lecture 1 basics - oct 12 - end

Practical Design to Eurocode 2

Paul Gregory

Regional Engineer

Course Outline

Foundations

Pads, Retaining Walls, Strut & tie, Piles11th October 2012

Slabs

Serviceability, Punching Shear, Tying systems4th October 2012

Columns

Axial load, Column Moments, Buckling, Fire27th September 2012

Beams

Bending, Shear, Detailing20th September 2012

Basics

EC0, Load cases, EC1, Materials, Cover13th September 2012

Basics

Lecture 1

13th September 2012

BS EN 1990 (EC0) : Basis of structural design

BS EN 1991 (EC1) : Actions on Structures

BS EN 1992 (EC2) : Design of concrete structures

BS EN 1993 (EC3) : Design of steel structures

BS EN 1994 (EC4) : Design of composite steel and concrete structures

BS EN 1995 (EC5) : Design of timber structures

BS EN 1996 (EC6) : Design of masonry structures

BS EN 1997 (EC7) : Geotechnical design

BS EN 1998 (EC8) : Design of structures for earthquake resistance

BS EN 1999 (EC9) : Design of aluminium structures

The Eurocodes

Each Eurocode Contains:

National front cover

Format of the Eurocodes



National foreword




National foreword

CEN front cover




National foreword

CEN front cover

Main text and annexes (which must be as produced by CEN)




National foreword

CEN front cover

Main text and annexes (which must be as produced by CEN)

Annexes - can by normative and/or informative


National Annex (NA)


The National Annex provides:

Values of Nationally Determined Parameters (NDPs)(NDPs have been allowed for reasons of safety, economy and durability)

Example: Min diameter for longitudinal steel in columnsmin = 8 mm in text min = 12 mm in N.A.

The decision where main text allows alternatives

Example: Load arrangements in Cl. 5.1.3 (1) P

The choice to adopt informative annexes

Example: Annexes E and J are not used in the UK

Non-contradictory complementary information (NCCI)

Example: PD 6687 Background paper to UK National Annexes

National Annex

The Eurocodes contain Principles (P) which comprise:

General statements and definitions for which there is no alternative, as well as:

Requirements and analytical models for which no alternative is permitted

They also contain Application Rules, which are generally rules which comply with the Principles

The Eurocodes also use a comma (,) as the decimal marker

Features of the Eurocodes

Eurocode 0

BS EN 1990:2002

EurocodeBasis of structural design

EN 1990 provides comprehensive information and guidance for all the Eurocodes, on the principles and requirements for safety and serviceability.

It gives the safety factors for actions and combinations of actions for the verification of both ultimate andserviceability limit states.

eg EC0 - Ultimate load can be 1.25 Gk + 1.5 Qk

Limit states are conditions beyond which some design criterion is violated.

Ultimate Limit State: Any condition that concerns the safety of people or structure

Generally the structure shall be verified at:

Serviceability Limit State:Corresponds to conditions in use of the structure. The limit state could be related to cracking, deformation or vibration.

Limit State Design

Ultimate Limit State:

Loss of equilibrium (EQU)

Ed,dst Ed,stbInternal failure or excessive structural deformation (STR)

Ed RdFailure or excessive deformation of ground (GEO)

Failure caused by time dependent effects such as fatigue (FAT)

Limit State Design

Principle: When using the partial factor method, it shall be verified that, in all relevant design situations, no relevant limit state is exceeded when design values for actions or effects of actions and resistances are used in the design models.

e.g. Ed RdEd is the design value of the effect of actions.

Rd is the design value of the corresponding resistance.

Verification by Partial Safety Factor Method

Fd = f FrepWhere: Frep = representative value of action

= FkAnd: f = partial factor for actions

See NA to BS EN 1990: Table NA.A1.2

converts the characteristic value of action to the representative value.

Compare to

Fd = f Fk BS8110

Design Value of Action

Each variable action may take one of four representative values,the main one being the characteristic value. Other representative values are obtained by the application of factors

can take one of four values, namely, 1.00 or 0 or 1 or 2. = 1.00 when only one variable action is present in a combination. 0Qk is the combination value of a variable action.1Qk is the frequent value.2Qk is the quasi-permanent value.

