Shear Reinforcement for Large Lightly Reinforced Concrete Members

Yoichi Yoshida

A thesis submitted in conformîty with the requirements for the Degree of Master of Applied Science Graduate Department of Civil Engineering

University of Toronto

O Copyright by Yoichi Yoshida, 2000

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Shear Reinforcement for Large Lightly Reinforced Concrete Members Master of Applied Science, 2000 Yoichi Yoshida Graduate Department of Civil Engineering Universisr of Toronto

Abstract

To obtain expenmental data about the shear capacity of very large concrete members,

four tests invofving 2m deep beams, which are believed to be the largest bearn-type specimens

tested in North Amerka were conducted. The four sections studied contained various arnounts

of shear reinforcement.

The following conclusions were arrived at fiom this study.

The specimen not containing transverse reinforcement failed at a shear which was only

47% of the failure load predicted by the shear provisions of the curent AC1 Building

Code.

Providing a small amount of shear reinforcement greatly enhanced the response of the

beams in terms of shear capacity and ductility. For the same total amount of stimps the

shear capacity increased as the spacing of transverse reinforcement decreased.

The procedures in the CSA code based on The Modified Compression Field Theory yield

generally good estimates of failure for al1 of the specimens.

Acknowledgments

First and foremost I would like to thank my s u p e ~ s o r , Professor Michael P. Collins for

giving me a chance to study and to do research with him on such an interesting research topic. I

also appreciate his expertise and guidance he has given me throughout this research.

1 want to express my appreciation to my fellow graduate students here at the University

of Toronto for their fnendship, their suggestions on vanous aspects of rny research, and their

generous assistance dunng the tests. Among them I name here only my roommates:

Evan C. Bentz, Almila Uzel, Young-Joon Kim, and Cao Sheng.

The experimental project wouldn't have succeeded without the help of the staff at the

Mark Huggins Structural Laboratory. 1 would like to take this opportunity to express al1 my

gratitude for their professional expertise and kind support. 1 also thank Mr. Peter Leesti for his

constant care regarding my research.

My stay at Toronto as a graduate student was made possible by Obayashi Corporation,

which 1 really thank for giving me the chance to study in Canada for two years and for providing

continuous financial support dunng my stay.

Table of Contents

Abstract Acknowledgments Table of Contents List of Tables List of Figures List of Appendices 1 Introduction ........................................................................................................................ 1

1.1 Background .................................................................................................................... I 1.2 Research Objectives and Layout of Work ....................................................................... 3

2 Review of Related Work and Code Provisions .................................................................... 4 ................................................................................................. 2.1 Review of Related Work 4

................................................................ 2.1.1 Effect of Member Size on Shear Strength 4 2.1.2 Effect of Minimum Shear Reinforcement on Shear Strength ................................... 6 2.1.3 Modified Compression Field ïheory ....................................................................... 7 2.1.4 Large Bearn Tests at the University of Toronto .............................................. 10 . .

2.2 Review of Code Provisions ........................................................................................... 1 3 2.2.1 AC1 3 18-99 ............................................................................................................ 13 2.2.2 C SA-A23 . 3-94 (Generai Method) ........................................................................ 14

2.3 Brief Introduction of Analysis Program ......................................................................... 18 2.3.1 Response-2000 ...................................................................................................... -18

3 Experimental Test Program ............................................................................................... 20 3.1 Specimen Details ......................................................................................................... 20 3.2 Matenal Properties ....................................................................................................... -24

3.2.1 Concrete Properties ................................................................................................ 24 3.2.2 S tee1 Properties ..................................................................................................... -26

3 -3 Specimen Construction .................................................................................................. 2 7 3.3.1 Form-work ................................................... ..............,,,...................... ............. -27 3 .3 .2 Concrete Pour and Cure ..................... ... ........ ..... ................................................... -30 3.3.3 Specimen Transportation ...................................................................................... 3 1

3.4 Test Rig Details ............................................................................................................. 34 3.4.1 Instrumentation and Data Acquisition .................................................................... 34

........................................................................... 3 .4.2 Strain Gauges on Reinforcement -37 ...............*.. ..*.*..*..........................*..*.....-..-.......................*. 3 -5 Load Procedure. ................... 3 9

3 -6 Reinforcement afker Test ................................................................................................ 39 4 Test Results and Analysis .................................................................................................. 42

........................................................................... 4.1 Overview of Result of YB2000 Series 42 ................................................................ 4.2 Effect of Member Depth on Shear Strength -49

.................................................. 4.2.1 Effect of Member Depth Observed in Test Result 49 ..................................... 4.2.2 Prediction of Beam's Shear Strength Using Design Codes 5 1

....................................... 4.3 Effect of Minimum S heu Reinforcement on Shear Strength - 3 5 4.3.1 Effect of Minimum S hear Reinforcemcnt in Test Results ...................................... .55 4.3.2 Prediction of Beam's Shear Strength ................................................................. 60

Table of Contents (Cont'd)

.................................................................................. 5 Conclusions and Recommendations -62 ................................................................................................................... 5.1 Conclusions 62

........................................................................................................ 5.2 Recomrnendations -63 Appendices

List of Tables

Table 2.1 Properties of BN Series Specimens ............................................................................ 11 Table 2.2 Values of ,û and @ for Section Not Containing Transverse Reinforcement .................. 16 Table 2.3 Values of and 0 for Section Containing Transverse Reinforcement ......................... 17 Table 3.1 Dimensions of Anchor Heads of T-headed bars ......................................................... 22 Table 3.2 Test S pecimen Details .............................................................................................. -22 Table 3.3 Concrete Properties ................................................................................................... -24 Table 3.4 Properties of Reinforcing Bars ................................................................................... 26 Table 4.1 Expenrnental Resuit for Bearns of YB Series and BN Series ..................................... .48 Table 4.2 Expenmental Result for Beams not containing shear reinforcement ........................... 49 Table 4.3 Prediction for Specimens without Transverse Reinforcement using AC1 3 18-99, CSA-

................................................................................... A23.3-94, and Response-2000 53 Table 4.4 Experimental Result for Beams of YB Senes ............................................................. 55 Table 4.5 Prediction for Specirnens of YB series using AC1 3 18-99, CSA-A23.3-94, and

Response-2000 .......................................................................................................... 61

List of Figures

Figure 1.1 Example of Liquid Natural Gas Tanks Constructed in Japan ...................................... 2 Figure 1.2 Example of Box Structure of Tokyo Highway Underpass .......................................... 2 Figure 2.1 Relationship between Shear Strength and Shear Span-Depth Ratio (Adapted from

Re f 9) ...................................................................................................................... 4 ....... Figure 2.2 Influence of Member Depth on Shear Strength at Failure (Adapted fkom Re f 9) 5

Figure 2.3 Size Effect Curves Suggested by Researchers (Adapted from Re f 3) ........................ 6 Figure 2.4 Modified Compression Field Theory ........................................................................ 8 Figure 2.5 Liuence of Mmber Dspth on Shear Stress at Failure (tests by Shioya) (Adapted

from Ref. 3) ................................................. .. ..................................................... 9 Figure 2.6 Geometric Details of BN Senes ................................................................................ 12 Figure 2.7 Values of Crack Spacing Parameter (Adapted fkom ReE 9) ...................................... -15 Figure 2.8 Values of P and 8 for Section Not Containhg Transverse Reinforcement (Adapted

from Ref. 9) ............................................................................................................ 16 Figure 2.9 Values of ,O and 6 for Section Containing Transverse Reinforcement (Adapted fkom

Ref. 9) .................................................................................................................... -17 Figure 2.10 Examples of the Screens of Response-2000 ............................................................ 19 Figure 3.1 Figure 3.2 Figure 3.3 Figure 3.4 Figure 3.5 Figure 3.6 Figure 3.7 Figure 3.8 Figure 3.9

T-headed bars ........................................................................................................... 21 Geometric Details of YB2000 Series Specimens ....................................................... 23 . Strength Development of Concrete ........................................................................... 25 S hrinkage Strain Development ................................................................................ -25 Longitudinal Rebars in YB2000/4&6 .............................. .. .................................... 26 Cross-sectional View of Form-work ......................................................................... 2 7 Bottom Rebar Cage .................................................................................................. 2 8 Form-work ............................................................................................................ -29 Rollen used to move the specimens ..................................................................... 31

Figure 3.10 Transportation Set-Up ............................................................................................ 32 Figure 3.11 Support ................................................................................................................... 32 Figure 3.12 Transporiation of Specimen .................................................................................... 33 Figure 3.13 Experirnental Test Set-Up ....................................................................................... 34

................................................................. Figure 3 .14 Layout of LVDT's for Beam DeBedon 35 Figure 3.15 Gnds of LVDT's .................................................................................................... 36

.............................................................................................. Figure 3.16 Zurich Target Layout 36 Figure 3.17 Measurement using Zurich Gauges ......................................................................... 3 7 Figure 3.18 Strain Gauges in Specimens .................................................................................... 38

............................................................... Figure 3.19 FaiIed End Reinforced by Dywidag Bars -40 .......................... Figure 3.20 Collapsed FIemiral Compression Zone on the Side of YB2000/6 ..41

