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The Shear Response of Circular Concrete Columns Reinforced with High Strength Steel Spirals

Young Joon Kim

A thesis su bmitted in conformity with requirements for the Degree of Master of Applied Science Graduate Department of Civil Engineering

University of Toronto

O Copyright by Young Jooa Kim, 2000

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Thesis Title: The Shear Response of Circulai- Concrete Colurnns Reinforced with High Strength Steel Spirals

Degree: Master of Applied Science Year of Convocation: 2000 Narne: Young Joon Kim Graduate Department: Civil Engineering Name of University: University of Toronto

Abstract

This report describes an experirnental investigation in which the shear strength

and shear behaviour of circular concrete rnembers reinforced with seven-wire hi&

strength transverse strand spirals compare to the strength and behaviow of members

reinforced with regular deformed bar spirals. Six large scale specimens were loaded

monotonically in shear. Two of the specimens were subjected to shear reversais afier

passing their peak rnonotonic shear capacities. The prime variables were the amount and

the yield strength of the transverse reinforcement which was either 1728 MPa for the

specimens reinforced with seven wire strands or 445 MPa for the specimens reinforced

with reinforcing bars.

The experimental results from the six specimens indicated that three analytical

modeis (AASHTO-LFRD, Response2000, TRiX97) based on the Modified Compression

Field Theory (MCFT) predicted the behaviow of the specimens reasonably well, with

both the predicted shear strengths and the predicted deformations agreeing well with the

actual test results. TRiX97 had a coefficient of variation of 6.3%. Response 2000 has a

coefficient of variation of 10.4% while AASHTO has a coefficient of variation of 1 1.9%.

Acknowledgments

1 would like to take the opportunity to express my sincere gratitude and

appreciation to al1 who assisted me in this thesis. Specifically 1 wish to thank Professor

M. P. Collins for his continual support throughout the last two years. Without his

assistance, this thesis could not have been completed.

Thanks are also extended to the many students who assisted me with this project.

1 appreciate their assistance. I would like to thank Gary McDonald, Yoichi Yochida,

Alrnila Uzel, Laurent Massan, Cao Shen and Juiius Lenart for their support. I am gratehl

for the help of Evan Bentz, who answered my questions and introduced me to his

sectional analysis prograrn, Response 20000. Special thanks go to Mr. P. Leesti, who

greeted me with instant help whenever 1 barged into his office with a problem.

1 would like to extend my gratitude to the management and persomet of the

structural laboratory. I want to thank John McDonald for his steadfast support, even

when 1 was in despair. 1 would also like to express my appreciation to Peter Heliopoulos

for his support. I am gratehl to Joel Babbin, Renzo Basset and Mehmet Citak for

helping me to solve my many problems. I am grateful to Giovanni Buzzeo and Allm

McCIenaghen for their assistance in the machine shop.

Finally, 1 wish to th& my farnily and my wife for their love and support.

Table of Contents

. . Abstract ............................................................................................... II ... Acknowledgmeats .... ............................................................... ............. 111

Table of Contents ................................................................................... iv List of Tables ......................................................................................... vi . . List of Figures ...................................................................................... VII

List of Appendices ................................................................................ ..xi . . Notations ............................................................................................. XII

1 . INTRODUCTION ................................................................................................................................ I

1.1. PROBLEM DESCRIPTION ........................................................................................................... 1

1.2. PREVIOUS WORK .......................................................................................................................... 5

............................................................................................ 1.3. OBJECTIVE OF CURRENT WORK 6

........................................................................................................... 4 . OUTLINE O F T H E THESIS 6

......................... 2 . REVIEW OF RELATED PREDICTION MODELS AND CODE PROVISIONS 8

.......................................................... 2.1. MODIFIED COMPRESSION FIELD THEORY (MCFT) 8

.......................................................................................................................... 2.1.. AASHTO LRFD 10

2.1.2. RESPONSE-2000 ........................................................................................................................ 14

....................................................................................................................................... 2.1.3. TRIX-97 14

..................... .....................*......*.......................................... 2.2. AC1 318M-99 CODE EQUATIONS ,., 15

................................................................................................................. 2.3. UCSD SHEAR MODEL 16

........................................................................................................ 3 . EXPERIMENTAL PROGRAM 18

...................................................................................................... OBJECTIVE O F T H E TESTS 18

TEST APPARATUS ................................................................................................................... 19

TEST SPECIMENS ................................................................................................................. 23

................................................................................................... GEOMETRIC PROPERTIES 24

.................... ............*........,....................*............... REINFORCING STEEL PROPERTIES ... 27

..................................................................................................... CONCRETE PROPERTIES 28

CONSTRUCTION ...................................................................................................................... 30

SPECIMEN INSTRUMENTATION ............................................................................................ 31

STRAIN GAUGES O N REINFORCEMENT ...................................................................... 32

Table of Contents (Cont'd)

3.4.2. LVDT LAY-OUT ........................................................................................................................ 35

3.5. TEST PROCEDURE .................................................................................................................. 3 6

4 . EXPERIMENTAL OBSERVATIONS ....................... .. ............................................................... 3 7

INTRODUCTION ................................................................................................................... 3 7

SPEClMEN YJCIOOR .................................................................................................................... 38

SPECIMEN YJClSOR .................................................................................................................... 44

MONOTONIC LOAD ................................ ,,., .. ..,.....,., ............................................ 44

REVERSE LOAD ....................................................................................................................... 49

SPECIMEN YJC2OOR .................................................................................................................... 52

MONOTONIC LOAD ................................................................................................................ 52

REVERSE LOAD ....................................................................................................................... 56

.................................................................................................................. SPECIMEN YJClOOW 59

.................................................................................................................. SPECIMEN YJCZOOW 65

SPECIMEN YJCCONTROL .................................................................................................... 70

LOAD-DEFLECTION CURVES FOR SIX SPECIMENS ......................................................... 74

5 . EXPERIMENTAL AND ANALYTICAL RESULTS .................................................................. 76

5.1. ULTIMATE SHEAR STRENGTH ............................................................................................... 76

5.2. TRANSVERSE STRAINS ............................................................................................................. 79

5.2.1. STlWIN DISTRIBUTION AROUND THE SPIRALS ........................................................... 79

5.2.2. VARIATION O F T H E SPIRAL STRAIN ALONG T H E TEST LENCTH .......................... 80

5.2.3. VARIATION O F TRANSVERSE STRAIN WITH SHEAR FORCE ................................... 80

5.3. SHEARSTRAINS .......................................................................................................................... 80

5.4. LONGITUDINAL STRAINS ...................................................................................................... 81

Reference ........................................................................................... 112 ........................................................................................ Appendices 114

List of Tables

Table 3 . 1 Transverse Reinforcement Detail ............................................................................................ 26

Table 3 . 2 Specimen Mater ia l Properties ................................................................................................ 30

Table 3.3 Strain Gauge Location on Longitudinal Reinforcement and Transverse Reinforcement .. 33

Table 1 . 1 Load history and shear strength of six specimens ................................................................ 38

Table 4 . 2 Test observations fo r Specimen YJC100R .............................................................................. 38

Table 4 . 3 Test observations for specimen YJC l5OR .............................................................................. 44

Table 1 . 4 Test observations for Reverse load of specimen YJClSOR ................................................... 49

Table 4 . 5 Test observations fo r specimen YJC200R ............................................................................. 52

................................................... Table 4 . 6 Test observations for Reverse load of specimen YJC2OOR 56

Table 4 . 7 Test observations for specimen YJClûûW ............................................................................ 59

Table 1 . 8 Test observations for specimen YJC200W ............................................................................. 65

.......................................................................... Table 4 . 9 Test observations fo r specimen YJCControl 70

List of Figures

Figure 1 . 1 Typical highway bridge piers wi th circular shape .................................................................. 2 Figure I . Z Circular column used i n high rise building ............................................................................. 3

Figure 1 . 3 Circular columns under the action o f lateral loads .............................................................. 3

Figure 1 . J Shear failure o f piers o f Hanshin Expressway ........................................................................ 4

Figure 2 . 1 A summary o f the relationship used i n the Modified Compression Field Theory ............... 9

Figure 2 . 2 MCFT analysis of beams and columns .................................................................................... 9

Figure 2.3 Values o f 8 and f3 fo r sections contain at least the minimum amount o f transverse

...................................................................................................................................... reinforcement 12

Figure 2.4 Values o f 0 and f3 for sections contain less than the minimum amount o f transverse

re in forcement ...................................................................................................................................... 13

Figure 2 . 5 y vs . Displacement Ductil i ty ............................................................................. 17

Figure 2 . 6 y vs . Curvature Ductil i ty ................................................................................. 17

................................................................................................ Figure 3 . 1 Loading simulated dur ing test 18

Figure 3 . 2 Testing r i g and specimen as positioned i n MTS testing machine ....................................... 19 Figure 3 . 3 Moment and shear force diagrams for test section ............................................................... 20

Figure 3 . 4 Specimen orientation. dimensions o f test r ig and location o f applied loads ....................... 21

Figure 3 . 5 Connection between the MTS machine and loading yoke ................................................... 22

.............................................................................. Figure 3 . 6 Hydraulic jack supported the end b lock 22

Figure 3 . 7 Post-tensioning the end blocks ............................................................................................ 23

Figure 3 . 8 Typical cross-section ofspecimen .......................................................................................... 24

Figure 3 . 9 Typical overall dimension o f specimen ............................................................................... 25 Figure 3 . 10 Typical reinforcing cage for the test specimens .................................................................. 26 Figure 3 . 1 1 Typical stress-strain ciirves for regular reinforcement bars (2SM & U.S.#3) ................. 27 Figure 3 . 12 Typical stress-strain curves for %" Seven Wire Strand (SWS) ......................................... 28 Figure 3 . 13 Stress-strain characteristics o f concrete ........................................... 29

Figure 3 . II Specimens were cast vertically ....................................................................................... 3 1

Figure 3 . IS Locations of Strain gauges i n reinforcement ................................................................... 32

Figure 3 . 16 Layou t for LVDTs ................................................................................................................. 36

Figure 4 . 1 Load- deflection curve fo r YJC100R .................................................................................. 39

Figure 4 . 2 Specimen YJCIOOR before peak load a t load stage 5 (Dri f t ratio = 1.4%) ........................ 39

Figure 4 . 3 Specimen YJCIOOR after peak Joad a t load stage 9 (Drift rat io = 6.1%) ........................... 40

vii

List of Figures (Cont'd)

Figure 4 . 1 Specimen YJClOûR removed from the MTS machine alter testing ................................... JO

Figure 1 . 5 Crack patterns for YJC100R (LSl to LS4) .......................................................................... 41

Figure 1 . 6 Crack patterns for YJClOOR (LS5 to LS8) ........................................................................... 42

Figure 4 . 7 Crack patterns for YJC1 OûR (LS9 and LS11) ................................................................... 43

Figure 1 . 8 Specimen YJClSOR belore peak load at load stage 5 (Drift ratio = 1.l0/0) ........................ 14

Figure 4 . 9 Specimen YJCISOR after peak load at load stage 9 (Drift rat io = 4.5%) ..................... ,, ... 45

Figure 1 . 10 Load- deflection curve for YJClSOR ............................................................................... 45

Figure 1 . I l Crack patterns for YJCISOR (LSl to LS1) ......................................................................... 46

Figure 4 . 12 Crack patterns for YJClSOR (LSS to LS8) ........................................................................ 47

Figure 4 . 13 Crack patterns for YJCISOR (LS9 to LS10) ..................................................................... 48

Figure 1 . II Load- deflection curve for YJC1 SOR (Reverse load) ........................................................ 49

Figure 4 . 15 Specimen YJC ISOR Reverse load at load stage 2 (Drift ratio = .2.4%) ........................... 50

Figure 4 . 16 Specimen YJClSOR Reverse load at load stage 3 (Drift ratio = .3.8%) ........................... 50

.................................................. Figure 1 . 17 Crack patterns for YJC150R Reverse load (LSI to LS3) S I

Figure J . 18 Specimen YJC2OOR belore peak load at load stage 4 (Drift ratio = 0.78%) .................... 52

Figure 4 . 19 Appearance of YJC2OOR at end o f test ............................................................................. 53

Figure 1 . 20 Load- deflection curve for YJC200R ............................................................................. 53

Figure 4 . 21 Crack patterns for YJC200R (LS1 to LS4) ....................................................................... 54

Figure -8 . 22 Crack patterns for YJCLOOR (LSS to LS7) ..................................................................... 55

Figure 4 . 23 Specimen YJC2OOR Reverse load at foad stage 2 (Drift ratio = .2.4%) ........................... 56

