 16.2) and plastic design approach

(Section 16.3) are given for all types of actions and all failure modes.

Requirements for the serviceability limit state, for fatigue and for seismic

actions are given in Sections 16.4 to 16.6. The provisions are valid when the

spacing between anchors of adjoining anchor groups or adjoining single

anchors or the distance between single anchors are a > scr,Np (scr,Np see

Equation (16.2-1b) (combined pullout and concrete cone failure), a > scr,N

(concrete cone failure in tension or pryout failure in shear), a > scr,sp (splitting

failure) and a > 3c1 (concrete edge failure in shear) (see Figure 1.2-8 to

Figure 1.2-10).

Abandoned drilled holes filled with high strength non-shrink mortar do

not have to be considered in the design of the anchorages.

In general, for the majority of structures the positioning and size of

existing reinforcement in the concrete member in which post-installed

anchors are placed is not known. However, in the following situations

detailed information may be available:

– during design of new construction anchor reinforcement for post-

installed anchorages is specified;

– drawings and construction protocols of existing structures are

available;

– detection tools based on scanning techniques are used to provide

information on existing reinforcement.

Where the existence of anchor reinforcement can be verified with respect

to size and positioning, this reinforcement may be taken into account for the

calculation of the characteristic resistance of the anchorage following the

approach for headed anchors given in Section 19.2. Tolerances on the

position of the post-installed anchors in respect to the location of the anchor

reinforcement should be taken into account in an unfavourable way such to

reduce the calculated resistance.



Provided the location as well as the size of the existing reinforcement is

known and the existing reinforcement fulfils the requirements to act as

anchor reinforcement, then this reinforcement may be taken into account in

the design of post-installed anchorages. The design should be carried out

following the approach for headed anchors given in Section 19.2 for the

verification of failure modes affected by anchor reinforcement (concrete cone

failure under tension loading and concrete edge failure under shear loading).

In the context of connections with bonded anchors no specific investigations

have so far been carried out to study the influence of anchorage

reinforcement on the combined pullout and concrete cone failure load. Hence

a verification of this failure mode is still required.

Note that for the typical range of embedment depth of post-installed

bonded anchors the consideration of anchor reinforcement may rather be

applicable for the calculation of the resistance to shear loading than for the

resistance to tension loads.

Because the exact location of the anchors with respect to the position of

anchor reinforcement may not be known, the corresponding tolerances need

to be taken into account in an unfavourable way, when designing post-

installed anchors including anchor reinforcement.


shear loads, cracks caused by the shear load will occur in the concrete well

before reaching the ultimate load. The width of these cracks is limited to

about 0.3 mm in the serviceability limit state. To avoid failure of the

tensioned anchors, the design should be performed using anchors suitable for

cracked concrete. Design for cracked concrete is not necessarily required

where the exponent in the interaction Equation (10.3-1d) (simplified

approach) or Equation (10.3-3) (alternative approach) is conservatively taken

as = 2/3 (see Section 19.2.3).

In case of combined tension and shear loads where the shear load is taken

up by anchor reinforcement, premature failure of the tension loaded anchors

due to excessive cracking caused by the shear load should be avoided. It is

therefore mandatory in such cases to use anchors suitable for cracked

concrete.



Start


(Sections 4.3.1 and 16.1)

Shear

(Section 16.2.2)

Tension

(Section 16.2.1)

Steel resistance Concrete resistance Steel resistance Concrete resistance

Combined

pullout and

concrete cone

(Sect. 16.2.1.3)

Concrete

cone

(Sect. 16.2.1.4)

Splitting

(Sect. 16.2.1.5)

Without

lever arm

(Sect. 16.2.2.2)

With

lever arm

(Sect. 16.2.2.2)

Concrete pryout

(Sect. 16.2.2.3)

Concrete

edge

(Sect. 16.2.2.4)

Find appropriate


Find smallest


Find appropriate


Find smallest

design resistance VSd

NSd NRd VSd VRd

If combined

tension and shear

(Section 16.2.3)

Fatigue

(Section 16.5)

Serviceability

limit state

(Section 16.4)

Seismic

(Section 16.6)

Fire

(Section 6.5)

Durability

(Section 7)

Section

16.2.1.2

End



member (Section 8)

Figure 16.1-1: Flowchart B for the calculation of the resistance of

post-installed bonded anchors (elastic design

approach)


from an Approval or they should be evaluated from the results of


- NRk,s (or As, fuk) See Sections 16.2.1.2 and 10.1.2

- hef See Section 16.2.1.3 and Figure 2.5-1

- Rk,cr, Rk,uncr See Section 16.2.1.3

- kcr, kuncr See Sections 16.2.1.4 and 10.1.4

- scr,N, ccr,N See Sections 16.2.1.4 and 10. .4

- ccr,sp , scr,sp See Sections 16.2.1.5 and 10.1.5

- cmin, smin, hmin See Sections 16.2.1.5 and 10.1.5

- VRk,s (or As, fuk and k2) See Sections 16.2.2.2 and 10.2.2.1

- 0

,Rk sM See Sections 16.2.2.2 and 10.2.2.2

- k4 See Sections 16.2.2.3 and 10.2.4

- d See Sections 16.2.2.4 and 10.2.5.1 and

Figure 2.5-1

- lf See Sections 16.2.2.4 and 10.2.5.1a)

- Type of steel (ductile, brittle) See Sections 16.2.2.2, 10.2.2.1, 16.3

and 4.3.2.1(4)


modes

See Section 3.4.2



See Section 8.3


The minimum values for member thickness and reinforcement as well as

for edge distance and spacing given in the relevant Approval should be

respected.



Shear

(Section 11.3)

Steel resistanceConcrete

resistance

Equation

(11.3-2)

Equation

(11.3-3)

End


(Section 16.4)

Fatigue

(Section 16.5)

Seismic

(Section 16.6)

Fire

(Sections 6.5)



member (Section 8)

Durability

(Section 7)

If combined

tension and shear

(Section 11.4)

Section

11.2.1

NSd NRd,s VSd VRd,s

Start


(Sections 4.3.2 and 16.3)

Tension

(Section 11.2)

Concrete

resistanceSteel resistance

Combined

pullout and

concrete cone

(Sect.11.2.2

and 16.3)

Concrete

cone

(Sect. 11.2.3)

Splitting

(Sect. 11.2.4)

Concrete

pryout

(Sect.11.3.3

and 16.3)

Concrete

edge

(Sect.11.3.4)

Without

lever arm

(Sect.11.3.2)

Equation

(11.2-2)

Equation

(11.2-3)

Figure 16.1-2: Flowchart C for the calculation of the resistance of

post-installed bonded anchors (plastic design

approach)



16.2 Ultimate limit state – elastic design

approach

In the elastic design approach the distribution of loads on the fixture to the

anchors of an anchor group is done according to the theory of elasticity

(see Section 4.3.1).

The field of application is given in Section 4.3.1.1.

16.2.1 Resistance to tension load

16.2.1.1 Required verifications

The design model for tension loading on bonded anchor groups has been

experimentally verified for groups up to 6 anchors and with numerical

simulation for groups as large as 9 anchors (Eligehausen et al., 2006-1; Appl

2009). Experimental verification of larger group sizes is not available; as

such, use of the design model given here for larger groups (e.g., 6 x 6) should

be approached with caution. In particular, the scatter associated with the

resistance of bonded anchors may result in a decrease of the group capacity

for larger groups as the anchor spacing approaches the characteristic spacing.

The required verifications are given in Table 16.2-1.


design approach)

Failure mode Single anchor

Anchor group a)

Most loaded anchor Anchor group a)

1 Steel failure ,

,

Rk s

Sd Rd s

Ms

NN N

,

,

Rk sh

Sd Rd s

Ms

NN N

2 Concrete

cone failure

,

,

Rk c

Sd Rd c

Mc

NN N

,

,

Rk cg

Sd Rd c

Mc

NN N

3

Combined

pullout and

concrete

cone failure

,

,

Rk p

Sd Rd p

Mp

NN N

,

,

Rk pg

Sd Rd p

Mp

NN N

4 Splitting

failure

,

,

Rk sp

Sd Rd sp

Msp

NN N

,

,

Rk spg

Sd Rd sp

Msp

NN N

a) Verification is performed for those anchors of a group loaded in tension

16.2.1.2 Steel failure

Section 10.1.2 applies.



16.2.1.3 Combined pullout and concrete cone failure

The characteristic resistance of an anchor and the tensioned anchors of a

group in the case of combined pullout and concrete cone failure may be

obtained by Equation (16.2-1).

0

, , , , , , ,Rk p Rk p A Np s Np g Np ec Np re NpN N (16.2-1)

The various factors of Equation (16.2-1) are provided below.

The bond strength may be dependent on the concrete strength. In general,

the influence varies and may conservatively be neglected. The value to be

used for the design is given in the Approval.

a) The characteristic resistance of a single bonded anchor 0

,Rk pN not

influenced by adjacent bonded anchors or edges of the concrete

member is:

0

, ,Rk p Rk cr efN d h cracked concrete (16.2-1a1)

0

, ,Rk p Rk uncr efN d h uncracked concrete (16.2-1a2)

with:

Rk,cr (Rk,uncr) = characteristic bond resistance corresponding to a given

concrete strength class in cracked (uncracked) concrete

given in the Approval or evaluated from the results of

suitable prequalification tests (see Section 1.3)

The bond strength decreases with time. The ratio bond strength under

sustained load to bond strength under short term loading is product

dependent. It should be evaluated by suitable prequalification tests.

According to ETAG 001, Part 5 (EOTA, 1997) and AC308 (ICC-ES, 2009),

bonded anchors are tested with a sustained load corresponding to about 55%

of the mean short-time bond strength (as measured in tests with wide

supports). If the displacement and residual strength criteria are satisfied at

this load level, the actual long term bond strength is higher than 55% of the

short-term bond strength due to the conservative criteria used to assess the

results of the creep tests (Eligehausen et al., 2010). In ETAG 001, Part 5

(EOTA, 1997) it is assumed that fulfilment of the creep test criteria is

sufficient to assure good performance under sustained loads.

To take the reduced long-term bond strength into account, an additional

verification according to Equation (3.3-1) should be performed for combined

pullout and concrete cone failure under tension load and combined tension

Under sustained load an additional verification according to Equation

(3.3-1) should be performed using the characteristic bond strength

under sustained load in cracked (uncracked) concrete.



and shear loading for the quasi permanent tension design load (permanent

load and that part of the variable load than can be considered as permanent)

using the characteristic bond strength under sustained tension loading in

Equation (16.2-1). The characteristic long-term bond strength used for this

check in ACI 318, Appendix D (ACI 318, 2011) or AC308 (ICC-ES, 2009) is

55% or 75%, respectively, of the characteristic bond strength as stated in the

Approval. In the Technical Report TR029 of EOTA (EOTA, 2007) no

reduction of the short-term bond strength as given in the Approval is deemed

necessary.

0

,p NA and Ap,N are calculated in the same manner as the reference areas

0

,c NA and Ac,N associated with concrete cone failure (see Figure 10.1-2 to

Figure 10.1-4), whereby the values scr,N and ccr,N are replaced by the values

scr,Np and ccr,Np, respectively.

If the bond strength is shown to vary with concrete strength, then the bond

strength corresponding to the minimum concrete strength specified in the

Approval (in general concrete strength class C20) should be used in Equation

(16.2-1b2). Note that the constant 7.5 in Equation (16.2-1b2) carries the unit

MPa.

b) The factor 0

, , ,/A Np p N p NA A takes into account the geometric effects of

axial spacing and edge distance on the characteristic resistance, where:

0

,p NA = reference bond influence area

= 2

,cr Nps (16.2-1b1)

Ap,N = actual bond influence area, limited by overlapping areas of

adjacent anchors (s ≤ scr,Np) as well as by edges of the

concrete member (c ≤ ccr,Np)

The value of the critical spacing for bonded anchors is determined as a

function of the bond strength and the anchor diameter, because the influence

zone around a tension-loaded bonded anchor does not grow laterally with

increasing embedment depth as for post-installed mechanical and cast-in-

place headed anchors, but rather with increasing bond area (anchor diameter)

and bond strength (Eligehausen et al., 2006-1; Appl, 2009). For higher bond

strengths and shallow embedments, this formulation can lead to the

calculation of critical spacings in excess of 3hef. This agrees with

observations of the behaviour of shallow headed anchors (Zhao, 1993).

However, for reasons of simplicity the critical spacing of mechanical and cast

in place headed anchors is constrained to scr,N = 3hef regardless of embedment

depth. Therefore, for consistency between the approach to the design of

bonded anchors and mechanical/headed anchors, an upper limit on scr,Np of

3hef is proposed in Part 5 of CEN/TS 1992-4:2009 (CEN, 2009). There are

two observations associated with this proposal:

scr,Np = ,

20 37.5

Rk uncr

efd h

(16.2-1b2)

with Rk,uncr corresponding to concrete C20

ccr,Np = 0.5scr,Np (16.2-1b3)



(1) For shallow embedment depths, where Rk is close to the value of bond

stress corresponding to concrete breakout (maxRk, see Equations

(16.2-1d4) and (16.2-1d5)), the imposition of a 3hef limit on scr,Np

results in prediction of higher failure loads for groups as compared to

predictions without this limitation. There are currently no test results

available for these cases. In order to reduce the effect of this

difference in the predicted resistances, a limit on the minimum

effective embedment as given in Table 16.1-1 is implemented.

(2) For the case where the limit on scr,Np is imposed, calculation of the

tension resistance for certain cases, e.g., anchors in a corner condition,

may result in declining predicted values for NRk,p with increasing

embedment, an anomalous artefact that has no theoretical or

observational explanation. Where the limit is not imposed, however,

changes in the predicted governing failure mode may occur, e.g., with

corner anchorages where the edge distance is progressively increased

for constant embedment.

Note that the limit of 3hef on scr,Np is not addressed in Eligehausen et al.

(2006-1) or Appl (2009).

As a simplification, the same characteristic spacing and edge distance is

used for calculations associated with cracked and uncracked concrete

conditions. This approach is used for other types of anchors as well and is

generally conservative.

c) The factor s,Np takes account of the distribution of stresses in the

concrete due to edges of the concrete member. For anchorages with

several edges, e.g., anchorages in a corner the smallest edge distance

should be inserted in Equation (16.2-1c)

,

,

0.7 0.3 1.0s Np

cr Np

c

c (16.2-1c)

In many applications the factor g,Np is relatively small (< 1.3). It may be

neglected for reason of simplification.

d) The factor g,Np takes account of the effect of the failure surface of

anchor groups.

0 0

, , ,

,

1 1.0 g Np g Np g Np

cr Np

s

s

(16.2-1d1)



with:

The value of n is limited in Equation (16.2-1d2) and (16.2-1d3) due to the

lack of test data for larger groups.

0

,g Np = 1.5

,

,

1 1.0max

Rk cr

Rk cr

n n

(16.2-1d2)

(cracked concrete)

= 1.5

,

,

1 1.0max

Rk uncr

Rk uncr

n n

(16.2-1d3)

(uncracked concrete)

n = number of tensioned bonded anchors

in a group (≤ 9)

The value maxRk represents the bond stress corresponding to a concrete

cone failure originating from the embedded end of the anchor. It is derived by

equating the expression for combined pullout and concrete cone failure with

that for concrete cone breakout, which is assumed to define the maximum

carrying capacity of the concrete. The value 7.7 in Equation (16.2-1d4)

(applications in cracked concrete) may be increased to 8.9 and the value 11.0

in Equation (16.2-1d5) (applications in uncracked concrete) to 12.7 if stated in

the relevant Approval. See Section 10.1.4 for the derivation of the

coefficients in Equations (16.2-1d4) and (16.2-1d5).

Figure 16.2-1: Determination of average spacing for typical cases

maxRk,cr =

7.7ef ckh f

d

(16.2-1d4)

maxRk,uncr = 11.0

ef ckh fd

(16.2-1d5)

Where anchors in a group are not spaced equally the average value of

the anchor spacing may be inserted as s in Equation (16.2-1d1).

Examples are shown in Figure 16.2-1.



For reason of simplification, the eccentricity factor may be taken as

ec,Np = 1.0 if the most stressed anchor is verified ( h h

Sd RdN N ) and the

characteristic resistance of this anchor is taken as , ,

h

Rk p Rk pN N n with NRk,p

according to Equation (16.2-1) with ec,Np = 1.0 and n = number of anchors

loaded in tension.

e) The factor ec,Np accounts for the reduction of the group capacity when


uniform.

,

,

11.0

1 2ec Np

N cr Npe s

(16.2-1e)

with:

eN = eccentricity of the resulting tensile load acting on the

tensioned anchors (see Section 4.3.1.2). Where there is an

eccentricity in two directions, ec,Np should be determined

separately for each direction and the product of both factors

should be inserted in Equation (16.2-1)

f) The factor re,Np accounts for the reduced strength of anchors with an

embedment depth hef < 100 mm, inserted in a concrete element with

closely spaced reinforcement.

, 0.5200

ef

re Np

h

for s < 150 mm (for any diameter ds)

or s < 100 mm (for ds ≤ 10 mm) (16.2-1f1)

, 1.0re Np for s ≥ 150 mm (for any diameter ds)


(16.2-1f2)

where s denotes the spacing of reinforcement within the concrete

element.

16.2.1.4 Concrete cone failure

In general, the maximum concrete capacity of anchorages with bonded

anchors is limited by the concrete cone resistance according to Equation

(10.1-2) with 0

,Rk cN as follows:

0 0.5 1.5

, 1 Rk c ck efN k f h

1 7.7crk k N / mm

cracked concrete

1 11.0uncrk k N / mm

uncracked concrete




Larger k1-values (kcr ≤ 8.9; kuncr ≤ 12.7) may be taken if stated in the

relevant Approval.

16.2.1.5 Splitting failure


16.2.2 Resistance to shear load



Table 16.2-2: Required verifications for shear loading (elastic design

approach)

Failure

mode Single Anchor Anchor group

a)

Most loaded anchor Anchor group

1

Steel

failure

without

lever arm

,

,

Rk s

Sd Rd s

Ms

VV V

,

,

Rk sh

Sd Rd s

Ms

VV V

2

Steel

failure

with

lever arm

,

,

Rk sm

Sd Rd sm

Ms

VV V

,

,

Rk smh

Sd Rd sm

Ms

VV V

3

Concrete

pryout

failure

,

,

Rk cp

Sd Rd cp

Mc

VV V

,

,

Rk cpg

Sd Rd cp

Mc

VV V

a)

4

Concrete

edge

failure

,

,

Rk c

Sd Rd c

Mc

VV V

,

,

Rk cg

Sd Rd c

Mc

VV V

b)


b) Verification is performed for the anchors assumed to generate concrete edge

failure; see Section 4.3.1.3





16.2.2.3 Concrete pryout failure

Because pryout and combined pullout and concrete cone failure under

shear load are generated by the same mechanism (see Section 3.2), for reason

of simplification both failure modes are covered by Equation (16.2-2).

Anchorage capacity may be limited by a concrete pryout failure at the side

opposite to the load direction. The corresponding characteristic resistance

VRk,cp may be calculated from Equation (16.2-2).

, 4 , ,min( ; )Rk cp Rk c Rk pV k N N (16.2-2)

with:

As a first indication the factor k4 may be taken as 1.0 for hef ≤ 60 mm and

2.0 for hef > 60 mm.

k4 = factor, which may be taken from the relevant Approval or

evaluated from the results of prequalification tests (see Section

1.3)

NRk,p = value according to Section 16.2.1.3

NRk,c = value according to Section 16.2.1.4

For group anchorages with shear forces (or components thereof) on the

individual anchors in opposing directions (e.g., anchorages loaded

predominantly by a torsion moment), the most unfavourable anchor should be

verified. When calculating the area Ac,N or Ap,N, it should be assumed that

there is a virtual edge (c = 0.5s) in the direction of the neighbouring anchor(s)

(see Figure 10.2-1).

16.2.2.4 Concrete edge failure

Section 10.2.5 applies. In Equations (10.2-5a) and (10.2-5a2) dnom should

be replaced by d.

16.2.3 Resistance to combined tension and shear load


16.3 Ultimate limit state – plastic design

approach

The use of bonded anchors in cases where plastic design is to be used

presents special problems. It is necessary to ensure that the unbonded length

is adequate to guarantee the necessary elongation associated with plastic

design. This may be accomplished by de-bonding a length of the anchor, or

Section 11 applies. However, in Equation (11.2-2) the value NRk,p should

be calculated according to Section 16.2.1.3 and in Equation (11.3-2) the value

VRk,cp should be calculated according to Section 16.2.2.3.



by providing sufficient rod length between the surface of the concrete and the

fixture (e.g., as in an anchor chair).

16.4 Serviceability limit state

Section 12 applies.

16.5 Fatigue

Section 13 applies.

As a first approximation Rk,fat may be taken as 0.5Rk (Spieth, 2002). The resistance NRk,p should be calculated using Equation

(16.2-1) replacing the value Rk in Equation (16.2-1a) by ,Rk fat . The value

Rk,fat should be taken from the relevant Approval or should be determined

from prequalification tests (see Section 1.3).