Figure 3 -2 1 Repaired Portion .............................................................................................. 41 ........ Figure 4.1 Load-Deflection Curves for YB2000/0, YB2000/4, YB2000/6, and YB2000/9 -43

................. ........................... Figure 4.2 Crack Pattern at the Final Load Stage of YB200010 .. 45 ................................................. Figure 4.3 Crack Pattern at the Final Load Stage of YB2000D 46

Figure 4.4 Crack Pattern at the Final Load Stage of YB200016 .................................................. 47 Figure 4.5 Crack Pattern at the Final Load Stage of YB2000/4 ............................................... -47 Figure 4.6 Cornparison of Crack Patterns .................................................................................. 50 Figure 4.7 S hear Force-Deflection Curve for YB2000/0 ........................................................... -52

vii

List of Figures (Cont'd)

Figure 4.8 Variation of failure shear stress ratio with beam depth .............................................. 54 ...................................................................... Figure 4.9 Load-deflection curve for YB2000/4 3 6 ...................................................................... Figure 4.10 Load-deflection curve for YB2000/6 56 ..................................................................... Figure 4.1 1 Load-deflection curve for YB2000/9 -57

Figure 4.12 Crack Pattern o f YB2000/4&6 at Load Stage Close to Failure ................................ 58 ................................................ Figure 4.13 Crack Pattern o f YB2000/9 at Failure of YB2000/0 59

............................................................. Figure 4.14 Shear force-deflection curve for YB2000/4 60

List of Appendica

Appendu A Calculations of AC1 3 18-99 and CSA423.3-94 (General Method) Code Predictions ................................................................................. 65

Appendix B Output of Experiment ..................................................................... 74

Appendk C Matenal Properties ........................................................................ 140

1 Introduction

1.1 Background

In recent years, some very large structures, containing members whose depth is more than

lm, have been constmcted. Some examples include iiquid natural gas tanks, one of which

contains a 9.8m deep bottom slab as shown in Figure 1.1. Figure 1.2 shows another example,

which is a box structure of a Tokyo highway underpass containing a 1.25m deep member as its

roof slab. These deep members usually have smaiî or sometimes no transverse reinforcement and

hence rely on the large contribution of concrete to shear strength of the members. However the

fact that the shear stress at failure decreases for members with larger depths has been known for

several decades and in 1967 Kani warned of the imporiance of this effect of member depth on

shear strength with his paper entitled "How safe are our large reinforced concrete beams?'. Since

then research on shear strength of concrete members has been one of the most active research

topics and as a result of it some theones have been deveioped and they afEord a capability to

explain shear behaviour rationally and also provide relatively precise estimates of shear capacity.

However the applicability of these theories for very deep members, say ones more than 2rn deep,

has not actually been assured by very many experiments due to the practical ditfinilty of

constructing and testing such large specimens. Hence a reliable shear design method for deep

memben with or without transverse reinforcement is still a significant need in current praaice.

The additional concern is that in the afiermath of some major earthquakes such as

Northridge Earthquake in California in 1994 and Hyogoken Nanbu Earthquake in Japan in 1995

design loads for earthquake in many design specifications have been increased. This change has

caused a need to retrofit existing concrete structures designed with old design codes especially

for shear capacity. One of the reinforcing methods for these deep slabs is the addition of

transverse reinforcement. While it is cost effective to minimire the number of reinforcing bars

placed as shear reinforcement, most design codes require a rather small spacing for such shear

reinforcement (e.g. In the AC1 and CSA codes this spacing may not exceed 600m even for very

deep members). Although wider spacing is believed to decrease the shear strength of members, it

is not clear how much and what kind of disadvantages sparsely reinforced memben really have.

Hence the eKea of spacing of shear reinforcement in large members also needs to be

investigated for a feasible repair scheme.

Figure 1.1 Example of Liquid Natural Gas Tanks Constmcted in Tapan

Figure 1.2 Example of Box Structure of Tolqo Highway Underpass

1.2 Research Objectives and Layout of Work

Considenng the situation briefly descnbed in the previous section, the following

objectives were set at the beginning of this research.

1. Foiiowing the series of l m deep beam tests done at the University of Toronto during the

last several years, obtain reliable experimental data about shear strength of 2m deep

bems using normal mength concrete :O investigate the vdidity of exisîLing analytical

models and design provisions

2. Xnvestigate the effect of minimum shear reinforcement on shear strength of such deep

members

3. Examine the effect of spacing of shear reinforcement on shear strength and behaviour of

deep concrete members

This thesis consists of the following chapters. Chapter 2 deals with previous work in

pursuit of sirnilar objectives as this research in order to give a background. Chapter 2 also

includes b k f explanations of shear provisions of some design codes and an analytical program,

which were later examined with experirnental results. Then Chapter 3 describes details of the

experimental program including design, construction, and instrumentation of the 2m deep beam-

type specimens. Test results and verification of the code provisions and the analytical program

are shown in Chapter 4. Finally Chapter 5 concludes this report with some recomrnendations for

fiiture research.

2 Review of Related Work and Code Provisions

2.1 Review of Related Work

In this section, previous research results are summarized about the topics related to this

research. It must be noted first that memben considered in this reseatch have relatively large

shear-span-to-depth ratios, a/d, so that they can be designed using sectional analysis ( d d > 2.5

according to Figure 2.1). For shorter members compression struts fom between the loading

point and the supports and the shear is carried by arch action. The behaviour of these short

members can be dealt with based on the strut-and-tie mode1 and hence this type of member,

which has no significant size effect, is not treated in this thesis.

Figure 2.1 Relationship between Shear Strength and Shear Span-Depth Ratio (Adapted f?om Ref. 9)

2.1.1 Effect of Member Ske on Shear Strength

Member size plays a significant role in determinhg the failure shear stress of memben

without web reinforcement. This effect means that the shear strengui of members doesn't

increase iineariy as the member depth increases. In other words, for deeper members, the shear

stress at failure is smaller than it is for smaller members.

This "size effect" in shear was investigated by Kani who conducted a series of beam tests

with specimens varying in depth f?om 200mm to 1200mm. More recently, Kani's observations

were extended by Shioya (shown as Shimizu in Figure 2.2) up to a member depth of 3000mm.

Figure 2.2 shows the infiuence of member depth observed by previous researches.

Figure 2.2 Infiuence of Member Depth on Shear Strength at Failure (Adapted from Ref. 9)

The cause of the size effect is mostly agreed among many researchers as being the wider

cracks which form in larger members. Since beams usualiy have longitudinal reinforcement only

at the top and the bottom, their capability to control crack distribution is very limited around the

mid-depth of the beams. From the observation of crack patterns in specirnens he tested, Shioya

suggested that the spacing of diagonal cracks was approximately the effective depth of the

specirnens. Some other researchers assume the crack spacing to be half of the effective depth or

0.7(d - c) where c represents depth of compression zone. As can be seen, crack spacing is nearly always related to member depth.

Shce the crack width is estimated as a produd of crack spacing and concrete strain, a

larger crack spacing results in wider cracks. One of the consequences of wider cracks is a

reduction of interface shear transfer, which is one of the mechanisms carrying shear in reidorced

concrete members. For normal strength concrete, the interface shear transfer is known as

addition, spacing requirement for shear reinforcement assures srna11 crack width at the s e ~ c e

load level for durability of the members.

Yoon et al tested 750mm deep specimens with various concrete strength to investigate

the concern that minimum shear reinforcement in cunent design codes rnay not be enough for

members made fiom high strength concretes. As a part of their project, normal strength concrete

specimens were also tested for cornparison. These exhibited very ductile behaviour afker the

formation of diagonal cracks and also the crack widths in the spechens were limiteci to very

smali values. They concluded that current requirements are reasonable for members having

normal concrete strength.

Although test results with regard to minimum shear reinforcement for large-size

specimens are very limiteci, current requirements may be conservative for deeper beams as long

as they are constructed with normal strength concrete. Since the required arnount as minimum

shear reinforcement is constant regardless of member sire, shear carried by stirrups increases as

d does (See Y, terms in Eqn.2.1 and Eqn.2.3) while shear carried by concrete doesn't increase

due to the size effect. Consequently there is sufficient reserve strength provided by the shear

reinforcement required by the current requirements. This conservative aspect of the existing

codes, in tum, leads to a possibility of smaller minimum reidorcement and larger spacing than

ones the design codes demand for these larger members.

2.1.3 Modified Compression Field Theory

With the aim of developing a rational shear design method, extensive research has been

done at the University of Toronto. With many results of membrane specimens tested with the

Panel Tester and the Shear Element Tester, the Compression Field Theory and Iater the Modified

Compression Field Theory (hereafler MCFT) were developed. In this section, a brief explanation

of the MCFT is presented.

MCFT considen not oniy equilibrium but also compatibility and stress-strain

relationships for cracked concrete element as shown in Figure 2.4. Assuming that angle of crack

inclination is equal to angle of principal compressive stress in the elements, MCFT determines

the angle of crack inclination satisfjring compatibility requirement. Concrete tension stsening

and compression softening are included in its stress-strain relationships as show in Figure 2.4.