Representative Values

Representative Values

Ref: Gulvanessian, H ICE Proceedings, Civil Engineering 144 November 2001 pp.8-13

For each critical load case design values of the effects of actions are determined by combining the effects of actions that are considered to act simultaneously

G, jGk,j + Q,1 Qk,1 + Q,i0,iQk,i Exp. (6.10)

Either

G, jGk,j + Q,1 0,1Qk,1 + Q,i0,iQk,i Exp. (6.10 a) or

G, jGk,j + Q,1Qk,1 + Q,i0,iQk,i Exp. (6.10 b)

Or (for STR and GEO) the more adverse of

The value for for the UK is 0.925

Combination of Actions

Perm. action + leading variable action + accompanying action

Dead + live (Office) + wind

G, jGk,j + Q,1 Qk,1 + Q,I0,IQk,I Exp. (6.10)or the more adverse of

G, jGk,j + Q,1 0,1Qk,1 + Q,I0,IQk,I Exp. (6.10 a) or

G, jGk,j + Q,1Qk,1 + Q,I0,IQk,I Exp. (6.10 b)

Example: ULS Combination of Actions for the STR Limit State

Table NA.A1.1 UK National Annex of BS EN 1990

Action 0 1 2Imposed loads in buildings, Category A : domestic, residential Category B : office areasCategory C : congregation areasCategory D : shopping areasCategory E : storage areas

0.70.70.70.71.0

0.50.50.70.70.9

0.30.30.60.60.8

Category F : traffic area, < 30kNCategory G : traffic area, 30 160 kNCategory H : roofs

0.70.70.7

0.70.50

0.60.30

Snow load: H 1000 m a.s.l. 0.5 0.2 0Wind loads on buildings 0.5 0.2 0

UK Values of Factor

Partial Factors for Actions (ULS)

G = 1.35 (NA 2.2.3.2 and Table NA.A1.2)Q = 1.5 (NA 2.2.3.2 and Table NA.A1.2)Relevant factors0 office areas = 0.7 (Table NA.A1.1)0 wind = 0.5 (Table NA.A1.1)


1.35 Gk + 1.5 Qk,1 + 0.75Qk,w Exp. (6.10)

1.35Gk + 1.05 Qk,1 + 0.75Qk,w Exp. (6.10 a)

or

1.25Gk + 1.5 Qk,1 + 0.75Qk,w Exp. (6.10 b)

Or the more adverse of


Design values of actions, ultimate limit state persistent and transient design situations (Table A1.2(B) Eurocode)

Combtionexpression reference

Permanent actions Leading variable action

Accompanying variable actions

Unfavourable Favourable Main(if any) Others

Eqn (6.10) G,j,sup Gk,j,sup G,j,inf Gk,j,inf Q,1 Qk,1 Q,i 0,i Qk,i

Eqn (6.10a) G,j,sup Gk,j,sup G,j,inf Gk,j,inf Q,10,1Qk,1 Q,i 0,i Qk,i

Eqn (6.10b) G,j,supGk,j,sup G,j,inf Gk,j,inf Q,1 Qk,1 Q,i 0,i Qk,i

Eqn (6.10) 1.35 Gk 1.0 Gk 1.5 Qk,1 1.5 0,i Qk,i

Eqn (6.10a) 1.35 Gk 1.0 Gk 1.5 0,1 Qk 1.5 0,i Qk,i

Eqn (6.10b) 0.925x1.35Gk 1.0 Gk 1.5 Qk,1 1.5 0,i Qk,i

Eurocode ULS (GEO/STR)

1.0

1.5

2.0

2.5

3.0

1 2 3 4 5 6

Eqn (6.10)Eqn (6.10a)Eqn (6.10b)

Ratio Gk/Qk

F

a

c

t

o

r

,

F

(

U

l

t

i

m

a

t

e

l

o

a

d

=

F

x

G

k

)

4.5

Eqn (6.10), (6.10a) or (6.10b)?

Design values of actions, ultimate limit state persistent and transient design situations (Table A1.2(A) Eurocode)

Combtionexpression reference

Permanent actions Leading variable action

Accompanying variable actions

Unfavourable Favourable Main(if any) Others

Eqn (6.10) G,j,sup Gk,j,sup G,j,inf Gk,j,inf Q,1 Qk,1 Q,i 0,i Qk,i

Eqn (6.10) 1.10 Gk 0.9 Gk 1.5 Qk,1 1.5 0,i Qk,i

Eurocode ULS (EQU)

Note - alternative method may be used when both EQU and STR should both be checked. See note below this table A1.2(A)

Combinations of Actions (SLS)

Characteristic combination Gk,j + Qk,1 + 0,IQk,I(typically irreversible limit states)

Frequent combination Gk,j + 1,1Qk,1 + 2,IQk,I(typically reversible limit states)

Quasi permanent combination Gk,j + 2,IQk,I(typically long term effects and appearance of the structure)

Partial Factors for Actions (SLS)

G = 1.00Q = 1.00

0 - combination value1- frequent value.2- quasi-permanent value.