16.6 Seismic loading



The resistance NRk,p should be calculated using Equation (16.2-1)

replacing the value Rk in Equation (16.2-1a) by Rk,eq. The value Rk,eq should

be taken from the relevant Approval or should be determined from suitable

prequalification tests in cracked concrete where crack width and cycling is

representative of seismic loading.

17 Connections with post-installed

reinforcing bars

17.1 Scope

The use of bonding material to embed reinforcing bars in hardened

concrete is a common construction practice, particularly in the strengthening

and renovation as well as the extension of existing structures. In order to

provide a monolithic connection between the new and the existing concrete

element post-installed reinforcing bar connections are established e.g., by

overlapping joints with existing reinforcement in a building component (see

This section addresses the prequalification, design and installation of

connections made with deformed reinforcing bars (fyk ≤ 500 MPa) and

polymer (epoxies, vinyl esters, etc.) or cementitious bonding systems in

existing structures made of normal weight concrete of strength class C12 to

C60 to resist predominantly static loads. Applications involving fatigue

and/or seismic loading are permitted provided that such applications are



Figure 17.1-1a) or by anchoring the reinforcement at a slab or beam support

(see Figure 17.1-1b). This type of structural connection is addressed in this

section of the Design Guide.

a)

b)

Figure 17.1-1: Example of connections with post-installed reinforcing

bars: a) overlap joint in slabs and beams; b) end

anchoring of slabs or beams

In this Design Guide, it is proposed that the design of post-installed

reinforcing bars follows the design rules given in Model Code 1990 (CEB,

1993) for cast-in reinforcing bars taking into account the rules for the design

of shear joints. The limit on the nominal yield strength of reinforcing is given

in Model Code 1990 as 500 MPa. When other design codes for reinforced

concrete are used for the design of post-installed reinforcing, the

corresponding limits on steel strength, spacing, etc. should be applied.

encompassed in the Approval or have been addressed in suitable


All configurations permitted in Model Code 1990 (CEB, 1993) for cast-in

straight deformed reinforcing bars are permissible for post-installed

reinforcing bars as well.

17.2 Prequalification testing

The basic requirements to be verified in the prequalification testing are as

follows:

Prequalification testing of systems for the installation of post-installed

reinforcing bars is necessary to both ensure suitability and durability of the



– ability of the drilling method to achieve straight and accurate holes

over the maximum embedment lengths anticipated for the system;

– ability of the injection system to place bonding material over the full

length of the maximum hole depth without the introduction of air

pockets;

– ability of the post-installed reinforcing bars to exhibit corrosion

resistance equivalent to or greater than cast-in reinforcing for the

applicable exposure class; and

– ability of the post-installed reinforcing bars to develop tension

capacities equivalent to or greater than cast-in reinforcing when

installed with normal concrete cover dimensions taking into account all

relevant influencing factors such as type of loading (short term, long

term, fatigue or seismic), temperature range and concrete cracking.

As a rule, reinforcing bars embedded with bonding material (polymer

and/or cementitious) should exhibit equal or superior strength and

comparable stiffness when tested side by side with cast-in-place deformed

reinforcing bars of equivalent diameter, embedment length, edge distance,

spacing, etc. Such tests should be conducted in the manner used to determine

permissible bond stress for cast-in bars; that is, in configurations where

splitting and pullout will control the behaviour. Testing regimes involving

testing close to edges have shown that the splitting forces are roughly

equivalent to cast-in-place bars (Spieth, 2002).

A primary factor is the ability of the bonding material to develop a

relatively uniform state of stress along the length of the bar. Overly stiff

bonding materials may result in zipper-type failures. Additional

considerations include the effect of concrete cracking along the bar caused by

tension stresses perpendicular to the bar direction on the bond behaviour and

the response to elevated in-service concrete temperatures. The ability of the

bonding material to provide a durable load transfer over the anticipated

service life under sustained load and a variety of environmental exposure

conditions should also be investigated. Since the bonding material will

prevent direct contact of the reinforcing steel with the concrete, the normal

passivation of the steel surface induced by the alkaline concrete environment

may not occur. It is therefore necessary to ensure that the bonding material

provides a similar level of corrosion protection for the reinforcement. The

bonding material for use in structural concrete as well as to verify the

effectiveness of the system for achieving an accurate installation and a

consistent strength.



performance of the system should be checked for the entire range of

applicable bar diameters, embedment lengths, concrete grades and in-situ

temperatures.

The prequalification tests should be performed on reinforcing bars

installed using the manufacturer’s printed installation instructions and in

conditions most similar to those that will be experienced on the job site. The

installation instructions should be of sufficient specificity to anticipate all

aspects of the installation process so as to provide for a low degree of job-site

improvisation and attendant installation error (see Section 3.5.2). The

maximal permissible anchorage depth in relation to the installation tools used

should be specified in the installation instructions and should be verified at

the specified extremes by means of handling tests during the product

evaluation. The ability of the drilling system to provide straight and accurate

holes of the required diameter and length, particularly in near-edge

conditions, should be verified.

17.3 Design

17.3.1 General

The design of the connection should take into account the condition of the

existing structure. The selection of the materials (bonding material,

reinforcing steel) for the joint should consider the applicable exposure class.

Post-installed reinforcing bar connections should be designed in

accordance with good engineering practice. The determination of internal

section forces to be transferred across the construction joint should conform

to the CEB-FIP Model Code 1990 (CEB, 1993). When ascertaining the

tensile force in the post-installed reinforcing bars, allowances should be made

for the in-situ effective position of the post-installed reinforcement taking

into account the expected variances from the nominal position due to

imperfect drilling.

At a minimum, the following information should be provided in the design

documents:

– strength of existing concrete and grade of post-installed reinforcing

bars;

– diameter, spacing, concrete cover and hole depth for the post-installed

reinforcing bars;

Only the drilling system(s) specified in the Approval should be used on

site.

– drilling system including drilling aid as necessary, e.g., for drilling

long holes close to edges and to other bars as required;



– joint preparation requirements, including the degree of surface

roughness;

– thickness of concrete cover or type, position and anchorage of

insulating material etc. as required for fire protection.

17.3.2 Dimensioning of the connection

The bond resistance of post-installed reinforcing bars may not increase

with increasing concrete strength in the same manner as for cast-in

reinforcing bars. In these cases, the bond strength corresponding to a limiting

concrete strength class may be mandated for applications in concrete with a

higher strength class (see Figure 17.3-1).

Figure 17.3-1: Example for determination of governing design bond

strength as a function of concrete strength class

The minimum concrete cover and bar spacing to avoid splitting of the

concrete during drilling are dependent on the method of drilling (hammer

drill, core drill, etc.). For hammer drilling a minimum spacing for post-

installed reinforcing bars of 4ds > 40 mm is advisable. In addition,

inaccuracies in the drilling trajectory associated with the drilling system used

should be accommodated in the minimum cover and spacing requirements.

As a result, the minimum cover and bar spacing may exceed those required

for cast-in bars. An example for minimum cover requirements as a function

of drilling method is given in Table 17.3-1. These values are valid for free-

hand drilling. They may be reduced if a suitable drilling aid is used. The

efficiency of such aids should be checked by tests.

The dimensioning of the connection should be performed according to the

CEB-FIP Model Code 1990 (CEB, 1993) assuming a bond resistance fbd as

given in the Approval. The bond resistance should not exceed that given for

deformed cast-in reinforcing bars in the code. Requirements for transverse

reinforcement should conform to those applicable to cast-in bars. The

following additional restrictions and requirements may apply:

– restrictions on the minimum concrete cover;

– restrictions on the minimum bar spacing;

– requirements for the minimum bond length;

– restrictions on concrete strength used in design.

For the transfer of shear forces across the joint, the design should consider

appropriate measures for the preparation of the concrete surface, e.g.,

roughening, keying, etc. in accordance with the assumptions made for the

design. The design should be in accordance with CEB-FIP Model Code 1990

Chapters 3.9, 3.10, 6.10 and 14.3 (CEB, 1993).



Table 17.3-1: Example of increased minimum cover requirements for

post-installed reinforcing bars

Drilling method Bar diameter ds required concrete cover (mm)

Rotary hammer drilling ≤ 20 mm 30 mm + 0.06

a)lv ≥ 2ds

25 mm 40 mm + 0.06a)

lv ≥ 2ds

Compressed air drilling ≤ 20 mm 50 mm + 0.08

a)lv ≥ 3ds

25 mm 60 mm + 0.08a)

lv ≥ 2ds

a) This term may be significantly reduced if a drilling aid is used

Care should be taken in the preparation of the joint to remove any

unsound concrete and loose material, and clean the exposed existing

reinforcement as required. Carbonated concrete in the location of the post-

installed reinforcing bars should be removed in order to reduce the potential

for corrosion. Revision of the design to accommodate the extent of removal

of existing concrete and the rehabilitation of the existing reinforcing bars may

be necessary.

17.4 Design for fire

Where structural fire design requirements control the design, possible

methods to improve the fire resistance of the joint are as follows:

– increase the concrete cover over the post-installed reinforcement to

reduce the internal concrete/bonding material temperature;

– increase the bond length of the post-installed reinforcing bars to

compensate for reduced bond resistance associated with increased

temperature;

– provide insulating material on the concrete surface to reduce the

internal concrete temperature.

The method employed should take into account the temperature response

of the bonding material as described in the Approval.

The organic materials in bonded anchor systems may be permanently

damaged through carbonisation during a fire. Verification of the competency

of the bonding material after a fire may be undertaken through local

investigation. Alternatively, if sufficient cover is provided, it may be possible

Where structural fire design requirements are in force, the joint should be

assessed accordingly taking into account the response of the bonding material

to increased temperature under fire exposure.



to establish that the bonding material has not been compromised, e.g., if an

assessment of the internal temperature in the concrete during the fire event

has not exceeded the critical carbonization temperature. No information in

respect to this topic is currently available in the literature.

17.5 Installation and job site quality control

The installation of post-installed reinforcing bars may place particular

demands on the training of the installation personnel. Accurate drilling of

long holes with close edge distances, cleaning of deep holes and installation

of large quantities of bonding material without voids in general requires

special training and equipment. Measures for the verification of the proper

installation on site may vary by country; e.g., emphasis may be placed on pre-

certification and training of installers as opposed to job-site inspection.

The installation of post-installed reinforcing bars should be carried out in

accordance with the manufacturer’s installation instructions.

The drilling and cleaning of the holes and the installation of the bonding

material and reinforcing bars should be performed with the equipment

specified by the manufacturer. The work should be performed by suitably

qualified personnel under adequate supervision. Job site quality control

measures should be provided and should verify the design conditions as

specified in the construction documents.


Part IV: 18 Scope 196

PART IV: CHARACTERISTIC RESISTANCE OF ANCHORAGES WITH CAST-IN

HEADED ANCHORS

18 Scope

a) b)

c)

Figure 18-1: Examples of headed anchors covered by this Design

Guide: a) headed bolt; b) headed stud welded to an

embed plate; c) group of headed studs welded to an

embed plate

Part I applies unless otherwise noted. Part IV applies to anchorages

accomplished with cast-in headed anchors (Figure 18-1) loaded by tension,

shear, combined tension and shear forces, as well as bending and torsional

moments. A variety of attachment options are addressed. Most commonly,

the anchors either pass through a hole in the fixture and are secured with a

nut and washer (Figure 18-1a) or, in the case of stud anchors, are welded

directly to the fixture (Figure 18-1b,c). One of the primary differentiating

characteristics between these two configurations from the standpoint of

resistance is that through-bolted cast-in anchors (Figure 18-1a) most often

feature an annular clearance between the anchor and the fixture whereas

welded anchorages do not. Anchors may also be threaded directly into the

fixture, in which case they may be assumed to share some of the

characteristics of welded anchorages.

This Part addresses both prestressed and non-prestressed anchors. Note

that welded anchorages as shown in Figure 18-1b,c cannot be prestressed.

Specialty inserts, strap-type anchors, L- and J-bolts are not covered in this

Design Guide.

This Part applies to members made of normal weight concretes ranging

between strength classes C20 and C90 as defined by CEB-FIP Model Code

1990 (CEB, 1993).

The following conditions should be fulfilled in order to ensure that the

behaviour of cast-in headed anchors conforms with the design model used in

this Design Guide:

1. the angle of inclination of the bearing surfaces of the head as

measured from the anchor longitudinal axis is greater than or equal to

45°, the thickness of the head is not less than 0.4d and the bearing

surface projection as given by 0.5(dh – d) is not less than the

maximum of 0.25d and 4 mm.



The wide variety of shapes and configurations of speciality inserts makes

it difficult to prescribe generalized tests and design equations for many insert

types. Hence, they have been excluded from the scope of this Design Guide.

While L- and J-bolts share some of the characteristics of headed cast-in

anchors covered by this Guide, their behaviour in groups and with respect to

concrete breakout, splitting, etc. has not been sufficiently investigated to

permit their inclusion in the design model used in this Design Guide.

The design model contains limits on the bearing stress in the concrete

under the head which relate to the relationship between splitting forces and

tension forces and controls the displacement of the anchor. This in turn

affects the concrete breakout behaviour. These limits are given in Section

19.1.1.3 (ultimate limit state) and Section 21 (serviceability limit state) and

will effectively dictate the size of the head. The tests used to determine these

limits did not involve fatigue or seismic loading of the concrete member.

2. in the case of anchors threaded directly into the fixture, the engaged

thread length is not less than the nominal anchor diameter.

3. the loading of the concrete member is limited to predominantly static

loading.

Suitability tests may be omitted if these conditions are met. Where these

requirements are not met, prequalification testing may be necessary

analogous to the tests specified in Section 1.3.

Prequalification testing may be necessary to evaluate the values ccr,sp, the

characteristic displacements under given loads and the characteristic fatigue

and seismic resistance.

As a minimum, the manufacturer and the grade and type of steel should be

marked on the anchor.

The plate dimensions, anchor spacing, edge distance and member

thickness provided for embed plates should ensure that full consolidation of

the concrete around the anchors and under the plate is facilitated.

Positioning and securing of anchors and embed plates in the formwork,

prior to placement of the concrete, should be carefully executed taking into

account the provisions in Section 3.5. Care should be taken during concrete

placement to ensure proper consolidation of concrete around the anchors and

under the fixture.

In general, the loading of the anchorage and the concrete member, in

which the anchorage is located, should be limited to predominantly static

loading. Anchors welded to or threaded into the fixture may be suitable for

fatigue loading if the conditions in Section 22 are met. Seismic loading may

be permissible if proper consideration is given to the effects of seismic

actions on the member and the anchorage. The requirements for the

anchorage are addressed in Section 23.



design value of the resistance. Equation (3.3-1) should be observed for all

loading directions on the anchors (tension, shear, combined tension and

shear) as well as all failure modes (steel failure, pullout failure, concrete cone

failure, splitting failure, side-face blowout failure under tension loading and

steel failure, pryout failure, concrete edge and pullout failure under shear

loading). Additionally, if anchor reinforcement is present it should be verified

for both reinforcement and anchorage failure.



The distribution of the actions acting on a fixture to the anchor(s) attached

to the fixture may always be calculated according to the theory of elasticity

(see Section 4.3.1). In certain cases, it may be permissible to calculate this

distribution according to the theory of plasticity (see Section 4.3.2).

Flowcharts for calculating the resistance of anchorages with headed

anchors according to the elastic and plastic design approaches are given in

Figure 18-2 to Figure 18-4.


resistance for both design approaches are given for all loading directions and

all failure modes. To use this Design Guide the following values should be

available either from an Approval or from suitable prequalification testing

and evaluation (see Section 1.3).

- NRk,s (or As, fuk) See Sections 19.1.1.2 and 10.1.2

- kcr, kuncr See Section 19.1.1.4

- hef See Section 19.1.1.4 and Figure 2.5-3

- scr,N, ccr,N See Sections 19.1.1.4 and 10.1.4

- ccr,sp , scr,sp See Sections 19.1.1.5 and 10.1.5

- cmin, smin, hmin See Table 18-1

- VRk,s (or As, fuk and k2) See Sections 19.1.2.2 and 10.2.2

- 0


- VRk,p (or k3) See Sections 19.1.2.3 and 10.2.3

- k4 See Sections 19.1.2.4 and 10.2.4

- d, dh See Sections 19.1.1.3, 19.1.2.3,

10.2.5.1, and Figure 2.5-3

- lf See Sections 19.1.2.5 and 10.2.5.1

- Type of steel (ductile, brittle) See Sections 19.1.2.2, 20, 10.2.2.1,

and 4.3.2.1(4)


modes

See Section 3.4.2



See Section 8.3




Start



Tension

(Section 19.1.1)


Shear

(Section 19.1.2)


Pullout

(Section

19.1.1.3)

Concrete

cone

(Section

19.1.1.4)

Splitting

(Section

19.1.1.5)

Without

lever arm

(Section

19.1.2.2.1)

With

lever arm

(Section

19.1.2.2.2)

Concrete

pryout

(Section

19.1.2.4)

Concrete

edge

(Section

19.1.2.5)

Find appropriate

partial factors (Sect. 3.4.2)

Find smallest


Find smallest

design resistance VRd

NSd NRd VSd VRd

Blowout

(Section

19.1.1.6)

Pullout

(Section

19.1.2.3)

If combined

tension and shear

(Section 19.1.3)

Fatigue

(Section 22)

Seismic

(Section 23)

Fire

(Section 6.5)


(Section 21)

Find appropriate


Durability

(Section 7)

Section

19.1.1.2

End



member (Section 8)

Figure 18-2: Flowchart B1 for the calculation of the characteristic

resistances of anchorages with headed anchors

without anchor reinforcement: elastic design approach

Anchorage resistance can be increased through the provision of suitably

dimensioned and detailed reinforcement.

For non-prestressed anchors the minimum values for spacing, edge

distance and member thickness given in Table 18-1 should be observed.

Table 18-1: Minimum values for spacing, edge distance and

member thickness for non-prestressed headed anchors

Minimum spacing smin = 5d ≥ 50 mm

Minimum edge distance cmin = 3d ≥ 50 mm

Minimum member thickness a) hmin = hef + th + c

a) th = thickness of anchor head

c = required concrete cover for reinforcement in conformance with CEB-FIP

Model Code 1990 (CEB, 1993)

For prestressed anchors, the values for minimum spacing, edge distance

and member thickness should be taken from the relevant Approval or should

be evaluated from the results of prequalification testing (see Section 1.3).

The provisions of Sections 19 and 20 are valid when the spacing between

the outer anchors of adjoining anchor groups or to single anchors or the

distances between single anchors are a > scr,N (concrete failure in tension or

pryout failure in shear), a > scr,sp (splitting failure) and a > 3c1 (concrete edge

failure in shear) (see Figure 1.2-8 to Figure 1.2-10).



Start



Tension

(Section 19.2.1)


Shear

(Section 19.2.2)


Pullout

(Section

19.2.1.3)

Splitting

(Section

19.2.1.5)

Anchor

reinf.

(Section

19.2.2.7)

Find appropriate


Find smallest


Find smallest

design resistance VRd

NSd NRd VSd VRd

Blowout

(Section

19.2.1.6)

Steel

strength

Section

(19.2.1.2)

Anchor

reinf.

(Section

19.2.1.7)

Anchor

reinf.

(Section

19.2.1.8)

Steel

strength

(Section

19.2.2.2)

Anchor

reinf.

(Section

19.2.2.6)

Concrete

pryout

(Section

19.2.2.4)

Pullout

(Section

19.2.2.3)

If combined

tension and shear

(Section 19.2.3)

Fatigue

(Section 22)

Seismic

(Section 23)

Fire

(Section 6.5)


(Section 21)

Find appropriate


Durability

(Section 7)

End



member (Section 8)

Figure 18-3: Flowchart B2 for the calculation of the characteristic

resistances of anchorages with headed anchors with

anchor reinforcement: elastic design approach



Start


(Sections 4.3.2.1, 11.1 and 20)

Tension

(Section 11.2)


Pullout

(Sect. 11.2.2

and 19.1.1.3)

Concrete cone

(Sect. 11.2.3

and 19.1.1.4)

Splitting

(Sect. 11.2.4

and 19.1.1.5)

Concrete.

pryout

(Sect.11.3.3

and 19.1.2.4)

Concrete edge

(Sect.11.3.4

and 19.1.2.5)

Without

lever arm

(Sect.11.3.2

and 19.1.2.2.1)

Equation

(11.2-2)Equation

(11.2-3)

Equation

(11.3-2)

Equation

(11.3-3)

Shear

(Section 11.3)



(Section 21)

Fatigue

(Section 22)

Seismic

(Section 23)

Fire

(Section 6.5)

Blowout

(Sect. 19.1.1.6

and 20)

If combined

tension and shear

(Sect.19.1.3)

Section

11.2.1

Durability

(Section 7)

NSd NRd,s VSd VRd,sEquation

(20-1)

End



member (Section 8)

Figure 18-4: Flowchart C for the calculation of the characteristic

resistances of anchorages with headed anchors

without anchor reinforcement: plastic design approach


Part IV: 19 Ultimate limit state – elastic design approach 202


approach

19.1 Anchorages without anchor reinforcement

When using anchors comprised of multiple headed anchors welded

together as shown in Figure 19.1-1, care should be exercised to align the

anchors properly during assembly in order to avoid secondary eccentric

moments. Consideration should also be given to the potential formation under

service loads of a premature concrete failure cone originating from the anchor

head closest to the concrete surface. To avoid this possibility, a soft material

should be placed around the anchor head, as shown in Figure 19.1-1. The

displacement to be accommodated by the soft material may be determined

through appropriate consideration of elastic strain in the anchor shaft and

corresponding head displacement under service loads. The soft material

should be properly secured to the head to avoid displacement during casting.