Aithough MCFT mainly deds with average values for strain and stress as representative values

of stress and strain States, it aiso checks the capability of shear transfer across the cracks by

calculating shear stress acting on crack surfaces.

A shear design method based on MCFT has been adopted by sorne design codes in North

Amenca; the Ontario Highway B d g e Design Code, the Canadian Standards Association

Concrete Design Code (CSA-A23.3-94), and the AASHTO LRFD specifications.

Stresses ut Cracks:

pXf- =&+I mi6+ v,.eotO p, f'& =/, + v tan8 - vd tan8

Geomelrlc Conditions:

Crack Widths:

Average Stress-Average Stmin Aelatlonships:

Concrete:

i\ltowable Shear Slress on Crack

Figure 2.4 Modified Compression Field Theory

MCFT explicitly accounts for the effect of member depth as follows. Since MCFT

assumes wider crack spacing for deeper beams, it Ieads to larger crack width, which is obtained

as a product of the crack spacing and average concrete strain. Consequently it becomes more

likely that the specimen's shear strength will be Iimited by the capacity of diagonal cracks to

transfer shear across the cracks. The wider the crack width becomes, the smaller the shear

transfer capability becomes.

Size effect predicted with MCFT is s h o w in Figure 2.5 with the experimenta.1 resrilts

done by Shioya. The curve indicated as Generai Method Prediction is based on the MCFT. As

show in this figure, actual shear stress at failure for the 3m (about 10 feet) deep barn member

was ody one-third of the shear stress at failure of the 200mm (8 inches) deep bearn.

2a ln. 0.6 12 In. (500 mm)

0.4

2.5 Influence of Member Depth on Shear Stress at Failure (tests by Shioya) (Adapted fiom ReE 3)

2.1.4 Large Beam Tests at the University of Toronto

M e r the development of design procedures based on the MCFT, an experimental

program was initiated at the University of Toronto in order to ve* the applicability of the

theory to members having depths up to lm. The largest specimens tested in the program were lm

deep, 0.3m wide, and 6m long. The beam properties varied in tenns of member sue, concrete

strength, longitudinal reinforcement ratio, the presence of distributed reinforcernent over the

depth of the beam, and the presence of minimum qriantities of shear reinforcement. Most of the

specimens had approximately 1% of longitudinal reinforcement. Details of this project can be

found in Ref. 2 and 13.

Conclusions deduced fiom this senes of tests related to objectives of this research are as

follows.

1. Tests of Iightly reinforced specimens with no transverse reinforcement exhiited a

significant size effect. The effect was related to the beam's capability to control crack

width and crack spacing rather than the absolute depth of the mernbers.

2. The amount of longitudinal reinforcement had a significant influence on shear

capacity. More longitudinal reinforcement resulted in larger shear capacity of beams

without transverse reinforcernent due to better ability to control crack width.

3. Providing a small amount of transverse reinforcement resulted in significant gains in

terms of reserve strength and ductility.

4. The shear design method based on MCFT, known as "the General Methoà" or "Beta

Method" (explained briefly in 2.2.2), yielded generally good predictions for the bearns

and it represented the trend of the effixts of member size and the amount and

distribution of longitudinal reinforcement which were found in the tests.

5. On the contrary, a considerable number of the specimens failed at loads lower than

those predicted by the procedures of the AC1 code (descnbed in 2.2.1). This was

prominent especially for members without transverse reinforcement where the size

effect was dominant.

Among the beams tested in the program, four beams in BN senes were selected to

compare with the results acquired in this 2m beam deep experirnental program. Their properties

and the cross-sectional details are given in Table 2.1 and Figure 2.6 respeaively.

Table 2.1 Properties of BN Series Specimens

Series 1 BN Senes s pecimen / ~ ~ 1 2 . 5 j ~ ~ 2 5 j BNSO 1 BNIOO

- -.

Beam Dimensions 1 1 - 1 1

Cross Sectionai Dimensions Width, k ( m m )

Shear Span Ratio, I ald 1 3.07 1 3.00 1 3.00 1 2.92

300

Shear Span a (mm)

~oncrete Cylinder Strength W a ) -

37.2 37.2 37.2 37.2

Height, h(mm) 1 125

Longitudinal Reinforcemen t 1 1 1

300

338

250

300

676

Bottom

300

500 1000

1350

3-Ml0 ( A = ~ o o ~ )

2700

3-MIS ( A = ~ o o ~ ' )

2-M20,l - M X ( A 4 ~OOIIUII~)

3-M30 ( ~ = 2 1 00m2)

BNIOO

BN50, BN25, and EN1 2 have dimensions 50%, 25%, and 12.5% of BNl O0 respectively.

BNIOO BN50 Figure 2.6 Geometric Details of BN Series

2.2 Review of Code Provisions

In this section, shear provisions in two codes are briefly reviewed. They are AC1

(American Concrete Institute) 3 18-99, CSA (Canadian Standard Association) 4 2 3 . 3 -94.

2.2.1 AC1 318-99

AC1 318-99 predicts that the shear strength of a concrete member is provided by the

concrete web and, if the member has shear reinforcement, by the sh= reinforcement. The s h w

strength provided by concrete, V,, is taken as the same value for beams with and without shear

reinforcement and was denved empiricdy from many experirnental data. The shear

reinforcement contribution, V,, is calculated based on the 45' tmss d o g y . As a result, for non-

prestressed concrete members with normal strength concrete and transverse reinforcement is as

follows.

[mm and MPa] (Eqn. 2.1)

AC1 3 18-99 requires that minimum shear reinforcernent have to be provided in members

where factored shear force exceeds one-half of V,. However slabs and footings are excluded

from this requirement.

42 A, = 0.33- [mm and MPa] (Eqn. 2.2) fY

When shear reinforcement is placed, the spacing has to be less than 610rnm (24") and

2.2.2 CSA423.3-94 (General Method)

CSA423.3 ado pted the General S hear Design Method (hereafter cded General Method)

that is based on MCFT as one part of its shear provisions.

The expression of the General Method for shear capacity consists of the concrete

contribution and shear reinforcement contribution in the same manner as AC1 3 18-99. However

both contributions are computed based on MCFT satisfjmg cornpatibiiity and stress-strain

relationship of cracked concrete. As a aeesult, General Method has the ability to consider some

factors which AC1 doesn't such as strain in longitudinal reinforcement, maximum aggregate size,

crack spacing, and so on.

The expression is as foUows.

v = v, + Y, =p + 4f,dv cote S

[mm and MPa] (Eqn. 2.3)

p is a measure to represent the ability of the concrete member to carry tensile stresses across potentid diagonai cracks. Since P determines the magnitude of concrete contribution, this General Method is also called Beta Method. The angle of diagonal cracks, 0, is assumed to be

the angle of principal compressive stress in cracked concrete with respect to longitudinal

reinforcement.

For members without web reinforcement, Table 2.2 or Figure 2.8 provides P and 0 with respect to strain in longitudinal reinforcement and the crack spacing parameter, %, which is

determineci by the layout of longitudinal reinforcement as show in Figure 2.7. The values in the

table and the figure were denved for a maximum aggregate size of 19mm. However the values

can be used for other

inaead of using st.

aggregate sizes using an equivalent spacing parameter, s, by Eqn. 2.4,

[mm] (Eqn. 2.4)

where a refers to a maximum aggregate size.

A table and a graph are also prepared for members with at least minimum web

reinforcement (See Table 2.3 and Figure 2.9). In this case, average shear stress induced at the

specific section should be referred to instead of the crack spacing parameter.

After the determination of and B, the strain in longitudinal reinforcement, E, has to be

checked if'its assumed value in detennining P and 6 is larger than the one calculated by Eqn. 2.5. Othenvise the values for ,8 and 8 should be revised using the ones for a higher E,

[mm and MPa] (Eqn. 2.5)

For members subjected to relatively low shear stress levels, the spacing of transverse

shear reinforcernent shall not exceed 0.7d or 600mm.

(II) Mmmkr wlthout atlrrups and wlth cont.ntrmted longltudinil nlnlorwment

(III) Mmikrrrtth0ul8ürrtIpr butwtth ml( dlrtrlbuld longltudlnil mlntorcmnent

Figure 2.7 Values of Crack Spacing Parameter (Adapted f?om Ref. 9 )

Table 2.2 Values of 1 and 0 for Section Not Containing Transverse Reinforcement --

Longitudinal ~train, t; < < s < -

0.ooos o.oo10 0.001s 0.0020 0.263 0.214 0.183 0.161 32" 34. 36O 38"

0.235 0.183 0.156 O. 138 370 4 1" 43" 45"

Figure 2.8 Values of and 0 for S edon Not Containing Transverse Reinforcement (Adapted f?om Ref 9 )

Table 2.3 Values of ,û and 8 for Section Containing Transverse Reinforcement

Figure 2.9 Values of p and û for Section Containing Transverse Reinforcement (Adapted nom Ref. 9)

2.3 Bnef Introduction of Analysis Program

Among the many programs for the analysis of reidorced concrete structures developed at

the University of Toronto based on the MCFT, a sectional anaiysis program was used for

analysis in this research.