Serviceability Limit State BS EN 1990 (6.5.3)

The UK National Annex refers only to Design Approach 1. Two combinations of partial load and partial soil factors need consideration.

Partial load factor Partial material factor, mGk Qk tan c cu

Combination 1 1.35 1.5 1.0 1.0 1.0

Combination 2 1.0 1.3 1.25 1.25 1.4

Note: where variable action is favourable Q = 0 angle of shearing resistance (in terms of effective stress)c cohesion intercept (in terms of effective stress)cu undrained shear strength

Normally Combination 2 will be critical for sizing the foundation The loads from Combination 1 should be used to design the concrete section

Geotechnical design EC7

Load Arrangements(BS EN 1992, Cl 5.1.3) Concise: 5.4.2

EC2

Load CasesEC2 clause 2.4.3 Combinations of actions:

Additional information is in PD 6687-1:2010

See clause 2.9 Simplified load combinations[BS EN 1992-1-1:2004, 5.1.3 (1)P]

EC2: Load cases & combinationsEC2: Cl 5.1.3 gives one option: Concise: 5.4.2

UK NA: Arrangement of Actions

All spans loaded

Alternate spans loaded

1.35 Gk or 1.25 Gk

1.5 Qk

1.35 Gk or 1.25 Gk

1.5 Qk

1.35 Gk or 1.25 Gk

1.5 Qk

NA gives additional options: Concise: 5.4.2

2. Continuous single-way slab. Using the Single load combination for a three span slab in an office building calculate the value of ULS total loading (kN/m2) using Exps (6.10), (6.10a) and (6.10b) (see BS EN 1990 Table A1.2(B) & UK NA).

Which of these expressions will lead to the most economic design?

1. Overhanging cantilever beam. Illustrate the load combinations that should be considered in the design :a) for equilibrium (EQU) (BS EN 1990, Table A1.2(A) & UK NA)b) for structural strength (STR) (BS EN 1990, Exp (6.10) & UK NA)

l a

5m 5m 5m

Gk = 6 kN/m2, Qk = 4kN/m2

Load Arrangement Exercise

l a

5m 5m 5m

6.10

6.10a

6.10b

EQU

STR

STR

Load Arrangement Exercise

a) Combination for equilibrium (EQU)BS EN 1990 Table A.1.2 (A) & UK NA

0.9Gk1.1Gk

1.5Qk

b) Combination for structural strength (STR) BS EN 1990 Table A.1.2 (B) & UK NA and BS EN 1992-1-1, Cl 5.1.3 & UK NA

1. Overhanging cantilever beam

1.35Gk1.35Gk

1.5Qk

1.35Gk 1.35Gk

1.5Qk

Load Arrangement Exercise Solution (1)

a) Value using Combination from BS EN 1990 Expression (6.10)G Gk + Q Qk 1.35 x 6 + 1.5 x 4 = 14.1 kN/m2

2. Continuous single-way slab (using BS EN 1990 and UK NA and BS 1992-1-2 Cl 5.1.3 & UK NA)

5m 5m 5m

b1) Value using Combination from BS EN 1990 Expression (6.10a)and UK National Annex

G Gk + Q 0Qk 1.35 x 6 + 1.5 x 0.7 x 4 = 12.3 kN/m2

b2) Value using Combination from BS EN 1990 Expression (6.10b)and UK National Annex

G Gk + Q Qk 1.35 x 0.925 x 6 + 1.5 x 4 = 13.5 kN/m2Expression (6.10b) gives the most economic design

Load Arrangement Exercise Solution (2)

Cantilever

EQU 1.1 Gk

1.5 Qk0.9 Gk

STR/GEO - 1 1.35 Gk or1.25 Gk

1.5 Qk

STR/GEO - 31.35 Gk or1.25 Gk

1.5 Qk

1.0 Gk

1.5 Qk

STR/GEO - 2

STR/GEO - 31.0 Gk

1.5 Qk

Frame see note in BS EN 1990 Table A.1.2 (A) & UK NA

Check EQU for uplift at A 1.35 Gk,N + 1.5 Qk,W + 1.5 x 0.7 Qk,N + 1.5 x 0.7 Qk,SN - 1.15 Gk,1 - 1.15 Gk,2 1.35 Gk,N + 1.5 Qk,N + 1.5 x 0.5 Qk,W + 1.5 x 0.7 Qk,SN - 1.15 Gk,1 - 1.15 Gk,2