Figure 19.1-1: Example of an anchorage with two anchors welded

together

In the elastic design approach, the distribution of the loads acting on the

fixture to the anchors is calculated according to the theory of elasticity (see

Section 4.3.1).

The field of application is given in Section 4.3.1.1.







design approach)

Failure

mode Single Anchor

Anchor group a)

Most Loaded

anchor Anchor group

a)

1 Steel

failure

,

,

Rk s

Sd Rd s

Ms

NN N

,

,

Rk sh

Sd Rd s

Ms

NN N

2 Pullout

failure

,

,

Rk p

Sd Rd p

Mp

NN N

,

,

Rk ph

Sd Rd p

Mp

NN N

3

Concrete

cone

failure

,

,

Rk c

Sd Rd c

Mc

NN N

,

,

Rk cg

Sd Rd c

Mc

NN N

4 Splitting

failure

,

,

Rk sp

Sd Rd sp

Msp

NN N

,

,

Rk spg

Sd Rd sp

Msp

NN N

5 Blowout

failure b)

,

,

Rk cb

Sd Rd cb

Mc

NN N

,

,

Rk cbg

Sd Rd cb

Mc

NN N


b) Verification is not required for anchors with c > 0.5hef in members with a thickness

of h ≥ hef + 2c1

The partial factors for Ms, Mp, Msp and Mc are given in Section 3.4.2.1.



19.1.1.3 Pullout failure

It may be necessary to reduce the pullout resistance according to Equation

(19.1-1) to fulfil the requirements in the serviceability limit state (compare

The characteristic pullout resistance NRk,p of an anchor is given by

Equation (19.1-1).



Section 21 and Equation (21-1)).

,Rk p k hN p A (19.1-1)

with:

pk = 7.5fck for cracked concrete (19.1-1a)

pk = 10.5fck for uncracked concrete (19.1-1b)

Ah = bearing area of the head

= 2 2 4hd d (for round head) (19.1-1c)


The values of kcr and kuncr depend on the concrete pressure under the head.

The values given in this Design Guide apply if the characteristic concrete

pressure pk according to Equation (19.1-1a,b) is observed. The critical

pressure to ensure a concrete cone failure according to Section 19.1.1.4 is

discussed in Eligehausen et al. (2006-2) and Furche (1994).

On the basis of a large experimental database including tests by Lee et al.

(2007) and numerical studies in Ožbolt, Eligehausen (1990), the mean

concrete cone failure load (mean resistance) of a single headed anchor in

uncracked concrete can be approximated by Eligehausen et al. (2006-2) with

Equation (10.1-3a) with k = 15.5.

The values of k1 used in Section 19.1.1.4a) are derived based on the

Equations (10.1-3a,b,c). However, the factor k = 15.5 has been used for cast-

in headed anchors.

The model used in this Design Guide assumes that for a group arranged

perpendicular to the edge and loaded by centric tension load, the edge

influences the whole group and not only the anchors closest to the edge. This

assumption may be unconservative for anchorages with an edge distance c

close to the minimum value according to Table 18-1. In such cases, it may be

advisable to provide supplementary reinforcement (stirrups and edge

reinforcement) in the region of the anchorage as shown in Figure 19.1-2 to

offer additional resistance for the near-edge anchors.

Section 10.1.4 applies with the following modifications:

a) The characteristic resistance 0

,Rk cN of a single anchor without edge

and spacing effects is calculated according to Equation (10.1-2a)

with k1 = kcr = 8.9 N / mm

(cracked concrete) or k1 = kuncr = 12.7

N / mm

(uncracked concrete).

b) The definition of embedment depth is given in Section 2.5 (see

Figure 2.5-3).



Figure 19.1-2: Example of a near-edge anchorage provided with

stirrups and edge reinforcement


Section 10.1.5 applies with the modifications explained in Sections

19.1.1.5.1 and 19.1.1.5.2.

19.1.1.5.1 Splitting failure associated with anchor installation

Headed anchors that are not torqued or prestressed (e.g., studs welded to

embed plates) do not generate splitting forces prior to application of load.

Splitting failure associated with prestressing or applying a torque moment

to headed anchors should be avoided by complying with minimum values for

edge distance, spacing, member thickness and reinforcement. These values

are given in the relevant Approval or should be evaluated from the results of

appropriate prequalification tests (e.g., analogous to Section 1.3).

19.1.1.5.2 Splitting failure due to anchor loading

Headed anchors complying with the provisions 1 to 3 in Section 18 are

generally suitable for applications in which the concrete is cracked. Where

cracked concrete conditions are assumed, verification of the splitting failure

mode is not necessary (see Section 10.1.5.2). If the characteristic splitting

resistance is calculated according to Equation (10.1-5), then the value 0

,Rk cN

should be calculated according to Section 19.1.1.4 and the values

ccr,sp = 0.5scr,sp = 2hef may be taken as a first approximation.

Section 10.1.5.2, applies.

19.1.1.6 Blowout failure

The model according to Equation (19.1-2) is based on Furche,

Eligehausen (1991) and Hofmann, Eligehausen (2009).

Verification of blowout failure is not required, when the edge distance of

the anchor in all directions is c > 0.5hef and the member thickness of



No tests are available with headed anchors in members with a small

thickness (h < hef + 2c1) in which blowout failure occurred. In these

applications Equation (19.1-2) may yield conservative results.

For an anchor group rectangular in shape, the characteristic resistance of

the group in the case of blowout failure should be calculated according to

Equation (19.1-2) for the row of anchors closest to the edge. This approach is

conservative.

For anchorages near a corner or in a narrow member with c2 < c1 the

concrete in the area of the anchor head should be confined by closely spaced

reinforcement (stirrup or spiral) with spacing ≤ 50 mm.

a) b)

Figure 19.1-3: Idealised concrete breakout body and area 0

,c NbA of an

individual anchor in the case of blowout failure:

a) side view; b) plan view

h > hef + 2c1. If verification is required, the characteristic blowout resistance

is given by Equation (19.1-2):

0

, , , , , ,Rk cb Rk cb A Nb s Nb g Nb ec NbN N (19.1-2)

with:

0

,Rk cbN = characteristic blowout resistance of a single anchor unaffected

by adjacent loaded anchors, proximate corners, or limited

member thickness

A,Nb = 0

, ,/c Nb c NbA A

= factor accounting for the geometric effects of loaded anchor

spacing, distance to proximate corners, and member thickness

s,Nb = factor to take into account the influence of a corner on the stress

distribution in the concrete

g,Nb = factor to take into account the influence of the anchor bearing

stress on the blowout resistance of an anchor group

ec,Nb = factor to take account of a group effect when different tension

loads are acting on the individual anchors of a group

The various factors of Equation (19.1-2) are explained below.

The average value of k5 has been quantified as 18.5 for headed bolts in

uncracked concrete on the basis of a large experimental database in respect to

the average blowout resistance of a single anchor for concrete strength

measured on cubes with side length of 200 mm (Hofmann, Eligehausen,

2009).

The values of k5 used in Equation (19.1-2a) are determined following the

procedure given in Equations (10.1-3a,b,c).

a) The characteristic resistance of a single anchor near an edge unaffected

by adjacent loaded anchors, proximate corners or limited member

thickness is given by:

0

,Rk cbN = 1

0.75 0.75

5 h ckk c A f (19.1-2a)

k5 = kcr = 11.1 [N0.25

/ mm0.25

] cracked concrete

k5 = kuncr = 15.8 [N0.25

/ mm0.25


Ah = see Equation (19.1-1c)



a)

b)

c)

Figure 19.1-4: Examples for the determination of Ac,Nb for different

arrangements of anchors: a) group of two anchors at

an edge; b) group of two anchors at a corner; c) group

of two anchors in a member with limited thickness

relative to the anchor embedment

b) The ratio 0

, , ,/A Nb c Nb c NbA A accounts for the geometric effects of

spacing, distance to a corner and member thickness, where:

0

,c NbA = projected area of the idealised concrete blowout failure

cone of a single tension-loaded anchor located near the

edge of the concrete member, taken as a pyramid with

height c1 and base length 4c1 (see Figure 19.1-3)

= 2

116c

Ac,Nb = projected area of the idealised concrete blowout failure

cone associated with the tension-loaded anchor group

located near the edge of the concrete member, as limited

by overlapping failure surfaces, proximate corners, or

limited member depth. Examples for the determination

of Ac,Nb are given in Figure 19.1-4

c) The factor s,Nb takes into account the influence of a proximate corner

on the distribution of the stresses in the concrete resulting from anchor

loading:

2,

1

0.7 0.3 1.02

s Nb

c

c (19.1-2b)

For anchorages in a narrow member, the value corresponding to the

lesser of the two distances to a corner should be taken for c2 in

Equation (19.1-2b).

d) The factor g,Nb accounts for the bearing areas of the individual

anchors of the group.

g,Nb = 1

(1 ) 1.04

sn n

c for s ≤ 4c1 (19.1-2c)

n = number of tension-loaded anchors in a row parallel to the

edge

The eccentricity should be determined for the row of tension-loaded

anchors nearest to the edge.

e) The factor ec,Nb accounts for the reduction of the group capacity when


uniform:



,

1

11.0

1 4ec Nb

Ne c

(19.1-2d)

eN = eccentricity of the resulting tension force of the tension-

loaded anchors with respect to their centre of gravity

19.1.2 Resistance to shear load

Embedded plates loaded in shear derive resistance from the embedded

plate as well as the anchors. Since the stiffness associated with the bearing of

the embed plate is initially much greater than that of the anchors, spalling of

the concrete at the leading edge of the embed plate may occur before the

anchors take up significant load. In general, such spalling is unlikely to

negatively influence the resistance of the anchorage. It may, however, pose

serviceability problems. Shear spalling may be avoided by placing a

compressible material around the outside edge of the embed plate. This

procedure is particularly recommended for anchorages close to edges.




19.1.2.2.1 Shear load without lever arm

Section 10.2.2.1 applies with the following modification:

The constant k2 = 0.6 compared with k2 = 0.5 in Equation (10.2-1), takes

into account the influence of welding on the shear resistance (Klingner,

Mendonca, 1982; Roik, 1982 and Anderson, Meinheit, 2000).

For embed plates with welded studs, the constant k2 in Equation (10.2-1)

may be increased to k2 = 0.6.

19.1.2.2.2 Shear load with lever arm

Section 10.2.2.2 applies.


In general pullout failure will not occur with headed anchors. However,

for headed anchors with small heads and large embedment depths pullout

may be decisive.

Section 10.2.3 applies. However, the value NRk,p used in Equation (10.2-3)

should be calculated according to Section 19.1.1.3.




Section 10.2.4 applies. However, the value 0

,Rk cN calculated according to

Section 19.1.1.4 should be used when calculating NRk,c in Equation (10.2-4).


Section 10.2.5 applies. In Equation (10.2-5a) and (10.2-5a2) dnom should be

replaced by d.



19.2 Anchorages with anchor reinforcement


Anchor reinforcement to take up tension loads should comply with the

following requirements (see also Figure 19.2-1).

a) The design tension force NSd,re in the anchor reinforcement associated

with each anchor should be calculated using the design load on the

anchor (see Figure 19.2-1c).

The limitation of yield strength and diameter of anchor reinforcement are

based on tests by Ramm, Greiner (1991).

b) The anchor reinforcement should consist of deformed bars

(fyk ≤ 500 MPa) with a diameter not larger than 16 mm. The anchor

reinforcement should be detailed in the form of stirrups or hoops with

bend diameters in accordance with the CEB-FIP Model Code 1990

(CEB, 1993).

c) The anchor reinforcement should be placed in close proximity to the

headed anchors and preferably tied to the anchors. Ideally, the anchor

reinforcement should enclose the surface reinforcement as well.

In the tests by Ramm, Greiner (1991) the anchor reinforcement was placed

in close proximity to the headed anchors. The limit on the spacing between

anchor reinforcement and headed anchor of 0.5hef is based on theoretical

considerations and it is conservative given the limits of utilization of hooked

bars according to Section 19.2.1.8.

d) Only those bars with a distance not larger than 0.5hef from the anchor

centreline should be assumed to resist the tension load from that

anchor.

e) The anchor reinforcement should be terminated in the assumed

failure cone by a bend, hook or loop with a minimum anchorage

length of 4ds.



a)

b)

c)

Figure 19.2-1: Example of a quadruple anchorage with anchor

reinforcement to take up tension loads: a), b) anchor

reinforcement at a distance ≤ 0.5hef from the anchors;

c) strut-and-tie model to calculate forces in the anchor

reinforcement

f) The anchor reinforcement should be anchored outside the assumed

failure cone with an anchorage length lb,net in accordance with CEB-

FIP Model Code 1990 (CEB, 1993).

g) In general, the anchor reinforcement (number and diameter)

determined to resist the force in the most-loaded anchor should be

provided for all anchors of the group.

Orthogonal surface reinforcement should be provided as shown in Figure

19.2-1a,b to resist the forces arising from the assumed strut-and-tie model

(see Figure 19.2-1c) and the splitting forces according to Section 8.3.



In practice, anchor reinforcement as shown in Figure 19.2-1 is provided to

increase the tension capacity of headed anchors. However, in many

applications it may be more effective to increase the embedment depth,

thereby providing a more direct load path.

Where such anchor reinforcement is included in the resistance of the

anchorage, it should be positioned roughly symmetrical with respect to the

anchor group in order to minimise the incompatibility of the resistance

mechanisms.

The limitation on the diameter of the anchor reinforcement and its

distance from the anchors are based on tests (Ramm, Greiner, 1991;

Eligehausen et al., 1992).


In the model presented below, it is assumed that the anchor reinforcement

is fully activated after the formation of a concrete breakout body starting

from the anchor head and takes up the total anchor load.


Table 19.2-1: Required verifications for tension loading –

anchorages provided with anchor reinforcement

Failure Mode Single anchor

Anchor group a)

Most loaded

anchor Anchor group

a)

1

Ste

el

Steel failure

of anchor

,

,

Rk s

Sd Rd s

Ms

NN N

,

,

Rk sh

Sd Rd s

Ms

NN N

2

Co

ncr

ete

Pullout

failure of

anchor

,

,

Rk p

Sd Rd p

Mp

NN N

,

,

Rk ph

Sd Rd p

Mp

NN N

3 Splitting

failure

,

,

Rk sp

Sd Rd sp

Msp

NN N

,

,

Rk spg

Sd Rd sp

Msp

NN N

4 Blowout

failure

,

,

Rk cb

Sd Rd cb

Mc

NN N

,

,

Rk cbg

Sd Rd cb

Mc

NN N

5 A

nch

or

rein

forc

emen

t Steel failure

,

, ,

,

Rk re

Sd re Rd re

Ms re

NN N

,

, ,

,

Rk reh

Sd re Rd re

Ms re

NN N

6 Anchorage

(bond) failure

, ,Sd re Rd aN N , ,

h

Sd re Rd aN N




The partial factors for Ms, Mp, Msp, Mc and Ms,re are given in

Section 3.4.2.1.

19.2.1.2 Steel failure of anchor


19.2.1.3 Pullout failure of anchor



Concrete cone failure needs not to be verified when sufficient anchor

reinforcement is provided to resist the applied tension load.




No tests with headed anchors with anchor reinforcement close to an edge

are available in which blowout failure occurred. It is assumed that the model

given in Section 19.1.1.6 applies. The model might be conservative.

Section 19.1.1.6 applies. However, a verification for blowout failure

should be performed in all applications.

19.2.1.7 Yielding of anchor reinforcement

The characteristic yield resistance NRk,re of the anchor reinforcement

provided to one anchor is given by:

, . ,Rk re s re yk reN n A f (19.2-1)

with:

As,re = cross-section of one bar of the anchor reinforcement

fyk,re = nominal yield strength of the anchor reinforcement

≤ 500 MPa

n = number of bars of the anchor reinforcement provided to one

anchor (see Section 19.2.1)



19.2.1.8 Anchorage failure of the anchor reinforcement in the

concrete cone

The design resistance NRd,a according to Equation (19.2-2) is based on the

provisions in CEB-FIP Model Code 1990 (CEB, 1993) for the anchorage of

tension reinforcement.

The factor re in Equation (19.2-2) takes account of the effect of the bend,

hook or loop on the anchorage capacity of the anchor reinforcement in the

assumed failure cone.

Table 19.2-2: Design bond stresses 0

bdf according to CEB-FIP

Model Code 1990 (CEB, 1993) for good bond

conditions

ckf [MPa] 20 30 40 50 60 70 80

0

bdf [MPa] 2.3 3.0 3.6 4.2 4.6 5.2 5.7

The design resistance NRd,a of the anchor reinforcement provided to one

anchor associated with anchorage failure in the assumed breakout cone is

given by:

, 1Rd a bd re

n

N l u f (19.2-2)

n = see Equation (19.2-1)

l1 = length of the anchor reinforcement in the assumed failure cone

(see Figure 19.2-1)

≥ 4ds

u = circumference of one bar

fbd = 0

6 7 bdk k f

0

bdf = design bond strength according to CEB-FIP Model Code 1990

(CEB, 1993) (see Table 19.2-2)

k6 = factor that considers the position of the bar during concreting:

k6 = 1.0 for good bond conditions, as for a) all bars with an

inclination of 45° to 90° to the horizontal during concrete

placement and b) all bars with an inclination less than 45° to

the horizontal which are up to 250 mm from the bottom or at

least 300 mm from the top of an individual concrete layer

during concrete placement

k6 = 0.7 for all other cases and for bars in structural parts

constructed with slip forms

k7 = factor to take into account the effect of concrete confinement

on the bond strength

= 1.0 for concrete cover of the anchor reinforcement ≤ 10ds

= 1.5 for concrete cover of the anchor reinforcement in all

directions > 10ds



re = factor taking into account the influence of the bend, hook or

loop

= 0.7

19.2.2 Resistance to shear loads

Anchor reinforcement to take up shear loads should be in the form of

stirrups or loops (Figure 19.2-3) or in the form of orthogonal surface

reinforcement (Figure 19.2-4). It should comply with the following

conditions:

In Equation (19.2-3) it is assumed that the total anchor shear force is

resisted by the anchor reinforcement.

Figure 19.2-2: Tension force in anchor reinforcement to take up shear

forces

For single anchors the design tension force in the anchor reinforcement

calculated according to Equation (19.2-3) is denoted NSd,re.

a) The design tension force ,

h

Sd reN in the anchor reinforcement provided

to one anchor, caused by the design shear force h

SdV acting on this

anchor is given by Equation (19.2-3).

, 1h h sSd re Sd

eN V

z

(19.2-3)

with (see Figure 19.2-2):

es = distance between axis of anchor reinforcement and shear

force acting on the fixture

z = internal lever arm of the concrete member

≈ 0.85d

d = distance between the opposite side of the concrete member

and anchor reinforcement

≤ min (2hef; 2c1)

If the anchor reinforcement is not parallel to the direction of the shear

force (see Figure 19.2-3c) then this should be taken into account in the

calculation of the design tension force in the anchor reinforcement.

The limitation on the diameter of the anchor reinforcement is based on

tests by Ramm, Greiner (1991) and Schmid (2010).

b) The anchor reinforcement should consist of deformed bars

(fyk ≤ 500 MPa) with a diameter not larger than 16 mm. In general, the

anchor reinforcement should be detailed in the form of stirrups or loops

with a bend diameter, db, in accordance with CEB-FIP Model Code

1990 (CEB, 1993).



c) In general the anchor reinforcement (number and diameter) determined

to resist the force in the most-loaded anchor should be provided for all

anchors of the group.

Anchor reinforcement according to Figure 19.2-3 should be in contact

with the anchor to ensure straining of the reinforcing bars with increasing

shear load or shear displacement of the anchor. If the anchor reinforcement is

not in contact with the anchor, a concrete strut is formed between anchor and

bend, which may fail at high pressure thus reducing the efficiency of the

anchor reinforcement. The reinforcement should conform to the minimum

bend diameter according to CEB-FIP Model Code 1990 (CEB, 1993). When

bend diameters larger than these are used, the efficiency of the anchor

reinforcement may also be reduced due to the increased flexural stresses in

the reinforcing near the bend.

d) If the shear force is taken up by anchor reinforcement according to

Figure 19.2-3, it should enclose and contact the anchor shank and

should be positioned as close as practical to the concrete surface taking

into account minimum concrete cover requirements. Where practical,

the anchor reinforcement may also be inclined away from the surface

of the concrete thus providing both additional cover and resistance to

splitting.