Figure 4 . 2 1 Specimen Y JC2OOR Re-loading at load stage 3 (Drift ratio = 5.7%) ................................ 57

Figure 1 . 25 toad- deflection curve for YJC2OR (Reverse Load) .................................................... 57

.................................................. Figure 4 . 26 Crack patterns for YJCZOOR Reverse load (LSI to LS4) 58

.................................................................................. Figure 4 . 27 Load- deflection cuve for YJC100W 60

Figure 4 . 28 Specimen YJClOOW belore peak load at load stage 4 (Drift ratio = 1.4%) ..................... 60

Figure 1 . 29 Specimen YJCIOOW alter peak load at load stage 10 (Drift ratio = 10.8%) .................... 61

.................................................................. Figure 4 . 30 Seven wire strands had broken in tension zone 61

........................................................................ Figure 4 . 31 Crack patterns for YJCIOOW (LS1 to LS4) 62

Figure 4 . 32 Crack patterns for YJClOOW (LSS to LS8) ...................................................................... 63

Figure 4 . 33 Crack patterns for YJCIOOW (LS9 to LS l I ) ...................................................................... 64

Figure 4 . 34 Specimen YJCZOOW before peak load at load stage 5 (Drift ratio = 0.72%) ................... 65

Figure 1 . 35 Specimen YJC2üOW alter peak load at load stage 9 (Drift rat io = 4.9%) ........................ 66

Figure 4 . 36 Load- deflection cuire for YJCZOOW .................................................................................. 66

Figure 4 . 37 Crack patterns for YJC2OOW (LS1 to LS4) ...................................................................... 67

viii


Figure 4 . 38 Crack patterns for YJC2OOW (LSS to LS8) ...................................................................... 68

Figure 4 . 39 Crack patterns for YJLZûOW (LS9) .................................................................................... 69

Figure 4 . 40 Specimen YJCControl at the failure load (Drift ratio = 0.48%) ....................................... 70

Figure 1 . 4 1 Appearance o f YJCControl at end o f test (Drift ratio = 4.6%) ......................................... 71

Figure 1 . 12 Load- deflection curve for YJControl ........................................................................... 71

.................................................................... Figure 1 . 43 Crack patterns for YJCControl (LSI to LS1) 72

.................................................................... . Figure 4 44 Crack patterns for YJCControl (LSS to LSS) 73

Figure 4 . 15 Load-deflection curves for specimens with reinforcing bar spirals ................................. 74

.......................... Figure 4 . 46 Load-deflection curves for spcimens with high strength stmnd spirals 75

Figure 5 . 1 Relationship bctween shear strength and amount of transverse reinforcement predicted

by ACI. AASHTO and Response2000 ......................................................................................... 78

Figure 5 . 2 Strain distribution along spiral at different load stages for YJCIOOR ............................... 83

Figure 5 . 3 Strain distribution along spiral at different load stages for YJCISOR ............................... 84

Figure 5 . 1 Strain distribution along spiral at different load stages for YJC2OOR .............................. 86

Figure 5 . 5 Strain distribution along spiral at different load stages for YJCIOOW .............................. 87

Figure 5 . 6 Strain distribution along spiral at different load stages for YJC2OOW .............................. 89

......... Figure 5 . 7 Variation of the transverse strain at the mid-depth along the length for YJC IOOR 90

......... Figure 5 . 8 Variation ofthe transverse strain at the mid-depth along the length for YJCISOR 90

......... Figure 5 . 9 Variation o f the transverse strain at the mid-depth along the length for YJC200R 91

...... Figure 5 . 10 Variation of the transverse strain at the mid-depth along the length for YJC100W 91

...... Figure 5 . 11 Variation of the transverse strain at the mid-depth atong the Iength for YJC2OûW 92

........ Figure 5 . 12 Variation of transverse strain in al1 specimens at the mid-depth o f the test section 94

Figure 5 . 13 Variation of the shear strain with applied shear load ................................................ 9 5

.......................... Figure 5 . 14 Longitudinal strain variation from five different sections forYJC1 OOR 97

......................... Figure 5 . 15 Longitudinal strain variation from five different sections for YJCISOR 98

Figure 5 . 16 Longitudinal strain variation from five different sections forYJC2OOR ........................ 100

....................... Figure 5 . 17 Longitudinal strain variation from five different sections forYJClOOW 101

....................... Figure 5 . 18 Longitudinal strain variation from five different sections forYJC2OOW 103

Figure 5 . 19 Longitudinal strain variation from five different sections forYJCControl .................... 104

Figure 5 . 20 Longitudinal strain distribution along the Iength for YJCIOOR ..................................... 105

Figure 5 . 2 1 Longitudinal strain distribution along the length for YJCISOR .................................... 105

Figure 5 . 22 Longitudinal strain distribution along the length for YJC200R ..................................... 106

Figure 5 . 23 Longitudinal strain distribution along the length for YJC100W .................................... 106

Figure 5 . 24 Longitudinal strain distribution along the length for YJC2OOW ................................... 107


................................. Figure 5 . 25 Longitudinal strain distribution along the length for YJCControl 107

Figure 5.26 Actual measured longitudinal strains of six specimens at failure and predictions of

.................................................................................. Response2000 at the predicted failure loads 109

List of Appendices

Appendix A Calculations of AASHTO-LRFD, AC1 3 18M-99 and UCSD Mode1 Predictions.. . . . .... 1 14

Appendix B Experimental Data.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -. ... 124

Notation

Ac A g

As Av bv bw D d dv ES f 'c

fy Mu Nu. P S

vc

vs

vu Es

V

= area of concrete cross-section = gross area of concrete cross-section = area of longitudinal reinforcernent on the flexwal tension side of the rnember = total cross-sectional area of shear reinforcement within distance s = effective width of cross-section = web width = overall diameter of section = effective depth = flexural lever arm = modulus of elasticity of steel = cglinder compressive strength of concrete = specified yield strength of reinforcement = moment at section = axial Ioad at section = spacing of shear reinforcement in direction parallel to longitudinal axis = shear force carried by concrete = shear force transferred by transverse reinforcement (stimps) = total shear force at section = longitudinal reinforcement strain = shear stress

xii

1. lntroductio

f -1. Problem Description

Circular reinforced concrete columns are often have been used to support

many bridges and buildings (as shown in Figure 1.1 .and 1.2). This is because such

columns are easy to constmct, have a pleasing appearance and provide equal strength

characteristics in ail directions under wind and seismic loads. Considenng the

widespread use of circular reinforced concrete columns, it is surprising that relatively

little research has been conducted on the shear strength of such members. The shear

strength of circular columns is critical in enabling them to support the structure

against lateral Ioads such as winds and earthquakes (see Figure 1.3). If the coIumns

do not have appropriate shear strength they will loose their load carrying capacity at

smaii deformations and a catastrophic collapse of the structure may occur. A

drarnatic example of such a collapse is the destruction of the Hanshin Expressway

during the 1995 Kobe earthquake [14]. The 3. lm diameter circular reinforced

concrete columns collapsed at a horizontal deformation of Iess than 1 % of their height

(see Figure 1.4). The collapse was due to an inadequate amount of hoop

reinforcement.

The shear strength of circular reinforced concrete columns depends on many

parameters such SLS: the diarneter and height of the column, the concrete cover, the

mount of longitudinal reinforcement and the amount of transverse reinforcement.

Although many parameters effect the shear strength of the column, the amount of

reinforcement (transverse and longitudinal) is typically most critical. A circular

column containing the appropriate amount of longitudinal reinforcement will have

adequate flexural and axial capacity. CSA A23.3-94 [IS] code States that the amount

of longitudinal reinforcement in circular column must be at Ieast 1% of the gross area

(A,) of the column. The maximum m o u n t of longitudinal reinforcement is usually

capped at 4% of the gross area (A,) of the column to avoid dificulties in placing and

compacting the concrete as well as placing reinforcement in bearn column joints. An

appropriate amount of transverse reidorcement will provide the column with

adequate confinement and shear strength against axial loads and lateral loads. The

CSA A23.3-94 code States that to quaMy as a spirally reinforced column the member

must contain a minimum amount of spiral reinforcement as given by Equation below.

In this equation the yield strength (f,) of the spiral reinforcernent rnust not be taken

greater than 500 MPa.

Where Ag is the gross area of the section and AC is the area of the concrete core

measured out-to-out of the spiral.

A well designed circula column must contain enough shear reinforcernent to

avoid a brittle shear failure when the column is subjected to lateral load. A sufficient

arnount of shear reinforcement in a column is an essential requirernent for the

ductility of the structure, whereby the structure can carry the load while sustaining a

large de formation.

Figure 1. 1 Typical highway bridge piers with circular shape

Figure 1.2 Circular column used in high rise building

Figure 1.3 Circular columns under the action of lateral loads

Figure 1. 4 Shear failure of piers of Hanshin Expressway

Priestley and Budek [13] have recently recommended the use of quarter inch

diameter, seven wire, prestressing strand (SWS) spirals in circular reinforced concrete

columns. This is a convenient-to-place and effective form of transverse confinement

reinforcement in circular colurnns. However code equations and analytical prograrns

used to predict the shear strength of circular columns usually restrict the yield

strength of the transverse reinforcement to about 500 MPa. The code equations

predicts that the higher the yield strength (fy) of the transverse reinforcement the

higher the shear capacity of the member will be. The geometric properties of the

member must also be considered. Seven wire prestressing strand has a much higher

yield strength than the maximum specified yield strength from the codes. Further,

there has been only a limited amount of investigation into circulai' reinforced

members with high strength transverse reinforcement. As well, little research has

been done with regards to the different shear behaviour of circular columns reinforced

with high strength seven wire strand spiral compared with regular reinforcing bar

spirals.

1.2. Previous work

From the review of the literature, it seerns that relatively few experiments

have been conducted to investigate the shear strength of circular reinforced members.

The amount of work done on members with circular columns is very limited when

compmed to the large number of shear tests of members with rectangular sections.

Farodji and Diaz de Cassio [ I l investigated the shear strength of twenty 250

mm diameter circular columns. However, only four of their columns contained

transverse reinforcement, and none were subjected to cyclic load reversals typical of

earthquake loading.

Some work on circular members was conducted at the University of Toronto

in 1974 by Aregawi [2]. He made and tested four specimens 457 mm in diameter.

An attempt was made to measwe hoop and longitudinal strains, however much of the

strain data was unreliable due to the dificulties he encountered rneasuring strains

over curved surfaces.

One study for circular member with shear reinforcement was performed at

University of Toronto in 1981 by Jamuel U. Khalifa and M.P. Collins [3]. Five

circular members were tested, of which four members contained shear reinforcement.

Four of the colwnns were tested with monotonie loading, while one column was

tested with load reversals.

A study involving 25 circular reinforced columns (24 columns containing

transverse reinforcement) was cmied out by Ang, Priestley and Paulay [4]. A series

of 25 circular columns were tested under axial loading, and cyclic reversals of

inelastic lateral displacements. Results from this series of tests indicated that the

shear strength was dependent on the amount of transverse spiral reinforcement; the

âuial load level; the column aspect ratio (MND), where D is the diameter of the

column; and the flexural displacement ductility factor.

Another study involving 16 circular reinforced columns (15 columns

containing transverse reinforcement) was carried out by Wong, Paulay and Priestley

[ 5 ] . Sixteen circular reinforced columns with different amounts of transverse

reinforcement were tested under reversed and various cyclic lateral load patterns (one

type of uniaxial pattern and two types of biaxial patterns). It was found that the shear

strength of the columns and the stisness of the shear-resisting mechanisms depends

on the amount of the transverse reinforcement, the axial compression load intensities

and various cyclic lateral load patterns.

Kowalsky and Priestley f 1 I ] recently presented an imprcved analytical model

(revised UCSD model) for the prediction of the shear strength of a circular reinforced

concrete colurnns. To validate their analyticai model, 47 circular columns (fiom

University of California San Diego database) of which 20 specimens suffered "brittie

shear failure" were analyzed. The c o l m database was an assembled fiom nine

different series of experiments. Kowalsky and Priestley concluded that the revised

anal ytical mode1 was an improvement on the original modet.

1.3. Objective of Current Work

The main objective of this research was to compare and examine experimentai

values with predicted values for the shear strength of circular reinforced members

containing high strength transverse reinforcement. The predicted values are

calculated by code provisions and analytical programs.

A secondary objective was to compare the shear behavior of circular

reinforced concrete members containing high strength seven wire strand as transverse

reinforcement and circular members containing regular reinforcing bar as transverse

reinforcement.

4 Outline of the Thesis

This thesis is comprised of the following:

Chapter 2 provides brief descriptions of the shear provisions of the design

codes and the analytical programs used to predict the shear strength of the columns.