Qk,W Gk,N Qk, N

Qk,S

Qk,1Gk,1Qk,SN

Qk,2Gk,2

Qk,2Gk,2

Qk,2Gk,2

A B

0 = 0.7 for Qk,20 = 0.7 for Qk,10 = 0.5 for Qk,W0 = 0.7 for Qk,S

Wind as leading variable action

Wind as accompanying variable action

EC1 Loads/Actions

BS EN 1991

Eurocode 1 has ten parts:

1991-1-1 Densities, self-weight and imposed loads 1991-1-2 Actions on structures exposed to fire 1991-1-3 Snow loads 1991-1-4 Wind actions 1991-1-5 Thermal actions 1991-1-6 Actions during execution 1991-1-7 Accidental actions due to impact and explosions 1991-2 Traffic loads on bridges 1991-3 Actions induced by cranes and machinery 1991-4 Actions in silos and tanks

Eurocode 1

Eurocode 1 Part 1-1: Densities, self-weight and imposed loads

Bulk density of mass concrete is 24 kN/m3

Bulk density of reinforced concrete is 25 kN/m3

This represents 1.84% reinforcement

Add 1 kN/m3 for wet concrete

The UK NA uses the same loads as BS 6399

Plant loading not given

Eurocode 1

Category Example Use qk (kN/m2)

Char. value of udl

Qk (kN)

Char. value of pt load

A1 All uses within self-contained dwelling units 1.5 2.0

A2 Bedrooms and dormitories 1.5 2.0

A3 Bedrooms in hotels and motels, hospital wards and toilets 2.0 2.0

A5 Balconies in single family dwelling units 2.5 2.0

A7 Balconies in hotels and motels 4.0 min 2.0

B1 Offices for general use 2.5 2.7

C5 Assembly area without fixed seating, concert halls, bars, places of worship

5.0 3.6

D1/2 Shopping areas 4.0 3.6

E12 General storage 2.4 per m ht 7.0

E17 Dense mobile stacking in warehouses 4.8 per m ht (min 15.0)

7.0

F Gross vehicle weight 30 kN 2.5 10.0

Eurocode 1 UK NA - Extracts

BS EN 1991 1-3 (NA)

Snow loads

BS EN 1991 1-4 (NA)

Wind speeds

vb,map

Eurocode 2

BS EN 1992

Design of concrete structures

BS EN 1992-1-1: General Rules and Rules For Buildings

BS EN 1992-1-2: Fire Resistance of Concrete Structures

BS EN 1992-2: Reinforced and Prestressed ConcreteBridges

BS EN 1992-3: Liquid Retaining Structures

Eurocode 2: Concrete StructuresBS EN 1992

1. General2. Basis of design3. Materials4. Durability and cover to reinforcement5. Structural analysis6. Ultimate limit state7. Serviceability limit state8. Detailing of reinforcement and pre-stressing tendons General9. Detailing of member and particular rules10. Additional rules for precast concrete elements and structures11. Lightweight aggregated concrete structures12. Plain and lightly reinforced concrete structures

Eurocode 2 Contents

BS EN 1992-1-1: General Rules and Rules For Buildings

A. (Informative) Modification of partial factors for materialsB. (Informative) Creep and shrinkage strainC. (Normative) Reinforcement propertiesD. (Informative) Detailed calculation method for pre-stressing steel

relaxation lossesE. (Informative) Indicative Strength Classes for durability Use BS8500F. (Informative) Reinforcement expressions for in-plane stress

conditionsG. (Informative) Soil structure interactionH. (Informative) Global second order effects in structuresI. (Informative) Analysis of flat slabs and shear wallsJ. (Informative) Examples of regions with discontinuity in geometry

or action (Detailing rules for particular situations) Alternative J in PD 6687

Eurocode 2 - AnnexesBS EN 1992-1-1: General Rules and Rules For Buildings

BS8110 vs EC2

Differences 1EC2:

1. Laid out to give advice on phenomena rather than by member type as in BS8110

2. Derived design formulae not included in code (contained in Non-contradictory complimentary information NCCI)

3. Design based on cylinder strength rather than cube strength

4. Higher strength concrete up to C90/105,

5. Applicable for ribbed reinforcement fy 400MPa 600MPa (Info on plain and mild steel given in PD 6687)

6. Reinforcement partial factor for material m = 1.15 but fy to BS4449 500MPa effect negligible

7. Effects of geometric imperfections (notional horizontal loads) considered in addition to lateral loads

BS8110 vs EC2

Differences -2

EC2:

8. Cover related to requirements for durability, fire and bond also subject to allowance for deviations due to variations in execution

9. Variable strut inclination method for shear

10. Punching shear checks at 2d from support

11. Rules for determining anchorage and lap lengths.

12. Serviceability checks

13. Decimal point replaced by comma

14. Units of stress MPa

15. 1/1000 expressed as

16. Axes changed from x, y to y, z

Eurocode 2

Materials

fcm = fck+ 8(MPa)

fctm = 0.30 fck(2/3) C50/60= 2.12 In(1+(fcm/10)) > C50/60

fctk;0,05 = 0,7fctm5% fractile

fctk;0,95 = 1,3fctm95% fractile

Ecm = 22[(fcm)/10]0,3(fcm in MPa)

Strength classes for concretefck (MPa) 12 16 20 25 30 35 40 45 50 55 60 70 80 90

fck,cube(MPa)

15 20 25 30 37 45 50 55 60 67 75 85 95 105

fcm(MPa)

20 24 28 33 38 43 48 53 58 63 68 78 88 98

fctm(MPa)

1,6 1,9 2,2 2,6 2,9 3,2 3,5 3,8 4,1 4,2 4,4 4,6 4,8 5,0

fctk,0,05(MPa)

1 1 1,3 1,5 1,8 2,0 2,2 2,5 2,7 2,9 3,0 3,1 3,2 3,4 3,5

fctk,0,95(MPa)

2,0 2,5 2,9 3,3 3,8 4,2 4,6 4,9 5,3 5,5 5,7 6,0 6,3 6,6

Ecm(Gpa)

27 29 30 31 32 34 35 36 37 38 39 41 42 44

c1 () 1,8 1,9 2,0 2,1 2,2 2,25 2,3 2,4 2,45 2,5 2,6 2,7 2,8 2,8cu1 () 3,5 3,2 3,0 2,8 2,8 2,8c2 () 2,0 2,2 2,3 2,4 2,5 2,6cu2 () 3,5 3,1 2,9 2,7 2,6 2,6

n 2,0 1,75 1,6 1,45 1,4 1,4c3 () 1,75 1,8 1,9 2,0 2,2 2,3cu3 () 3,5 3,1 2,9 2,7 2,6 2,6

Concrete properties(Table 3.1)

Design Strength Values(3.1.6)

Design compressive strength, fcdfcd = cc fck /c

Design tensile strength, fctdfctd = ct fctk,0.05 /c

cc (= 0.85 (flexure) and 1,0 (shear)) and ct (= 1,0) are coefficients to take account of long term effects on the compressive and tensile strengths and of unfavourable effects resulting from the way the load is applied

Elastic Deformation(3.1.3) Values given in EC2 are indicative and vary according to

type of aggregate.

Ecm(t) = (fcm(t)/fcm)0,3Ecm

Tangent modulus, Ec , may be taken as 1,05 Ecm

Poissons ratio for uncracked concrete = 0,2 for cracked concrete = 0

Linear coef. of thermal expansion = 10 x 10-6 K-1

Creep(3.1.4)

01,02,03,04,05,06,07,0100

50

30

1

2

3

5

10

20

t 0

(t 0)

SN R

100 300 500 700 900 1100 1300 1500

C20/25C25/30C30/37C35/45C40/50C45/55C50/60 C55/67C60/75 C70/85

C90/105C80/95

h 0 (mm)

Inside conditions RH = 50%Example: 300 thick slab, loading at 30 days, C30/37 - = 1,8

h0 = 2Ac/u where Ac is the cross-section area and u is perimeter of the member in contact with the atmosphere

Shrinkage(3.1.4)

Shrinkage Strain, cs, is composed of two components: Drying Shrinkage Strain, cd, develops slowly Autogenous Shrinkage Strain, ca, develops during the hardening of the

concrete.