After the formation of the concrete breakout body, the anchor shear load is

transferred to the anchor reinforcement by compression struts (see

Figure 19.2-4). Anchor reinforcement close to the anchor or between the

anchors is effective. Because the shape of the breakout body might vary, the

distance of the anchor reinforcement to the anchor should be limited to 0.5c1.

The anchorage length of the anchor reinforcement in the assumed failure

cone should be equal to or larger than the minimum value according to CEB-

FIP Model Code 1990 (CEB, 1993) to ensure a force transfer according to

Equation (19.2-5). For reasons of equilibrium an edge reinforcement should

be provided (see Figure 19.2-4).

e) If the shear force is resisted by surface reinforcement as shown in

Figure 19.2-4, the following requirements should be met:

- Only bars with a distance ≤ 0.5c1 from the anchor and bars between

anchors with s ≤ 3c1 should be assumed as effective.

- The minimum anchorage length of the surface reinforcement in the

assumed concrete breakout body is:

minl1 = 10ds straight bars with or without welded transverse

bars

= 4ds bars with a hook or bend

- Continuous edge reinforcement designed for the forces

corresponding to an appropriate strut-and-tie model (see Figure

19.2-4) should be provided. As a simplification, the angle of the

compression struts may be taken as 45°.

f) The anchor reinforcement should be anchored outside the assumed

failure cone with an anchorage length lb,net according to CEB-FIP

Model Code 1990 (CEB, 1993).



a)

b)

c)

Figure 19.2-3: Detailing of the anchor reinforcement in the form of

hairpins. Values cmin, lb,net and db according to CEB-

FIP Model Code 1990 (CEB, 1993)



Figure 19.2-4: Surface reinforcement to take up shear forces with

simplified strut and tie model to design anchor and

edge reinforcement





Table 19.2-3: Required verifications for shear loading – anchorages

provided with anchor reinforcement

Failure Mode Single anchor

Anchor group a)

Most loaded

anchor Anchor group

b)

1

Ste

el f

ailu

re

Shear force

without lever

arm

,

,

Rk s

Sd Rd s

Ms

VV V

,

,

Rk sh

Sd Rd s

Ms

VV V

2 Shear force

with lever arm

,

,

Rk sm

Sd Rd sm

Ms

VV V

,

,

Rk smh

Sd Rd sm

Ms

VV V

3

Co

ncr

ete Pullout failure

,

,

Rk p

Sd Rd p

Mp

VV V

,

,

Rk ph

Sd Rd p

Mp

VV V

4 Pryout failure ,

,

Rk cp

Sd Rd cp

Mc

VV V

,

,

Rk cpg

Sd Rd cp

Mc

VV V

5

An

cho

r re

info

rcem

ent

Yielding

,

, ,

,

Rk re

Sd re Rd re

Ms re

NN N

,

, ,

,

Rk reh

Sd re Rd re

Ms re

NN N

6

Anchorage

failure in the

concrete

breakout

body b)

, ,Sd re Rd aN N , ,

h

Sd re Rd aN N


b) Only for anchor reinforcement according to Figure 19.2-4



The partial factors for Ms, Mp, Mc, and Ms,re are given in

Section 3.4.2.1.

19.2.2.2 Steel failure of anchor





In the case of anchorages with anchor reinforcement the anchors may be

significantly deformed before failure. This will increase the force causing

pryout failure. The reduction of the factor k4 is based on tests by Ramm,

Greiner (1991).

Section 19.1.2.4 applies. However, the factor k4 given in Section 10.2.4.

should be multiplied by 0.75.


Concrete edge failure need not be verified when sufficient anchor

reinforcement is provided to resist the applied shear load.

19.2.2.6 Yielding of anchor reinforcement

Tests by Ramm, Greiner (1991) indicate that the efficiency of an anchor

reinforcement according to Figure 19.2-3 may be reduced significantly by

small deviations in the position of the anchor reinforcement (e.g., not in

contact with the anchor shaft, placed not as closely as possible to the fixture)

and spalling of the concrete cover in the region of the hairpin bend. The

factor k8 = 0.5 takes into account usual tolerances. It is valid for anchors with

a fixture embedded in the concrete (embed plates) and may be unconservative

for surface-mounted fixtures. If the correct position of the anchor

reinforcement is ensured (e.g., by welding to the anchor), then the efficiency

factor may be increased to k8 = 1.

The characteristic yield resistance NRk,re of the anchor reinforcement of

one anchor may be calculated according to Equation (19.2-4).

, 8 , ,Rk re s re yk reN k n A f (19.2-4)

with:

k8 = efficiency factor

= 0.5 anchor reinforcement according to Figure 19.2-3

= 1.0 anchor reinforcement according to Figure 19.2-4

n = number of bars of the anchor reinforcement of one anchor


concrete breakout body

The anchor reinforcement according to Figure 19.2-3 is strained by the

shear displacement of the anchor. Therefore, no check of the anchorage

resistance is required.

For an anchor reinforcement in the form of hairpins or stirrups as shown

in Figure 19.2-3 no check of the anchorage resistance is required.



The design resistance NRd,a according to Equation (19.2-5) is based on the

provisions in CEB-FIP Model Code 1990 (CEB, 1993) for the anchorage of

tension reinforcement.

For anchor reinforcement as shown in Figure 19.2-4, the design resistance

NRd,a of the anchor reinforcement provided to one anchor associated with

reinforcement anchorage failure in the assumed concrete breakout body is

given by:

, 1Rd a bd re

n

N l u f (19.2-5)

n = see Equation (19.2-4)

l1 = length of the anchor reinforcement in the assumed failure cone

(see Figure 19.2-4)

u = circumference of one bar

fbd = design bond strength; see Section 19.2.1.8

Straight bars should be used as anchorage reinforcement only if the

anchorage length provided is large enough so that the design yield force of

the reinforcing bar can be anchored.

re = 1.0 for straight bars

= 0.7 for bars with a hook, bend or loop at the end or welded

wire mesh with at least one welded wire within the anchorage

length

= 0.5 for welded wire mesh with at least one welded wire within

the anchorage length and a hook or bend at the end

19.2.3 Resistance to combined tension and shear loads


shear loads only, failure cracks will occur in the concrete well before

reaching the ultimate load (see cracks 1 in Figure 19.2-5). These cracks will

reduce the tension capacity of the anchorage. Also, the shear capacity of

anchorages with anchor reinforcement to take up tension loads only might be

reduced by the early formation of a concrete cone.

Anchorages provided with anchor reinforcement to take up tension and

shear loads may be designed in accordance with Section 10.3. Failure of the

anchor reinforcement should be treated as concrete failure.

Anchor channels close to an edge with anchor reinforcement to take up the

shear load have been tested by Potthoff (2008). The test results indicate a

linear interaction between the tension and shear capacity (Equation (10.3-3)

with ). No tests have been performed with headed anchors. Because of

the higher shear capacity of anchorages with headed anchors, more concrete

cracking and thus a reduced interaction capacity may be anticipated.

Therefore, a conservative interaction equation ( = 2/3) is proposed.

For anchorages that are provided with anchor reinforcement to take up

tension or shear loads only, Equation (10.3-1d) (simplified approach) or

Equation (10.3-3) (alternative approach) should be used with = 2/3.



Figure 19.2-5: Anchorage at the edge with an anchor reinforcement

to take up shear loads under combined tension and

shear loads

20 Ultimate limit state – plastic design

approach No tests have been performed on anchorages with anchor reinforcement

designed according to the plastic design approach. However, if the anchor

reinforcement is designed to ensure yielding of the headed anchors, a

redistribution of anchor forces as assumed in the plastic design approach

should occur.

Section 11 applies. However, the modifications for the calculation of the

characteristic resistances for the different load directions and failure modes

given in Section 19 should be taken into account when applying the

provisions given in Section 11. Furthermore, to avoid blowout failure either

the edge distance should be c1 > 0.5hef or Equation (20-1) should be satisfied

for the anchors closest to the edge.

g

Rk ,cb Rk ,s instN N 0.6 (20-1)

with NRk,cb according to Equation (19.1-2), g

Rk ,sN according to Equation

(11.2-1) and inst according to Section 3.4.2.1.2.

For anchorages with anchor reinforcement the following additional

modifications apply:

a) Anchor reinforcement is provided to take up tension loads. Instead of

Equation (11.2-3) verify Equation (20-2):

Rk ,re c Rd ,a Rk ,s instmin N ; N N 0.6 (20-2)

with:


Part IV: 21 Serviceability limit state 222

NRk,re = value according to Equation (19.2-1)

NRd,a = value according to Equation (19.2-2)

c = 1.5

NRk,s = characteristic steel resistance of one anchor according to

Section 10.1.2

inst = value according to Section 3.4.2.1.2

b) Anchor reinforcement is provided to take up shear loads. Instead of

Equation (11.3-3) verify Equation (20-3):

Rk ,re c Rd ,a Rk ,smin N ; N V 0.6 (20-3)

with:

NRk,re = value according to Equation (19.2-4)

NRd,a = value according to Equation (19.2-5)

c = 1.5

inst = value according to Section 3.4.2.1.2

VRk,s = characteristic steel resistance of one anchor according to

Section 19.1.2.2

21 Serviceability limit state Section 12 applies with the following additions:

If the characteristic displacements under tension load have not been

evaluated by suitable prequalification tests, then the following information

may be taken as a first approximation (Furche, 1994).

The short-time displacement under the characteristic tension load may be

calculated from Equation (21-2):

,0s

N s head

s

lE

(21-2)

with:

s = steel strain of anchor

Under long-duration loading the displacements will increase. To limit the

displacements under the characteristic tension load to an acceptable value

( , 2N mm), the concrete bearing pressure p under the head should be

smaller than the value padm specified below:

Skadm

h

Np p

A (21-1)

with:

NSk = characteristic tension load on anchor calculated according to

Section 4.4



Es = modulus of elasticity of steel

ls = length of anchor with uniform strain

head = slip of anchor head

=

2

9

10

ck

k p

k f

(21-2a)

k9 = 15 for d ≤ 10 mm

= 25 for d > 10 mm

k10 = 200 for cracked concrete

= 400 for uncracked concrete

p = concrete pressure under the head

= /Sk hN A (21-2b)

Nsk = characteristic tension load on anchor calculated according

Section 4.4

Ah = bearing area of the head, as defined in Equation (19.1-1c)

A significant increase of displacement will occur when the anchor is

located in a crack and the crack width varies due to a variation in the live load

on the concrete member. Furthermore, the displacement will increase under

sustained load due to creep of the highly compressed concrete under the head.

To limit this increase of displacement, the pressure under the head should be

limited. The value given in Equation (21-1a) has been evaluated from tests on

headed anchors that were assessed using the displacement criteria given in

EOTA (1997). The value given in Equation (21-1b) is based on current

experience.

Ah = bearing area of the head, as defined in Equation (19.1-1c)

padm = admissible concrete pressure under the anchor head

= 2.5fck for cracked concrete (21-1a)

= 4.0fck for uncracked concrete (21-1b)

For an anchor group, NSk in Equation (21-1) should be replaced by h

SkN .

If anchor reinforcement is present to take up the tension and/or shear loads

on the anchorage, the concrete breakout body might form under service load.

The width of the corresponding crack should be limited to acceptable values.

This is obtained by designing the anchorage capacity of the anchor

reinforcement according to CEB-FIP Model Code 1990 (CEB, 1993).

The short-time displacements under the characteristic shear load may be

calculated from Equation (21-3)

,0 11 2

SkV

Vk

d (21-3)

with:


Part IV: 23 Seismic loading 224

k11 = 12 [mm3 / kN]

VSk = characteristic shear load on anchor [kN] calculated according to

Section 4.4.

d = anchor diameter [mm]

For an anchor group, VSk in Equation (21-3) should be replaced by h

SkV .

The long-time displacement under shear load may be assumed to be

V, 1.5V,0. This is an estimate based on limited test data.

22 Fatigue loading For embed plates with welded headed studs (insert type of welding) the

following values were developed:

k,fat = 100 MPa (Usami et al., 1988)

k,fat = 35 MPa (Naithani et al., 1988)

These values are valid for 62 10 load cycles. For a larger number of load

cycles they should be reduced.

If the anchor is threaded into the baseplate, values for k,fat and k,fat

should be taken from the relevant code of practice for bolts in bearing-type

connections.

Fatigue loading of the anchorage is allowed when the anchor is welded to

the fixture or threaded into the fixture. Section 6.3 applies. Values for k,fat

and k,fat should be taken from the relevant Approval or evaluated from the

results of suitable prequalification tests (see Section 1.3).

23 Seismic loading Tests by Hoehler (2006) indicate that the displacement of headed anchors

might increase significantly during seismic loading. However, it is believed

that this increase in anchor displacement is acceptable if the pressure under

the head is limited according to Equation (21-1).





PART V: CHARACTERISTIC RESISTANCE OF ANCHORAGES WITH CAST-IN

ANCHOR CHANNELS 24 Scope Shear forces applied in the direction of the longitudinal axis of the channel

are not covered in this Design Guide due to a lack of a generalized model to

describe the slip behaviour of the channel connection and the near edge

behaviour under shear loads. In general, product-specific Approvals are

required for these applications.

Torsional moments causing shear forces perpendicular to the longitudinal

channel axis (Figure 24-1) are admissible; however, the provision in this

Design Guide should be used with engineering judgement.

Figure 24-1: Example of an anchor channel loaded by a torsional

moment

Part I applies unless otherwise noted. Part V applies to anchorages with

cast-in anchor channels, whereby an essentially rigid connection exists

between the channel and the anchor elements (see Figure 1.2-7). The anchor

may be welded or forged to the channel. The anchor channel may be loaded

by tension, shear perpendicular to the longitudinal axis of the channel, or a

combination of tension and shear loads. Shear applied longitudinally along

the channel axis is not addressed in this Design Guide. The concrete members

in which the channel anchor is embedded should be comprised of concrete

containing normal weight aggregate and belonging to a strength class of at

least C20 and at most C90 according to CEB-FIP Model Code 1990 (CEB,

1993).

The anchor channels should be placed flush with the concrete surface. A

fixture is connected to the channel by channel bolts (hammer head or hooked

bolts) with nuts and washers (see Figure 1.2-7).

The design provisions given in this Part of the Design Guide are valid for

channels with a height 15 mm ≤ hch ≤ 50 mm and a corresponding width

25 mm ≤ bch ≤ 75 mm.

At least two anchors should be provided on an anchor channel. The

maximum number of anchors is not limited. The spacing between anchors

should not be smaller than 5d or 50 mm and not be larger than the smallest of

5cmin and 400 mm. The distance between the end of the channel and the

nearest anchor should be about 25 mm.


Part V: 24 Scope 226

The authors are not aware of testing to address the behaviour of anchor

channels subjected to seismic loading. This load condition is therefore not

addressed in this Design Guide.

a1) a2) a3)

In general, within the approach used in this Part of the Design Guide it is

assumed that the loading of the anchorage and the concrete member in which

the anchorage is located is limited to predominantly static loading. Fatigue

and seismic loading are not addressed in this Part of the Design Guide.

To ensure suitability of anchor channels in concrete, prequalification

testing is necessary (e.g., analogous to the tests specified in Section 1.3).

As a minimum, the manufacturer and the size of the channel should be

marked on the channel.

Welding of the anchors to the channel should be done according to the

corresponding code of practice. Anchors made of carbon steel may be welded

to channels produced from stainless steel. However, in general, anchors made

of stainless steel may not be welded to a channel made of carbon steel.

Care should be taken during concrete placement to ensure proper

consolidation of concrete around the anchors and under the fixture (see

Section 3.5).

a4) a5) a6)

b1) b2) b3) b4)

Figure 24-2: Failure modes of anchor channels:

a) Tension: a1) steel failure of channel bolt; a2) flexural failure of

channel lips; a3) flexural failure of channel; a4) failure of

connection between channel and anchor; a5) steel failure

of anchor; a6) concrete cone failure. Pullout, splitting and

blowout failure not shown (compare Figure 3.2-1)



design value of the resistance. Equation (3.3-1) should be observed for all

loading directions (tension, shear, combined tension and shear) as well as all

failure modes (see Figure 24-2) (steel failure (failure of channel bolt, local

failure by flexure of channel lips, failure by flexure of channel, failure of

connection between anchor and channel, failure of anchor), pullout failure,

concrete cone failure, splitting failure, blowout failure under tension loading

and steel failure (failure of channel bolt, failure by flexure of channel lips,

failure of connection between anchor and channel, failure of anchor), pullout

failure, pryout failure, and concrete edge failure under shear loading). If

anchor reinforcement is present it should be verified for steel and anchorage

failure instead of concrete cone failure (tension loading) and/or concrete edge

failure (shear loading).



b) Shear: b1) steel failure of channel bolt; b2) flexural failure of

channel lip; b3) concrete edge failure; b4) concrete

pryout failure. Failure of anchor, failure of connection

between anchor and channel and pullout failure not

shown.

Flowcharts for calculating the design resistance of anchor channel are

shown in Figure 24-3 and Figure 24-4.

The calculation of the distribution of the actions acting on a fixture to the

anchors of the channel should be performed according to the theory of

elasticity (see Section 25). Plastic design of the anchorage is not covered in

this Design Guide.

In Section 26, equations for calculating the characteristic resistances for

the elastic design approach are given for all loading directions covered in this

Design Guide and all failure modes. This Design Guide applies only to

anchor channels with distance s ≥ scr,N (tension loading) and s ≥ scr,V (shear

loading) to neighbouring anchor channels.


from an Approval or they should be determined from the results of suitable

prequalification tests e.g., according to EOTA (2004-1) or ICC-ES (2010-2).

- bch, hch See Section 26.1.1.4 and

Figure 2.5-4

- Iy See Section 25.1.2

- NRk,s, NRk,s,a, NRk,s,c, NRk,s,l,

MRk,s,flex

See Section 26.1.1.2

- hef See Section 26.1.1.4 and

Figure 2.5-4

- ch,N See Section 26.1.1.4

- cmin, smin, hmin See Section 26.1.1.5.1

- ccr,sp , scr,sp See Section 26.1.1.5.2

- d, dh See Sections 26.1.1.3 and 19.1.1.3

- Ah for I-Anchors See Section 26.1.1.6

- VRk,s, VRk,s,l, VRk,s,c, VRk,s,a See Section 26.1.2.2


Part V: 24 Scope 228

Start


(Section 24)

Tension

If combined

tension and shear

(Section 26.1.3)


(Section 27)

Blowout

(Section

26.1.1.6)

Splitting

(Section

26.1.1.5)

Distribution of

tension load NSd

(Section 25.1.2)


Concrete

cone

(Section

26.1.1.4)

Pullout

(Section

26.1.1.3)

Anchor

Anchor / channel

Channel lips

Channel bolt

Bending of channel

(Section 26.1.1.2)

Channel and

channel bolt

MSd,flex MRd,s,flex NSd NRd

Shear

VSd VRd

Find appropriate partial

factor (Section 3.4.2)



Find smallest design

resistance NRd


reistance VRd

Fire

(Section 6.5)

Distribution of

shear load VSd

(Section 25.1.3)


Concrete

edge

(Section

26.1.2.5)

Without lever arm

With lever arm

Anchor / Channel

Anchor

Channel lips

(Section 26.1.2.2)

Channel and

channel bolt

Pullout

(Section

26.1.2.3)

Pryout

(Section

26.1.2.4)

Durability

(Section 7)

End



member (Section 8)

Figure 24-3: Flowchart B1 for the calculation of the design

resistances of anchor channels without anchor

reinforcement: elastic design approach

- 0


- VRk,p (or k3) See Sections 26.1.2.3 and 19.1.2.3

- k4 See Section 10.2.4

- ch,V See Section 26.1.2.5

- Type of steel (ductile, brittle) See Sections 26.1.1.2 26.1.2.2,

26.2.1.2, 26.2.2.2, 26.2.2.6 and

10.2.2.1

- Mi for different failure modes See Section 3.4.2



See Section 8.3


The minimum value for edge distance, member thickness and

reinforcement given in the Approval should be observed.

The behaviour of anchor channels can be improved by suitably

dimensioned and detailed reinforcement crossing the failure surface. The

influence of this reinforcement on the strength of anchor channels is taken

into account in Section 26.2.



Start


(Section 24)

Tension

If combined

tension and shear

(Section 26.2.3)


(Section 27)

Blowout

(Section

19.2.1.6)

Splitting

(Section

19.1.1.5)

Distribution of

tension load NSd

(Section 25.1.2)


Pullout

(Section

19.1.1.3)

Shear

Distribution of

shear load VSd

(Section 25.1.3)


Pullout

(Section

26.2.2.3)

Pryout

(Section

26.2.2.4)

VSd VRd

Anchor

reinf.

(Section

26.2.2.7)






resistance MRd, NRd


reistance VRd

Anchor

reinf.

(Section

26.2.2.6)

Anchor reinf.

(Sect.

