Shear Resistance of High Strength Concrete I-Beams with ... · Shear Resistance of High Strength...

Shear Resistance of High Strength Concrete I-Beams with Large Shear Reinforcement Ratios

by

Roger Yuan Xu

A thesis submitted in conformity with the requirements for the degree of

Master of Applied Science

Graduate Department of Civil Engineering

University of Toronto

© Roger Yuan Xu 2012

Shear Resistance of High Strength Concrete I-Beams with Large

Shear Reinforcement Ratios

Roger Yuan Xu

Master of Applied Science, 2011

Graduate Department of Civil Engineering University of Toronto

Abstract

Experiments were performed to examine the shear resistance of heavily reinforced I-beams. Six I-beams

with identical cross sections were constructed using high strength self-consolidating concrete, and were

tested under monotonic anti-symmetric loading. All specimens had almost the same amount of

longitudinal reinforcement, which provided sufficient flexural capacities. There were two variables: shear

span and shear reinforcement ratio.

Test results showed that ACI code was too conservative in predicting the shear strengths of heavily shear

reinforced I-beams, and the shear strength limit for deep beams should be increased to account for the

benefit of high strength concrete. However, doubling the amount of stirrups did not improve the ultimate

shear resistance much. The three beams that contained around 2.45% stirrups showed over-reinforced

shear failures. Longitudinal flange cracking occurred to every specimen due to lack of cross tie

reinforcement in the flanges, and it was believed to have reduced the ultimate shear strength.

ii

Acknowledgments

I would like to express my deepest gratitude to my supervisors, Professor M. P. Collins and

Professor E. C. Bentz. They granted me with this valuable opportunity to step into my desired

field of study. Within the past two years, I have benefited tremendously from their inspiring ideas,

insightful comments, and constant encouragements. I have been and will always be greatly

influenced by their enthusiasm and professionalism.

I thank every staff member in the Structures Laboratory. Renzo J. Basset, John MacDonald, and

Xiaoming Sun have pointed out many mistakes I made and given me numerous constructive

suggestions throughout my experiments, I have learned a lot from their expertise. Giovanni

Buzzeo and Joel Babbin taught me on using every tool I needed in the lab, and they always

showed kindness and patience even when I bothered them during their coffee breaks.

I also appreciate Innocon for supporting this research by supplying the concrete at a discounted

price.

I am grateful to my friends and colleagues: Paolo Calvi, Loreto Caprara, Andrew Cheung, Cyrille

Dunant, David Johnson, Robert Netopilik, Stephen Perkins, David Ruggiero, Min Sun, and

Liping Xie. Without their generous help, the success of this project would be impossible. I

especially thank Dr. Boyan Mihaylov, who not only helped me many times in the lab, but also

taught me lots of valuable knowledge and skills.

Finally, I want to dedicate this thesis to my parents.

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Table of Contents

1 Introduction 1

1.1 Motivation of Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Current Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2 Experimental Programme 6

2.1 Specimen Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.1.1 Specimen Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.1.2 Specimen Dimensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.1.3 Reinforcement Layout . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2.1.4 Formwork . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