Drying shrinkage, cdcd(t) = ds(t,ts)kh cd,0 (EC2, Exp (3.9)

Autogenous shrinkage, caca(t) = as(t)ca() (EC2, Exp (3.11)

Annex B Creep and Shrinkage

Creep 0 is the notional creep coefficient (in Figure 3.1 the notation

used is (,t0)) (t,t0) is the creep at any time, t after time of loading, t0

Shrinkage cd,0 is the basic drying shrinkage strain cd,(t) = ds(t,ts)kh cd,0 (Section 3)

fcd

c2

c

cu2 c0

fck

For section analysis

Parabola-rectangle

c3 cu30

fcd

c

c

fck

Bi-linear

fcm

0,4 fcm

c1

c

cu1 c

tan = Ecm

For structural analysis

Schematic

c1 () 0,7 fcm0,31cu1 () =

2,8 + 27[(98-fcm)/100]4 fcm)/100]4

for fck 50 MPa otherwise 3.5

c2 () = 2,0 + 0,085(fck-50)0,53for fck 50 MPa otherwise 2,0

cu2 () = 2,6 + 35 [(90-fck)/100]4for fck 50 MPa otherwise 3,5

n = 1,4 + 23,4 [(90- fck)/100]4for fck 50 MPa otherwise 2,0

fn

cc cd c c2

c2

1 1 for 0

f forc cd c2 c cu2 c3 () = 1,75 + 0,55 [(fck-50)/40]

for fck 50 MPa otherwise 1,75

cu3 () =2,6+35[(90-fck)/100]4for fck 50 MPa otherwise 3,5

Concrete Stress Blocks(3.1.5 and 3.1.7)

As

d

fcd

Fs

x

s

x

cu3Fc

Ac

= 1,0 for fck 50 MPa= 1,0 (fck 50)/200 for 50 < fck 90 MPa

400)508,0 ck (f for 50 < fck 90 MPa

= 0,8 for fck 50 MPa

Rectangular Concrete Stress Block (3.1.7, figure 3.5)

Confined Concrete(3.1.9)

c2,c cu2,c

c

c

fck,c

fcd,c

0

A 2 3 ( = 2)

1 = fck,c

fck

cu

fck,c = fck (1.000 + 5.0 2/fck) for 2 0.05fck= fck (1.125 + 2.50 2/fck) for 2 > 0.05fck

c2,c = c2 (fck,c/fck)2cu2,c = cu2 + 0,2 2/fck

Reinforcement (1)(3.2.1 and 3.2.2) EC2 does not cover the use of plain reinforcement

Principles and Rules are given for deformed bars, decoiled rods, welded fabric and lattice girders.

EN 10080 provides the performance characteristics and testing methods but does not specify the material properties. These are given in Annex C of EC2

Product form Bars and de-coiled rods Wire Fabrics Class

A

B

C

A

B

C

Characteristic yield strength fyk or f0,2k (MPa)

400 to 600

k = (ft/fy)k

1,05

1,08

1,15

0.2% uk

f0.2kft = kf0.2k

ft = kfykt

uk

fyk

Hot rolled steel Cold worked steel

The design value for Es may be assumed to be 200 GPa

Reinforcement (3)(3.2.4, figure 3.7)

ud

fyd/Es

fyk

kfyk

fyd = fyk/skfyk/s

Idealised

Design

uk

ud= 0.9 ukk = (ft/fy)k

Alternative design stress/strain relationships are permitted:- inclined top branch with a limit to the ultimate strain horizontal - horizontal top branch with no strain limit

Reinforcement (4) Design Stress/Strain Curve (3.2.7, Figure 3.8)

Prestressing Steel (1)(3.3.1 and 3.3.2)

Unlike EN 10080 the harmonised standard for prestressing steel, EN10138, provides all the mechanical properties. The reason given is that there are only a few types of prestressing steel and they can all be included within the Standard.

Prestressing steel losses are defined for: Class 1: wire or strand ordinary relaxation Class 2: wire or strand low relaxation Class 3: hot rolled and processed bars

Adequate ductility is assumed if fpk/fp0,1k 1.1 the mean density of prestressing tendons may be taken as 7850

kg/m3

Strand type

Steel Number

Nominal tensile

strength (MPa)

Nominal diameter

(mm)

Cross-sectional

area (mm2)

Nominal mass

(kg/m)

Charact-eristic

value of maximum force (kN)

Maximum value of

maximum force(kN)

Charact-eristic value

of 0.1% proof force

(kN)

12.9 Super

1.1373 1860 12.9 100 0,781 186 213 160

12.7 Super

1.1372 1860 12.7 112 0.875 209 238 180

15.7 Super

1.1375 1770 15.7 150 1.17 265 302 228

15.7 Euro

1.1373 1860 15.7 150 1.17 279 319 240

15.2 Drawn

1.1371 1820 15.2 165 1.290 300 342 258

Pre-stressing Strands Commonly Used in the UK

Prestressing Devices(3.4)

Anchorages and Couplers should be in accordance with the relevant European Technical Approval.