26.2.1.8

and

19.2.1.8)

Fire

(Section 6.5)

Anchor

Anchor / channel

Channel lips

Channel bolt

Bending of channel

(Section 26.1.1.2)

Without lever arm

With lever arm

Anchor

Anchor / channel

Channel lips

(Section 26.1.2.2)

Channel and

channel bolt Channel and

channel bolt

MSd,flex MRd,s,flex NSd NRd

Anchor reinf.

(Sect.

26.2.1.7

and

19.2.1.7)

Durability

(Section 7)

End



member (Section 8)

Figure 24-4: Flowchart B2 for the calculation of the design

resistances of anchor channels with anchor

reinforcement: elastic design approach


Part V: 25 Determination of action effects 230

25 Determination of action effects –

25.1 Derivation of forces acting on anchors of

anchor channels

– 25.1.1 General

The distribution to the anchors of tension loads acting on the channel may

be calculated using a beam on elastic support (anchors) with a partial restraint

of the channel ends. The resulting anchor forces depend significantly on the

assumed anchor stiffness and degree of restraint. For shear loads the load

distribution is also influenced by the pressure distribution in the contact zone

between channel and concrete.

As a simplification for anchor channels with two anchors, the loads on the

anchors may be calculated assuming a simply supported beam with a span

length equal to the anchor spacing.

As an alternative in the following the triangular load distribution method

to calculate the distribution of tension and shear loads to the anchors is

introduced.

– 25.1.2 Tension loads

The rationale for the triangular load distribution method is given in Kraus

(2003).

– The tension force ,

a

Sd iN in each anchor due to a tension load NSd acting on

the channel is calculated according to Equation (25.1-1), which assumes a

linear load distribution over the influence length lin and takes into account

equilibrium. The influence length lin should be calculated according to

Equation (25.1-2). An example for the calculation of the forces acting on the

anchors is given in Figure 25.1-1.

,

a

Sd i i SdN k A N (25.1-1)

with:

'

iA = ordinate at the position of the anchor i of a triangle

with the unit height at the position of load NSd and

the base length lin

k =

1

1n

i

i

A

(25.1-1a)



Example:

'

2

1.25 1

6

in

in

l sA

l

,1 ,5 0a a

Sd SdN N

'

3

0.25 5

6

in

in

l sA

l

,2

1 2 1

6 3 9

a

Sd SdN N N

'

4

0.75 1

2

in

in

l sA

l

,3

5 2 5

6 3 9

a

Sd SdN N N

' ' '

2 3 4

1 2

3k

A A A

,4

1 2 1

2 3 3

a

Sd SdN N N

Figure 25.1-1: Example for the calculation of anchor forces

according to the triangular load distribution method

for an anchor channel with 5 anchors – the influence

length is assumed as 1.5inl s

n = number of anchors on the channel within the

influence length lin to either side of the applied load

NSd (see Figure 25.1-1)

0.0513in yl I s s (25.1-2)

The moment of inertia Iy of the channel should be taken from the relevant

Approval or should be calculated from the channel cross section.

If several tension loads are acting on the channel, a linear superimposition

of the anchor forces for all tension loads may be assumed.

If the exact position of the load on the channel is not known, the most

unfavourable loading position should be assumed for each failure mode (e.g.,

load acting over an anchor for the case of steel failure of anchor, failure of the

connection anchor/channel or pullout failure and load acting between anchors

in the case of bending failure of channel).

The assumption of a simply supported beam to calculate the bending

moment is a simplification which neglects the influence of partial end

restraints, continuous beam action for channels with more than 2 anchors and

catenary action after yielding of the channel. The characteristic values of the

moments of the resistance given in the Approval or evaluated from the results

of suitable prequalification tests, e.g., EOTA (2004-1) or ICC-ES (2010-2),

– The design bending moment in the channel, MSd,flex, due to design tension

loads acting on the channel may be calculated assuming a simply supported

beam with a span length equal to the anchor spacing.


Part V: 26 Ultimate limit state – elastic design approach 232

should take these effects into account. They may be larger than the plastic

moment calculated from the section dimensions of the channel and the

nominal yield strength of the channel steel.

25.1.3 Shear loads

In reality, shear loads applied perpendicular to anchor channels are

transferred mainly by compression stresses at the interface between channel

and concrete. A part of the shear load is transferred by the anchors via

bending of the channel. In addition, for reasons of equilibrium the anchors are

stressed by tension forces.

In the approach presented below it is assumed that shear forces are

transferred by bending of the channel to the anchors and by the anchors into

the concrete. This simplified approach has been chosen to allow a simple

interaction between tension and shear forces acting on the channel.

Shear loads applied to the fixture are transferred to the channel by channel

bolts. The provision given in Sections 4.3.1.4 and 4.3.1.5 should be used to

determine whether the shear loads act on the channel bolts with or without a

lever arm.

The shear forces of each anchor due to a shear load acting on the channel

perpendicular to its longitudinal axis may be calculated as described in

Section 25.1.2.


approach –

26.1 Anchor channels without anchor

reinforcement

26.1.1 Resistance to tension loads

– 26.1.1.1 Required verifications

The failure modes of anchor channels under tension loading are shown in

Figure 24-2a. In addition to failure modes for headed anchors shown in

Figure 3.2-1 failure of the connection between anchor and channel, local

failure of channel lips due to flexure and flexural failure of channel might

occur.




While for group anchorages with post-installed anchors or headed anchors

the design resistances for concrete cone failure, splitting failure and blowout

failure are calculated for the group of tensioned anchors, for anchor channels

these resistances are calculated for a single anchor taking into account the

influence of neighbouring loaded anchors. These resistances are compared

with the design loads acting on the anchors determined according to Section

25. Instead of verifying all anchors it is sufficient to verify the most

unfavourable anchor and the channel bolt with the highest load.

For steel failure and pullout failure the most unfavourable anchor is the

highest loaded anchor. For concrete cone failure, splitting failure and blowout

failure the most unfavourable anchor is the anchor with the highest ratio a

Sd RdN N . Therefore, it might be necessary to verify several anchors.

Table 26.1-1: Required verifications for anchor channel without

anchor reinforcement under tension loading

Failure Mode Channel Anchor

b) Channel

bolt c)

Design

resistance d)

1

Ste

el

Anchor , ,

a

Sd Rd s aN N

, ,

, ,

Rk s a

Rd s a

Ms

NN

2 Channel /

anchor , ,

a

Sd Rd s cN N

, ,

, ,

,

Rk s c

Rd s c

Ms c

NN

3 Channel

lip , ,Sd Rd s l

N N , ,

, ,

,

Rk s l

Rd s l

Ms l

NN

4 Channel

bolt ,Sd Rd s

N N ,

,

Rk s

Rd s

Ms

NN

5 Flexure of

channel , , ,Sd flex Rd s flex

N N , ,

, ,

,

Rk s flex

Rd s flex

Ms flex

NN

6

Co

ncr

ete

Pullout ,

a

Sd Rd pN N

,

,

Rk p

Rd p

Mp

NN

7 Concrete

cone ,

a

Sd Rd cN N

,

,

Rk c

Rd c

Mc

NN

8 Splitting ,

a

Sd Rd spN N

,

,

Rk sp

Rd sp

Msp

NN

9 Blowout a)

,

a

Sd Rd cbN N

,

,

Rk cb

Rd cb

Mc

NN

a) Not required for anchors with c > 0.5hef and h > hef + 1.5c1

b) Verification required for most unfavourable anchor

c) Verification required for channel bolt with highest tension load

d) Recommended partial factors see Section 3.4




The characteristic resistances NRk,s,a (failure of anchor) and NRk,s (failure of

channel bolt) may be determined according to Equation (10.1-1).

The characteristic resistances for failure of the connection between anchor

and channel (anchor forged to channel), local failure of channel lips and

flexure of channel should be evaluated from the results of suitable

prequalification tests, e.g., according to EOTA (2004-1) or ICC-ES (2010-2),

because no sufficiently accurate design equations are available.

The characteristic resistance NRd,s,flex is calculated from MRd,s,flex taking into

account the static system. For a single load in the middle between anchors

NRd,s,flex = 4MRd,s,flex/s is obtained.

– The characteristic resistances NRk,s,a (failure of anchor), NRk,s (failure of

channel bolt), NRk,s,c (failure of the connection between anchor and channel),

NRk,s,l (local failure by flexure of channel lips), and MRk,s,flex (failure by flexure

of channel) should be taken from the relevant Approval or determined from

the results of suitable prequalification tests, e.g., according to

EOTA (2004-1) or ICC-ES (2010-2).

– 26.1.1.3 Pullout failure

For I-anchors welded to the channel the load bearing area Ah should be

taken from the Approval or calculated from the results of suitable


– Section 19.1.1.3 applies.

– 26.1.1.4 Concrete cone failure

The model for calculating the characteristic resistance for concrete cone

failure is based on the Concrete Capacity Method (see Section 10.1.4). It has

been adapted for anchor channels (Kraus, 2003). Note, that the characteristic

resistance of one anchor and not of a group (as for post-installed anchors and

headed anchors) is determined by Equation (26.1-1).

– The characteristic resistance of one anchor of an anchor channel in the

case of concrete cone failure may be calculated according to Equation

(26.1-1).

0

, , , , , ,Rk c Rk c s N e N c N re NN N (26.1-1)

with:

0

,Rk cN = characteristic resistance of a single anchor without edge and

spacing effects

s,N = factor to take into account the influence of neighbouring

loaded anchors

e,N = factor to take into account the influence of edges

c,N = factor to take into account the influence of a corner

re,N = factor accounting for the negative effect of closely spaced

reinforcement in the concrete member on the strength of

anchors with limited embedment depth (hef < 100 mm).



The various factors in Equation (26.1-1) are explained below.

a) The basic characteristic resistance of one anchor not influenced by

adjacent anchors, edges or corners of the concrete member is obtained

by:

0 1.5

, 1 , Rk c ch N ef ckN k h f [N] (26.1-1a)

with:

The values of k1 are calculated as in Section 19.1.1.4.

k1 = kcr = 8.9 N / mm

cracked concrete

k1 = kuncr = 12.7 N / mm

uncracked concrete

As a first approximation the factor ch,N may be estimated from Equation

(26.1-1a1) (Kraus, 2003).

0.15

, 1.0180

ef

ch N

h

[-] (26.1-1a1)

In Equation (26.1-1a1) the constant 180 carries the unit [mm].

Figure 26.1-1: Example of an anchor channel with different anchor

tension forces

ch,N = factor taking into account the influence of the channel

on the concrete cone failure load. It should be taken

from the relevant Approval or determined from the

results of suitable prequalification tests, e.g., according

to EOTA (2004-1) or ICC-ES (2010-2).

b) The influence of neighbouring anchors on the concrete cone resistance

is taken into account by the factor s,N according to Equation

(26.1-1b).

, 1.5

,

1 , ,0

1

1 1

s Nn

Sd ii

i cr N Sd

Ns

s N

(26.1-1b)


si = Distance between the anchor under

consideration and neighbouring loaded anchors

[mm] ≤ scr,N

scr,N = 2 2.8 1.3 180 3 ef ef efh h h (26.1-1b1)

NSd,i = design tension force on an influencing anchor

NSd,0 = design tension force on the anchor under

consideration



a) b)

Figure 26.1-2: Anchor channel at an edge or in a narrow member

n = number of anchors within a distance scr,N to

both sides of the anchor under consideration.

c) The influence of an edge of the concrete member on the characteristic

resistance is taken into account by the factor e,N according to Equation

(26.1-1c).

1,

,

1.0e N

cr N

c

c (26.1-1c)

Figure 26.1-3: Definition of the corner distance of an anchor channel

in the corner of a concrete member

d) The influence of a corner of the concrete member on the characteristic

resistance is taken into account by the factor c,N according to Equation

(26.1-1d).

2,

,

1.0c N

cr N

c

c (26.1-1d)

with:

c2 = corner distance of the anchor under consideration (see Figure

26.1-3)

If an anchor is influenced by two corners (example see Figure 26.1-4a),

then the factor c,N should be calculated for the values c2,1 and c2,2 and

the product of the factors c,N should be inserted in (26.1-1).

The factor re,N according to Equation (26.1-1e) is the same as in Section

10.1.4(e).

e) The factor re,N takes into account that the strength of anchors with an

embedment depth hef ≤ 100 mm is reduced by reinforcement with a

small bar spacing s.

, 0.5200

ef

re N

h

For s < 150 mm (for any diameter ds)

or s < 100 mm (for ds ≤ 10 mm)

(26.1-1e1)

, 1re N For s ≥ 150 mm (for any diameter ds)


(26.1-1e2)



a) b)

Figure 26.1-4: a) Anchor channel with influence of an edge and two

corners; b) anchor channel with influence of two edges

and one corner

Equation (26.1-1f) is valid for anchor channels with a constant anchor

spacing s.

f) Special cases - For anchor channels in an application with influence of

an edge and two corners (Figure 26.1-4a) or with two edges and one

corner (Figure 26.1-4b) with edge distances less than ccr,N from the

anchor under consideration the calculation according to Equation

(26.1-1) may lead to conservative results. More precise results are

obtained if the value hef is substituted by '

efh according to Equation

(26.1-1f) in Equation (26.1-1a) and the values '

,cr Ns and '

,cr Nc

calculated with '

efh according to Equations (26.1-1b1) and (26.1-1c1),

respectively are inserted in Equations (26.1-1b), (26.1-1c) and

(26.1-1d).

' max

, ,

;ef ef ef

cr N cr N

c sh max h h

c s

(26.1-1f)

with:

cmax = maximum distance from centre of an anchor to the edge or

corner of the concrete member ≤ ccr,N. In the example in

Figure 26.1-4a it would be the maximum value of c1, c2,1 and

c2,2.


At the time of writing this document, the characteristic splitting resistance

cannot be predicted very accurately. However, it is believed that the

following provisions are conservative.

If the edge distance of an anchor is smaller than the value ccr,sp (see

Section 26.1.1.5.2), then a longitudinal reinforcement should be provided

along the edge of the member.

26.1.1.5.1 Splitting failure due to tightening of the channel bolt

The minimum values for spacing, edge distance and member thickness

shall ensure that full compaction of the concrete in the region of the

anchorage is possible and that during the application of a torque moment to

the channel bolts no splitting cracks occur in the concrete cover.

Splitting failure is avoided during tightening of the channel bolt by

complying with minimum values for edge distance cmin, spacing smin, member

thickness hmin, maximum allowed torque moment Tinst and requirements on

reinforcement. These values should be taken from the relevant Approval or

determined from the results of prequalification tests, e.g., according to EOTA

(2004-1) or ICC-ES (2010-2).



26.1.1.5.2 Splitting failure due to loading

Anchor channels with a rigid connection between channel and anchor and

a sufficiently large anchor head are suitable for use in cracked concrete.

Therefore, in general, splitting failure should be avoided by complying with

the condition b) in Section 26.1.1.5.2 (1). If in certain cases the characteristic

splitting resistance is calculated according to Equation (26.1-2), then the

values ccr,sp = 0.5scr,sp = 2hef may be used as a first indication.

(1) No verification of splitting failure is required if this is stated in the

relevant Approval or if one of the following conditions is fulfilled:

a) The edge distance in all directions is c ≥ 1.0ccr,sp. The characteristic

values of edge distance and spacing in the case of splitting under

load, ccr,sp and scr,sp, as a function of the member thickness should be

taken from the relevant Approval or determined from the results of

prequalification tests, e.g., according to EOTA (2004-1) or ICC-ES

(2010-2).

b) The characteristic resistance for pullout failure, concrete cone

failure and blowout failure is calculated for cracked concrete and

reinforcement is present to resist the splitting forces and to limit the

crack width to wk ≤ 0.3 mm.

(2) If the conditions in (1) above are not fulfilled, then the characteristic

resistance of one anchor of an anchor channel should be calculated

according to Equation (26.1-2).

0

, , , , , , ,Rk sp Rk c s N e N c N re N h spN N (26.1-2)

with 0

,Rk cN , s,N, e,N, c,N, re,N, according to Section 26.1.1.4.

However, the values ccr,N and scr,N should be replaced by ccr,sp and scr,sp

in Equations (26.1-1b) to (26.1-1f). The values ccr,sp and scr,sp are valid

for the member thickness hmin.

The factor h,sp takes into account the influence of the actual member

depth h on the splitting resistance. It should be calculated according to

Equation (26.1-2a).

The member thickness influences the splitting failure load up to a limiting

value. The value hef + 1.5c1 is based on experimental investigations by Asmus

(2007). The factor ψh,sp is limited to 2.0 because in tests a larger increase of

the splitting failure load due to an increase of the member depth has not been

observed.

2 / 32 / 3 1

, minmin

+1.52.0

1.0

ef

h sp

h ch

hh

(26.1-2a)

For anchorages affected by more than one edge, e.g., anchorages in the


distance should be inserted for c1 in Equation (26.1-2a).




The model for calculating the characteristic resistance for blowout failure

is the same as given in Section 19.1.1.6. However, it has been adopted for

anchor channels. For anchor channels oriented perpendicular to the edge,

only the most unfavourable anchor with respect to location and loading

should be verified.

No tests are available with anchor channels in members with a small depth

(h < hef + 2c1) in which blowout failure occurred. In these applications

Equation (26.1-3) may yield conservative results.

Verification of blowout failure is not required, when the edge distance of

the anchor in all directions is c > 0.5hef and the member depth is h > hef + 2c1.

If verification is required, the characteristic blowout resistance of one anchor

is given by Equation (26.1-3):

0

, , , , , ,Rk cb Rk cb s Nb c Nb h Nb g NbN N (26.1-3)

with:

0

,Rk cbN

= characteristic blowout resistance of a single anchor unaffected

by adjacent anchors, a corner or the member thickness

s,Nb = factor to take into account the influence of neighbouring

loaded anchors

c,Nb = factor to take into account the influence of a corner

h,Nb = factor to take into account the influence of the member

thickness

g,Nb = factor to take into account the influence of the anchor bearing

area on the behaviour of an anchor group

The various factors in Equation (26.1-3) are explained below.

a) The characteristic resistance of a single anchor near an edge unaffected

by adjacent loaded anchors, a corner or limited member thickness is

given by Equation (26.1-3a).

Equation (26.1-3a) is identical with Equation (19.1-2a).

For I-anchors the load bearing area Ah should be taken from the Approval

or evaluated from the results of suitable prequalification tests.

0

,Rk cbN = 0.75 0.75

5 1 h ckk c A f (26.1-3a)

k5 = 11.1 [N0.25

/ mm0.25

] cracked concrete

= 15.8 [N0.25

/ mm0.25


Ah = as defined in Equation (19.1-1c)

b) The influence of neighbouring anchors on the blowout resistance is

taken into account by the factor s,Nb, which may be calculated

according to Equation (26.1-3b).



, 1.5

,

1 1 ,0

1

1 14

s Nbn

Sd ii

i Sd

Ns

c N

(26.1-3b)

with s, NSd,i NSd,0 as defined in Section 26.1.1.4b).

c) The influence of a corner of the concrete member on the characteristic

blowout resistance is taken into account by the factor c,Nb according to

Equation (26.1-3c).

2,

1

1.02

c Nb

c

c

(26.1-3c)

with:

c2 = corner distance of the anchor under consideration (see

Figure 26.1-3).

If an anchor is influenced by two corners (example see Figure 26.1-4a),

then the factor c,Nb should be calculated for the two corner distances

c2,1 and c2,2 and the product of the factors c,Nb should be inserted in

Equation (26.1-3).

Figure 26.1-5: Anchor channel at the edge of a thin concrete member

d) The influence of a limited member thickness is taken into account by

the factor h,Nb according to Equation (26.1-3d).

,

1

1.04

ef

h Nb

h f

c

(26.1-3d)

with:

f = distance between the anchor head and the lower surface of the

concrete member (see Figure 26.1-5)

≤ 2c1



e) The factor g,Nb takes account of the bearing areas of the individual

anchors of a group.

g,Nb = 1

(1 )4

sn n

c for s ≤ 4c1 (26.1-3e1)

= 1.0 for s > 4c1 (26.1-3e2)

with:

n = number of tensioned anchors in a row parallel to the edge

26.1.2 Resistance to shear loads





While for group anchorages with post-installed anchors or headed anchors

the design resistances for concrete pryout failure and concrete edge failure

are calculated for the group of anchors loaded in shear, for anchor channels

these resistances are calculated for a single anchor taking into account the

influence of neighbouring loaded anchors. These resistances are compared

with the design loads acting on the anchors determined according to Section

25. Instead of verifying all anchors it is sufficient to verify the most

unfavourable anchor and the channel bolt with the highest load.

For steel failure and pullout failure the most unfavourable anchor or

channel bolt is the highest loaded anchor or channel bolt. For pryout failure

and concrete edge failure the most unfavourable anchor is the anchor with the

highest ratio a

Sd RdV V . Therefore, it might be necessary to verify several

anchors.