2.3.1 Response-2000

Response-2000 has been devrlcped by Bentz as a part of his Ph.D. research project under

the supervision of Collins. This is a two-dimensionai sectional anaiysis program for beams and

columns. In this program, cross-sections are discretized into concrete layers and longitudinal

reinforcing bar elements. Longitudinal strain in each of the layers and elements follows the

comrnon assurnption of "plane sections remain plane".

The program finds out a satisfactory state for the longitudinal strain distribution and the

shear stress distribution across the cross-section based on MCFT. Even though it was developed

based on MCFT, it is capable of using some other concrete matenal models suggested by other

researchers in tenns of compressive stress-strah curve, tension stiffening, and compression

sofiening of concrete. In this research, default selection automatically chosen by the program

was used throughout the analysis, which are: Popovicsmiorenfeldt/Collins for compressive

stress-strain curve, Vecchio-Collins 1986 for compression sofiening, Bentz 1999 for tension

stiffening. Tensile strength of concrete was calculated using 0.33JfC; rather than using the

value the program automatically gives.

In spite of being a sectional analysis program, Response-2000 is able to predict full

member response such as deflected shapes and the Ioad-deflection curve of a span by perforrning

sectional analysis for a number of sections dong the span and then integrating the calculation

results. In this research this &naion was fully used to analyze experimental results. However,

since Response-2000 can't take into account a combination of a dead load and an applied load,

the analysis was undertaken by considenng only the applied Ioad.

Response-2000 and its manual are available fieely for use fiom the World Wide Web at

the address of http://www.ecf utoronto.ca/-bentz/rîk-htm.

heu on Cnek

-. - . .- - -

Figure 2.10 Exarnples of the Screens of Response-2000

3 Experimental Test Program

As descnbed in 2.1.1, the data accumulation of shear strength of deep beams, especiaiiy

ones with over l m in depth, is very limited. Therefore an experimental project involving tests of

2m deep beams was initiated as a part of this research. The details of this test program are

explained in this chapter.

5 . Specimen Detaiis

Two lightly reinforced beam specimens were constmcted and tested in the Mark Huggins

Stmchiral Laboratory at the University of Toronto. Table 3.2 sumrnarizes the properties of the

specimens and their geometric properties are given in Figure 3.2.

The dimensions of the specimens were 12m in length, 2m in depth, and 300mm in width.

The size of the specimens was determined considenng the laboratory layout and the capacity of

the indoor Crane. The length of shear span is 5 . 4 ~ which resulted in a shear-span-to-effective

depth ratio of 2.86.

Both specimens contained 0.74% of bottom longitudinal reinforcement provided by six

M30 rebars. Three M20 rebars at the top were placed in order to provide some bending strength

against unexpected loads dunng moving of the large beams. Ail of the covers and the spacings of

longitudinal reinforcement satisfied the requirements of the CSA code.

Shear reinforcement was provided not by usual stirrups but by T-headed bars (as shown

in Figure 3.1). T-headed bars have a round head at each end and the heads are designed to work

as anchors. More importantly this anchorage syaem is easy to place for deep slabs which these

specimens were intended to represent. The round heads had an area equal to about 7 t h e s the

bar area and the dimensions of the heads are shown in Table 3.1. The length of the bars was

about 1890mrn fiom inside to inside of the heads. Headed Reinforcement Corp. in California

manufactured the bars used for this project.

Each end of the two specimens was designed to have a dEerent configuration of shear

reinforcement with the intention of obtaining a total of four different test regions. The fust

specirnen had no shear reinforcement in one of the ends and one USA #9 T-headed bar at the

middle of the other end. The other specimen contained USA #6 T-headed bars at a spacing of

1350mm in an end and USA #4 T-headed bars at a spacing of 590mm in the other end. The site

of the bars and their corresponding spacing were determined so that each end has the minimum

Avf, shear reinforcement ratio required in AC1 3 18-99, which is - - - 0.33MPa. 4"s

The target concrete strength was 30MPa and it had a maximum aggregate size of 10mrn.

The four test regions were narned according to their depth and the size designation of the

rebars used for the T-headed bars ("0" was used for non-shear-reinforced end). For example

YB2000!9 contained #9 T-hendet! bar in it. The beans ncre identified by a combinadon of the

names of both ofits ends, such as YB2000/0&9.

Figure 3.1 T-headed bars

Table 3.1 Dimensions of Anchor Heads of T-headed bars

. . . - . - .

Table 3.2 Test Specirnen Details

1 Beam 1 YB2000/0&9 YB2000/4&6

S pecimen

T-headed bar

Specirnen

YB2000/9 USA #9

(e28.7rnm)

75

20 Anchor Head

1 East End 1 West End 1 East End 1 West End

Diameter (mm)

Thickness (mm)

YB2000/6 USA #6

1 Shear Spm 1 cAnn

YB2000/4 USA #4

Cross Sectional Dimensions Width, b, (mm)

Height, h (mm) Beam Dimensions

t

1 Shear Span Ratio, a/d

( e 1 9 . lmm) . (+12.7mm) I

I t 1

55

17

300

1

Longitudinal Reinforcement

TOP

I I

Transverse Reinforcement 1 1 1 1

38

11

300

Bottom

d (mm)

Bar Designation

3-M20 (~=900mm')

Yield Strength fi W a )

S hear Reinfo r- cernent Ratio

f , A A s ma)

2000

34420 (~=900rnm~)

6-M3 O (A4200mrn2)

1890

2000

6-M3 O (~=4200rnm')

1890

USA #9 ( ~ ~ 4 5 r n r n ' )

2700

USA #6 (A,-285 mm2)

1350

I

USA #4 (A*= 1 27mm2)

590

Beam ~~2000/0&9 fi

Beam YB2000/4&6

Beam YB2000/0&9 Beam

EAST

Figure 3.2 Geometnc Details of YB2000 Series Specirnens

3.2 Material Properties

3.2.1 Concrete Properties

Dufferin Concrete, a local ready-mi. concrete plant, provided the concrete for this

projea. Concrete cylinders were made at the pouring. Since a total of two tmcks were needed to

cast the two specimens sirnultaneously, concrete cylinders were taken fiom each truck to

determine the properties of each of the concretes. The volume of the concrete ftom the fkst

truck, dled batch ttl, was 9m3 and one h m the second tmclg called batch #2, was 6Sm3.

Theoretically the amount of 14.4m3 out of the total 15.5m3 was used to cunstnict the two

specimens.

The development of the compressive strength was observed by testing the cylinden at the

age of 7 days, 14 days and 28 days ( a h 21 days for batch #2) using a load controlled test

machine. The strengths at the age of the tests were obtained using a 4,448kN high stifniess test

machine (MTS) with its stress-strain responses. Properties of the concrete are shown in Table

3.3. The stress-strain curves are presented in Appendk C.

In addition to the strength properties, the s W a g e strain for the specimens was

monitored dunng the maturing process by recording the readings of three strain gauges on the

longitudinal reinforcernent in each bearn. Figure 3.4 shows the shrinkage strain development.

Final values were listed in Table 3.3.

Table 3.3 Concrete Properiies

S pecimen 1 YB2000/0 1 YB200019 1 YB2000/6 1 YB2000/4 -

Cast Date 1 - c t . 13, 1999 1 Oct. 13, 1999

YB2000/4&6 B eam

Test Date 1 Dec. 16, 1999 1 Dec. 17, 1999 1 Feb. 2,2000 [ Feb. 11,2000

YB2000/0&9

Age at Test Date 1 64 1 65 1 112 1 121

--

' Shrinkage Strain on Test Date

(microstrain)

f c o n Test Date

w a )

1 The average of the readings of the three strain gauges on longitudinal reinforcement

Batch #l

Batch #2

35.4

3 1.8

3 5.4

3 1.8

37.3

34.5

37.7

35.0

56 84 112 Age of Concrete (Days)

Figure 3.3 Strength Developrnent of Concrete

-300 ' Figure 3.4 Shrinkage Strain Developrnent

3.2.2 Steel Properties

The stress-strain responses of steel coupons taken from the rebars were obtained using a

1,000kN universal dynamic test machine (MTS). The properties are s u d e d in Table 3.4.

M30 and M S O rebars were used as longitudinal reinforcernent and USA #9, #6, and #4 rebars

were placed as shear reinforcement. The stress-strain responses for the reinforcing bars are given

in Appendix C.

The stress-strain results for the M30 longitudinal rebars hdicated that the bars may have

corne f b m different heats (named as type A and type B). Therefore additional tensile tests were

undertaken for coupons cut f?om YB2000/4&6 afker its tests so as to identify the strength of each

longitudinal rebar. The identified location is shown Ui Figure 3.5.