External non-bonded tendons situated outside the original section and connected to the structure by anchorages and deviators only, should be in accordance with the relevant European Technical Approval.

Eurocode 2

Durability and Cover

Concrete Cover

The Nominal Cover, Cnom, the cover specified on the drawings, is defined as:

Cnom = Cmin + Cdev

Cmin = max{Cmin,b; Cmin,dur; 10mm}

Bond durability

Durability of Structures

Cover density and quality is achieved by:

Controlling the maximum water/cement ratio

Controlling the cement content.

but Annex E does not apply. The UK has produced its own tables

Exposure Classes

Table 4.1 (based on EN 206-1) provides the definitions of exposure classes for different environmental conditions.

XO no risk of corrosion or attack XC risk of carbonation-induced corrosion XS risk of chloride-induced corrosion (sea water) XD - risk of chloride-induced corrosion XF risk of freeze/thaw attack XA (DC - BS8500) risk of chemical attack in ground

Minimum Cover for Durability, cmin,dur The UK National annex provides a table for cmin,dur

In EC2 this can be modified by further factors

But in the UK these are all 0

ie: Values of cdur,, cdur,st and cdur,add are taken as 0 in the UK unless reference is made to specialist literature.

Subclause Nationally Determined Parameter

Eurocode Recommendation

UK Decision

4.4.1.2 (5) Structural classification and values of minimum cover due to environmental conditions cmin,dur

Table 4.3N for structural classification Tables 4.4N and 4.5N for values of cmin,dur

Use BS 8500-1:2006, Tables A.3, A.4, A.5 and A.9 for recommendations for concrete quality for a particular exposure class and cover reinforcement c.

Cmin,dur = Cover for Durability 50 year life. Taken from BS 8500

Minimum Cover for Bond, Cmin,b

For bars: Cmin,b = Bar diameter

For Post-tensioned tendons: Circular ducts: Duct diameter Rectangular ducts: The greater of:

the smaller dimension or half the greater dimension

For pre-tensioned tendons: 1,5 x diameter of strand or wire 2,5 x diameter of indented wire

Cminb= lCminb= m

ml

Allowance in Design for Deviation

cdev: Allowance for deviation = 10mm

A reduction in cdev may be permitted: quality assurance system, which includes measuring

concrete cover, 10 mm cdev 5 mm where very accurate measurements are taken and non

conforming members are rejected (e.g. precast elements), 10 mm cdev 0 mm

RECAP : cnom = cmin + cdev

Fire

BS EN 1992 1-2

Tabular Data

Simplified Methods

Axis Distance a is specified (not cover). This is distance from the face to the centre of the main bar.

(Fire will be covered in Lecture 3)

a AxisDistance

Cover Example (Fire and Durability) What are the nominal cover and element size for a car

park slab with hour fire resistance?

Assume the max bar size in the slab is 20mm.

Assume the concrete is C28/35 with cement type IIIB

Assume design life 50 years and in-situ construction

Cover Example

BOND

EC2-1-1 Table 4.2 (4.2)

DURABILITY

EC2-1-1 Table 4.1 (Table 4.1)

BS8500-1:2006 Table A.4 (Table 4.2)

DEVIATION

EC2-1-1Cl. 4.4.1.3 (4.5)

FIRE


Cminb =.

Durability Class.

Cmindur =.

Cdev =

Min thickness hs=..

Min axis distance a=..

Nominal Cover governed by = ..mm

Cover Example

BOND

EC2-1-1 Table 4.2 (4.2)

DURABILITY


BS8500-1:2006 Table A.4 (Table 4.2)

DEVIATION

EC2-1-1Cl. 4.4.1.3 (4.5)

FIRE


Cminb = 20mm

Durability Class = XD3

Cmindur = 45mm

Cdev = 10mm

Min thickness hs= 60mm

Min axis distance a= 10mm

Nominal Cover governed by durability = 55mm

Eurocode 2

Structural Analysis

Structural Analysis(5.1.1) Common idealisations used:

linear elastic behaviour

linear elastic behaviour with limited redistribution

plastic behaviour

non-linear behaviour

Local analyses are required where linear strain distribution is not valid: In the vicinity of supports Local to concentrated loads In beam/column intersections In anchorage zones At changes in cross section