Table 26.1-2: Required verifications for anchor channels without

anchor reinforcement under shear loading

Failure Mode Channel Anchor

a) Channel

bolt b)

Design

resistance c)

1

Ste

el

Anchor , ,Rd s a

a

SdV V

, ,

, ,

Rd s a

Rk s a

Ms

VV

2 Anchor /

Channel , ,Rd s c

a

SdV V

, ,

, ,

,

Rd s c

Rk s c

Ms c

VV

3 Channel lip , ,Sd Rd s lV V

, ,

, ,

,

Rk s l

Rd s l

Ms l

VV

4 Channel bolt ,Sd Rd s

V V d)

,Sd Rd smV V

e)

,

,

Rk s

Rd s

Ms

VV

d)

,

,

Rk sm

Rd s

Ms

VV

e)

5

Co

ncr

ete

Pullout ,

a

Sd Rd pV V

,

,

Rk p

Rd p

Mp

VV

6 Pryout ,

a

Sd Rd cpV V

,

,

Rk cp

Rd cp

Mc

VV

7 Concrete edge ,

a

Sd Rd cV V

,

,

Rk c

Rd c

Mc

VV

a) Verification required for most unfavourable anchor

b) Verification required for channel bolt with highest shear load

c) Partial factors see Section 3.4.2

d) Shear loads without lever arm

e) Shear loads with lever arm




The characteristic resistances of the channel for the failure modes failure

of anchor, failure of connection between anchor and channel (anchor forged

to channel) and local failure of channel lips due to flexure should be

evaluated from the results of suitable prequalification tests, e.g., according to

EOTA (2004-1) or ICC-ES (2010-2), because no sufficiently accurate design

equations are available. Bending failure of the channel is prevented by the

concrete.

As a first indication the characteristic shear resistance of the anchor,

VRk,s,a, the connection between anchor and channel, VRk,s,c and for local failure

of channel lips, VRk,s,l may be taken equal to the values valid for tension

loading.

The characteristic shear resistances VRk,s,a (failure of anchor), VRk,s,c (failure

of connection between anchor and channel) and VRk,s,l (local failure of channel

lips) should be taken from the relevant Approval or determined from the

results of suitable prequalification tests, e.g., according to EOTA (2004-1) or

ICC-ES (2010-2).

The characteristic resistance VRk,s (failure of channel bolt in case of shear

load without lever arm) may be determined according to Equation (10.2-1).

The characteristic resistance VRk,sm (failure of channel bolt in case of shear

load with lever arm) may be determined according to Equation (10.2-2).

The characteristic resistances of the channel bolt (VRk,s and 0

,Rk sM ) should

be taken from the relevant Approval.


For I-anchors see also Section 26.1.1.3. Section 19.1.2.3 applies.


The characteristic resistance for concrete pryout failure should be

calculated according to Equation (26.1-4).

, 4 ,Rk cp Rk cV k N (26.1-4)

k4 = see Equation (10.2-4)

NRk,c = characteristic resistance according to Section 26.1.1.4,

determined for the most unfavourable anchor loaded in shear


The model for calculating the characteristic resistance for concrete edge

failure is based on the Concrete Capacity Method (compare Section 10.2.5).

It has been adopted for anchor channels (Potthoff, 2008).

For anchor channels with an edge distance in all directions

c ≥max(10hef; 60d) (d = diameter of channel bolt), a check of the

characteristic concrete edge resistance may be omitted.



The characteristic resistance of one anchor loaded perpendicular to the

edge corresponds to:

0

, , , , , 90 , ,Rk c Rk c s V c V h V V re VV V (26.1-5)

with:

0

,Rk cV = characteristic resistance of a part of an anchor channel with one

anchor loaded perpendicular to the edge not influenced by

neighbouring loaded anchors, member thickness or corner

effects

s,V = factor to take into account the influence of neighbouring

loaded anchors

c,V = factor to take into account the influence of a corner

h,V = factor to take into account the influence of the member

thickness

90°,V = factor to take into account the influence of a shear load acting

parallel to an edge

re,V = factor to take into account the influence of an edge

reinforcement

The various factors of Equation (26.1-5) are explained below.

As default value ch,V = 2.5 N / mm

(cracked concrete) or ch,V = 3.5

N / mm

(uncracked concrete) may be taken.

a) The basic characteristic resistance of a part of an anchor channel with

one anchor loaded perpendicular to the edge not influenced by

neighbouring loaded anchors, member thickness or corner effects is:

1.50

, , 1 Rk c ch V ckV f c (26.1-5a)

with:

ch,V = factor N / mm

. It should be taken from the relevant

Approval or determined from the results of suitable

prequalification tests, e.g., according to EOTA (2004-1) or

ICC-ES (2010-2).



Figure 26.1-6: Example of an anchor channel with different anchor

shear forces

b) The influence of neighbouring loaded anchors on the concrete edge

resistance is taken into account by the factor s,V according to Equation

(26.1-5b).

, 1.5

,

1 , ,0

1

1 1

s Vn

Sd ii

i cr V Sd

Vs

s V

(26.1-5b)


si = distance between the anchor under

consideration and the neighbouring anchors

≤ scr,V

scr,V = 4c1 + 2bch (26.1-5b1)

VSd,i = design shear force of an influencing anchor

VSd,0 = design shear force of the anchor under

consideration

n = number of anchors within a distance scr,V to

both sides of the anchor under consideration

a) b)

Figure 26.1-7: Example of an anchor channel with anchors influenced

by a) one or b) two corners, anchor 2 is under

consideration

c) The influence of a corner on the characteristic edge resistance is taken

into account by the factor c,V.

2,

,

1.0c V

cr V

c

c (26.1-5c)

with:

, , 10.5 2cr V cr V chc s c b (26.1-5c1)

If an anchor is influenced by two corners (example see Figure

26.1-7b), then the factor c,V according Equation (26.1-5c) should be

calculated for each corner and the product of the factors c,V should be

inserted in Equation (26.1-5).



The factor h,V as given in Equation (26.1-5d) has been used, e.g., in

Potthoff (2008).

Figure 26.1-8: Example of an anchor channel influenced by the

member thickness

d) The influence of a member thickness h < hcr,V (example see Figure

26.1-8) is taken into account by the factor h,V.

,

,

1.0h V

cr V

h

h

(26.1-5d)

with:

, 12 2h V chh c c (26.1-5d1)

An exponent = 2/3 in Equation (26.1-5d) was established from testing

with rectangular channel geometries and is assumed to be conservative for

other channel cross section shapes.

The exponent in Equation (26.1-5d) should be taken from the

relevant Approval or evaluated from suitable prequalification tests. In

the absence of prequalification tests = 2/3 may be used.

When a shear load is applied parallel to the edge, failure is initiated by

splitting forces perpendicular to the edge. The ratio of the splitting force to

the shear force applied parallel to the edge depends on the pressure in front of

the anchors in the direction of loading related to the concrete compressive

strength (compare Section 10.2.5.1.1f). The load transfer area in front of an

anchor channel is much larger compared to anchors. Therefore, for a given

shear force the splitting forces in front of an anchor channel are much smaller

than in front of an anchor. This induces that the factor 90°,V = VRk,c,/VRk,c, is

larger for anchor channels than for anchors.

The results of numerical investigations (Grosser et al., 2010) and the

evaluation of limited test data (Roik, 2009) show that the assumed factor

90°,V = 2.5 for anchor channels arranged and loaded as shown in Figure

26.1-9 with an edge distance close to the value valid for steel failure is

conservative. For anchor channels with a smaller edge distance the factor

e) The factor 90°,V takes into account the influence of shear loads acting

parallel to the edge (see Figure 26.1-9).

90 , 2.5V (26.1-5e)



90°,V increases. For anchor channels with more than two anchors or with

load applied not only on the anchor closest to the edge the factor 90°,V = 2.5

may be used as well.

Figure 26.1-9: Anchor channel loaded by shear loads parallel to the

edge

f) The factor re,V takes into account the influence of an edge

reinforcement in cracked and uncracked concrete.

, 1.0re V for anchor channels without

supplementary reinforcement as defined

in Figure 10.2-7.

(26.1-5f1)

, 1.4re V for anchor channels with edge

reinforcement (ds ≥ 12 mm) and closely

spaced stirrups (spacing ≤ 100 mm and

≤ 1.5c1) (see Figure 10.2-6).

(26.1-5f2)

g) Special cases - For an anchor channel in a narrow, thin member (see

Figure 26.1-10) with c2,max ≤ ccr,V (ccr,V according to Equation

(26.1-5c1)) and h < hcr,V (hcr,V according to Equation (26.1-5d1)), the

calculation according to Equation (26.1-5) leads to conservative

results. More precise results are achieved if c1 is substituted by '

1c

according to Equation (26.1-5g) in Equations (26.1-5a), (26.1-5b1),



Figure 26.1-10: Illustration of an anchor channel influenced by two

corners and member thickness. In the example the

value c2,2 is decisive for the determination of '

1c

(26.1-5c1) and (26.1-5d1)

'

1 2,maxmax ( ) / 2;( 2 ) / 2ch chc c b h h (26.1-5g)

with:

c2,max = largest of the two edge distances parallel to the direction

of load


For anchor channels the interaction should be verified separately for the

channel bolt and the anchor channel since the location of the failure in each

case is not coincident.

For the verification of combined tension and shear loads the channel bolts,

the channel and the individual anchors of an anchor channel should be

checked according to Section 10.3. The interaction should be verified

separately for the channel bolt and the anchor channel. The highest loaded

channel bolt and the most unfavourable anchor are decisive.

For channel bolts Equation (10.3-2) with = 2.0 is valid.

For the verification of the anchor channel a simplified and an alternative,

more accurate approach are distinguished:

26.1.3.1 Simplified approach

In the simplified approach according to Equations (10.3-1a) to (10.3-1c) or

Equation (10.3-1d) with = 1.5 the following values should be inserted: for

NSd and VSd the maximum value of the design actions valid for the anchor or the

channel bolt, for NRd the minimum value of NRd,s,a, NRd,s,c, NRd,s,l, NRd,s,flex, NRd,p,

NRd,c, NRd,sp and NRd,cb, and for VRd the minimum value of VRd,s,a, VRd,s,c, VRd,s,l,

VRd,p, VRd,cp, and VRd,c. This approach is often conservative, because failure

modes are assumed to interact even if the failures occur at different locations.

Case A: Equations (10.3-1a) to (10.3-1c) or Equation (10.3-1d) with

= 1.5 may be used provided that

VRd,s,ch ≤ NRd,s,ch

where:

VRd,s,ch = design shear resistance of the anchor channel (minimum value of

VRd,s,a, VRd,s,c and VRd,s,l); and



NRd,s,ch = design tension resistance (minimum value of NRd,s,a, NRd,s,c and

NRd,s,l).

Where the concrete resistance is not much lower than the steel resistance

of the channel and the design shear resistance of the anchor channel VRd,s,ch

exceeds the design tension resistance NRd,s,ch, limited testing at the University

of Stuttgart with VRd,s,ch/NRd,s,ch ~ 1.8 indicates that this interaction approach

may not be conservative. Due to the lack of additional experimental data a

conservative linear interaction is proposed for the whole range of

VRd,s,ch > NRd,s,ch.

Case B: For VRd,s,ch > NRd,s,ch Equation (10.3-1d) with = 1.0 should be

used.


Alternatively, the interaction may be performed separately for steel failure

modes and concrete failure modes of the channel, whereby both interactions

should be satisfied (see Figure 10.3-2).

Separate verifications should be performed for failure of the anchor and

the connection between anchor and channel and for the channel (local failure

of channel lips and flexural failure of channel) since the locations of the

failures are not coincident.

The verification of steel failure modes should be performed as follows:

Limited testing at the University of Stuttgart indicates that the use of

= 2.0 in Equation (10.3-2) for verification of the anchor channel is valid

only if the design shear resistance VRd,s,ch of the anchor channel is not larger

than the design tension resistance NRd,s,ch. If the design shear resistance VRd,s,ch

of the anchor channel is larger than the design tension resistance NRd,s,ch the

power on the interaction equation (10.3-2) should be evaluated from the

results of prequalification tests. A linear interaction is considered to be

conservative.

Case A: For VRd,s,ch ≤ NRd,s,ch, Equation (10.3-2) with = 2.0 is valid.

Case B: For VRd,s,ch > NRd,s,ch, Equation (10.3-2) is valid with determined

from suitable prequalification tests ( ≤ 2.0). If prequalification tests are

omitted then = 1.0 should conservatively be used.

The use of the tri-linear interaction equations (10.3-1a) to (10.3-1c) or

Equation (10.3-3) with = 1.5 is considered conservative for concrete

failure.

For the verification of concrete failure modes Equation (10.3-3) with

= 1.5 is valid independent of the ratio VRd,s,ch/NRd,s,ch.



26.2 Anchor channels with anchor

reinforcement

For the field of application Section 24 applies.


a) b)

Figure 26.2-1: Arrangement of anchor reinforcement: a) anchor

channel at an edge; b) anchor channel in a narrow

member

For anchors channels with anchor reinforcement to take up tension loads

the requirements given in Section 19.2.1 should be met. In addition, for

anchor channels parallel to the edge of a concrete member or in a narrow

concrete member, the plane of the anchor reinforcement should be located

perpendicular to the longitudinal axis of the channel (see Figure 26.2-1).


For the most unfavourable anchor see Section 26.1.2.1. The required verifications are given in Table 26.2-1.



Table 26.2-1: Verifications for anchor channels with anchor

reinforcement under tension loading

Failure Mode Channel Anchor a) Channel

bolt b) Design resistance

c)

1

Ste

el

Anchor , ,

a

Sd Rd s aN N

, ,

, ,

Rk s a

Rd s a

Ms

NN

2 Channel /

anchor , ,

a

Sd Rd s cN N

, ,

, ,

,

Rk s c

Rd s c

Ms c

NN

3 Channel

lip , ,Sd Rd s l

N N , ,

, ,

,

Rk s l

Rd s l

Ms l

NN

4 Channel

bolt ,Sd Rd s

N N ,

,

Rk s

Rd s

Ms

NN

5

Flexure

of

channel , , ,Sd flex Rd s flex

N N , ,

, ,

,

Rk s flex

Rd s flex

Ms flex

NN

6

Co

ncr

ete

Pullout ,

a

Sd Rd pN N

,

,

Rk p

Rd p

Mp

NN

7 Splitting ,

a

Sd Rd spN N

,

,

Rk sp

Rd sp

Msp

NN

8 Blowout ,

a

Sd Rd cbN N

,

,

Rk cb

Rd cb

Mc

NN

9

An

cho

r

rein

forc

emen

t Steel

Failure ,

a

Sd Rd reN N

,

,

,

Rk re

Rd re

Ms re

NN

10

Anchorage

(bond)

failure ,

a

Sd Rd aN N ,

1

Rd a

nbd

i s

i

Nf

l d

a) Verification required for the most unfavourable anchor

b) Verification required for channel bolt with highest tension load









Concrete cone failure does not need to be verified when sufficient anchor

reinforcement is provided.




No tests with anchor channels with anchor reinforcement close to an edge

are available in which blowout failure occurred. It is assumed that the model

given in section 26.1.1.6 applies. The model might be conservative.

Section 26.1.1.6 applies. However, verification for blowout failure should

be performed in all applications.

26.2.1.7 Steel failure of anchor reinforcement


26.2.1.8 Anchorage failure of anchor reinforcement in the

concrete cone


a) b)

Figure 26.2-2: Reinforcement to take up shear forces; detailing of

reinforcement: a) cross section; b) plane view with

simplified strut and tie model

26.2.2 Resistance to shear failure

For anchor channels with anchor reinforcement to take up shear loads the

requirements given in Section 19.2.2 should be met. However, the

reinforcement configurations shown in Figure 19.2-3 are not as effective for

anchor channels as for headed anchors and should therefore not be used. Only

anchor reinforcement in the form of surface reinforcement as shown in Figure

19.2-4 and Figure 26.2-2 is covered in this Design Guide.

The force acting on the reinforcement, NSd,re, should be calculated

according to Equation (19.2-3).





Table 26.2-2: Required verifications for anchor channels with

anchor reinforcement under shear loading

Failure Mode Channel Anchor a) Channel

bolt b)

Design resistance

c)

1

Ste

el

Channel

lip , ,Sd Rd s l

V V , ,

, ,

,

Rk s l

Rd s l

Ms l

VV

2 Channel

bolt

,Sd Rd sV V

d)

,Sd Rd smV V

e)

,

,

Rk s

Rd s

Ms

VV

d)

,

,

Rk sm

Rd s

Ms

VV

e)

3

Co

ncr

ete Pullout ,

a

Sd Rd pV V

,

,

Rk p

Rd p

Mp

VV

4 Pryout ,

a

Sd Rd cpV V

,

,

Rk cp

Rd cp

Mc

VV

5

An

cho

r

Rei

nfo

rcem

ent

Steel

failure

, ,

a

Sd re Rd reV N

,

,

,

Rk re

Rd re

Ms re

NN

6

Anchorage

(bond)

failure ,

a

Sd Rd aV N

,

1

Rd a

nbd

i s

i

Nf

l d

a) Verification required for most unfavourable anchor or channel bolt

b) Verification required for channel bolt wit highest shear load


d) Shear load without lever arm

e) Shear load with lever arm






Section 19.1.2.3 applies. However, the factor k3 in Equation (10.2-3)

should be taken as 1.5.


Section 26.1.2.4 applies. However, the factor k4 in Equation (26.1-4)

should be multiplied by 0.75.


Concrete edge failure does not need to be verified when sufficient anchor

reinforcement is provided.

26.2.2.6 Steel failure of the anchor reinforcement

Section 19.2.2.6 applies. However, the reinforcement configurations in

Figure 19.2-3 should not be used for anchor channels and are therefore not

covered in this Design Guide.


concrete breakout body

Section 19.2.2.7 applies. However, the reinforcement configurations in

Figure 19.2-3 should not be used for anchor channels and are therefore not

covered in this Design Guide.

26.2.3 Resistance to combined tension and shear loads

For anchor channels with anchor reinforcement, Section 26.1.3 applies

with the following modifications. Failure of the anchor reinforcement should

be treated as concrete failure.

26.2.3.1 Anchor channels with anchor reinforcement to take up

tension and shear loads

For verification of the channel of anchor channels with anchor

reinforcement to take up tension and shear loads Section 26.1.3.1 (simplified

approach) or Section 26.1.3.2 (alternative approach) are valid.



26.2.3.2 Anchorages with anchor reinforcement to take up

tension or shear loads only

For verification of the channel of anchor channels with anchor rein-

forcement to take up tension or shear loads, the following provisions apply:


shear loads, failure cracks will occur in the concrete well before reaching the

ultimate load (see cracks 1 in Figure 19.2-5). These cracks will reduce the

tension capacity of the anchorage. Also, the shear capacity of anchorages

with anchor reinforcement to take up tension loads might be reduced by the

early formation of a concrete cone. According to Potthoff (2008) a linear

interaction equation is adequate.

In the simplified approach Equation (10.3-1d) with = 1.0 should

conservatively be used.

In the alternative approach, steel and concrete failure modes may be

verified separately. For steel failure modes Section 26.1.3.2 is valid. For the

verification of concrete failure modes of anchor channels Equation (10.3-3)

with = 1.0 should be used.

27 Serviceability limit state If the characteristic displacements under tension and shear load are not

given in the Approval or have not been evaluated by prequalification tests,

then the following information should be considered as a first approximation.

The displacement of an anchor channel under tension load is composed of

the displacement of the anchor and the displacement of the channel due to

bending and local opening of the channel lips and deformation in the area of

the connection of the anchor and the channel. The displacement of the

anchors can be calculated according to Section 21. The displacement due to

bending of the channel may conservatively be calculated using simple beam

analysis. No formulas are currently available for calculating the displacement

due to local opening of the channel lips and this displacement should

therefore be determined from suitable tests.

No method for calculating the displacement of an anchor channel under

shear loading is currently available.

Section 21 applies.

28 Fatigue loading Fatigue loading of anchor channels is not covered in this Design Guide.

29 Seismic loading Seismic loading of anchor channels is not covered in this Design Guide.



References ACI 355.2 (2007): ACI 355.2-07: Qualification of post-installed mechanical anchors in concrete and

commentary. American Concrete Institute (ACI), Farmington Hills, Michigan, USA, 2007.

ACI 318 (2008): Building code requirements for structural concrete (ACI 318-08) and commentary

(ACI 318R-08). American Concrete Institute (ACI), Farmington Hills, Michigan, USA, 2008.

ACI 318 (2011): Building code requirements for structural concrete, Appendix D: Anchoring to

concrete. American Concrete Institute (ACI), Farmington Hills, Michigan, USA, to be published in

2011.

ANSI (1994): ANSI B212.15-94: American national standard for cutting tools – Carbide-tipped

masonry drills and blanks for carbide-tipped masonry drills. American National Standard Institute

(ANSI), New York, New York, USA, 1994.

ASCE (2006): ASCE/SEI 7-05: Minimum design loads for buildings and other structures. American

Society of Civil Engineers (ASCE), Reston, Virginia, USA, 2006.

ASTM (2009): ASTM A193-09: Standard specification for alloy-steel and stainless steel bolting

materials for high temperature or high pressure service and other special purpose applications.