These predictions are later used for cornparison with experimental results.

Chapter 3 specifies the detailed descriptions of the geometric and material

properties of each specimen. In addition, the experimental program incIuding the test

apparatus, construction, and instrumentation of the six circular reinforced columns is

presented.

The experimentai observations made during the loading of each specimen are

presented in Chapter 4. Load-deformation curves and crack patterns at different load

stages are given.

The experimental and analytical results obtained are then compared and

discussed in Chapter 5. The actual shear strengths of the specimens are compared

with the predictions of severai code provisions and analytical prograrns. Strain

analysis is also presented. The actual strains are compared to the strains predicted by

Response2000 (Analytical program based on the Modified Compression Field

Theory).

Finally, Chapter 6 presents the conclusions of this thesis.

Appendix A contains the calculations for the predicted shear strengths from the

various approaches. The experimental data are present in Appendix B.

2. Review of related prediction models and code provisions

This chapter will discuss analytical models based on the Modified Compression

Field Theory (MCFT) [6]. In addition the code equations of the American Concrete

Institute (ACI) 3 1 8M-99 [l O] and a new analytical mode1 proposed by researchers

from the University of California, San Diego (UCSD) [ I l ] will be presented. Sample

calculations for predictions of column shear capacity using these modeIs and code

provisions are provided in Appendix A.

2.1. Modified Compression Field Theory (MCFT)

Figure 2.1 summarizes the equilibrium, compatibility and stress-strain

relationships used by the MCFT [6]. In the relationships, 0 is the angle between the

x - a i s , and the direction of the principal compressive average strain. Note that these

average strains are rneasured over base lengths that are greater than the crack spacing.

For specified applied loads, the angle 0, the average stresses and the average strains

c m be detennined by solving the given equilibrium equations in terms of average

stresses. the given compatibility equations in terms of average strains, and the given

average-stress average-strain relationships.

This section will describe the use of three models based on MCFT [6] to

predict the shear response of circular reinforced concrete columns: AASHTO-LRFD

[7] (American Association of State Highway and Transportation Officiais) Bridge

Design Specifications, Response-2000 [8] and TRIX-97 [9]. Figure 2.2 illustrates

these three MCFT models. A simple AASHTO-LRFD spreadsheet and Response-

2000 (including manual) are available for use from the World Wide Web at the

address of

http:/lwww.ecf.utoronto.ca/-bentdaashto-htm

&

htt~://www.ecf.utoronto.ca~-bentdr2k.htm

Average Stresses:

SbwseratC&:

p, f,, =/, + v cote + v* cote

p,, fv =4 + v îan0 - vd tinû

Allowabk S b a r S b n r on C m k :

Figure 2. 1 A summary of the relationship used in the Modilied Compression Field Theory

m - 9 7

Treak entire beam as array of biaxial eiements

MSHTOlFRO

Treats weô of beam as one b i d e(ernent

Figure 2.2 MCFf analysis of beams and columns

2.1.1. AASHTO LRFD

In the derivation of this method, just one biauial element within the web of

the section is considered and the shear stresses and angle 0 are assumed to remain

constant over the depth of the member (Figure 2.2).

The shear strength of a non-prestressed section containing at least the

minimum amount of transverse reinforcement can be express as Equation 2.1

where for a circula member the effective width, b ~ , can be taken as D and the

effective depth, d ~ , can be taken as 0.72D .

where A v is the area of the two legs of the hoop reinforcement.

The minimum amount of transverse reinforcement required is

Equation 2. 1

Equation 2.2

The vatues of P and 8 as s h o w in Figure 2.3 (at least the minimum

amount of transverse reinforcement) and Figure 2.4 (less than the minimum

amount of transverse reinforcement) depend on the longitudinal strain, E,, at mid

depth of the member shear stress on the member, v, given by

Equation 2 .3

The value of E, can be determined by performing a plane sections analysis

of the section subjected to moment MU, axial load Nu (tension positive,

compression negative) and equivalent tension Vucote.

As a simple hand calculation E, can be taken as half the strain in the

flexural tension chord of an equivalent tniss. Thus,

Equation 2.3

Where As is the area of longitudinal reinforcement on the flexural tension side of

the member. If the value of E, is negative then the stifkess of the concrete in

compression must be taken into account by replacing the term ASES by ASES +AcEc

where Ac is the area of concrete on the flexural tension side of the member.

Members containing less than minimum amount of transverse reinforcement have

less capacity for redistribution and hence, for such members the highest

longitudinal strain in the web should be used as E, and the term ASE ES replaced by

AsEs.

Shear causes tensile stresses in the longitudinal reinforcement as well as in

the transverse reinforcement. If a member contains an insufficient amount of

longitudinal reinforcement, its shear strength will be limited by the yielding of

this reinforcement. To avoid this type of failure, the longitudinal reinforcement

on the flexural tension side of the member should satisfy the following

requirement:

Mu A.& 2 - + 0.5 Nu + (Vu - 0.5Vs) CO^ 0

dv Equation 2.5

--------

tension side - -

Typkrl Section

Figure 2.3 Values of8 and f3 for sections contain at least tbe minimum amount of transverse reinforcement.

Figure 2. 4 Values of 0 and f3 for sections contain less than the minimum amount of transverse rein forcement.

This cornputer program was developed at the University of Toronto by

Evan Bentz 171 as a part of his Ph-D. research project supervised by Michael P.

Collins. This two-dimensional sectional analysis program for beams and columns

will calculate the strength and ductility of a reinforced concrete cross-section

subjected to shear. moment, and axial load (Figure 2.2). Al1 three loads are

considered simultaneously to find the full load-deformation response. Response-

2000 is able to calculate the strength of beams and coiumns with rectangular

sections as well as or better than traditional methods and, more importantly, is

able to make predictions of shear strengths for sections that cannot easily be

modeled by such traditional methods such as circular columns containing high-

strength reinforcement.

Response-2000 analyses sections subjected to axial load, moment and

shear. It also includes a method to integrate the sectional behaviour for simple

prismatic members. This program treats each cross-section as a stack of biaxial

element (figure 2.2). As stated by Evan Bentz [73 "The assumptions implicit in

the program are that plane sections remain plane, and that there is no transverse

clamping stress across the depth of the beam. For sections of a beam or column a

reasonable distance away fiom a support or point load, these are excellent

assumptions. These are the sarne locations in beams that are usually the critical

locations for brittle shear failures."

TRIX-97 is a non-Iinear finite element program based on the MCFT. This

program was developed by F.J. Vecchio. [9] at the University of Toronto. T m -

97 is the most complete implementation of MCFT and can analyse the complete

member. This program treats an entire bearn or column as an array of biaxiat

elements (Figure 2.2). In addition, this program c m treat both the "disturbed

regions" near the locations of point loads and supports and the "bearn regions"

which are about the depth of the beam away fiom such disturbances.

2.2. AC1 3181111-99 Code Equations

According to AC1 3 18M-99 [IO], the shear strength of a non-prestressed

section c m be calculated as

Vu = Vc + Vs Equation 2.6

For member subjected to axial compression, NU,

where Ag is the gross area of the section.

For members subjected to axiai tension,

Equation 2. 7

Equation 2.8

where NU is negative for tension.

In either case, the shear contribution of the transverse reinforcement, VS is given by:

Equation 2.9

For a circular member the web width? b ~ , can be taken as diameter, D, and

the depth, d, can be taken as 0.8D.

2.3. UCSD Shear model

Kowalsky and Priestley [ I 1) recently presented an "improved andytical

model" for the shear strength of circular reinforced concrete columns. In their

method

The concrete mechanism tenn VC is

Vc- = a b f i ( 0 . 8 4 ~ ~ )

The term a accounts for the column aspect ratio and is given by

Equation 2. 10

Equation 2. 11

M 1 S a = 3 - - 11 .5 Equation 2. 12

KD

The factor P accounts for the longitudinal reinforcement ratio (p) and given by

Equation 2. 13

The factor y accounts for the decrease in concrete shear resisting

mechanisms as the displacement of the column increases. Figure 2.5 shows the

value of y as a function of the displacement ductility. Figure 2.6 shows the value

of y as a function of the curvature ductility. Both figures are in term of uniaxial

ducti My.

Figure 2. 5 y vs. Displacement Ductility Figure 2.6 y vs. Cuwature Ductility

The contribution of the transverse reinforcement VS is taken as

Equation 2. t4

where c is the calculated depth of the compression zone under the axial

compression, P. and the moment, M, and cov is the concrete cover to the outside

of the longitudinal reinforcement. In the UCSD model, 0 is asswned to be 30".

The contribution of the axial compression Vp is taken as

Equation 2. 15

for axial compression and

vP = 0 Equation 2. 16

for axial tension. In Equation 2.15, L is the length o f the column fiom the critical

section to the point of contraflexure.

3. Experimental Program

3.1. Objective of the tests

Six circular reinforced concrete columns were tested under simulated lateral

loads (Fig 3.1). The key variables in the experimental study were the amount of

transverse reinforcement and the strength of the transverse reinforcement. The pitch

of the spiral controlled the amount of transverse reinforcement in each specimen. The

same longitudinal reinforcement was used for al1 six specimens and was designed to

be suficiently strong such that the al1 specirnens would fail in shear rather than

flexure.

Figure 3. 1 Loading simulated during test.

3.2. Test Apparatus

The test apparatus developed by Sadler Cl21 in 1978 was utilized for this

study. This rig provided a uniform transfer of shear into the end regions of the test

section of the specimen (Fig 3.2). Two steel yokes gripped the end blocks of the

specimen and applied the transverse load to the specimen. Twenty high strength bolts

threaded through the end blocks of the specimen and clarnped the specimen to the

loading yokes (Fig 3.2). These bolts were highly torqued, so as to provide enough

friction to prevent slip between the specimen and the yoke plates during application

of the transverse load.

The tests were performed in the Sanford Fleming Labotatory of the

Department of Civil Engineering at the University of Toronto. The transverse load

was applied by a 2700kN MTS testing machine. Figure 3.3 illustrates a bending

moment and shear force diagrams for test section. The orientation of the specimen,

the overall dimensions of the test rig, and the applied loads are illustrated in Figure

3.4. The MTS machine grips the clevises attached to the yokes and applies the load

(Fig 3 3).

Figure 3.2 Testing rig and specimen as positioned in M T S testing machine.

Dead Load

M=1255V

Bendirig M o m e n t ( k N - m m >

Figure 3.3 Moment and shear force diagrams for test section.

Figure 3 .5 Connection between the MTS machine and loading yoke

The self-weight of the specimen including the two loading yokes was 55kN.

To prevent this dead weight fiom causing a difference in moment at the two ends of

the specimen, a 30 ton double acting hydraulic jack with a 5 inch stroke supported

each end block (Fig. 3.6). This produced a constant shear across the test section of

the specimen (Fig 3.3). During the test the pressure supplied to these jacks was kept

constant so that the dead load of the rïg and the specimen "floated" on these jacks

which had sphencal bearings at the top and bottom of each jack. Thus, the bending

moment at the mid-length of the test section \vas maintained at a value of close to

zero.

Figure 3.6 Hydraulic jack supported the end block.

In order to strengthen the rectangular end blocks of the specimens they were

post-tensioned with four 1" D W D A G bars. A 60 ton hydraulic jack was used for

applying the pst-tensioning. Post-tensioning was applied just p ior to testing to

minirnize creep losses (Fig. 3.7). Each bar was stressed to a stress of 470 MPa which

generated approximately 3 MPa of compressive stress in the concrete of the end block

(560x6 1 Omrn). This increased the effective cracking strength of the end blocks and

hence reduced the chance of cracks developing in the end blocks when transverse

Ioad was applied to the specimen.

Figure 3.7 Post-tensioning the end blocks

3.3. Test specimens

A total of six columns were constructed and tested. These six specimens were

called the YJC series. One specimen (called YJCControl) contained no transverse

reinforcement. In the other specimens two different types of transverse reinforcement

wsre used. The name given to each specimen was assembled by a nurnber, which

espressed the pitch of the spiral in mm, and either the letter R (U.S.#3 reinforcing

bar) or W (%" diameter seven wire strand).

3.3.1. Geometric Properties

The exterior geometric dimensions and the longitudinal reinforcement of al1

specimens were identical (Fig. 3.8 and Fig. 3.9). The test section for al1 specimens

was 1670mm long and had a 445rnm diameter. Twelve 25M longitudinal bars were

placed symmetrically around the circumference and ran the entire length of specimen.