Soil/Structure Interaction(5.1.2)

Where soil/structure interaction has a significant affect on the structure use EN 1997-1

Simplifications (see Annex G) include: flexible superstructure rigid superstructure; settlements lie in a plane foundation system or supporting ground assumed to

be rigid

Relative stiffness between the structural system and the ground > 0.5 indicate rigid structural system

Second Order Effects(5.1.4)

For buildings 2nd order effects may be ignored if they are less than 10% of the corresponding 1st order effects

Two alternative methods of analysis are permitted: Method A based on nominal stiffnesses (5.8.7) Method B based on nominal curvature (5.8.8)

Linear elastic analysis may be carried assuming: uncracked sections (concrete section only) linear stress-strain relationships mean value of the modulus of elasticity

Linear elastic analysis may be used for both ULS and SLS

For thermal deformation, settlement and shrinkage effects at ULS a reduced stiffness corresponding to cracked sections may be assumed.

Linear Elastic Analysis(5.4)

In continuous beams or slabs which are mainly subject to flexure and for which the ratio of adjacent spans is between 0,5 and 2 0,4 + (0,6 + 0,0014/cu2)xu/d 0,7 for Class B and C reinforcement 0,8 for Class A reinforcement

where is (distributed moment)/(elastic moment)xu is the neutral axis depth after redistribution

For column design the elastic values from the frame analysis should be used (not the redistributed values).

Linear Elastic Analysis with Limited Redistribution (5.5)

05

10

15

20

25

30

35

0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60x /d

%

r

e

d

i

s

t

fck =70 fck =60 fck =50

Redistribution Limits for Class B & C Steel

05

10

15

20

25

0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60x /d

%

r

e

d

i

s

t

fck =70 fck =60 fck =50

Redistribution Limits for Class A Steel

Beam: Span 3h otherwise it is a deep beam Slab: Minimum panel dimension 5h

One-way spanning

Column: h 4b and L 3h otherwise it should be considered as a wall

Ribbed or waffle slabs need not be treated as discrete elements provided that:rib spacing 1500mmrib depth below flange 4bflange depth 1/10 clear distance between ribs or 50mm transverse ribs are provided with a clear spacing 10 h

Idealisation of the structure (5.3)

bb1 b1 b2 b2

bw

bw

beff,1 beff,2

beff

beff = beff,i + bw bWhere beff,i = 0,2bi + 0,1l0 0,2l0 and beff,I bi

l3l1 l2

0,15(l1 + l2 )l =0

l0 = 0,7 l2 l0 = 0,15 l2 + l3l0 = 0,85 l1

l0, is the distance between points of zero moment. It may be taken as:

Effective Flange Width(5.3.2.1)

leff = ln + a1 + a2

The design moment and reaction for monolithic support should generally be taken as the greater of the elastic and redistributed values ( 0,65 the full fixed moment).

leff

ai ln

h

t

ln

leff

a = min {1/2h; 1/2t }i

Permitted reduction, MEd = FEd.supt/8

Effective Length of Beam or Slab(5.3.2.2)

Geometric Imperfections(5.2)

Deviations in cross-section dimensions are normally taken into account in the material factors and should not be included in structural analysis

Imperfections need not be considered for SLS

Out-of-plumb is represented by an inclination, ll = 0 h m where 0 = 1/200h = 2/l; 2/3 h 1m = (0,5(1+1/m)l is the height of member (m) m is the number of vert. members

ei

N

Hi

N

l = l0 / 2

ei

N

l = l0Hi

N

ei = i l0/2 for walls and isolated columns ei = l0/400

Hi = iN for unbraced membersHi = 2iN for braced members

or

Unbraced Braced

Isolated Members(5.2)

Na

Nb

Hi

l

i

iNa

Nb

Hi

/2i

/2i

Bracing System Floor Diaphragm Roof

Hi = i (Nb-Na) Hi = i (Nb+Na)/2 Hi = i Na

Structures(5.2)

lx (> ly)

ly

ly/4 ly/4

ly/4

ly/4

= lx - ly/2

= ly/2

= ly/2 A

B

B

A Column strip

B Middle strip

Negative moments Positive moments Column Strip

60 - 80%

50 - 70%

Middle Strip

40 - 20%

50 - 30%

Note: Total negative and positive moments to be resisted by the column and middle strips together should always add up to 100%.

Equivalent Frame Analysis Annex I

Eurocode 2MaterialsDurability and CoverStructural Analysis

lecture 1 basics - oct 12 - end

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