American Society for Testing and Materials (ASTM), Philadelphia, Pennsylvania, USA, 2009.

Anderson, Meinheit (2000): Anderson, N. S.; Meinheit D. F.: Design Criteria for Headed Stud

Groups in Shear. Part 1 – Steel Capacity and Edge Effects. PCI Journal, September-October 200, pp.

46-75.

Anderson, Meinheit (2005): Anderson, N. S.; Meinheit D. F.: PCI’s headed stud design redefined.

Structure Magazine, April 2005, pp. 26-29.

Anderson, Meinheit (2007): Anderson, N. S.; Meinheit D. F.: A review of headed-stud design criteria

in the sixth edition of the PCI design handbook. PCI Journal, V. 52, No. 1, 2007, pp. 2-20.

Appl (2009): Appl, J.: Tragverhalten von Verbunddübeln unter Zugbelastung (Load carrying

behaviour of bonded anchors under tension loading. PhD thesis, University of Stuttgart, Stuttgart,

Germany, 2009 (in German).

Asmus (2007): Asmus, J.: Design Method for Splitting Failure Mode of Fastenings. Eligehausen, R.;

Fuchs, W.; Genesio, G.; Grosser, P. (Editors): “Connections between Steel and Concrete”. Ibidem-

Verlag, Stuttgart, Germany, 2007, pp. 505-517.

Bruckner et al. (2001): Bruckner, M.; Eligehausen, R.; Ožbolt, J.: Influence of bending compression

stresses on the concrete cone capacity. In: Eligehausen, R. (Editor): “Connections between Steel and

Concrete”. RILEM Publications, Cachan, France, 2001, pp. 647-657.

CEB (1991): Fire design of concrete structures in accordance with CEB-FIP Model Code 90. Comité

Euro-International du Béton (CEB), CEB, Bulletin d'Information 208, Lausanne, Switzerland, 1991.

CEB (1993): CEB-FIP Model Code 1990. Comité Euro-International du Béton (CEB), Thomas

Telford, London, UK, 1993.

CEB (1994): Fastenings to concrete and masonry structures, state of the art report. Comité Euro-

International du Béton (CEB), Thomas Telford, London, UK, 1994.

CEB (1997): Design of fastenings in concrete – Design Guide - Parts 1 to 3. Comité Euro-

International du Béton (CEB), CEB Bulletin d'Information 233, Thomas Telford, London, UK, 1997.

CEN (2000): EN 206-1:2000: Concrete. Part 1: Specification, performance, production and

conformity. Comité Européen de Normalisation (CEN), Brussels, Belgium, 2000.


258 References

CEN (2002-1): EN 1990:2002: Eurocode: Basis of structural design. Comité Européen de

Normalisation (CEN), Brussels, Belgium, 2002.

CEN (2002-2): EN 1991:2002: Eurocode 1: Actions on structures. Comité Européen de


Part 1-1: General actions - Densities, self-weight, imposed loads for buildings

(EN 1991-1-1:2002)

Part 1-2: General actions - Actions on structures exposed to fire (EN 1991-1-2:2002)

Part 1-3: General actions - Snow loads (EN 1991-1-3:2003)

Part 1-4: General actions - Wind actions (EN 1991-1-4:2005)

Part 1-5: General actions - Thermal actions (EN 1991-1-5:2003)

Part 1-6: General actions - Actions during execution (EN 1991-1-6:2005

Part 1-7: General actions - Accidental actions (EN1991-1-7:2006)

Part 2: Traffic loads on bridges (EN1991-2:2003)

Part 3: Actions induced by cranes and machinery (EN1991-3:2006)

Part 4: Silos and tanks (EN1991-4:2006)

CEN (2004-1): EN 1992-1-1:2004: Eurocode 2: Design of concrete structures. Part 1-1: General

rules and rules for buildings and civil engineering structures. Comité Européen de Normalisation

(CEN), Brussels, Belgium, 2004.

CEN (2004-2): EN 1992-1-2:2004: Eurocode 2: Design of concrete structures. Part 1-2: General

rules. Structural fire design. Comité Européen de Normalisation (CEN), Brussels, Belgium, 2004.

CEN (2005): EN 1993-1-8:2005: Eurocode 3: Design of steel structures. Part 1-8: Design of joints.

Comité Européen de Normalisation (CEN), Brussels, Belgium 2005.

CEN (2007): EN 13501-2:2007: Fire classification of construction products and building elements.

Part 2: Classification using data from fire resistance tests, excluding ventilation services. Comité

Européen de Normalisation (CEN), Brussels, Belgium, 2007.

CEN (2009): CEN/TS 1992-4:2009: Design of fastenings for use in concrete. Comité Européen de


Part 4-1: General (CEN/TS 1992-4-1:2009)

Part 4-2: Headed fasteners (CEN/TS 1992-4-2:2009)

Part 4-3: Anchor channels (CEN/TS 1992-4-3:2009)

Part 4-4: Post-installed fasteners - Mechanical systems (CEN/TS 1992-4-4:2009)

Part 4-5: Post-installed fasteners - Chemical systems (CEN/TS 1992-4-5:2009)

Cook, Klingner (1992): Cook, R. A.; Klingner, R. E.: Ductile Multiple-Anchor Steel-to-Concrete

Connections. Journal of Structural Engineering, ASCE, V. 118, No. 6, 1992, pp. 1645-1665.

Cook et al. (1998): Cook, R. A.; Kunz, J.; Fuchs, W.; Konz, R. C.: Behavior and design of single

adhesive anchors under tensile load in uncracked concrete. ACI Structural Journal, V. 95, No. 1,

1998, pp. 9-26.

DAfStb (1991): Hilfsmittel zur Berechnung der Schnittgrößen und Formveränderungen von

Stahlbetontragwerken: nach DIN 1045, Ausg. Juli 1988 (Aids for the calculation of action effects and

deflections in concrete structures: according to DIN 1045, vers. July 1988). Deutscher Ausschuss für

Stahlbeton (DAfStb), Heft 240, Ernst & Sohn, Berlin, Germany, 1991 (in German).

DIBt (2002): Merkblatt über die Kennwerte, Anforderungen und Prüfungen von Mauerbohrern mit

Schneidkörpern aus Hartmetall, die zur Herstellung der Bohrlöcher von Dübelverankerungen

verwendet werden (Technical bulletin for characteristic values, requirements and tests for masonry

drill bits with carbide cutting edges which are used to drill holes for anchors). Deutsches Institut für

Bautechnik (DIBt), Berlin, Germany, 2002.



DIBt (2009): Approval Certificate Z-30.3-6: Erzeugnisse, Verbindungsmittel und Bauteile aus

nichtrostenden Stählen (Products, fasteners and components made of stainless steels). Deutsches

Institut für Bautechnik (DIBt), Berlin, Germany, 2009 (in German).

Eligehausen et al. (1992): Eligehausen, R.; Fuchs, W.; Ick, U.; Mallée, R.; Reuter, M.;

Schimmelpfennig, K.; Schmal, B.: Tragverhalten von Kopfbolzenverankerungen bei zentrischer

Zugbeanspruchung (Behavior of headed anchors under centric tension loading tension). Bauingenieur

67, 1992, pp. 183-196 (in German).

Eligehausen et al. (2006-1): Eligehausen, R.; Cook, R. A.; Appl, J.: Behavior and design of adhesive

bonded anchors. ACI Structural Journal, V. 103, No. 6, 2006, pp. 822-831.

Eligehausen et al. (2006-2): Eligehausen, R.; Mallée, R.; Silva, J. F.: Anchorage in Concrete

Construction. Ernst & Sohn, Berlin, Germany, 2006.

Eligehausen, Grosser (2007): Eligehausen, R.; Grosser, P.: Experimentelle und numerische

Untersuchungen zur Bemessung von Befestigungen am Bauteilrand unter Querlasten (Experimental

and numerical investigations on anchorages close to the edge under shear loading). Research Report

EL 72/13-2, University of Stuttgart, Stuttgart, Germany, 2007, (in German).

Eligehausen et al. (2010): Eligehausen, R.; Blochwitz, R.; Fuchs, W.: Behavior, testing and design of

bonded anchors under sustained tension load in concrete. ACI Spring Convention, March 2010,

Chicago, Illinois, USA.

EOTA (1997): ETAG 001: Guideline for European Technical Approval of Metal Anchors for Use in

Concrete. European Organisation for Technical Approvals (EOTA), Brussels, Belgium, 1997.

Part 1: Anchors in general (1997), amended 2006

Part 2: Torque-controlled expansion anchors (1997), amended 2006

Part 3: Undercut anchors (1997), amended 2010

Part 4: Deformation-controlled expansion anchors (1998), amended 2006

Part 5: Bonded anchors (2002), amended 2006 and 2008

Part 6: Anchors for multiple use for non-structural applications (2003), amended 2010

Annex A: Details of test (1997), amended 2001 and 2006

Annex B: Tests for admissible service conditions, detailed information (1997), amended

2001 and 2006

Annex C Design methods for anchorages (1997), amended 2001, 2006 and 2010

EOTA (2003-1): Technical Report TR 018: Assessment of torque-controlled bonded anchors.

European Organisation for Technical Approvals (EOTA), Brussels, Belgium, 2003.

EOTA (2003-2): Steel plate with cast-in anchor(s) - Common Understanding of Assessment

Procedure (CUAP) for a European Technical Approval. European Organisation for Technical

Approvals (EOTA), Brussels, Belgium, 2003.

EOTA (2004-1): Anchor channels - Common Understanding of Assessment Procedure (CUAP) for a

European Technical Approval. European Organisation for Technical Approvals (EOTA), Brussels,

Belgium, 2004.

EOTA (2004-2): Technical Report TR 020: Evaluation of Anchorages in Concrete concerning

Resistance to Fire. European Organisation for Technical Approvals (EOTA), Brussels, Belgium, 2004.

EOTA (2007): Technical Report TR 029: Design of Bonded Anchors. European Organisation for

Technical Approvals (EOTA), Brussels, Belgium, 2007.

Fichtner, Eligehausen (2007): Fichtner, S.; Eligehausen, R.: Stiffness requirements for baseplates. In:

Eligehausen, R.; Fuchs, W.; Genesio, G.; Grosser, P. (Editors): “Connections between Steel and

Concrete”. Ibidem-Verlag, Stuttgart, Germany, 2007, pp. 1059-1072.


260 References

Fuchs, Eligehausen (1989): Fuchs, W.; Eligehausen, R.: Tragverhalten von Befestigungsmitteln im

gerissenen Beton bei Querzugbeanspruchung (Load-bearing behaviour of fasteners in cracked

concrete under shear load). Test report No. 1/41-89/15 (in German), University of Stuttgart, Germany,

1989.

Fuchs (1992): Fuchs, W.: Tragverhalten von Befestigungen unter Querlasten in ungerissenem Beton

(Load-bearing behaviour of fastenings under shear loading in uncracked concrete). Deutscher

Ausschuss für Stahlbeton (DAfStb), Heft 424, Beuth Verlag, Berlin, Germany, 1992 (in German).

Fuchs et al. (1995): Fuchs, W.; Eligehausen, R.; Breen, J.E.: Concrete Capacity Design (CCD)

Approach for Fastening to Concrete. ACI Structural Journal, V. 92, No. 1, 1995, pp. 73-94.

Furche, Eligehausen (1991): Furche, J.; Eligehausen, R.: Lateral blow-out failure of headed studs

near a free edge. In: Senkiw, G. A.; Lancelot, H. B. (Editors): Anchors in Concrete - Design and

Behavior. ACI Special Publication 130, Detroit, Michigan, USA, 1991, pp. 235-252.

Furche (1994): Furche, J.: Zum Trag- und Verschiebungsverhalten von Kopfbolzen bei zentrischem

Zug (Load-bearing and displacement behaviour of headed anchors under axial tension loading). PhD

thesis, University of Stuttgart, Stuttgart, Germany, 1994 (in German).

Grosser (2008): Grosser, P.: Tragverhalten von parallel zum Bauteilrand angeordneten

Zweifachbefestigungen unter Torsionsbeanspruchung im ungerissenen Beton (Load-bearing

behaviour of groups with two anchors arranged parallel to the edge under torsion loading in

uncracked concrete). Test report No. E 08/01 – G07100/02, University of Stuttgart, Germany, 2008

(in German).

Grosser, Eligehausen (2008): Grosser, P.; Eligehausen, R.: Fastenings under shear loading parallel

to the edge. Test report No. E 08/02 – G07100/03, University of Stuttgart, Germany, 2008.

Grosser, Cook (2009): Grosser, P.; Cook, R.: Load bearing behavior of anchor groups arranged

perpendicular to the edge and loaded by shear towards the free edge. UF Structures Report 2009-1,

University of Florida, Florida, USA, 2009.

Grosser et al. (2010): Grosser, P.; Eligehausen, R.; Ožbolt, J.: 3D FE analysis of anchor channels and

headed anchors under shear load close to the edge. In: Proceedings of the 7th International

Conference on Fracture Mechanics of Concrete and Concrete Structures, Jeju, Korea, May 23 – 27,

2010, Korea Concrete Institute, 2010, Seoul, Republic of Korea.

Grosser (2011): Grosser, P.: Adhesive anchors with deep embedments under shear load located close

to the edge and loaded perpendicular to the edge. Test report No. fHW/17-11/01, University of

Stuttgart, Germany, 2011.

Hoehler (2006): Hoehler, M. S.: Behavior and testing of fastenings to concrete for use in seismic

applications. PhD thesis, University of Stuttgart, Stuttgart, Germany, 2006.

Hofmann (2005): Hofmann, J.: Tragverhalten und Bemessung von Befestigungen am Bauteilrand

unter Querlasten mit beliebigem Winkel zur Bauteilkante (Load-bearing behaviour and design of

fasteners close to an edge under shear loading under an arbitrary angle to the edge). PhD thesis,

University of Stuttgart, Stuttgart, Germany, 2005 (in German).

Hofmann, Eligehausen (2009): Hofmann, J., Eligehausen, R.: Tragfähigkeit von randnahen

Kopfbolzen bei der Versagensart seitlicher Betonausbruch (Load bearing capacity of headed studs in

case of blow out failure mode. Beton- und Stahlbetonbau 104 (2009), Heft 7, pp. 386-393 (in

German).

ICC-ES (2009): AC308: Acceptance criteria for post-installed adhesive anchors in concrete elements.

International Code Council-Evaluation Service (ICC-ES), Whittier, California, USA, 2009.



ICC-ES (2010-1): AC193: Acceptance criteria for mechanical anchors in concrete elements.


ICC-ES (2010-2): AC232: Acceptance criteria for anchor channels in concrete elements.


ISO (1992): ISO 898-2:1992: Mechanical properties of fasteners made of carbon steel and alloy steel.

Part 2: Nuts with specified proof load values, coarse thread. International Organization for

Standardization (ISO), Geneva, Switzerland, 1992.

ISO (1999): ISO 834-1:1999 “Fire resistance test-elements of building constructions. Part 1: General

requirements”. International Organization for Standardization (ISO), Geneva, Switzerland, 1999.

ISO (2009-1): ISO 898-1:2009: Mechanical properties of fasteners made of carbon steel and alloy

steel. Part 1: Bolts, screws and studs with specified property classes – coarse thread and fine pitch

thread. International Organization for Standardization (ISO), Geneva, Switzerland, 2009.

ISO (2009-2): ISO 3506-1:2009: Mechanical properties of corrosion-resistant stainless steel-

fasteners. Part 1: Bolts, screws and studs”. International Organization for Standardization (ISO),

Geneva, Switzerland, 2009.

ISO (2009-3): ISO 3506-2:2009: Mechanical properties of corrosion-resistant stainless steel

fasteners. Part 2: Nuts. International Organization for Standardization (ISO), Geneva, Switzerland,

2009.

Klingner, Mendonca (1982): Klingner, R. E.; Mendonca, J. A.: Shear Capacity of Short Anchor Bolts

and Welded Studs: A Literature Review. ACI-Journal, September / October 1982, pp. 339-349.

Kraus (2003): Kraus, J.: Tragverhalten und Bemessung von Ankerschienen unter zentrischer

Zugbelastung (Load-bearing behaviour and design of anchor channels under axial tension). PhD

thesis, University of Stuttgart, Stuttgart, Germany, 2003 (in German).

Lee et al. (2007): Lee, N.H.; Kang, S.K.; Chang, J.B.; Park, K.R.: Tensile-headed anchors with large

diameter and deep embedment in concrete. ACI Structural Journal, V. 104, No. 4, 2007, pp. 479-486.

Lee et al. (2010): Lee, N.H.; Park, K.R.; Suh, Y.P.: Shear behavior of headed anchors with large

diameters and deep embedments. ACI Structural Journal, V. 107, No. 2, 2010, pp. 146-156.

Lieberum et al. (1987): Lieberum, K. W.; Reinhardt, H.-W.; Walraven, J. C.: Fastenings of anchors

in the shear zone of concrete slabs. Beton + Fertigteil-Technik 1987, No. 10, pp. 708-715.

Lotze (1993): Lotze, D.: Tragverhalten und Anwendung von Dübeln unter oftmals wiederholter

Belastung (Load-bearing behaviour and application of anchors under frequently repeated loading).

PhD thesis, University of Stuttgart, Stuttgart, Germany, 1993 (in German).

Mallée (2001): Mallée, R.: “Behaviour and design of anchors close to an edge under torsion”. In:

Eligehausen, R. (Editor): “Connections between Steel and Concrete”. RILEM Publications, Cachan,

France, 2001, pp. 178-187.

Mallée (2002): Mallée, R.: Dübelgruppen am Bauteilrand unter Torsionsbeanspruchung (Anchor

groups close to an edge under torsion). Beton- und Stahlbetonbau, V. 97, No. 2, 2002, pp. 69-77 (in

German).

Mallée, Pusill-Wachtsmuth (2007): Mallée, R.; Pusill-Wachtsmuth, P.: Design of anchors close to an

edge under shear loading – Engineering approach for consideration of load direction. Beton- und

Stahlbetonban V. 102, 2007, Special Edition, pp 7-15.


262 References

Nilsson, Elfgren (2009): Nilsson M.; Elfgren, L.: Fastenings (Anchor Bolts) in Concrete Structures –

Effect of Surface Reinforcement. Proceedings of Nordic Symposium on Nuclear Technology, Inspecta,

Stockholm 25-26 Nov 2009, Paper B2-4.

Naithani et al. (1988): Naithani, K. C.; Gupta, V. K.; Gudh, A. D.: Behavior of shear connection

under dynamic loads. Materials and Structures V. 21, No. 5, 1988, pp. 359-363.

Newmark, Hall (1982): Newmark, N. M.; Hall, W. J.: Earthquake spectra and design. Engineering

monographs on earthquake criteria, structural design, and strong motion records, No. 3, Earthquake

Engineering Research Institute (EERI), Oakland, California, USA, 1982.

Ožbolt, Eligehausen (1990): Ožbolt, J.; Eligehausen, R.: Numerical analysis of headed studs

embedded in large plain concrete blocks. In: Bicanic, N., Mang, H. (Editors): Computer Aided

Analysis and Design of Concrete Structures. Pineridge Press, London, 1990.

Periškić (2006): Periškić, G.: Einzel- und Zweifachbefestigungen mit Verbunddübel senkrecht zum

Rand unter Querlast zum Rand im ungerissenen Beton (Single anchors and Groups with two anchors

loaded in shear towards the edge in uncracked concrete). Report No. E06/01-E01301/1, University of

Stuttgart, Stuttgart, 2006 (in German).

Periškić (2010): Periškić, G.: Entwicklung eines 3D thermo-hygro-mechanischen Modells für Beton

unter Brandbeanspruchung und Anwendung auf Befestigungen unter Zuglasten (Development of a

thermo-hydro-mechanical Model for concrete under fire and application to fastenings loaded in

tension). PhD thesis, University of Stuttgart, Stuttgart, 2010 (in German).

Potthoff (2008): Potthoff, M.: Tragverhalten und Bemessung von Ankerschienen unter Querbelastung

(Load bearing behavior and design of channel bars under shear load). PhD thesis, University of

Stuttgart, Stuttgart, Germany, 2008 (in German).

Ramm, Greiner (1991): Ramm, W.; Greiner, U.: Verankerungen mit Kopfbolzen – Randnahe

Verankerungen unter Querzugbeanspruchung und randferne Verankerungen unter zentrischer

Zugbeanspruchung – Untersuchung des Einflusses von speziellen Rückhängebewehrungen

(Anchorages with headed anchors – anchors close to an edge under shear loading and anchors

remote from an edge under axial tension loading – Investigation of the influence of special

supplementary reinforcement). Research Report, Universität Kaiserslautern, Kaiserslautern, Germany,

1991 (in German).

Reick (2001): Reick, M.: Brandverhalten von Befestigungen mit großem Randabstand in Beton bei

zentrischer Zugbeanspruchung (Behavior of fastenings remote from an edge in concrete under axial

tension). PhD thesis, University of Stuttgart, Stuttgart, Germany, 2001 (in German).