Table 3.4 Properties of Reinforcing Bars

South 1

Rebar Size

USA #4

USA #6

USA #9

M20

WeA

Figure Longitudinal Rebars in YB2000/4&6

Diameter '-)

12.7

19.1

28.7

19.5

IM301xI 29.9 ( 700

Cross- Sectional

Area (mm2)

127

285

645

300

462

Yield Stress a )

468

465

470

433

447

658

Ultimate Stress W a )

68 1

657

692

63 8

610

13.7

'train hardening

Strain wl

( d m ) 4.4

13.8

4.5

14.1

14.8

129 200000

Rupture Strain htt

(mdm)

113

132

132

148

129

Theoreticai Young's Modulus

W a )

200000

200000

200000

200000

200000

3.3 Specimen Construction

3.3.1 Form-work

The construction of form-work was commenceci at the end of June, 1999 after design

calculations were done so that it would hold the pressure of fksh concrete safely during the pour.

The form-work was also designed so that the two spechens could be cast sirnultaneously. The

forrn-work was presented schematically in Figure 3.6 and in more detail in Figure 3.8.

2*6 lumber

Threaded steel rods

ma. 0.0 O Q O 0 0 0

Figure 3.6 Cross-sectional New of Fom-work

Shce the form-work was very long, it was designed to wnstnict it as a series of five

panel cornponents. Four of the five panels were 8 feet (2438rnrn) long and the last panel

measured 2247m.m. Ail walls were constmcted fiom ?4 hch sheets of plywood specially

processed to be able to be reused for future pouring. The extenor walls were stiffened by two-by-

sixes running vertically, while the rniddle walls, which were shared by both specimens, were

reinforced by two-by-fours. The extenor waiis were supported laterally at three points: a sheet of

plywood screwed to the base sheets at the bottom of the fom-work, and doubled channels at the

middepth and aiso at the top. Threaded steel rods were used to tie the both sides of the channels

together. To cut the fiction between concrete and the threaded steel rods at the middepth, the

rods were covered by PVC pipes in the fonn-work

The construction of the fom-work consiaed of the following procedures.

Firstly, a layer of base sheets was laid on the laboratory floor by adjusting its elevation to

keep them nearly level throughout the entire length of the forni-work. Then two rows of 3OOmm

wide plywood were screwed to the base sheets so that they would provide a groove to hold the

bottom side of the middle walls. Then the middte waiis were built on the base sheets.

After strain gauges were applied to longitudinal rebars, bottom rebar cages were

assembled on the base sheets (Bearns YB2000/0&9 on the south side and Beam YB2000/4&6 on

the north side). The location of each rebar was secured by means of many sets of a 50mm hi&

plastic chair and a 5rnm thick plastic plates, 50mm concrete cubes, and Ml0 bars as show in

Figure 3.7. After the T-headed bars were hooked and tied to the longitudinal rebars the exterior

walls and end walk were built with the aid of the indoor Crane. Then the doubled channels were

attached to the form-work with the threaded steel rods and the plywoods were screwed at the

bottom as weI1.

Findly the top rebats, which were prefabricated with 300m long Ml0 bars on the floor,

were hung nom the top threaded steel rods with wires. 300mm long wood spacen were dso

placed in both beam forms at the top to keep the width unifonn during the cast. AU surfaces of

the plywood contacting the concrete were oiled prior to their installation.

In case of unbalanced lateral force by fiesh concrete pressure, some support pipes were

placed outside of the form-work in order to provide extra lateral raistance. The support pipes

were used to adjust the plumbness of the form-work as well.

\ Base Plywood Figure 3.7 Bottom Rebar Cage

3.3.2 Concrete Pour and Cure

Concrete was cast on October 13th 1999. Since the total volume required to cast two of

the beams was about 14.4m3, two 9m3 tmcks were used to transport the concrete from the

concrete plant. On the arriva1 of the trucks, the slump of the concrete was checked and

superplasticizer was added to the rnk to ensure an appropriate placement of the concrete.

A large concrete bucket with the capacity of 0.9m3, maneuvered by the 10-ton Crane in

the labor;itory, was used for the connete pour. Concrcte was evenly distributed h t o tha two

molds in the fom-work to avoid laterai displacement of the form-work. As a result, when the

batch #1 concrete was poured both beams were cast up to almost the same height. Hence the

batch #1 concrete was located at the bottom part of the two beams, which was assumed to be

approximately 1.1 to 1.2m deep, and the rest of the beams was made fkom batch #2 concrete (0.8

to 0.9m deep).

On the south side of the fom-work, a fïxed scaffolding covering east side of the fom-

work was built in advance and the rest was covered by a rolling tower so that people could climb

up on the fon-work. A 3m long vibrator was employed fiom the top side of the forrn-work to

fulfill concrete in the form-work. The wooded spacen placed at the top of the forrn-work were

removed when the pour was near completion. The pour started at 9 o'clock in the rnoming and

finished at approximately 1 o'clock.

M e r the initial setting of concrete, the specimens and cylinders were covered with moist

burlap and plastic sheets to rninimize the moisture loss during the cure. The beams were kept

under this condition for a week. M e r that the exterior walls were split ofFfiom the specimens,

which were then cured in air dry condition until their tests.

From shortly after the completion of the pour, three of the strain gauges on longitudinal

reinforcement in each bearn were kept measured with a main indicator for the purpose of

obtaining their shrinkage strain.

3.3.3 Specimen Transportrtion

Because each beam weighed almost 17 ton, the 10-ton crane of the laboratory couldn't

carry the whole beam. Therefore the following procedure was taken utilizing a total of four sets

of rollen (See Figure 3.9) in order to transport the beams from the construction area to the

testing area under the Baldwin loading machine in the laboratory.

Firstiy one of the ends of the specimen in the fom-work was lifted by the crane and

shifted to the side of the form-work with the other end remaining in the form-work. Then the

other end was lifted and shifted in the sarne way. Then each end was set on a steel pedestal and

fastened to two bracing stnits of the pedestal with bolts. Pnor to the transportation the laboratory

floor was cleaned and some lines were drawn on the floor as guides. M e r two sets of rollers

were placed under each steel pedestal (See Figure 3-10), the crane dragged the specimen laterally

to the testing position under the loading machine (See Figure 3.12).

M e r settling the specimen to the right position, the specimen was unfastened from the

bracing stnits and supports (See Figure 3.1 1) were placed under the specimen.

Figure 3.9 Rollers used to move the specimens

Figure 3.10 Transportation Set-Up

Figure 3.11 Support

Figure 3.12 Transportation of Specirnen

3.4 Test Rig Detrils

Because of the magnitude of force required for the tests and the size of the specimens, a

5,400kN Baldwin universal test machine (load-control actuator) was chosen for the tests. The

specimens were tested under the condition of three point loading. Between the Baldwin jack and

the specimen, a rocker type support was placed in order to allow only rotation there. Anticipating

large bearing stress under the loading jack, a steel plate (1 1.5" long, 12" wide, and 1" thick) was

placed undemeath the suppon. At each end of the specimens, a steel rollet support was placed on

the steel holder providing free rotation and longitudinal displacements. Mixed plaster was placed

at al1 supports in order to create tight comection; thereby minimiUng stress concentrations due

to irregularities of the surface of the concrete.

3.4.1 Instrumentation and Data Acquisition

Figure 3.13 shows a photograph of the test set-up. Ail of the sides of the specimens w

painted white with Bat latex paint to emphasize crack patterns.

Figu ire 3.13 Experimental Test Set-Up

Ten LVDT's (Linear Varying Displacement Transfomiers) were placed as shown in

Figure 3.14 to measure the deflected shape of the specimen. Two of the LVDT7s, which were

able to measure î50mm, were mounted on each side of the specimen at the midspan to see ifany

tilting occurs dunng testing and aiso to obtain more accurate midspan deflection by taking the

average of both readings. The other eight LVDT's (A25mm) were placed directly under the

centre-line of the beam.

Measured midspan deflettion at the second test of each b a n (Le. Specimen YB200019

of Bearn YB2000/0&9, Specimen YB2000/4 of Beam YB2000/4&6) was modified in the

following way. For those specimens the acquired data of midspan deflection were replaced with

the deflection data of the first specirnen up to the maximum load attained at the first test. And the

following data were shifted to make a load-deflection curve. This adjustment was done to

counter the effects of cracks formed during the fint test.

Figure 3.14 Layout of LVDT's for Beam Deflection

On the nonh side six grids of LVDT's were located in order to provide average shear

strain of the grids (See Figure 3.15). For compression stmt of the grids, LVDT's measuring

*15mm were mounted and for tension struts LVDT's measuring k25rnrn were employed. At the

rniddle of each bar, a d e r support was glued on the concrete to prevent the bar from sagging.

L 1

1750 1500 1 500 1250 . 1250 1500 -- 1500 1750 A

EAST WEST

-

1900*1900rnm grid Figure 3.15 Grids of LMT' s

On the south side, a total of 164 mrich targets were giued to capture the strain

distribution of the concrete surface. Hand-held mnch gauges were used to measure the length of

horizontal, vertical, and diagonal spacings of the grids. Pnor to the test, initial readings were

taken and strains in following load stages were cdculated by subtracting the reading obtained at

the load stage from the initial reading. The meamred concrete strains in d m units are

presented in Appendix B.

Dunng the tests, nirich reading was perfonned ody for the end expected to fail at the test

except for the test of YB2000/6. At the test of YB2000/6, both ends were measured because

there was a small possibility that YB2000/4 might fail first. With the help of three people the

time taken to measure the grids in an end was about 25 minutes at each load stage.