Figure 3.8 shows the typical cross-section of specimen. The test section c o ~ e c t e d

two end blocks, which were 56Ox610mm in cross-section. These end blocks were

heavily reinforced with 15M bars in both directions to avoid failure when transverse

load was applied to the specimen. The end blocks contained twenty 32mm diameter

PVC pipes to accommodate the 25mm diarneter high-strength bolts, which were

connected to the loading yokes. These PVC pipes were removed afier casting to

provide larger tolerances for the 25mm diameter high-strength bolts. In addition, four

38mm diameter PVC pipes were placed in the longitudinal direction of the end blocks

to allow for application of the post-tensioning. Figure 3.10 shows a typical

reinforcing cage for the test section and the end blocks.

Figure 3.8 Typical cross-section of specimen

For the transverse reinforcement, pre-fabricated U.S.ff3

spirals or !ha' diameter seven wire strand (SWS) were used. The

diameter for each specimen are listed in Table 3.1.

Table 3. t Transverse Reinforcement Detail

reinforcing

spiral pitch

bar

YJCControI YJC 1 OOR

I Measured inside-to-inside 2 SWS (Seven Wire Strand)

YJC 150R YJC2OOR YJCIOOW

Figure 3. 10 Typical reinforcing cage for the test specimens.

--- 1 -- U.S. Rr3 1 71 U.S. #3 US. #3 i / , SWS'

-- 100

7 1 7 1 23

3 75 35 25

150 200 100

375 375 375

25 25 28.2

3.3.2. Reinforcing Steel Properties

Since the main variables for this experimental program are the amount and

yield strength of the transverse reinforcement, identical longitudinal reinforcing

bars were used for al1 specimens. The longitudinal reinforcement consisted of

25M bars (area = 500mmz) with a yield strength of 459 MPa. The transverse

reinforcement consisted of either U.S.#3 bars (area = 71 mm') or %" diameter

seven vire strand (SWS) (area = 23 mm?). The spiral for the U S . #3 bars was

prefabricated while the spiral for the %" SWS was wound on the specimen by

hand. Properties of the reinforcing steel are listed in Table 3.2. Figure 3.1 1 and

3.12 give the typical stress-strain curves for the reinforcing steel.

Figure 3. 1 1 Typical stress-strain curves for regular reinforcement bars (25M & U.S.#3)

Figure 3. 12 Typical stress-strain curves for !hW Seven Wire Strand (SWS)

3.3.3. Concrete Properties

A local ready-mix plant supplied the concrete. On the arriva1 of the truck,

the slump of the concrete was checked and superplasticizer was added to the mix.

Pea grave1 aggregate with a maximum size of 1 Omm was used. Twelve standard

12" X 6" diarneter cylinders were cast for each specimen. Concrete properties of

the specimens are listed in Table 3.2. Figure 3.13 gives typical stress-strain

curves for the concretes used in constructing the different specimens.

Figure 3. 13 Stress-strain characteristics of concrete

Table 3. 2 Specimen Material Properties

1 SPECIMEN 1 CONCRETE ] LONGITUDMAL 1 TRANSVERSE REMFORCEMENT 1 PROPERTIES RECNFORCEMENT~

Y ield, 1 Ultimate, Size 1 Yield, [ Ultimate, 1 Avfy /Ds

I Longitudinal steel consists of 25M bars. (Area = 500mrn2) 3 S W S (Seven Wire Strand) * 0.2% Offset D = diameter of the colurnn (445mm) s = pitch o f spiral Es (SWS) = 303000 MPa Es (U.S.#3) = 223000 MPa Es (25M) = 183600 MPa

3.3.4. Construction

AI1 specimens were cast vertically as is the normal practice for reinforced

concrete columns (Fig 3.14). The reinforcing cage of the test section and the two

end block cages were produced individually. First, the cage of the test section

was transferred to a prefabricated steel form. Subsequently the end block cages

were transferred to the form. Finally the three cages were assembled together.

Once assembled the steel form was closed and ready for casting. It should be

noted that venting was incorporated into the design of the steel fomwork. This

allowed any trapped air to escape during casting of the specimens. During the

casting, a form vibrator and an immersion vibrator were used to ensure even

dispersion of the concrete mix in the formwork.

Figure 3. 14 Specimens were cast verîically

3.4. Specimen Instrumentation

The LVDT readings, steel strains, and applied loads were recorded continuously

during testing by means o f a data acquisition system and a microcornputer. A load

ce11 built into the MTS testing machine monitored the transverse load.

3.4.1 .Strain Gauges on Reinforcement

Reinforcement in the test section was instmented with strain gauges. Each

specimen contained 20 strain gauges (5rnm gauge length) on the longitudinal

reinforcing bars and 20 strain gauges (2mm gauge length) on the transverse

reinforcing bars. Shear failures were expected to occur in a region centred about

300rnm (effective depth, d, = 3 0 0 m ) frorn the edge of the test section. Transverse

strain gauges were placed at five different locations along the length of the test

section: 1 OOrnm, 400mm, 835mrn (middle of the test section), 1270mm, and 1 S70rnm

ftom the edge of the end blocks (Fig. 3.15).

Figure 3. 15 Locations of Strain gauges in reinforcement.

Four gauges were installed at each location, one on each quadrant, one north edge,

one south edge, one west edge, and one east edge, see Fig. 3.15, where north, south,

east and west refer to the orientation of the specimen during casting. Note that

because the specimen were cast in a vertical position but were tested in a horizontal

position during testing the north edge became the top edge while the West edge

becarne the south edge. In placing the strain gauges on the spiral reinforcement

account was taken of the fact that the four quadrants where the gauges were to be

installed were not located on the same vertical plane. Consequently, the four gauges

were placed at somewhat different distances along the test section of the specimen to

provide an average indication of the strain at one particular location. For example, for

specimen YJClOOR, at about lOOmm fiom the bottom edge of the test section, four

gauges were installed (one on each quadrant) at 80mm, 95mm, 120mrn, and 150rnm

from the edge of the test section.

Longitudinal strain gauges were placed at five different locations along the

length of the test section: Ornm, 417.5mm9 835mm (middle of the test section),

I252.5mm, and 1670rnm(edge of the test section) from the edge of the end block

(Fig. 3.15). These strain gauges were intended to capture the longitudinal strain

variation along the length of the test section. In each location, four gauges were

installed, one on each quadrant (See Fig. 3.15).

The locations of al1 the strain gauges on transverse and longitudinal

reinforcement are listed in Table 3.3.

Table 3.3 Strain Cauge Locations on Longitudinal Reinforcement and Transverse Reinforcement for al1 Specirnens

Strain Cauges on Longitudinal Reinforcement

NORTH Label of Strain Gauge N1 N2 N3 N4 NS

Distance from cdge (mm) O 4 17.5 83 5 1252.5 1670

EAST WEST Label of Strain Gauge El E2 €3 €4 E5

SOUTH Labei of Strain Gauge W1 W 2 W 3 W4 ,

WS

Distance from edge (mm) O 4 17.5 83 5 1252.5 1670

Label of Strain Gauge S 1 S2 S3 S4 S5

Distance from edge (mm) O 4 17.5 835 1252.5 1670

Distance fiorn edge (mm) O 4 17.5 835 1252.5 1670

Table 3.3 continued

Strain Gauges on Transverse Reinforcement

For YJC 1 OOR

For YJC 150R

NORTH Label o f 1 Distance

For YJC2OOR

EAST Label o f 1 Distance

NORTH

For YJC 1 O0 W

SOUTH Label of / Distance

Label of Strain Gauge NIS N2S N3 S N4S N5S

WEST Label o f 1 Distance

Distance from edge (mm) 155 460 770 123 O 1530

EAST

1 Strain 1 fiom edge 1 Strain 1 from edge 1 Strain 1 from edge 1 Strain 1 from edge 1

Label o f Strain Gauge EIS E2S E3S E4S E5S

NORTH

' NORTH 1 EAST SOUTH WEST

Distance frorn edge (mm) 1 12.5 422.5 882.5 1337.5 1487.5

SOUTH

Label of Strain Gauge NI S N2S N3S N4S N5S

EAST SOUTH

Label o f Strain Gauge SIS S2S S3S S4S S5S

WEST

Distance From edge (mm) 205 410 S 1s' 1220 1620

Label o f Strain Gauge EIS E2S E3S E4S E5S

Label o f Strain Gauge SIS S2S S3S S4S S5S

WEST

Label o f 1 Distance LabeI of 1 Distance ! Label o f 1 Distance

Distance from edge (mm) 80 380 83 5 1295 1595

Label o f Strain Gauge WIS W2S WjS W4S W5S

Distance from edge (mm) 165 3 70 780 1185 1585

Distance fiom edge (mm) 105 3 10 910 13 I O 1515

Label o f Strain Gauge WIS W2S W3S W4S W5S

Label o f 1 Distance

Distance fiom edge (mm) 192.5 347.5 807.5 1262.5 1 562.5

Distance fiom edge (mm) 60 465 8 10 1320 1630

Table 3.3 continued

For YJCSOO W

NORTH Label o f ( Distance

3.4.2. LVDT Lay-Out

Strain Gauge N I S N2S N3S N4S N5S

The specimens were instnimented with Linear Varying Displacement

Transfomers (LVDTs) to measure the specimen deformations. A total of nine

LVDTs were mounted. Six LVDTs, 3 sets of two, were used to measure the surface

shear strain deformation for al1 columns except YJC200R (where only four LVDTs

were used). Two LVDTs measured the displacernent of the end blocks with respect

to the test section to help in assessing yieid penetration of the tensile bars. One large

LVDT was used to measure the tangential deformation of one end of the specimen

with respect to the other end. Figure 3.16 shows the layout of the LVDTs.

EAST Label of 1 Distance

frorn edge (mm) 210 410 815 1210 1610

SOUTH Label of 1 Distance

WEST Label o f 1 Distance

Strain Gauge E1S E2S E3S E4S E5S

fiom edge (mm) 145 3 50 750 1345 1545

Strain , Gauge

S1S S2S S3 S S4S SSS

fiom edge (mm) I O5 500 900 1295 1490

Strain Gauge W1S W2S W3S W4S W5S

fiom edge (mm) 65 460 855 1255 1650

LVJT ARRANGEMENT - NORTH SIDE VIEW

Label of LVDTs

1 .E-TE-B W 2.E-TW-BE 3.C-TE-B W 4.C-TW-BE 5. W-TE-B VI 6.W-TW-BE 7.EH-TOP 8.WH-BOT

Figure 3. 16 Layout for LVDTs.

3.5. Test Procedure

The transverse load was applied in stages. At each load stage, the

displacement of the head of the MTS machine was held constant while the crack

widths were measured, and the crack patterns were photographically documented.

4. Experimental Observations

4.1. Introduction

In this chapter, the experimental observations made of the six specimens are

discussed. The main observations at each load stage are presented in tabular form. In

addition, load-deflection curves and crack patterns at selected load stages are

presented. Al1 the cracks pattern diagrams are presented from a South view of the test

arrangement. The specimens were aligned East-West during testing. During the test,

the top of the specimen (with respect to the direction of casting) was placed on the

East-Side of the testing arrangement and the bottom of the specimen faced the West-

Side of the testing arrangement for al1 the specimens except YJC200R which was

placed inverse to the direction of the other specimens due to a change in the test

arrangement.

As mentioned in the previous chapter, 5" stroke hydraulic jacks were used to

carry the dead load of the specimen. Once the displacement at one end of a specimen

reached about Y, the jacks had to be reset. To do this, the load on the whole system

had to be reduced to zero. In the load-deflection curves the unloading to zero and

reloading are shown.

To help observe and record the location and orientation of the cracks, a square

grid was marked on the surface of the specimens. The side lengths of each square - were originally 116.5mm which was one-twelfih of the circumference of the circular

specirnens.

As the purpose of this research was to investigate the shear capacity of

circular reinforced concrete colurnns, al1 specimens were loaded only with a pnmarily

monotonically increasing shear load until the peak capacity was reached. Two

specimens were loaded under revened loading after reaching their peak capacities.

The load history and shear strength of the six specimens are listed in Table 4.1.

For the specimens with reinforcing bar spirals, the loading was stopped

because the maximum displacement of the MTS loading machine as set for that test

was being approached. For the specimens reinforced with seven wire strands (S WS),

the final failures involved rupturing of the strand.

Table 4. 1 Load history and shear strength of six specimens r

Specimen

YJC IOOR YJC ISOR

YJC200R

Load History

Monotonic Monotonic then

YJCIOOW

4.2. Specimen YJC100R

Table 1.2 Test observations for Specimen YJCIOOR

Reverse-Direction Monotonic then

YJC20OW Y JCControl

Stage Force '"/,L,)

Monotonic Shear strength

W) 479 41 1

Reverse-Direction 1 Monotonic 1 433

Shear strength Reverse direction

OcN)

-175

3 23

--- Monotonie Monotonic

I 1

5 1 0.3 1 First flexural crack a ~ ~ e a r e d at both ends.