Reuter, Eligehausen (1992): Reuter, M.; Eligehausen, R.: Einfluß der Lasteinleitung durch

Befestigungen auf die Tragfähigkeit von Stahlbetonbauteilen (Influence of load transmission by

fastenings on the load-bearing capacity of reinforced concrete elements). Bauingenieur V. 67, No. 10,

1992, pp. 461-474 (in German).

Rieder, Bergmeister (2010): Rieder, A.; Bergmeister, K.: Simulated and tested seismic response of

post-installed metal anchors in concrete. Proceedings of 3rd

fib International Congress, 2010,

Washington, DC, USA.

Roik (1982): Roik, K.: Verbundkonstruktion (Composite construction). Stahlbau-Handbuch, Vol. 1,

Stahlbau-Verlags-GmbH, Köln, Germany, pp. 627-672 (in German).

Roik (2009): Roik, M.: Tastversuche zum Tragverhalten von senkrecht zum Rand eingebauten

Ankerschienen, belastet durch Querzug parallel zum Rand (Preliminary tests to anchor channels

arranged perpendicular to the edge and loaded by a shear load parallel to the edge). Halfen GmbH,

Langenfeld, Germany, 2009 (in German).



Scheer et al. (1987): Scheer, J.; Peil, U; Nölle, P.: Schrauben mit planmäßiger Biegebeanspruchung

(Screws under bending). Report No. 6079, TU Braunschweig, Braunschweig, Germany, 1987 (in

German).

Schmid (2010): Schmid, K.: Der Einfluss einer Rückhängebewehrung auf das Tragverhalten von

Befestigungsmitteln unter Querlasten senkrecht zum Rand (Influence of anchor reinforcement on the

behaviour of anchors loaded by shear towards the edge). PhD thesis, University of Stuttgart, Stuttgart,


Silva (2002): Silva, J. F.: Design Considerations for Earthquake Resistant Anchorages. In: Fuchs, W.;

Reinhardt, H.-W. (Editors): “Befestigungstechnik, Bewehrungstechnik und… . Festschrift zu Ehren

von Prof. Dr. –Ing. Rolf Eligehausen anlässlich seines 60. Geburtstages – aktuelle Beiträge aus

Forschung und Praxis”. Ibidem Verlag, Stuttgart, Germany, 2002, pp. 511-521.

Spieth (2002): Spieth, H. A.: Tragverhalten und Bemessung von eingemörtelten Bewehrungsstäben

(Behavior and design of post-installed reinforcing bars). PhD thesis, University of Stuttgart, Stuttgart,


Usami et al. (1988): Usami, S.; Abe, Y.; Nagano, T.; Kowada, A.; Kobayashi, J.; Kodama, J.; Koike,

K.: Studies on the fatigue strength of anchors for supporting equipment and piping. Tensile fatigue

strength against cone-shaped concrete failure. Proceedings of the Annual Meeting of Kanton Branch

of Architectural Institute of Japan, Tokyo, Japan, 1988.

Utescher (1978): Utescher, G.: Beurteilungsgrundlagen für Fassadenverankerungen (Assessment

principles for fastening of façades). Verlag Wilhelm Ernst & Sohn, Berlin, Germany, 1978 (in

German).

Zhao et al. (1989): Zhao, G.; Fuchs, W.; Eligehausen, R.: Einfluss der Bauteildicke auf das

Tragverhalten von Dübelbefestigungen im ungerissenen Beton unter Querzugbeanspruchung

(Influence of member thickness on the behaviour of anchors in non-cracked concrete under shear

loading). Report No. 10/12A-89/5, University of Stuttgart, Stuttgart, Germany, March 1989 (in

German).

Zhao (1993): Zhao, G.: Tragverhalten von randfernen Kopfbolzenverankerungen bei Betonbruch

(Behaviour of headed anchors remote to an edge at concrete failure). PhD thesis, University of

Stuttgart, Stuttgart, Germany, 1993 (in German).


264 References

Related documents

ACI 355.1 (1991): ACI 355.1R-91: State of the art report on anchorage to concrete. American

Concrete Institute (ACI), Detroit, Michigan, USA, 1991.

CEB (1978): International system of unified codes of practice for structures. Volume 1: Common

unified rules for different types of construction and material. Comité Euro-International du Béton

(CEB), Bulletin d'Information 125, Paris, France, 1978.

CEB (1988): General principles on reliability for structures - a commentary on ISO 2394. Comité

Euro-International du Béton (CEB): CEB, Bulletin d'Information 191, Lausanne, Switzerland, 1988.

CEN (2000-2): EN 12390-1:2000 Testing hardened concrete. Part 1: Shape, dimensions and other

requirements for specimens and moulds. Comité Européen de Normalisation (CEN), Brussels,

Belgium, 2000.

CEN (2000-3): EN 12390-2:2000 Testing hardened concrete. Part 2: Making and curing specimens

for strength tests. Comité Européen de Normalisation (CEN), Brussels, Belgium, 2000.

CEN (2000-4): EN 12390-5:2000 Testing hardened concrete. Part 5: Flexural strength of test

specimens. Comité Européen de Normalisation (CEN), Brussels, Belgium, 2000.

CEN (2000-5): European Committee for Standardization (CEN) (2000): EN 12390-6:2000 Testing of

hardened concrete. Part 6: Tensile splitting strength of test specimens. Comité Européen de


CEN (2000-6): EN 12390-7:2000: Testing hardened concrete. Part 7: Density of hardened concrete.

Comité Européen de Normalisation (CEN), Brussels, Belgium, 2000.

CEN (2000-7): EN 12504-1:2000: Testing concrete in structures. Part 1: Cored specimens - Taking,

examining and testing in compression. Comité Européen de Normalisation (CEN), Brussels, Belgium,

2000.

CEN (2001): EN 10002-1:2001: Metallic materials - Tensile testing of metallic materials. Part 1:

Method of test at ambient temperature. Comité Européen de Normalisation (CEN), Brussels, Belgium,

2001.

CEN (2004-2): EN 1994-1-1:2004: Eurocode 4: Design of composite steel and concrete structures.

Part 1-1: General rules and rules for buildings. Comité Européen de Normalisation (CEN), Brussels,

Belgium, 2004.

CEN (2004-3): EN 1998-1:2004: Eurocode 8: Design of structures for earthquake resistance. Part 1:

General rules, seismic actions and rules for buildings. Comité Européen de Normalisation (CEN),

Brussels, Belgium, 2004.

CEN (2005-1): EN 1993-1-1:2005: Eurocode 3: Design of steel structures. Part 1-1: General rules

and rules for buildings”. Comité Européen de Normalisation (CEN), Brussels, Belgium 2005.

CEN (2005-3): EN 1998-3:2005: Eurocode 8: Design of structures for earthquake resistance. Part 3:

Assessment and retrofitting of buildings. Comité Européen de Normalisation (CEN), Brussels,

Belgium 2005.

CEN (2005-4): EN 10080-1:2005: Steel for the reinforcement of concrete. Weldable reinforcing steel.

Part 1: General. Comité Européen de Normalisation (CEN), Brussels, Belgium 2005.

CEN (2005-5): EN 10088-2:2005: Stainless steels. Part 2: Technical delivery conditions for

sheet/plate and strip of corrosion resisting steels for general purposes. Comité Européen de

Normalisation (CEN), Brussels, Belgium 2005.



CEN (2005-6): EN 10088-3:2005: Stainless steels. Part 3: Technical delivery conditions for semi-

finished products, bars, rods, wire, sections and bright products of corrosion resisting steels for

general purposes. Comité Européen de Normalisation (CEN), Brussels, Belgium 2005.

CEN (2008): EN ISO 13918:2008: Welding - Studs and ceramic ferrules for arc stud welding. Comité

Européen de Normalisation (CEN), Brussels, Belgium, 2008.

Eligehausen (2001): Eligehausen, R. (Editor): Connections between Steel and Concrete. RILEM

Proceedings PRO 21, RILEM, Cachan, France, 2001.

Eligehausen et al. (2007): Eligehausen, R.; Fuchs, W.; Genesio, G.; Grosser, P. (Editors):

Connections between Steel and Concrete. Ibidem-Verlag, Stuttgart, Germany, 2007.

Fichtner (2011): Fichtner, S.: Untersuchungen zum Tragverhalten von Gruppenbefestigungen unter

Berücksichtigung der Ankerplattendicke und einer Ausgleichsschicht (Investigations on the behavior

of anchor groups taking into account baseplate thickness and thickness of mortar layer). PhD thesis,

University of Stuttgart, Stuttgart, Germany, 2011 (in German).

ISO (1979): ISO 273:1979 Fasteners clearance holes for bolts and screws. International Organization

for Standardization (ISO), Geneva, Switzerland, 1979.

ISO (1997-3): ISO 1803:1997 Building construction, tolerances, expression of dimensional accuracy,

principles and terminology. International Organization for Standardization (ISO), Geneva,

Switzerland, 1997.

ISO (2005): ISO 5922:2005 Malleable cast iron. International Organization for Standardization (ISO),

Geneva, Switzerland, 2005.


fib – fédération internationale du béton – the International Federation for Structural Concrete – is grateful for the invaluable support of the following National Member Groups and Sponsoring Members, which contributes to the publication of fib technical bulletins, the Structural Concrete Journal, and fib-news.

National Member Groups AAHES – Asociación Argentina del Hormigón Estructural, Argentina CIA – Concrete Institute of Australia ÖVBB – Österr. Vereinigung Für Beton und Bautechnik, Austria Belarussian Nat. Techn. University GBB – Groupement Belge du Béton, Belgium ABCIC – Associação Brasileira da Construção Industrializada de Concreto, Brazil ABECE – Associação Brasileira de Engenharia e Consultoria Estrutural, Brazil fib Group of Canada CCES – China Civil Engineering Society Hrvatska Ogranak fib-a (HOFIB) – Croatian Group of fib Cyprus University of Technology Ceska betonarska spolecnost, Czech Republic Dansk Betonforening DBF – Danish Concrete Society Suomen Betoniyhdistys r.y. – Concrete Association of Finland AFGC – Association Française de Génie Civil, France Deutscher Ausschuss für Stahlbeton, Germany Deutscher Beton- und Bautechnik-Verein e.V. – dbv, Germany FDB – Fachvereinigung Deutscher Betonfertigteilbau e.V., Germany Technical Chamber of Greece Hungarian Group of fib, Budapest University of Technology & Economics The Institution of Engineers (India) Technical Executive (Nezam Fanni) Bureau, Iran IACIE – Israeli Association of Construction and Infrastructure Engineers Consiglio Nazionale delle Ricerche, Italy JCI – Japan Concrete Institute PCEA – Prestressed Concrete Engineering Association, Japan Administration des Ponts et Chaussées, Luxembourg Betonvereniging – fib Netherlands New Zealand Concrete Society Norsk Betongforening – Norwegian Concrete Association Polish Academy of Sciences Committee of Civil Engineering, Silesian Technical University, Poland GPBE – Grupo Portugês de Betão Estrutural, Portugal Society For Concrete and Prefabricated Units of Romania Technical University of Civil Engineering, Romania Association for Structural Concrete (ASC), Russia


Association of Structural Engineers, Serbia Slovak Union of Civil Engineers Slovenian Society of Structural Engineers ACHE – Asociacion Cientifico-Técnica del Hormigon Estructural, Spain Svenska Betongföreningen, Sweden Délégation nationale suisse de la fib, EPFL, Switzerland ITU – Istanbul Technical University, Turkey Research Institute of Build. Constructions, Ukraine fib UK Group ASBI – American Segmental Bridge Institute, USA PCI – Precast/Prestressed Concrete Institute, USA PTI – Post Tensioning Institute, USA Sponsoring Members Preconco Limited, Barbados Liuzhou OVM Machinery Co., Ltd , China Consolis TECHNOLOGY Oy Ab, Finland FBF Betondienst GmbH, Germany FIREP Rebar Technology GmbH, Germany MKT Metall-Kunststoff-Technik GmbH, Germany Verein zur Förderung und Entwicklung der Befestigungs-, Bewehrungs- und

Fassadentechnik e. V. – VBBF, Germany Larsen & Toubro Ltd ECC Division, India Sireg S.P.A., Italy Fuji P. S. Corporation Ltd., Japan Obayashi Corporation, Japan Oriental Shiraishi Corporation, Japan P.S. Mitsubishi Construction Co., Ltd, Japan PC BRIDGE Company Ltd., Japan SE Corporation, Japan Sumitomo Mitsui Construct. Co.Ltd., Japan BBR VT International Ltd., Switzerland SIKA Services AG, Switzerland VSL International Ltd , Switzerland China Engineering Consultants, Inc, Taiwan (China) PBL Group Ltd, Thailand CCL Stressing Systems Ltd, United Kingdom Strongforce Engineering PLC, United Kingdom


fib Bulletins published since 1998

N° Title

1 Structural Concrete – Textbook on Behaviour, Design and Performance;

Vol. 1: Introduction - Design Process – Materials Manual - textbook (244 pages, ISBN 978-2-88394-041-3, July 1999)

2 Structural Concrete – Textbook on Behaviour, Design and Performance

Vol. 2: Basis of Design Manual - textbook (324 pages, ISBN 978-2-88394-042-0, July 1999)

3 Structural Concrete – Textbook on Behaviour, Design and Performance

Vol. 3: Durability - Design for Fire Resistance - Member Design - Maintenance,

Assessment and Repair - Practical aspects Manual - textbook (292 pages, ISBN 978-2-88394-043-7, December 1999)

4 Lightweight aggregate concrete: Extracts from codes and standards State-of-the-art report (46 pages, ISBN 978-2-88394-044-4, August 1999)

5 Protective systems against hazards: Nature and extent of the problem Technical report (64 pages, ISBN 978-2-88394-045-1, October 1999)

6 Special design considerations for precast prestressed hollow core floors Guide to good practice (180 pages, ISBN 978-2-88394-046-8, January 2000)

7 Corrugated plastic ducts for internal bonded post-tensioning Technical report (50 pages, ISBN 978-2-88394-047-5, January 2000)

8 Lightweight aggregate concrete:

Part 1 (guide) – Recommended extensions to Model Code 90; Part 2 (technical report) –

Identification of research needs; Part 3 (state-of-art report) – Application of lightweight

aggregate concrete (118 pages, ISBN 978-2-88394-048-2, May 2000)

9 Guidance for good bridge design: Part 1 – Introduction, Part 2 – Design and

construction aspects. Guide to good practice (190 pages, ISBN 978-2-88394-049-9, July 2000)

10 Bond of reinforcement in concrete State-of-art report (434 pages, ISBN 978-2-88394-050-5, August 2000)

11 Factory applied corrosion protection of prestressing steel State-of-art report (20 pages, ISBN 978-2-88394-051-2, January 2001)

12 Punching of structural concrete slabs Technical report (314 pages, ISBN 978-2-88394-052-9, August 2001)

13 Nuclear containments State-of-art report (130 pages, 1 CD, ISBN 978-2-88394-053-6, September 2001)

14 Externally bonded FRP reinforcement for RC structures Technical report (138 pages, ISBN 978-2-88394-054-3, October 2001)

15 Durability of post-tensioning tendons Technical report (284 pages, ISBN 978-2-88394-055-0, November 2001)

16 Design Examples for the 1996 FIP recommendations Practical design of structural concrete

Technical report (198 pages, ISBN 978-2-88394-056-7, January 2002)

17 Management, maintenance and strengthening of concrete structures Technical report (180 pages, ISBN 978-2-88394-057-4, April 2002)


N° Title

18 Recycling of offshore concrete structures State-of-art report (33 pages, ISBN 978-2-88394-058-1, April 2002)

19 Precast concrete in mixed construction State-of-art report (68 pages, ISBN 978-2-88394-059-8, April 2002)

20 Grouting of tendons in prestressed concrete Guide to good practice (52 pages, ISBN 978-2-88394-060-4, July 2002)

21 Environmental issues in prefabrication State-of-art report (56 pages, ISBN 978-2-88394-061-1, March 2003)

22 Monitoring and safety evaluation of existing concrete structures State-of-art report (304 pages, ISBN 978-2-88394-062-8, May 2003)

23 Environmental effects of concrete

State-of-art report (68 pages, ISBN 978-2-88394-063-5, June 2003)

24 Seismic assessment and retrofit of reinforced concrete buildings State-of-art report (312 pages, ISBN 978-2-88394-064-2, August 2003)

25 Displacement-based seismic design of reinforced concrete buildings State-of-art report (196 pages, ISBN 978-2-88394-065-9, August 2003)

26 Influence of material and processing on stress corrosion cracking of prestressing steel

– case studies. Technical report (44 pages, ISBN 978-2-88394-066-6, October 2003)

27 Seismic design of precast concrete building structures State-of-art report (262 pages, ISBN 978-2-88394-067-3, January 2004)

28 Environmental design State-of-art report (86 pages, ISBN 978-2-88394-068-0, February 2004)

29 Precast concrete bridges

State-of-art report (83 pages, ISBN 978-2-88394-069-7, November 2004)

30 Acceptance of stay cable systems using prestressing steels Recommendation (80 pages, ISBN 978-2-88394-070-3, January 2005)

31 Post-tensioning in buildings

Technical report (116 pages, ISBN 978-2-88394-071-0, February 2005)

32 Guidelines for the design of footbridges Guide to good practice (160 pages, ISBN 978-2-88394-072-7, November 2005)

33 Durability of post-tensioning tendons Recommendation (74 pages, ISBN 978-2-88394-073-4, December 2005)

34 Model Code for Service Life Design Model Code (116 pages, ISBN 978-2-88394-074-1, February 2006)

35 Retrofitting of concrete structures by externally bonded FRPs. Technical Report (224 pages, ISBN 978-2-88394-075-8, April 2006)

36 2006 fib Awards for Outstanding Concrete Structures Bulletin (40 pages, ISBN 978-2-88394-076-5, May 2006)

37 Precast concrete railway track systems State-of-art report (38 pages, ISBN 978-2-88394-077-2, September 2006)

38 Fire design of concrete structures – materials, structures and modelling State-of-art report (106 pages, ISBN 978-2-88394-078-9, April 2007)


N° Title

39 Seismic bridge design and retrofit – structural solutions State-of-art report (300 pages, ISBN 978-2-88394-079-6, May 2007)

40 FRP reinforcement in RC structures Technical report (160 pages, ISBN 978-2-88394-080-2, September 2007)

41 Treatment of imperfections in precast structural elements State-of-art report (74 pages, ISBN 978-2-88394-081-9, November 2007)

42 Constitutive modelling of high strength / high performance concrete State-of-art report (130 pages, ISBN 978-2-88394-082-6, January 2008)

43 Structural connections for precast concrete buildings Guide to good practice (370 pages, ISBN 978-2-88394-083-3, February 2008)

44 Concrete structure management: Guide to ownership and good practice Guide to good practice (208 pages, ISBN 978-2-88394-084-0, February 2008)

45 Practitioners’ guide to finite element modelling of reinforced concrete structures State-of-art report (344 pages, ISBN 978-2-88394-085-7, June 2008)

46 Fire design of concrete structures —structural behaviour and assessment State-of-art report (214 pages, ISBN 978-2-88394-086-4, July 2008)

47 Environmental design of concrete structures – general principles Technical report (48 pages, ISBN 978-2-88394-087-1, August 2008)

48 Formwork and falsework for heavy construction Guide to good practice (96 pages, ISBN 978-2-88394-088-8, January 2009)

49 Corrosion protection for reinforcing steels Technical report (122 pages, ISBN 978-2-88394-089-5, February 2009)

50 Concrete structures for oil and gas fields in hostile marine environments State-of-art report (36 pages, IBSN 978-2-88394-090-1, October 2009)

51 Structural Concrete – Textbook on behaviour, design and performance, vol. 1 Manual – textbook (304 pages, ISBN 978-2-88394-091-8, November 2009)

52 Structural Concrete – Textbook on behaviour, design and performance, vol. 2 Manual – textbook (350 pages, ISBN 978-2-88394-092-5, January 2010)

53 Structural Concrete – Textbook on behaviour, design and performance, vol. 3 Manual – textbook (390 pages, ISBN 978-2-88394-093-2, December 2009)

54 Structural Concrete – Textbook on behaviour, design and performance, vol. 4 Manual – textbook (196 pages, , ISBN 978-2-88394-094-9,October 2010)

55 fib Model Code 2010, First complete draft – Volume 1 Draft Model Code (318 pages, ISBN 978-2-88394-095-6, March 2010)

56 fib Model Code 2010, First complete draft – Volume 2 Draft Model Code (312 pages, ISBN 978-2-88394-096-3, April 2010)

57 Shear and punching shear in RC and FRC elements. Workshop proceedings.

Technical report (268 pages, ISBN 978-2-88394-097-0, October 2010)

58 Design of anchorages in concrete

Guide to good practice (282 pages, ISBN 978-2-88394-098-7, July 2011)

Abstracts for fib Bulletins, lists of available CEB Bulletins and FIP Reports, and

an order form are available on the fib website at www.fib-international.org/publications.


resources/fib... · subject to priorities defined by the technical council and the presidium, the...

Documents