2.2 Material Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

2.2.1 Concrete . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

2.2.2 Reinforcement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

2.3 Test Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

2.4 Instrumentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

2.4.1 LVDTs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

2.4.2 Clinometers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

2.4.3 Zurich Targets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

2.4.4 Strain Gauges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

2.4.5 Optical Scanner and LEDs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

2.5 Test Arrangement and Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

3 Experimental Observation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

3.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

3.2 Specimen Behavior . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

3.2.1 L1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

3.2.2 L2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

3.2.3 M1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

3.2.4 M2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

3.2.5 S1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

iv

3.2.6 S2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

4 Evaluation of Test Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

4.1 LVDT Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

4.1.1 Deflection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

4.1.2 Shear Strain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

4.2 Strain Gauge Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

4.2.1 Longitudinal Strains . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

4.2.2 Transverse Strains . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

4.3 Zurich Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

4.3.1 L1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

4.3.2 L2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

4.3.3 M1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

4.3.4 M2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

4.3.5 S1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

4.3.6 S2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

4.4 Clinometer Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

5 Comparison of Experimental and Analytical Results. . . . . . . . . . . . . . . . . . . . . . . . . . . 70

5.1 ACI Code . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

5.2 CSA Code . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

5.3 Predicted Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

6 Conclusions and Recommendations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

6.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

6.2 Recommendations for Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

A Material Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

B Method for Estimating the Vertical Displacement . . . . . . . . . . . . . . . . . . . . . . . . . . 82

C Test Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

v

List of Tables

2.1 Specified Dimensions of Beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2.2 As-built Dimensions of Beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2.3 Concrete Compressive Strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

2.4 Reinforcement Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

2.5 Shear Forces at the End of Each Load Stage (kN) . . . . . . . . . . . . . . . . . . . . . . . 37

3.1 Summary of Test Results for Beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

5.1 Shear Strength Predictions (kN) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

vi

List of Figures

1.1 Shear Strength as a Function of ρt fyt/ fc′ (Lee and Hwang, 2010) . . . . . . . . . . . . . . . . 3

2.1 Sample View of the Specimen Geometry, Loading Condition, and Deflected Shape. . .6

2.2 Specified Cross Sectional Dimensions for the I-section of Each Beam (units: mm) . . .8

2.3 Longitudinal Dimensions, Shear Force Diagram, and Bending Moment Diagram for

Group L Beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.4 Longitudinal Dimensions, Shear Force Diagram, and Bending Moment Diagram for

Group M (Left) and Group S (Right) Beams . . . . . . . . . . . . . . . . . . . . . . . . . . .10