- 194

Tangential Displacement (mm)

3 15 213

23 1 1 -4 1 Previous cracks opened widely and extended. More cracks

-- -

Drift Ratio* (%)

Observations

Diagonal cracks fonned at both ends. New diagonal cracks appeared in regions 5-6 and 10- 1 1 . Previous cracks extended. More diagonal cracks appeared. Previous cracks extended.

10 13

18

increased. More cracks formed. Cracks in regions 3-6 and 10- 12 widening-

0.6 0.8

1 .O

29

3 8 1 2.3 1 Load curve more flat, although deformation was increased.

1.7

in al! regions. Additional cracks develokd in end blocks. S~ecirnen was assumed to have failed.

formed in the regions 5-7 and 8- 10. Load curve started to flatten and deformation was being

65 3 -9

102

Cracks more uniformly distributed. Load peaked and started to drop. Crack patterns uniform

145

1 1 curve is still riding on a plateau.

6.1

168

Drift ratio = Tangential displacement / Test length of the specimen Test length of the specimen = 1670mm

Specimen was unloaded and kept at zero for a half-hour. Hydraulic jack has been reset to zero stroke, then Ioad

8.7 increased. Crack pattern unifonn in al1 regions. Load curve got flat

10.1 and forrned a plateau. Concrete started to crush on bottom of regions 1-4. Load

YJC100R Force Vs Tangential displacement

Tangentid displacement (mm)

Figure 4.1 Load- deflection cuwe for YJCIOOR

Figure 4. 2 Specimen YJCIOOR before peak load at load stage 5 (Drift ratio = 1.4%)

Figure 4.3 Specimen YJCIOOR after peak load at load stage 9 (Drift ratio = 6.1%)

Figure 4 . 4 Specimen YJCIOOR removed from the MTS machine after testing

YJCl WR SOUTH V = 1SOkN

LOAD STAGE: 1 A = 5mm

LOAO STAGE: 2 A =10mm

YJClOOR SOUTH V = 3 0 0 k N

LOAD STAGE: 3 A =13mm

YJCl OOR SOUTH V = 350 kN

LOAD STAGE: 4 A = lamm

Figure 4.5 Crack patterns for YJCIOOR (LSI to LS4)

(Crack widths in mm)

u

YJClOOR SOUTH

LOAO STAGE: 5

u

YJC100R SOUTH

LOAO STAGE: 6

v

YJClOOR SOUW V = 460 kN


u

YJCl OOR SOUTH

LOAD STAGE: 8

Figure 4.6 Crack patterns for YJClûûR (LS5 to LS8)


YJCl WR SOUTH

LOAD STAGE: 9

u

YJC1 WR SOUTH

LOAD STAGE: 11

Figure 4.7 Crack patterns for YJCIOOR (LS9 and LSI 1)


4.3. Specimen YJCISOR

4.3.1. Monotonic load

Table 4 .3 Test observations for specimen YJClSOR

- - - 1 3 1 250 1 10 1 0.6 1 New cracks fonned and previous cracks extended. Load

Load Stage

1 2

defornation nearly linear. New diagonal crack developed in regions 5-7. Previous

Shear Force (W 150 200

cracks opened widely and extended. More diagonal cracks developed in regions 10- 13. Cracks

Previous cracks extended and widened. Regions 7-9 still uncracked. Slope of load-deflection curve flattens. Load peaked and started to drop while deformation was being increased. Cracks in regions 3-6 and IO- 12 opened widely. Specimen was assurned to have failed. Crack patterns uniform in al1 regions. After readings taken specimen unloaded to zero for one hour md jack reset to zero strokes.

Tangential Displacement (mm)

I

8 1 350 1 42 1 2.5 1 A large S shape diagonal cracks formed through the test

Drift Ratio* (%)

110 1260 1 IL10 f 8.3 ( More cracks developed and uniforrnly distributed. Load

Observations

1 1 1 stayed uniform while deformation increased. Drift ratio = Tangential displacement / Test length of the specimen

First flexural cracks appeared at both ends Previous cracks extended and became inclined.

4 6

I

Test length of the siecimen = 1670mm -

0.2 0.36

75 9

Figure 4. 8 Specimen YJCISOR before peak load at load stage 5 (Drift ratio = 1.1%)

300 4.5 section. Load dropped further although deformation was increased. Load curve formed plateau. More S shape diagonal cracks developed in 211 regions. New cracks appeared in al1 regions.

Figure 4. 9 Specimen YJCISOR alter peak load at load stage 9 (Drift ratio = 4.5%)

YJC15OR Force Vs Tangerrtial displacement

. - - -- - - - - -- - - - - -- -- -- --.

[ l--- - - -- - - - - - - - - 1- -- -- - -

O 20 40 60 80 100 120 140 160

Tangentid displicement (mm)

Figure 4. 10 Load- deflection curve for YJCl50R

. YJC1 SOR SOUTH

LOAD STAGE: 1

u

YJC1 SOR SOUTH

LOAO STAGE: 2 A =6mm

u YJCISOR SOUTH

LOAD STAGE: 3

u YJC150R SOUTH


Figure 4.11 Crack patterns for YJCISOR (LS1 to LS4)


u

YJCl SOR SOUTH

LOAD STAGE: 5

u

YJCl SOR SOUTH

LOAD STAGE: 6

LOAD STAGE: 7

YJC150R SOUTH

LOAD STAGE: g

Figure 4. 12 Crack patterns for YJCISOR (LSS to LS8)


YJC1 S R SOUTH V=300kN


LOAD STAGE: 10 A = 140 mm

Figure 4. 13 Crack patterns for YJCISOR (LS9 to LSIO)

(Crack widtbs in mm)

4.3.2. Reverse load

The 5" stroke hydraulic jacks were removed when the reverse load was applied.

The shear force listed in the table accounts for half of the dead load o f the specimen

which was 28kN. No strain gauge readings were taken.

Table 4.4 Test observations for Reverse load of specimen YJClSOR

Load Stage

O 1

7

I I top of regions 6-8. Most concrete cover popped out in al1 reoions. I

1

* Drift ratio = Tangential displacement / Test length of the specimen Test length of the specimen = l67Omm

;plled off on the bottom of regions 1-4.

YJCISOR L a d revened Force Vs Tangential dkplacement

Shear Force (W 19 -80

-145

Figure 4. 14 Load- deflection cuwe for YJCISOR (Reverse load)

Tangential Displacement (mm) 126 8

-40

Drift Ratio* (%) 7 3 0.48

-2.4

3 1 -175 , -64

Observations

Most of the previous cracks closcd New cracks appeared in al! regions. Large diagonal crack appeared at the mid-depth of the regions 5- 10. Previous cracks extended in both directions. Cracks patterns more uniform. Concrete cmshed and cover

-3.8 Extensive spalling of cover fiom bottom of regions 1-4 to

Figure 4. 15 Specimen YJClSOR Revenc load at load stage 2 (Drift ratio = -2.4%)

Figure 4. 16 Specimen YJClSOR Reverse load at load stage 3 (Drift ratio = -3.8%)

LOAD STAGE: 1 (Remme Laad) A = 8 m m

YJCl 50R S o m V = -145 kN

LOAD STAGE: 2 (Reverse Load) A =40rnm

YJC1 S R SOUTH V = -175kN

LOAD STAGE: 3 (Reverse Load) A =*mm

Figure 4. 17 Crack patterns for YJClSOR Reverse load (LSI to LS3)


4.4. Specimen YJCZOOR

4.4.1. Monotonie load

Table 4. 5 Test observations for specimen YJCZOOR

Load Stage

2 3

l l Cracks in regions 1-4 widened and developed as shear cracks. Afler readings taken specimen unloaded and jack

4

Shear Force

180 -- 333

Drift Ratio*

Tangential Displacement

23

5

(Peak 1 1 1 1 inçreased. New S ;hape diagonal cracks fonned in regions

Observations

6 9

6

13

3 O0

increased. Cracks uniformly distributed. Concrete crushed and cover spalled off on the bottom of regions 3-

0.36 0.54

3 23

Load) 7

1 1 J

* Drift ratio = Tangential displacement / Test Iength of the specirnen Test length of the specimen = l67Omrn

Previous cracks extended. New flexural cracks appeared in regions 8- 12. Previous

0.78

15

Figure 4. 18 Specimen YJC200R before peak load at load stage 4 (Drift ratio = 0.78%)

cracks extended and widened. No Eracks in region 4-8. One large diagonal crack developed in region 8-1 1.

18

368

0.9 reset to zero strokes. More diagonal cracks appeared in regions 8-1 3 and 1-4.

1.1

70

StilI no cracks in regions 4-8. Load started to drop although deformation was being

4 -2

- 6-12. Specimen was Gsumed to have failed. Load kept almost constant while deformation was

Figure 1. 19 Appearance of YJC2ûûR at end of test

YJCZOOR Force Vs Tangential displacement

O 10 20 30 40 50 60 70 80 90 1 M)

Tanganthl displacement (mm)

Figure 4.20 Load- deflection cuwe for YJC200R

u

YJC200R SOUTH

LOAD STAGE: 1

u

YJCÎOOR SOUTH

LOAO STAGE: 2

YJC200R SOUTH

LOAD STAGE: 3

u

YJC2ûûR SOUTH


Figure 4.2 1 C r a c k patterns for YJCZOOR (LS1 to LSJ)


YJC2WR SOüTH

LOAll STAGE: 5

u

YJCZOOR SOUM

LOAD STAGE: 6

u

YJC200R SOUTH

LOAD STAGE: 7

Figure 4.22 Crack patterns for YJC2OOR (LSS to LS7)


4.4.2. Reverse load

The hydraulic jacks were removed when the reverse load was applied. The shear

force listed in the table accounts for half of the dead load of the specimen which kvas

28kN. No strain gauge readings were taken.

Table 4.6 Test observations for Reverse load of specimen YJC2OOR

~an~ent ia l Observations 1 Displacernent 1 1 i 1 -129 1 -6 1 -0.48 1 New cracks appeared in al1 regions. Concrete crushed and 1 O

1 1 1 1 pattern more uniform. Concrete crushed and cover spalled 1

(kW 19

2

(mm) 50

- 194

3

* Drift ratio = Tmgential displacement / Test length of the specimen Test length of the specimen = 1670mm

4

Figure 4.23 Specimen YJC2OOR Reverse load at load stage 2 (Drift ratio = -2.4%)

(%) 3

40

180

Most of the previous cracks ciosed

200

-2.4

96 regions 1-81 r oit concrete cover popped out in an regions. At regions 6-9 (middle of the test section), most cover spalled off tiom the top to the bottom. Specimen still took more load. Loao-deflection curve is still riding on a

cover spalled off on the bottom of regions 3-8. Previous cracks extended in both directions. Cracks

5.7 off on the bottom of regions 1-4. Extensive spalling of cover fiom bonom to mid-depth of

Figure 4.24 Specimen YJC200R Re-loading at load stage 3 (Drift ratio = 5.7%)

YJCZOOR Load revemed Force Vs Tangential displacement

-- Tangmntial Dispiamant (mm)

Figure 4.25 Load- deflection curve for YJC200R (Reverse Load)

YJC200R SOUTH V = -129kN

LOAO STAGE: f (Reverse Load) A =-6 mm

YJCZOOR SOUTH V=200kN

LOAD STAGE: 4 (Re-Loading) A =180mm

YJCPWR SOUTH V = -194 kN

LOAD STAGE: 2 (Reverse Load) A =4Omm

LOAD STAGE: 3 (Re-Loading) A =96mm

Figure 4.26 Crack patterns for YJC200R Reverse lord (LS1 to LS4)


4.5. Specimen YJC100W. Table 4.7 Test observations for specimen YJClOOW

Stage

4

5 1 (Peak

Load)

6

7

8

9

1 O

1 1

Shear 1 Tangential 1 Drift 1 Observations 1

More diagonal cracks fomed at both sides. An S shaped diagonal crack formed from bottom of 1 to top of 9. Load-deflection curve started to flanen. More S shaped diagonal cracks formed. Still, not many cracks appeared at the middle of section. Specimen was assumed tg have

Force

150 250 3 O0

3 70

~is~lacement (mm) c 11 17

24

4 10

1 likely that some wires had broken. Load started to drop 1 although deformation was being increased. More diagonal

342

I * Drift ratio = Tangential displacement

Ratio* (%) 0.3 0.7 1 .O

1.4

54

cracks a ~ ~ e a r e d across entire section.