-- -

Figure 3.16 Zurich Target Layout

Figure 3.17 Measurement using Zurich Gauges

3.4.2 S train Gauges on Rein force ment

Reinforcement in the beam specimens was instnimented with many strain gauges as

shown in Figure 3.18. S train gauges wit h 1Om long leadwires in 3-wire syaem, FLA-5- 1 1- 1 OLT,

produced by Tokyo Sokki Kenkyujo Co. Ltd. were used for the project. The leadwires were tied

to rebars with reinforcing tapes and they ail came out fiom the top of the specimen in the vicinity

of the centre support. For longitudinal rebars two strain gauges were attached at the sarne

location on both sides of the rebar because of an expectation that some of the strain gauges

would be destroyed dunng the pour. If both gauges s u ~ v e d the strain at the location was

calculated by taking the average of the two gauges.

Strain Gauaes on Lonaitudinal Reinforcernent œ

Strain Gaucies on Transverse Reinforcement

B

South

Figure 3.18 Strain Gauges in Specimens

North

T'-heoded bar

?ries

tries

3.5 Load Procedure

The tests were done by applying a venical downward load at the bearn's midspan until

ultimate conditions were attained. In order to keep the area under the loading jack intact and to

test the other half span, Ioading was done very carefully especially near failure. During the tests,

load stages were taken for measurement of crack width, crack pattern, and zurich reading. The

applied load was leveled off at each load stage and decreased by approximately 10 % of the load

for the salie of çafety duRng the load stage.

3.6 ReinforcementafterTest

Since each end contains a difEerent configuration of shear reinforcement, &er the fks t

test of the beam, the failed end had to be reinforced to recover the strength for the next test for

the other end. Five sets of Dywidag high-strength bars with a diarneter of 1" were employed and

the failed end was strapped with them as shown in Figure 3.19. During the test, width of major

cracks in the previously failed end was observed to confirm that the reinforcing system was

working well.

At the fint test of Bearn YB2000/4&6, the fiexural compression zone on the side of

YB2000/6 collapsed severely due to the siippage of a major shear crack (See Figure 3.20). Hence

the cmshed zone was repaired in the following way. Firstly the crushed zone was chipped off

and al1 unstable concrete was removed. Then a fast hardening mortar, EMACO S88 CI, produced

by Master Builders Inc. was used to fil1 up the void. Two days later two 4" mortar cyünders,

which were taken at the pour, were tested and the strength was found to be more than the

strength of the original concrete. A % inch thick steel plate was placed on the portion and it was

clamped to the specimen by two of the five sets of prestressing bars. The portion after the repair

is s h o w in Figure 3.2 1.

Figure 3.19 Failed End Reinforced by Dywidag Bars

Figure 3.20 Collapsed Flexural Compression Zone on the Side of YB200016

6 . d AG5

Figure 3.21 Repaired Portion

4 Test Results and Analysis

In this chapter, the test results are discussed. In addition, some analysis was performed

and the results are compared to the expenmental results. The validity of the code provisions for

shear strength is also investigated.

The shear forces shown in this chapter were calculated at the cntical section for shear,

which is d, away from the applied load, considenng the effect of the self-weight of the beam.

The shear force due to the self-weight of the beam, Va is

Vd = y.h*w*d,, = y-hw0.9d = 23.5kN/m3x2mx0.3mx0.9x1.89m = 24.0kN

This Vd was added to the half of the applied load to obtain the shear force at the critical section.

4.1 Overview of Result of YB2000 Series

Table 4.1 shows main result obtained fiom the tests of YB2000 senes beams. To

investigate the effect of member depth on shear strength, four beams in the BN series (See Table

2.1 for details of these beams) are listed in the table as well. The Ioad-deflection curves acquired

fiom the tests are shown in Figure 4.1.

Beam YB2000/0&9 containhg Specimen YB2000/0 and YB2000/9 was tested on

December 16th and 17th 1999. Specimen YB2000/0, with no transverse reinforcement,

undenvent a very bnttle failure. Pnor to the fdure, flexural cracks, which initially propagated

vertically, inclined their directions towards the loading point as the load increased. Finaliy at a

load of 461 kN, the plot of load-deflection curve showed its peak and went into the post-peak

stage. At the maximum load the defection was only 8.0mm at midspan. That is the failure

deflection was 1/675th of the span.

M e r reinforcing the failed end, Specimen YB2000/9 was tested on the following day.

The end showed a big improvement due to the addition of only one bar of USA $9 and finally

carried an applied load of 897kN before the compression mne near the loading point was pushed

up to collapse.

The next two tests were done in February 2000. Beam YB2000/4&6 demonstrated a good

distribution of cracks than Beam YB2000/0&9. A similar failure mode as Specimen YB2000/9

o c m e d on the side of Specimen YB2000/6 when a load of 1053kN was applied. At failure of

YB2000/6 Specimen YB2000/4 seemed to be very close to failure judghg from the high strains

in the transverse reinforcement and the very wide shear cracks.

M e r the repair was done as explained in 3.6, SpecimenYB2000/4 was tested ten days

later. At an applied load of approximately l25OlcN (midspan deflection of 45mm), the specimen

showed flexural yielding of longitudinal reinforcement and the deflection continued to increase.

The magnitude of the load was almost the sarne as an estimate by Response-2000 (it prediaed

that a load when the longitudinal reinforcernent starteci to yield was 1220kN). Finally the

compression zone failed at a midspan defieaion of 94mq and the maximum applied load

obtained during the flexural yielding was 1300M.

YB 2000 senes - Load vs. Deflection

Midspan Defiedion (mm) Figure 4.1 Load-Deflection Curves for YB2000/0, YB2000/4, YB2000/6, and YB200019

The photographs in the following pages show cracking pattern obtained at failwe of the

specimens. The shear failure loads labeled on the specimens in the photos were calculated as the

shear force at 2m away from the loading point based on less accurate reading from the operating

console of the testing machine. Their values are somewhat difSerent fiom the ones s h o w later in

this chapter, which were obtained as the shear force at d, away from the loading point based on

data from the computerized data acquisition system.

Figure 4.2 Crack Pattern at the Final Load Stage of YB2000/0

Figure 4.4 Crack Pattern at the Final Load Stage of YB2OOO/6

Figu

Table 4.1 Expenmental Result for Beams of YB Series and BN Series

6, at

failure

1 The first value shows the strength of batch #1 of concrete and the second one is for batch #2. 2 Failed in flexure

4.2 E f k t of Member Depth on Shear Strength

4.2.1 Effect of Member Depth Observeci in Test Result

The expenmental results of Specimen YB2000/0 and the specimens in BN series clearly

shows the significant decrease in shear stress at fdure that occurs as mernber size increases (See

Table 4.2). The specimens in this table aii contained about the sarne percentage of longitudinal

reinforcement and their concrete strengths were also very similar. This result atnrms the

importance of the effea of menber size and it is very simi1ar to the result of Shioya (See Figure

2.5).

It is noted that as the member size Uicreases the strain in the longitudinal reinforcement at

failure decreases. Thus large size elements are more likely to fail in shear and hence it is

necessary to have an accurate prediction method for shear strength of such members.

Table 4.2 Expenmental Result for Beams not containing shear reinforcement

The fint value shows the strength of batch #1 concrete and the second one is for batch #2.

Specimen

YB2000/0

BNlOO

BNSO

BN25

BN12

The Modified Compression Field Theory explains the eflect of member depth by the

increase of effective crack spacing which results in large crack widths and decreased shear

transfer capacity across the crack. The crack patterns of Specimens YB2000/0, BN100, and

BN50 show very similar pattems regardless of the difference of member depth (See Figure 4.6).

This indicates that the approach of MCFï to size effect is correct because a member with larger

depth has larger spacing and wider cracks. For Specimen YB200010, the crack spacing at the

d (mm)

1 890

925

450

225

110

6, at

failure

8.0

5.9

5.4

5 .O

2.6

f c W a )

35.4/3 1 -8 ' 37.2

37.2

37.2

37.2

EX

(X 10-~)

0.83

1 .O

1.5

1.7

2.5

vw (w 255

192

132

73

40

7-

0.45

0.69

0.98

1 .O8

1.21

middepth is almost d , which is approximately 1.8m according to the calculation in Appendix A,

and the maximum crack width measured larger than Specimens BNlOO and BNSO.

WEST YB2000/9 Içouth y ~ ~ o o o / o s . . . . . a

EAST

. . . . . . . . o . . . * . . . . . O . . . . .

25

- . - BNSO

Figure 4.6 Cornparison of Crack Patterns

4.2.2 Prediction of Beam's Shear Strength Using Design Codes

Even though the influence of mernber depth on Mure shear stress has been discussed for

many years, not al design codes appreciate the eEect sufficiently. In this section, a cornparison

between the experimental results and predictions using some design codes are made. In addition,

the specirnens were analyzed using Response-2000. Table 4.3 shows the experimentd results and

estimation using AC13 18-99, CSA-A23.3-94, and Response-2000.

The K I code predias ml! the shev apacity for the specimens with relatively small

depths. However Specimens YB2000/0 (d=1890mm) and BNlOO (d=925mm) had much smaiier

shear strength than the ones the AC1 code predicts. Therefore it is of a considerable concem to

use the AC1 code for mernbers with no shear reinforcement which are deeper than about 0.75m.

The AC1 code requires that beams contain a minimum area of shear reinforcement if the factored

shear force exceeds O.Sc$,V, and this requirement usually mitigates the concem for its

unconservative prediction. However, the trend of the size effect shown in Table 4.2 indicates that

the actual strength can be less than 0.43 (=0.5$.=0.5x0.85) times the predicted strength for

members with over 2m depths. Besides the 0.54,Vc requirement does not apply to slabs and

footings. Therefore the shear design according to the AC1 code possibly leads to very

unconservative design for large depth memben.

The CSA code, on the other hand, yields conservative predictions for the BN senes and

gives a close but somewhat unconservative estimate for the failed load of Specimen YB2000/0.

The unconservative aspect of the predictions seems to increase as the rnember depth increases.

Hence funher improvernent to provide more accurate predictions seems to be necessary for the

CSA method with more expenmental data for the shear strength of larger specimens being

acquired.

Fairly accurate estimates were made by Response-2000 throughout the range of member

size. Figure 4.7 compares the load-deflection curve obtained fiom the test of YB200010 with the

curve calculated by Response-2000. Although the andysis result doesn't take into account the

dead load of the specimen itself0.e. the curve starts at zero point), the behaviour of the specimen

was wel1 reproduced by Response-2000 while it predicts somewhat higher stifihess after initial

crac king.

Figure 4.8 shows variation of failure shear stress ratio ( ~ 1 6 , d f i ) with beam depth and

the prediction results. It is evident fkom Figure 4.8 that the CSA code and Response-2000

represent size effect on shear strength relatively weil.

i

I 1

j

O 1 2 3 4 5 6 7 8 9 10

Midspan Deflecb'on (mm)

Figure 4.7 Shear Force-Deflection Curve for YB200010

Table 4.3 Prediction for Specimens without Transverse Reinforcement using AC1 3 18-99, CSA-A23.3-94, and Response-2000

Specimen

YB2000/0

b

BN100

SR,, at failure (mm)

5.7

Figure 4.8 Variation of failure shear stress ratio with bearn depth

4.3 Effect of Minimum Shear Reinforcement on Shear Strength

4.3.1 Effect of Minimum Shear Reinforcement in Test Results

Table 4.4 summarizes the results of the specimens with transverse reinforcement. Results

h m Specimen YB200010, which contains no transverse reinforcernent, are aiso included. In

addition Figure 4.9 to Figure 4.11 compare the load versus midspan deflection relationships of

YB200014, YB2000/6, and YB2000/9 with YB2000/0.

Table 4.4 Experimental Result for Bearns of YB Senes

1 The fist value shows the strength of batch #1 concrete and the second one is for batch #2. 2 Failed in flexure

S p ecimen

L

YB200014

YB200016

YB200019

YB200010

Al1 of the specimens with transverse relliforcement showed a signifiant increase in load

capacity and ductility in cornparison to Specimen YB200010. Specimen YB2000/4 actuaily failed

d (mm)

1890

1890

1890

1890

in flexure at a load that was almost shear capacity judging fiom the main readings of transverse

reinforcement. The shear capacity of Specimen YB2000/4 was at least 2.64 tirnes as great as

Specimen YB200010 due to the presence of just minimum transverse reinforcement. Specimen

f c W a )

35.4/31.8 ' 37.3134.5 ' 37.7135.0 ' 35.413 1.8 '

YB200016, which contained bigger T-headed bars spaced wider apart than SpecimenYB2000/4,

gained less increase in shear strength but was still 2.16 times as strong as YB2000/0. The one

s (m)

large T-headed bar in YB200019 resulted in this specimen being 1.85 times as strong as

YB2000/0. Moreover ail three specimens with T-headed bars fded at a peak rnidspan deflection

PV fv @@a)

which was three to four times larger than that of Specimen YB2000/0. These results prove that

this srnaii amount of shear reinforcement, A, = 0 . 3 3 Q 7 was adequate to serve as minimum fY

b O

590 1 0.33

shear reinforcernent for these large specimens.

674

550

472

255

1350

2700

-

b at

failure

0.33

0.37

-

Ex

(XIO-~)

- * 34

27

8.0

I

- 2

2.1

1.5 I

0.83

Midspan Defiedion (mm) Figure 4.9 Load-deflection curve for YE2000/4

O 5 10 15 20 25 30 35 40 45 50

Midspan Defiedion (mm) Figure 4.10 Load-deflection curve for YB2000/6

Midspan Defiedion (mm) Figure 4.11 Load-deflection curve for YB200019

The crack patterns of the specirnens with transverse reinforcement (See Figure 4.3 to

Figure 4.5) show well distributed cracks compared to Specimen YB2000/0. In addition it

indicates that more cracks and smaller crack widths as the spacing of the shear reinforcement

becornes closer. This is clearly shown in the photographs of YB2000/4&6 at the same load stage

(See Figure 4.12). In the photographs YB2000/4 end shows relatively more distributed aacks

and its maximum crack width is 4.0rnm compared to 6.0mm at almost the same location on

YB2000/6 side.

This crack behaviour is certainly one of the reasons why, while keeping the sarne amount

of shear reinforcement, closer spaced shear reinforcement results in a greater increase in shear

capacity. That is, the capability to control crack width of the closer spaced shear reinforcement

resulted in bigger shear transfer across the cracks. Figure 4.13 shows the ability of a T-headed

bar to control cracks. In the photograph, though the side of YB2000/0 has failed, the end with a

transverse bar has only a few cracks and no visible crack crossing the bar.

Figure 4.12 Crack Pattern of YB2OOO/4&6 at Load Stage Close to Failure

Figure 4.13 Crack Pattern of YB2OOOI9 at Failure of YB200010

4.3.2 Prediction of Beam's Shear Strength

Estimations of the shear capacity of the specimens were made using AC1 318-99, CSA-

A23.3-94, and Response-2000. The results are surnmarized in Table 4.5. It should be noted that

among the three specimens only YB200014 satisfies 600rnm maximum spacing of shear

reinforcement requirement in these codes. The code predictions for YB2000/6 and YB200019,

neglecting the violation of the limit, are shown to help in judging the need for this requirement.

Table 4.5 shows a very good agreement of the failure ioad with the prediction using the

CSA code while the AC1 code also made a relatively accurate estimate considering that the reai

shear capacity was somewhat higher than the value shown in Table 4.5 as shear strength.

Previous research shows members with at least minimum shear reinforcement are tess influenceci

by the size effect of member size. The AC1 code, which doesn't consider this effect, can be used

with only a smail loss in safety for large memben with normal strength concretes as long as they

satisQ the minimum shear reinforcement requirements.

Response-2000 gives somewhat conservative estimate for specimen YB200014 and it

predicts that the specimen fails in shear rather than in flexure as really occurred. Figure 4.14

compares the experimental result and analytical result using Response-2000.

i

i

I 1 est Result 1 4 Response2000 Result

O 5 I O 15 20 25 30 35 40 45 50

Mfdspan Deflection (mm)

Figure 4.14 Shear force-deflection curve for YB2000/4

Table 4.5 Prediction for Specimens of YB series using AC1 3 18-99, CSA423.3-94, and Response-2000

1 Failed in flexure 2 Prediction for shear capacity

Specimen

YB200014

YB2000/6

YB200Ol9

f c ( M W

37.7 .

350

37,3 - 34.5

35.4

31.8

Vcw (kW

674 '

550

472

VACI (W

772

7512

764

742

776

746

Vcs A (W

655

639'

649

633

658

636

VR‘S- (W

563

562

548

547

572

571

cd VACI

0.87

0.90

0.72

0.74

0.6 1

0.63

VaqJ VCSA

1 .O3

1 .O5

0.85

O, 87

0.72

O. 74

Veld V R ~

1.20

1.20

1 .O0

1 .O1

0.83

0.83

6~ at failure

(mm)

1

34

27

g~apmv at failure

(mm)

30

30

30

3 1

30 b

3 1

5 Conclusions and Recommendations

5.1 Conclusions

1. It is possible for a 2m deep member made fiom approximately 35MPa concrete and not

containing transverse reinforcement to fd at the very low shear stress of 0.45 MPa

Cornparisons with shdower specimens show that this fdure stress is sigdcantiy

eEected by rnember depth due to iarger crack spacings and wider crack widths.

AY 1' 2. The addition of a srnaii amount of shear reinforcement (- = 0.33hPa) greatly b w s

improves the shear capacity and ductility of large members. Midspan deflections at

failure for the specimens with minimum transverse reinforcement were three to four times

larger than those for the specimen without transverse relliforcement.

3. The increase in shear capacity due to the presence of shear reinforcement varied fiom

85% to 164% depending on the spacing of transverse reinforcement. As the spacing

becarne closer, the capacity becarne bigger because of the better crack control ability.

However it is noted that adding only one transverse bar at the rniddle of the haif span

dmost doubled the shear capacity of the specimen.