Some flexural cracks appeared at both ends. Diagonal cracks fomed in regions 4-7 and 10- 13. Previous flexunl cracks extended. More diagonal cracks appeared. No cracks formed in regions 7-9. Cracks in regions 4-8 and 9-1 3 extended and widened.

90

Concrete started crushing and wide S shape diagonal

3.2

cracks formed. Loaddeflection curve formed a plateau although deformation was being increased. After readings taken specimen unloaded to zero and jacks reset to zero

failed. Load started to drop. Cracks more uniformly disuibuted. Previous cracks extended. Afier readings taken specimen unloaded to zero and jack reset to zero strokes then load

5.4 continued to be applied. Small sharp sounds came from the specimen and it seemed

Test

500

180

220

Iength of the

175

192

200

specimen Test lenpth of the siecirnen 1 I670mm

10.5

10.8

12.0

strokes then load continued to be applied. Concrete crushed and cover spalled off in regions 1-1 1. Small sounds came out continuously. Broken wires still did not show up. Load dropped suddeniy with a loud bang fiom 3OOkN to 175kN. Some wires break and show up on the bonom of regions 2-5, which is in the tension zone. More concrete crushed and cover spalled off in most regions. Again, the load dropped suddeniy fiom 220kN to 100kN.

YJClWW Force Vs Tangential displacement

O 20 40 60 80 1 O0 120 140 1W 180 200

Tangmntial displacement (mm)

Figure 4.27 Load- deflection curve for YJCIOOW

Figure 4. 28 Specimen YJCIOOW before peak load at load stage 4 (Drift ratio = 1.4%)

Figure 1. 29 Specimen YJCIOOW alter peak load at load stage 10 (Drift ratio = 10.8%)

Figure 4.30 Seven wire strands had broken in tensioo zone

u YJCl W W SOUTH

LOAD STAGE: 1

LOAû STAGE: 2 A =il mm

u

YJClûûW SOUTH

LOAD STAGE: 3

u YJCl W W SOUTH

LOAD STAGE: 4

Figure 4.31 Crack patterns for YJCIOOW (LS1 to LS4)


I

YJClûûW SOUTH


YJClOOW SOUTH V = 410kN


YJClOOW SOUTH V = 342W


u

YJClûûW SOUTH

LOAD STAGE: 8 A =152 mm

Figure 4.32 Crack patterns for YJCIOOW (LSS to LS8)


YJCl WW SOUTH V=300kN


YJCI OOW SOUTH v = 180w


YJC1 OOW SOUTH V = 220 kN

LOAD STAGE: 1 1 A =2ûûmm

Figure 4.33 Crack patterns for YJC100W (LS9 to LSI 1)


4.6. Specirnen YJCZOOW Table 4.8 Test observations for specimen YJCtOOW

Load Stage

1 3 - 3 4

Drift Ratio* (%) 0.18 0.24

5

6

8 1 235 151 ( 3.1 1 Load dropped suddenly from 235kN IO 125kN with a very 1

Shear Force (kN) 1 O0 150

Observations

SrnaIl flexural cracks appeared. New flexural cracks formed.

200 725

Tangential Displacernent (mm) 3 4

250

3 O0 !

1 1 ( middle section. Again, wires break. 1 * Drift ratio = Tangential displacernent / Test length of the specimen

7 1 O

27 7 (Peak Load)

9

Test length of the specimen = 1670mm

12

20

3 15

Figure 4.34 Specimcn YJC200W before peak load at load stage 5 (Drift ratio = 0.72%)

0.32 0.6

1.6

170

- Diagonal cracks formed at both ends. Diagonal cracks formed in regions 9-1 3 and load dropped suddenlv. Previous cracks extended.

0.72 Large diagonal crack developed fiom bottom of region 1 I to top of region 9 with a bang. Load dropped suddenly

diagonal cracks developed: Specimen was assumed to have failed. Load started to drop.

1.2

82

form 25OkN to 2 1 OkN. Previous crack started to open more wideiy and more

4.9 loud bang. Wires break. Another big bang and load dropped fiom 170kN to 60kN. Concrete crushed and cover spalled off on bottorn of

Figure 4.35 Specimen YJC200W after peak load at load stage 9 @rift ratio = 4.9%)

YJCZOOW Force Vs Tangential displacement

Figure 4.36 Load- deflection cuwe for YJC2OOW

LOAD STAGE: 1

LOAD STAGE: 2 A = 4 m m

YJC200W SOUTH V = 2 0 0 W


J v

YJC2ûûW SOClTH

LOAD STAGE: 4

Figure 4.37 Crack patterns for YJC200W (LSI to LS4)


u YJC2WW SOUM

LOAD STAGE: 5

YJCZûûW SOUTH

LOAD STAGE: 6

.

u YJC2CûW SOUTH


YJCPWW SOUTH

LOAD STAGE: 6

Figure 4.38 Crack patterns for YJC2OOW (LS5 to LSS)


YJC2ûûW SOUM

LOAD STAGE: 9

Figure 4.39 Crack patteriis for YJCZOOW (LS9)


4.7. Specimen YJCControl

Table 4.9 Test observations for specimen YJCControl 7

1 3 1160 14 ( 0.24 1 No diagonal cracks. ~revio& Eiexural crack extend and

Load 1 Shear Stage ( Force

1 3 -

Tangential Displacement

(W 100 130

1 3 1 200

Drift Ratio*

(mm) 2 3

6 Load drop~ed suddenty fiom 2 13 kN to 1 14kN without bang while deformation was increased. Specimen was assurned to have failed. Diagonal cracks formed in

5 (Peak ! Load)

6

1 1 1 1 ( increased. Diagonal cracks extended to top of region

Observations

1 become sornewhat incl ined. 0.36 ! Flexural cracks more inciined.

7

(96) 0.12 0.18

213

90

Smali flexural cracks appeared at both ends. More tlexural cracks form.

7 5

1 8 1 69

Test length of the specimen = l6îOrnrn

8

23

1

Figure 4.40 Specimen YJCControl at the failure load (Drift ratio = 0.48%)

0.48

1 regions 1-8. -

1.4 1 Load dropped Further although deformation was being

48

7 7 regions 1 - 1 0. Still no diagon& crack appeared on bottom of regions 1 1 - 14. Load drop suddenly from 69kN to 40kN.

* Drift ratio = Tangential displacement / Test length of the specimen

2.9

4.6

increased. Load remained almost constant while deformation was

10- 1 3. ~oncrete started to be crushed. Concrete crushed and cover spalled off in rniddle of

Figure 4.41 Appearance of YJCControl at end of test (Drift ratio = 4.6%)

YJCConbol Force Vs Tangontirl displacement

-10 O 10 20 30 40 50 00 70 80 90

Tangontirl displacement (mm)

Figure 4. 42 Load- denection cuwe for YJControl

CONTROL S o m

LOAD STAGE: 1

u

CONTROL SOUTH

LOAD STAGE: 2

CONTROL SOUTH V=lsOl rN


CONTROL SOUTH

LOAD STAGE: 4

Figure 4.43 Crack patterns for YJCControl (LSI to LS4)


u CONTROL SOUTH


u CONTROL SOüTH


u CONTROL SOUTH

LOAD STAGE: 7 A = 48mm

CONTROL SOUTH V = 69 kN

LOAD STAGE: 8 A = n m m

Figure 4.44 Crack patterns for YJCControl (LSS to LS8)


4.8. Loaddeflection curves for six specimens

The observed load-deflection CUI-ves of ail six specimens are shown in Figure

4.45 and Figure 4.46. As would be expected, the addition of transverse reinforcernent

increased both the failure load and the post-peak ductility of the specimens.

For Specimens with U.S.#3 Force Vs Tangenthl displacernent

O 20 40 60 80 1 O0 120 140 160 180 200

Tangential dbplacament (mm)

Figure 4. 45 Load-deflection cuwes for spccimens with reinforcing bar spirals

For specimens with SWS Force Vs T angential displacement

O 20 40 60 80 100 120 140 160 180 200

Tangential displacement (mm)

Figure 4.16 Loaddeflection curves for specimens with high strength strand spiral5

5. Experimental and Analytical Results In this chapter the experimental resuits are discussed. In addition, shear strength

predictions for the test specimens using the analytical procedures contained in AASHTO-

LRFD [7]. TRIX97 [9] (Non-Linear Finite Element program based on MCFT), AC1

3 18M-99 [ l O] and University of Califomia, San Diego (UCSD) [ I l ] mode1 are compared

wïth the experimental results. Response 2000 [8] (Computer Software based on MCFT)

is used to predict the shear strengths, strains and the behavior of test specimens.

5.1. Ultimate Shear Strength

The ultimate shear strengths of the six specimens are sumrnarized in TableS. 1. It

is obvious that as the amount of transverse reinforcernent is increased, the shear

capacity of the specimens is also increased.

Table 5. 1 Experimental and prediction Shear Strengths of the specimens

-- - ~ -

* calculated using fi = IOOOMPa

In Figure 5.1, the shear strengths of the six specimens have been plotted against

the amount of transverse reinforcement. In addition, AAS HTO, Response2000, and

Specirnens

YJC l OOR YJCI SOR YJCîOOR YJClOOW Y 3 ~ 2 0 0 W

YJCControl

AC1 predictions were included in the same figure. For the three prediction models, an

UCSD OcN)

474 397 3 72

413* 3 18, 224

AASHTO (W

447 37 1 339 503 358 187

TRiX97 (kW

450 390 330 390 330 220

average concrete cylinder strength of 36 MPa was used. AASHTO and

Response 2000 (kW

457 3 73 33 1 462 339 176

AC 1 (kW

3 84 309 28 1 442 293 147

Av.Q/D.s

1.42 0.95 0.7 1 1.79 0.89

O

Response2000 assumed that the failure of the specimens occwred at 320mm

(Effective Depth (4) = 0.720 = 0.72*445 = 320mm) fiom the edge of the test section

Experimental (kN)

where the bending moment was equal to 0.51 SV ( M N = 0.5 1 Sm). A study of Fig.

' Monotonie

479 41 1 323 433 3 15 2 12

5.1 and Table 5.1 indicates that the three MCFT models (Response 2000, AASHTO

Reversed Loading -eV

182 200 ---

----- --

and TRIX97) predict the observed shear strength of the six specimens reasonably

well. As might be expected the most accurate estimates are made by TRIX97 with an

average value of experimentdpredicted of 1.02 and a coefficient of variation of

6.3%. Response 2000 has an average of 1-03 and a coefficient of variation of 10.4%

while AASHTO has an average of 1.00 and a coefficient of variation of 11.9%.

Response2000 overestimates the shear capacity by about 7% of the specimens

reinforced with the seven wire strand (SWS). A possible reason for this may be that

for the specimens with SWS spirals most of the concrete cover spafled off pnor to

failure. However, Response2000 assumes that the spalled concrete cover still carries

the load. The average difference between the actual shear strength of the specimens

with SWS and the Response2000 predicted values was reduced to 2% fiom 7% if the

concrete cover was ignored in the predictions.

The AC1 expressions typically underestimated the shear capacity of the specimens

with an average value of experimentdpredicted of 1.20 and a coefficient of variation

of 14.1%. The UCSD expressions, on the other hand. gave accurate estimates

(experimental/predicted = 0.98. coeficient of variation = 6.8%) after the suggested

limit of 1000 MPa was placed on the yield strength of the transverse reinforcement.

Specirnens with low transverse reinforcement ratios, especially YJCControl with

no transverse reinforcement, show noticeably higher shear failure compared to three

of the predictions (AASHTO, Response2000 and ACI). A possible reason for this

could be that the cracking strength of the concrete was higher than the assurned value

( 0 . f ) The shear strength of YJCControl (no transverse reinforcement) depends

totally on the cracking strength of concrete. The cracking strength of the concrete is

affected by many parameters such as the curing conditions of the specimen and this

may significantly affect the strength of mernbers with no transverse reinforcement.

The specimens containing seven wire strand spirals were less stiff than specimens

with U.S.#3 bar spirals and had wider cracks. For instance, at V=300 kN, YJC lOOR

had an average crack width of 0.20mm while YJC100W had 0.29mm. Moreover,

YJC100W had a larger deformation. It was observed that the shear strength for the

specimens with SWS spirals is lower than comparable specirnens with reinforcing bar

spirals (e-g. YJC 1 OOR and YJC 1 OOW), although the transverse reinforcement ratio

(Av.fyA2.s) is higher. A possible reason for this could be that the failure of the

specimens would occur by the crushing and slipping of concrete due to the wide

cracks and the larger deformations. The final failures of specimens reinforced with

S WS involved the rupture of the strands.

After specimens YJC I SOR and YJCZOOR reached the peak load, the specimens

were untoaded and then the load was reversed. For the reversed loading of YJC200R,

the load reached about 194kN (drift ratio = 3%) for the first reverse loading and still

reached 200kN (drift ratio=IO%) when the Ioad was reversed once more.