4. Methods based on The Modified Compression Field Theory, CSA-A23.3-94 and

Response-2000, generally predict well the shear capacity for members with or without

transverse reinforcement and the trend of the size effect was followed by the methods.

S. It is of considerable concem that the AC1 code predicted shear strength for the member

without reinforcement more than twice the experimentdly determined faiiure load.

Recognizing that the AC1 code pemits slabs and footings not to have shear reinforcement

until the applied factored Ioad exceeds the predicted shear strength, the code may

possibly produce severely unconservative members especially for large lightiy reinforced

elements,

5.2 Recommendations

1. Since not only member depth but aiso amount of longitudinal reinforcement has a

sigmficant effect on the shear capacity of members, tests should be conducted with large

specimens having amounts of longitudinal reinforcement different than the 0.74% used in

this study. Other major parameters such as concrete strength should also be investigated.

2. Although the minimum arnount of shear reinforcement has proved to be enough for the

specirnens in tfiis resemh, specimens witth higher strengtfi conmte should be tested to

check the validity of the current design requirements for minimum shear reinforcement.

3. The results of this research indicate that the spacing of shear reinforcement significantiy

influences shear strength. Experiments should be conducted to accumulate more data on

this effea so that the current code rules which prohibit the use of spacings greater than

600mrn even for very deep members can be verified.

References

1. AC1 Committee 3 18, "Building Code Requirements for Reinforced Concrete (AC1 3 18-99) and Commentary AC1 3 18 R-99", American Concrete Institute, Detroit, 1999

2. Angelakos, D., "The Influence of Concrete Strength and Longitudinal Reinforcement Ratio on the Shear Strength of Large-Size Reinforced Concrete Bearns with, and without, Transverse Reinforcement", M.ASc. Thesis, University of Toronto, Department of C ' i Engineering, 1999, 181pp.

3 . .ASCE-MI Cornmittee 445 on Shear and Torsion, ''Recent Approaches to Sheat Design of S tmctural Concrete", Journal of Structurai Enginee~g, Dec. 1998, pp. 1375-14 17

4. Bentz, E.C., "Sectional Analysis of Reinforced Concrete Members," Ph.D. Thesis, Department of Civil Engineering, University of Toronto, 2000, 3 10 pp.

5. Canadian Portland Cernent Association, "Concrete Design Handbook", Ottawa, 1995

6. Collins, M.P. and Kuchma, D., "How safe Are Our Large, Lightly Reinforced Concrete Bearns, Slabs, and Footings?', AC1 Structural Journal, Jui.-Aug. 1999, pp. 482490

7. Collins, M.P., Mitchell, D., Adebar, P., Vecchio, F.J., "A General Shear Design Method", AC1 Structural Journal, Jan.-Feb. 1996, pp. 36-45

8. Collins, M.P., Mitchell, D., "Prestressed Concrete Structures", Response Publications, Canada, 1997,766 pp.

9. CSA Cornmittee A23.3, "Design of Concrete Stnictures with Explanatory Notes*, Canadian Standard Association, Rexdal+ 1994, 199 pp.

10. Kani, G.N. J., Wow Safe Are Our Large Reinforced Concrete Beams?", AC1 Journal, Mar. 1967, pp. 128-141

11. Kuchma, D., Végh, P., Simionopoulos, K., Stanik, B., and Collins, M.P., 'The Influence of Concrete Strength, Distribution of Longitudinal Reinforcement, and Member Size, on the Shear Strength of Reinforced Concrete Beams", CEB Bulletin d'Information No. 237, pp. 209-229

12. Shioya, T., "Shear Properties of Large Reinforced Concrete Membef, Special Report of Institute of Technology, Shi- Corporation, No.25, Feb. 1989, 198pp.

13. Stanik, B ., 'The Infiuence of Concrete S trength, Distribution of Longitudinal Reinf'orcement, Amount of Transverse Reinforcement and Member Size on Shear Strength of Relliforced Concrete Members", M.kSc. Thesis, University of Toronto, Depariment of Civil Engineering, l998,7 1 1 pp.

14. Yoon, Y., Cook, W.D., Mitchell, D., "Minimum S hear Reinforcement in Normai, Medium and Hi&-Strength Concrete Bearns", AC1 Structural Journal V.93, NOS, Sept.-Oct. 1996, pp.576-584

Appendix A

Calculations of AC1 3 18-99 and CSA43.3-94 (General Method) Code Predictions

Estimation of Shear Failure Load Using CSA-A23.3-94 (Gened Method)

Sam~Ie Calculation for S~ecimen YB2000/0

Concrete Strength: f ;=3 5.4 MPa (batch #1) Maximum Aggregate Size: 10 mm Yield Strength of Longitudinal Rebars: 455 MPa (Average of Type A and Type B) Shear Span Length: a=5.4m Unit Weight of Concrete: 23.5 kN/rn3

1. Find the flexural lever arm, d,

a d,, =d--=1890- 455 x 6 x 7OO/(O.8O x 35.4 x3OO) 3 3

= 1777mm

2. Calculate sectionai forces due to dead load Critical section for shear is taken d, away from the applied load.

VD =23 .5~0 .3~2 .0~ l.777=25.l kN MD=183.3 kNm

3. Calculate the equivalent crack spacing parameter, s,

Hence s,d2000mm, s,,=2000mrn

4. Assume a value for the strain in longitudinal reinforcemeni, gr and select values for @ and 0 fiom Table 2.2

Assume e = 0.0005. From Table 2.2, P = 0.126 and O= 59'. x 354~300~1777/1000=399.7~ V, =/?J?;'b,,,dv =0.126 J-

The sectional forces acting on the critical section are calculated as: Shear force due to the applied load

Y, -Y, =399.7 -25.1=374.6W Bending moment

Mu = M D +M, = M D +V'(a-dv) = 183.3 +374.6x(5.4 -1.777) = 1540.5kNm

5. Check the strain in longitudinal reinforcement

The strain in longitudinal reinforcement is calculated as:

This hdicates that our assumption was unconservative. We must choose a bigger value for

6. Second Iteration

Assume E~ = 0.0009. From Table 2.2, P = 0.084 and 8= 66'. x 354~300~1777/1000=266.4kN V, = p a b W d Y = 0.084 4-

The sectional forces acting on the critical section are calculated as: Shear force due to the appiied load

Vp = V, - V' = 266.4 - 25.1 = 241.3kN Bending moment Mu = M D + M p =MD +Yp@-d , ) =l83.3+241.3~(5.4-1.777) = lOS7.SkMm

Check the arain in longitudinal reinforcement The strain in longitudinal reinforcement is calculated as:

MM f dv + OSV, cot 9 Ex =

E A

- - 1057.5 x 106 / 1777 + 0.5 x 266.4 x 1000 x cot66O 200000 x 6 x 700

= 0.00078 < 0.0009 This indicates that our second assumption was sornewhat conservative. However we can use this value as a shear capacity of the section when we design this member.

Vu= 266.4kN

In this research, linear interpolation was used in selecting and 6 &om Table 2.2 for more accurate value for shear capacity. The result is as foiiows.

/3 = 0.0945;O = 64.3*;~, = 0.000875 V, = 299.8W

Mu = M D +(V, -&)(a-d,) = 183.3+(299.8-25.1)(5.4-1.777) =1178.5RNm Mu Id, +0.5V, cote 1178.5 x lo6/1777 +OS x 299.8 x 1000xcot64.3~

8, = - - EsAs 200000 x 6 x 700

= 0.000875

Therefore prediction by the CSA code is V2=300kN

Sample Calculation for Soecimen YB2000/4

Concrete Strength: Maximum Aggregate Size: Yleld Strength of Longitudinal Reban: Yield Strength of Transverse Reban: Area of a Transverse Rebar: Spacing of Transverse Rebars: Shear Span Length: Unit Weight of Concrete:

f ,=37.7 MPa (batch #1) 10 mm 455 MPa (Average of M 3 O Type A and Type B) 468 MPa (#4) 127 mm2 (a) 590mm a=5.4m 23.5 ]th/m3

1. Find the flexural lever arm, d,,

2. Calculate sectional forces due to dead load Critical section for shear is taken d, away from the applied load.

VD =23.5~0.3~2.0~1.784=25.1 kN Mp183.2 kNm

3. Calculate the shear force

4. Select values for p and B fiom Table 2.3

V Assume E, a 0.0020 and 7 0.050. From Table 2.3, f l= 0.143 and O= 43.0'.

f,

V, = 3286.lp + 179.7 cot 6 = 3286.1 x 0.143 + 179.7 x cot 43 .O0 = 662.6W The sectional forces acting on the critical section are calculated as: Shear force due to the applied load

Vp = V, - V' = 662.6 - 25.1 = 637SW Bending moment Mu =MD + M, = M D + Vp(a - d,) = 183.2 + 637.5 x (5.4 - 1.784) = 2488.4WVm

V 5. Check E, and -

L'

The strain in longitudinal reinforcement is calculated as:

v 662.6 x 1000/(300 x 1784) = o.o328 < o.o5o -= L' 37.7

This indicates that Our assumption of gX was somewhat unconservative. We must choose a bigg