Shear strength Vs Quantity of transverse reinforcement

O 1 O 0.05 O. 1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

Quantity of transverse reinforcement AvlDs (96)

Figure 5. 1 Relationship between shear strength and amount o f transverse reinforcement predicted by ACI, AASHTO and Response2000.

5.2. Transverse Strains

Transverse strains were measured using strain gauges attached to the transverse

reinforcement. Some of the strain gauges were darnaged during the casting of the

specimens and hence not al1 strain locations were available. Three sets of plots

showing values of transverse strain have been prepared.

5.2.1. Strain distribution around the spirals

The first set of plots shows the transverse strain distributions around the

circurnference of the spiral. Strain distributions at five different locations

(1 OOrnm, 400mm, 835mm(middle of test section), 1270mm and 1507mm from the

edge of test section) for each specirnen are shown in the Figures 5.2 through 5.6.

The spirals in the specimens with U.S.#3 bar showed yielding in critical regions

well before failure, while the spirals in the specimen with SWS were not detected

to yield by the strain gauges. Although SWS spirals did not record yield strain

pnor to the peak load, the SWS spirals had higher strains than the #3 bar spirals in

comparable specimens. For exarnple, at V = 300kN, the average mid-depth strain

at the critical section for YJCIOOW was 2506pe, while for YJClOOR, it was

168 1 pe. This may be the reason that the specimens with SWS spirals were less

stiff (larger deformations) than the specirnens with #3 bars spirals. As mentioned,

the SWS had a yield strain four times larger than U.S.#3 bars. For YJC 1 OOW, the

highest strain recorded was only 43% of the yield strain (E, = 8510ps). The

patterns of strain distribution between the two different spirals are very similar to

each other. For the regions at 400mm and 1270mm from the edge o f the test

section (the critical section = 320mm), it is observed that strains (U.S.#3) at mid-

depth (North Side (NS) and South Side (SS)) started yielding at earlier load

stages. Strains (U.S.#3) from the Top and Bottom did not start yielding until the

failure of the specimen. For the spirals with SWS, the strains at the mid-depth

(NS and SS) were higher than the strains from the Top and Bottom. For a region

835mm from the edge (middle of test section), the strains were observed to be

generally higher at mid-depth (SS and NS) as compared to the Top and Bonom of

the specimen. For the regions lOOmm and 1570mm from the edge of the test

section (high moment region), the four strains (NS, SS, Top and Bottom) are more

or less uniform. For the most part, the four strains did not reach the yield strain

until failure happened.

5.2.2. Variation of the spiral strain along the test length

The second set of strains plotted in Figures 5.7 through 5.1 1 shows the

variation of the transverse strain at the mid-depth ( N S and SS) of the test section

along the test length. The average of the NS and SS strains were used. It was

observed that the spirals had higher strains at 4 0 0 m and 1270mm fiom the edge

of the test section as expected. For the specirnens with U.S.#3 bars, the strains in

these regions reached the yield strain at earlier load stages. However the strains

from 1 OOmm, 835mm(middle of the section) and 1570mm from the edge did not

reach the yieid strain until failure happened. For the specimens with SWS. none

of the spirals yield was recorded to until the specimen failed. It should be noted

that in these specimens the strands ruptured after the peak load was attained and

hence very high strains did eventually develop in the spirals.

5.2.3. Variation of transverse strain with shear force

The third set of strains plotted in Figure 5.12 show the variation of

transverse strain in al1 specimens at the mid-depth of the test section (NS and SS)

with increasing applied load. The strains at the mid-depth have been plotted for

the locations at 400mm and 1270mm frorn edge of the test section. On the same

plot, transverse strains predicted by Response2000 [8] are also given. It is

observed that Response2000 predicts the strains reasonably well for al1 of

specimens.

5.3. Shear strains

The shear strains were measured using Linear Variable Di fferential

Transducers (LVDTs) attached on the surface of the test section. The variation of

shear strain with applied shear load is shown in Figure 5.13. The shear strains at

4 2 5 m and 1245mm from che edge of the test section were plotted. (The plot for

YJCZOOR is based on location at 225mm and 1445mm from the edge of the test

section.) Again, it was observed that Response2000 predicts the strains with

reasonabl y accuracy.

5.4. Longitudinal strains

Longitudinal strains were measured with strain gauges attached to the

longitudinal reinforcement. Figures 5.14 through 5.19 show the longitudinal strain

variations of the four strains ( N S , SS, Top and Bottom) fiom five diflerent sections

(Omm, 4I 7.5mm, 835mm, 1252Smm and 1670mm fiom the edge). Strains of the

Top and Bottom were higher than the strains of the NS and SS. In most specimens,

strains did not reach the yield strain (f,, = 459 MPa) until afier peak load except at the

edge of the test section (Omm aïid 1670rnm from the edge of the specimen). Figures

5.20 and 5.25 show the longitudinal strain distribution dong the length of the test

section. Strains from the Top (tensile strain) were used for the sections -835mm and

-4 1 7.5rnm. Strains from the Bottom (tensile strain) were used for section 4 1 7.Smm

and 835mrn. At the middle of the specirnen (Omm), the average strains of the Top

and Bottom were used. Longitudinal strains increased from the middle of the test

section to the edge of the test section as the bending moments increased. Figure 5.25

shows the actual measured longitudinal strains at the measured failure load and the

longitudinal strains predicted by Response2000 at the predicted failure loads. The

Iongitudinai strains at 41 7.5mm and 1252.5mm from the edge of the test section were

plotted. It was observed that Response2000 predicts the strains reasonably weli for al1

the specimens.

. r , ; t l 1 1 :;

100mm from edge of the test section

V = 150

.e V 250

-6- V = 300 -*- V = 350 - Va400 * -V n 432

-.*- V c 460

- v = 479 - Yield

,- -- > -. . -500 O 500 1000 1500 2000 2500

Strain Guaga Reading (microstrain)

4OOrnrn fiom d g s of the test sbctlon

-2000 O 2000 4000 8000 8000

Stnin Gauge Reading (mlcrortnln)

- V = 150 ' -.-V = 250

-.-v=300 *V = 350 -0-v 400 -0- V m 432

- - V u 460 - V u 4 7 8 - neld

-500 O 500 1000 1500 2000 2500

Stnin Gaugo Reading (mlcrartnin)

i/,! ::' ! ,* 1270m from edge of the test section

Stnin Guige Reading (micrortraln)

1 l . l , q d ,';<, 1 ' .


100mm h m eâge of t h test section

Figure 5.2 Strain distribution along spiral at difirent load stages for YJCIOOR

Strain Gurge Reading (mlcroatnln)

.,1 \ . < ,,,J!\ (. . a > t c

lOOmm fiom the edge of the test section

r-- -----r-- - - . ..-- - , . . ..--..-.l--.l-l -500 O 500 1OOO 1500 2000 2500

Slrrln Gui* Reading (microstrrln)

4OOmm ftom the aigo of the test section

Figure S. 5 Strain distribution almg spiral at diffcrcnt load stages for YJClOOW

'if , J ~ I :)>'<I,.'~U 1OOmm from edge of the test sectfon

-2000 O 2000 4000 6000 8000

Stnln Guage Reading (micrortrrln)

-2000 O 2000 4000 rn 8000 10000 Stnin G I J ~ ~ O Rerdlng (micrortnln)

L

(1 i ion *

\ \ \ l l , / 1 , '11


1 1- - - . - - - y - - . _ _ , _ .- - . , . . . . - . - .. . , - -- - . . . . . , - -. - . . . - -

- 2000 O 2000 4000 eooo Bo00 I , 10000

Slriin Gurge Rsrdlng (mlcrostnin)

-.-V 3 IO0

- m - V a 150 -.- V = 200 +- V = 225 -a- V = 250 0 - V u 300

- - V a 315 - Yield

Figure 5.6 Strain distribution along spiral at differcnt load stages for YJC2OOW

Transverse strain variation along the section for YJC1 OOR

length

...-

of test

- . . -

+v = 150 - c V = 250

- e V = 300 +V = 350 +V = 400 +V = 432 -V = 460

- Yield A

-900 -700 -500 -300 -100 100 300 500 700 900

-1000 - - - - - - - - -- - - - - - . -- - - - - - - - - - - - -

Distance from Specimen Centre Line (mm)

Figure 5. 7 Variation of the transverse strain at the mid-depth along the length for YJCIOOR

Transverse strain variation along the length of test section for YJCISOR

-900 -700 -500 -300 -100 100 300 500 700 900 -500 - . -

Distance from Specimen Centre Line (mm)

Figure 5.8 Variation of the transverse strain at the mid-depth a

+V= 250 * V = 300 +V = 350

+V= 390 +V=411

- Yield

ong the length for YJCISOR

Transverse strain variation along the length of test yJ@@~R section for YJCZOOR

+-v = 120 - c V = 180

+V=225

+ v = 2 6 4

+V = 300 + V = 323. - Yield - '

-900 -700 -500 -300 -100 100 300 500 700 900

-500 - Distance from Specimen Centre Line (mm)

Figure 5.9 Variation of the transverse strain at the mid-depth along the length for YJC200R

Transverse strain variation along the length of test yyJ@j@$'$$' section for YJC100W

Distance from Smcimen Centre Line (mm)

-.-

+ V = 150

+V = 250

+V=300

-+t-V= 370

+ v = 433

+ Yield

Figure 5. 10 Variation o f the transverse strain at the mid-depth along the length for YJClOOW

Transverse strain variation along the length of test VJw&fj section for YJCZOOW

Distance from Specimen Centre line (mm)

-v = 100 +v= 150 +v = 200 + V = 225 +V = 250 +v = 300' +V = 315 - Yield

Figure 5. 1 I Variation of the transverse strain at the mid-depth along the length for YJC200W

O O O O O O O O Z "

L/: 'Y.

, dT \, 3 - S c -

+. - - > - z -- - *- -:

L <- a - a '. .&' 4 - -

L -, - - ,- - CI , . u

Longitudinal strain distribution along the length fo , l M % i ~ ~ YJC1 OOR

Tq

t V = 250 t V = 300 +V = 350

- t V = 4 3 2 -V = 460

.900 -700 -500 -300 -100 100 300 5 0 0 700 900

Distance from the Centre of Test Section

Figure 5. 20 Longitudinal strain distribution along the length for YJCIOOR

VJG41m8 Longitudinal strain distribution along the length for

---

+ V = 1501

+v = 200

+V = 250

-.eV = 300 -+V= 350 +-V = 390 -V=411

- Y ield -.


Figure 5. 21 Longitudinal strain distribution along the length for YJCISOR

Tj'JrnB Longitudinal strain distribution along the length for

+V = 120 + V = 180 +V = 225 +V = 264

- V = 300 + V = 323 - Yield

-900 -700 -500 -300 -100 100 300 500 700 900


Figure 5. 22 Longitudinal strain distribution along the length for YJC200R

Longitudinal strain distribution along the length for yJtj$rn

C .- E 2000

3i = 1500 c .- = tooo

-900 -700 -500 -300 -100 IO0 300 500 700 900


+ V = 150

+V = 250

-a-V = 300 +-V = 370

+v = 433 - Yield

Figure 5. 23 Longitudinal strain distribution along the length for YJCIOOW

Longitudinal Strain (microstrain) Longitudinal Strain (microstrain)

6. Conclusions The results obtained in this investigation indicate that the shear strength for circular

members predicted from Response2000, AASHTO, and TRIX97 (al1 based on the

Modified Compression Field Theory) are reasonably accurate. The shear strengths

predicted by the AC1 code are more conservative and have somewhat more scatter. The

UCSD (University of California, San Diego) mode1 provides much more consistent

estimates of the shear capacity of the members than the AC1 code expressions.

Predictions from Response 2000 overestimated somewhat the shear strength for the

specimens reinforced with high strength seven wire strands (SWS). A possible reason for

this may be that for the specimens with SWS most of the concrete cover spalled off pnor

to failure.

The shear strength of the specimens with regular reinforcing bar spirals was higher

than the shear strength of the comparable specimens with SWS although the specimen

with S WS contained a larger amount of transverse reinforcement (Av.fy/D.s). Specimens

with SWS were less stiff and had wider cracks. In addition, the SWS specimens had

larger tangential deforrnations compared to the specimens with regular reinforcing bar.

Detailed strain analyses showed that the spirals from specimens with S WS had higher

strain than the spirals with reinforcing bar. In the critical region, the strains from the

reçular reinforcing bar spirals at mid-depth of the test section started yielding pnor to

failure. The Top and the Bottom strains of the test section were below yield until failure

occurred. SWS spirals did not reach the yield strain until afier failure. For YJClOOW,

the highest transverse strain in the critical region reached only 43% of the yield strain.

Response2000 predicted the transverse reinforcement strains and shear strains reasonably

well, right up to failure.

In most regions of the test section, longitudinal strains did not reach the yield strain

until specimen failure, except at the extreme edge of the test section. Longitudinal strains

increased from the middle of the test section (M=O) to the edge of the test section

(M=835V) as the bending moment increased. Response2000 predicted the longitudinal

strains reasonably well for ail specimens.

It may be concluded that the Modified Compression Field Theory (MCFT)

models are capable o f accurately predicting the shear strengths and the deformations o f

circular reinforced concrete colurnns reinforced with high strength seven wire strands and

regular reinforcing bars.

Faradji, M.J., and Diaz de Cassio, R., "Diagonal Tension in Concrete Members of Circular Section" (in Spanish), Ingenieria, Mexico, April 1965, pp. 257-280. (Translation by Portland Cement Assoc., Foreign titerature Study No. 466)

Aregawi, M., "An Expenmental Investigation of Circular Reinforced Concrete Bearns in Shear", M.A.Sc. Thesis, Depanment of Civil Engineering, University of Toronto, 1974.

Khali fa, J. U. and Collins, M.P., "Circular Reinforced Concrete Members Subjected to Shear", Publication 8 1-08, Department of Civil Engineering, University of Toronto, Dec. 198 1.

Ang, B.G., Priestley, M.J.N. and Paulay, T., "Seismic Shear Strength of Circular Reinforced Concrete Columns", AC1 Structural Journal, Vol. 86, No. 1, 1989, pp. 45- 59.

Wong, Y.L., Paulay, T. and Priestley. M.J.N., "Response of Circular Reinforced Concrete Colurnns to Multi-Directional Seismic Attack, AC1 Structural Journal, Vol. 90, No. 2, 1993, pp.180-191.

Vecchio, F.J., and Collins. M.P., "The Modified Compression Field Theory for Reinforced Concrete Elements Subjected to Shear", AC1 Structural Journal, Vol. 83, No. 2, 1986, pp. 2 19-33 1.

"AASHTO L W D Bridge Design Specifications", Second Edition 1998 with ZOO0 updates. Amencan Association of State Highway and Transportation Oficials, Washington. IW8, 109 1 pp.

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

Vecchio, F.J., c'Nonlinear Finite Element Analysis of Reinforced Concrete Membranes", AC1 Structural Journal, Vol. 86, No. 1, 1989, pp. 25-35.

10. AC1 Cornmittee 3 18, "Building Code Requirements for Structural Concrete (3 18-99) and Commentary (3 18R-99)", American Concrete Institute, Detroit, 1999, 3 19pp.

1 1. Kowalsky, M.J., and Priestley, M.J.N., 'Tmproved Analytical Mode1 for Shear Strength of Circular Reinforced Concrete Colurnns in Seismic Regions", AC1 Structural Journal, Vol. 97, No. 3,2000, pp. 388-396.

12. Sadler. C., "lnvestigating Shear Design Criteria for Prestressed Concrete Girders", M. A.Sc. Thesis, Department of Civil Engineering, University of Toronto, 1978.

13. Priestley, M.J.N., and Budek, A.M., "Improved Analyticai Mode1 for Shear Strength of Circuiar Reinforced Concrete Columns in Seismic Regions", Private Communication, San Diego, Juiy 2000.

14. Tanabe, T., "Discussion about the Collapse of the Piers of Hanshin Expressway No. Y. Communication to the Concrete Committee of the Japan Society of Civil Engineering, Nagoya, 1995, 13 pp.

1 5 . CSA Committee A23.3, "Design of Concrete Structures: Structures (Design), Canadian Standard Association, Rexdale, 1 994, pp. 37-38.

Calculation of AASHTO-LRFD, AC1 3 18M-99 and UCSD Mode1 Predictions

Estimation of Shear Failure Load Using AASHTO-LRFD

For the spreadsheet AASHTO-LRFD (http://www.ecf.utoronto.ca/-bentz/aashto.htm)

Sample Calculation for Specimen YJC200R

Concrete Strength ( f~ ' ) = 40.4 MPa Yield Strength of Transverse Reinforcing bars (fy) = 445 MPa Area of Transverse Reinforcing bars (A") = 71 mm' Diameter (D) = 445 mm Effective Width ( b ~ ) = D = 445 mm EMective Depth ( d ~ ) = 0.72D = 0.72 x 445 = 320.4 mm Pitch of Spiral (s) = 200 mm

From Equation 2.1

Assume a value for the strain in longitudinal reinforcement, cx and select valuesB for

and 8 from Figure 2.3.

Assume E, 5 0.00025 and v/fc' 1 0.75 From Figure 2.3, f3 = 2.94 and 0 = 26.6"

Check the strzin in longitudinal reinforcement The critical section is taken effective depth ( d ~ ) away from the appiied load where the moment to shear ratio is 0.5 15m and Axial force (NU) is zero.

The strain in longitudinal reinforcement (E,) is calculated as Equation 2.4 AS = 500x6 = 3000mm" ES = 183600 MPa

.-.This indicates that our assurnption was unconservative. We must choose a bigger value for E,.

Second Iteration

Assume E, 5 0.0005 and v/fc9 1 0.75 From Figure 2.3, P = 2.59 and 0 = 30.5"

Check the strain in longitudinal reinforcement

MU / d,. + OSNU + OSVU cot 0 0.5 15x368300 / 320.4 + 0 .5~368300~ cot 30.5 Er = - -

2 AsEr 2~500~6~183600

:.This indicates that our assumption was unconservative. We must choose a bigger value for E,.

Third Interation

Assume E, I 0.00075 and v/&' 1 0.75 From Figure 2.38, P = 2.38 and 9 = 33.7"

Check the strain in Iongitudinal reinforcement

This indicates that our third assumption was a bit conservative. However, we can use this value as a shear capacity of the member when we design this member practically. Vu = 332.1 kN -

In this research, linear interpolation was used in selecting P and 0 fiom Figure 2.3 for more accurate value for shear capacity. The result is as follows.


:. Therefore prediction by the AASHTO-LRFD is VU = 339 kN

Estimation of Sbear Failure Load Using AASHTO-LFWD

For the spreadsheet AASHTO-LRFD (http://www.ecf.utoronto.ca~-bentz/aashto-htm)

Sample Calculation for Specimen YJC 15OR

Concrete Strength (fc') = 36.0 MPa Y ield Strength of Transverse Reinforcing bars (fy) = 445 MPa Area of Transverse Reinforcing bars (A") = 71 mm' Diameter (D) = 445 mm Effective Width (bV) = D = 445 mm Effective Depth (dv) = 0.72D = 0.72 x 445 = 320.4 mm Pitch of Spiral (s) = 150 mm

From Equation 2.1

Assume a value for the strain in longitudinal reinforcement, E, and select vaiuesp for and 8 From Figure 2.3.

Assume E, 2 0.00075 and v/fci 1 0.75 From Figure 2.3, P = 2.38 and 0 = 33.7"

+ Check the strain in longitudinal reinforcement The criticat section is taken effective depth ( d ~ ) away from the applied load where the moment to shear ratio is 0.5 1 Sm and Axial force (NU) is zero.

The strain in longitudinal reinforcernent (E,) is calculated as Equation 2.4 AS = 500x6 = 3000mm2 ES = 1 83600 MPa

= 0.0008 2 0.00075

:. This indicates that our assumption was unconservative. We must choose a bigger value for E,.

Second Iteration

Assume E, I 0.00 1 and v/fci 10.75 From Figure 2.3, P = 2.23 and 8 = 36.4"


v/fcg = Vu / bvdvfc' = 342000/(445~320.4~36.0) = 0.0666 I 0.075 (0 .K)

This indicates that our third assumption was a bit conservative. However we can use this value as a shear capacity of the member when we design this member practicaily. VU = 342 kN -

In this research, linear interpolation was used in selecting P and 8 fiom Figure 2.3 for more accurate value for shear capacity. The result is as follows.


:. Therefore prediction by the AASHTO-LRFD is VU = 371 IrN

Summarv of calculations for s~ecimen in YJC series

* ~ o t e chat the specimen YJCControl used the Figure 2.4 to find the value of p and 8.

For spreadsheet AASHTO-LRFD (htt~://www.ecf.utoronto.c&benWaashto.htm~

Estimation of Shear Failure Load Using AC1 318M-99

Sample Calculation for Specimen YJC 1 SOR

Concrete Strength ( f~' ) = 36.0 MPa Yield Strength of Transverse Reinforcing bars (fy) = 445 MPa Area of Transverse Reinforcing bars (Av) = 7 1 mm2 Diameter (D) = 445 mm Effective Width (bv) = D = 445 mm Effective Depth (dv) = 0.8D = 0.8 x 445 = 356 mm Pitch of Spiral (s) = 150 mm

From Equation 2.7 NU = O (no axial load)

From Equation 2.9

From Equation 2.6

Vu=Vc+V\ =I58630+149970

Therefore prediction by the AC1 code is VU = 309 kN

Estimation of Shear Failure Load Using UCSD

Sample Calculation for S~ecimen YJC 150R

Concrete Strength (fc') = 36.0 MPa Yield Strength of Transverse Reinforcing bars (fy) = 445 MPa Area of Transverse Reinforcing bars (Av) = 71 mm' Diarneter (D) = 445 mm Effective Width (bv) = D = 445 mm Pitch of Spiral (s) = 150 mm Longitudinal reinforcement ratio (p) = 0.0386 Gross section area Ag = 155449.6 mm' Length (L) = 835 mm (for single curvature)

From Equation 2.12 (accounts for the column aspect ratio) M = 0.835V (for maximum moment) M N D = 0.835V/0.445V = 1.876

From Equation 2.13 (accounts for the longitudinal reinforcement ratio) p = AS / Ag = (1 2x500) /(3.14~(445/2)~) = 0.03856 = 3.856%

From Figure 2.4 (curvature ductility)

:.y = 0.29 (Shear capacity is larger than flexural capacity)

From Equation 2.1 1 (concrete shear strength)

From Equation 2.14 (transverse reinforcement shear strength) c = I50mrn (distance fiom Neutral-Axis to surface of the column)

From Equation 3.10 Vp = O (no axial load)

Therefore prediction by the UCSD is VU = 397 IcN

Experimental Data

The following pages contain the measured longitudinal reinforcement strains

and transverse reinforcement strains. The LVDTs outputs are also presented and

expressed in mm. Al1 reported strains are expressed in microstrain (FE). Tensile

strains are positive. Strains are identified by the names of the strain gauge and

LVDT.

Table B. 1 Table B.2 Table B.3 Table B.4 Table B.5 Table B.6 Table B.7 Table B.8 Table B.9 Table B.10 Table B. 1 1 Table B.12 Table B.13 Table B.14 Table B. 15 Table B. 16 Table B.17

Longitudinal Reinforcement Strain for YJC IOOR Transverse Reinforcement Strain for YJC 1 OOR LVDTs Reading for YJC 1 OOR Longitudinal Reinforcement Strain for YJC 1 SOR Transverse Reinforcernent Strain for YJC 1 SOR LVDTs Reading for YJC1 SOR Longitudinal Reinforcement Strain for YJC200R Transverse Reinforcement Strain for YJC200R LVDTs Reading for YJC2OOR Longitudinal Reinforcement Strain for YJC 1 OOW Transverse Reinforcement Strain for YJC 100W LVDTs Reading for YJC 100 W Longitudinal Reinforcement Strain for YJC200W Transverse Reinforcement Strain for YJC200W LVDTs Reading for YJC200W Longitudinal Reinforcement Strain for YJCControl LVDTs Reading for YJCControl

Table B.1 Specimen YJCIOOR Longitudinal Reinforcernent Strains

Table 8.2 Specimen YJCIOOR Transverse Reinforcernent Strains

Table 8.4 Specirnen YJCISOR Longitudinal Reinforcement Strains

Table B.5 Specimen YJCISOR Transverse Reinforcement Strains

Table B.6 Specimen YJCISOR LVDTs Readings

Table 8.9 Specimen YJCZOOR LVDTs Readings

Table 6.1 1 Specimen YJClOOW Transverse Reinforcement Strains

Table BA2 Specirnen YJ LVDTs Readings

CIOOW

Table 8.13 Specimen YJC2OOW Longitudinal Reinforcement Strains

Table B.14 Specimen YJC2OOW Transverse Reinforcement Strains

Table 8.1 5 Specimen YJC2OOW LVDTs Readings

Table B.46 Specimen YJCControf Longitudinal Reinforcement Strains

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