2.5 Reinforcement Details at the Cross Sections for All Specimens . . . . . . . . . . . . . . . . 14

2.6 Typical Upper and Lower Reinforcement Cages . . . . . . . . . . . . . . . . . . . . . . . . 15

2.7 Reinforcement Cages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

2.8 Dimensions and Reinforcement Details for L1 . . . . . . . . . . . . . . . . . . . . . . . 17

2.9 Dimensions and Reinforcement Details for L2 . . . . . . . . . . . . . . . . . . . . . . . 18

2.10 Dimensions and Reinforcement Details for M1 and M2 . . . . . . . . . . . . . . . . . 19

2.11 Dimensions and Reinforcement Details for S1 and S2 . . . . . . . . . . . . . . . . . . 20

2.12 Formwork containing all Reinforcement Cages . . . . . . . . . . . . . . . . . . . . . . 21

2.13 Selected Pictures of Styrofoams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

2.14 Stress Strain Relationship of One Cylinder Sample . . . . . . . . . . . . . . . . . . . . 24

2.15 Stress Strain Relationships of Reinforcement Steel (10M & 25M) . . . . . . . . . . . 25

2.15 Stress Strain Relationships of Reinforcement Steel (Dywidag & D4) . . . . . . . . . 26

2.17 Illustration of Loading Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

2.18 Typical Test Setup (M1) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

2.19 Arrangements of LVDTs and Clinometers . . . . . . . . . . . . . . . . . . . . . . . . 30

2.20 Arrangement of Zurich Targets for L1 and L2 . . . . . . . . . . . . . . . . . . . . . . 31

2.21 Arrangement of Zurich Targets for M1, M2, S1 and S2 . . . . . . . . . . . . . . . 32

2.22 Strain Gauge Layout for L1 and L2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

2.23 Strain Gauge Layout for M1, M2, S1 and S2 . . . . . . . . . . . . . . . . . . . . . . 34

2.24 Arrangement of LED Targets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

vii

viii

3.1 L1 Crack Diagrams for Selected Load Stages . . . . . . . . . . . . . . . . . . . . . . 41

3.2 L1 after Failure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

3.3 L2 Crack Diagrams for Selected Load Stages . . . . . . . . . . . . . . . . . . . . . . 43

3.4 L2 during Failure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

3.5 L2 after Failure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

3.6 M1 Crack Diagrams for Selected Load Stages . . . . . . . . . . . . . . . . . . . . . . 45

3.7 M1 after Failure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

3.8 M2 Crack Diagrams for Selected Load Stages . . . . . . . . . . . . . . . . . . . . . . 47

3.9 M2 during Failure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

3.10 M2 after Failure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

3.11 S1 Crack Diagrams for Selected Load Stages . . . . . . . . . . . . . . . . . . . . . . 49

3.12 S1 after Failure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

3.13 S2 Crack Diagrams for Selected Load Stages . . . . . . . . . . . . . . . . . . . . . . 51

3.14 S2 after Failure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

4.1 Deflections of Beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

4.2 Shear Force vs. Shear Strain (L1, M1, M2, and S1) . . . . . . . . . . . . . . . . . . 56

4.3 Shear Force vs. Shear Strain (S2) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

4.4 Longitudinal Strain (L1 and L2) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

4.5 Longitudinal Strain (M1, M2 and S1) . . . . . . . . . . . . . . . . . . . . . . . . . . 59

4.6 Longitudinal Strain (S2) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

4.7 Transverse Strain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

4.8 L1 Zurich Strains and Web Deformations at Selected Load Stages . . . . . . . . . . 63

4.9 L2 Zurich Strains and Web Deformations at Selected Load Stages . . . . . . . . . . 64

4.10 M1 Zurich Strains and Web Deformations at Selected Load Stages . . . . . . . . . . 65

4.11 M2 Zurich Strains and Web Deformations at Selected Load Stages . . . . . . . . . . 66

4.12 S1 Zurich Strains and Web Deformations at Selected Load Stages . . . . . . . . . . 67

4.13 S2 Zurich Strains and Web Deformations at Selected Load Stages . . . . . . . . . . 67

4.14 Inclinations at West Reaction Support . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

CHAPTER 1

Introduction

1.1 Motivations of Study As high strength concrete became more widely used nowadays, many studies were also performed on

examining the shear behavior of high strength reinforced concrete members. While high strength concrete

can certainly bring up the shear strength, its brittleness also increases compare to normal strength concrete.

With a stronger interface between the cement paste and the aggregate, the failure surface of high strength

concrete is smoother and thus lead to a weaker post-cracking shear resistance due to less aggregate

interlock (Cladera and Mari, 2005). Therefore, to re-evaluate the failure shear strength, most of the

previous studies involved testing members with either no shear reinforcement or minimum of shear

reinforcement. Not many tests, however, have been done in the past on high strength concrete beams that

are heavily reinforced in shear. While brittle failure that occurs due to lack of shear reinforcement is

dangerous, it is also believed that having too much stirrups can cause sudden shear failure when the

concrete crushes before stirrups yield (Lee and Hwang, 2010). Therefore, each of the two major concrete

design codes in North America: CSA A23.3-04 and ACI 318-08, imposes a shear strength upper limit that

is governed only by the concrete strength and the sectional geometry of a member.

In CSA A23.3-04, the shear design equations for reinforced concrete members with no prestress and axial

load are given below (units: mm/N):

Vc = 'β cf vwdb Where 'cf 8 MPa,

Vs = θcots

dfA vytv

Vn = Vc + Vs 0.25fc′ (1-1) vwdb

In ACI 318-08, the shear design equations for members with no prestress and axial load are given below

(units: in/lb):

Vc = (1.9 'cf +2500 wu

u

M

dV) dbw 3.5 'cf dbw (1-2)

Where 'cf 100 psi,

1

Vs = s

dfA ytv 8 'cf dbw (1-3)

For deep beams, Clause 11.7.3 states that:

Vn = Vc + Vs 10 'cf dbw (1-4)

As shown above, Eq. (1-1) and Eq. (1-4) set the shear strength upper limits for CSA A23.3-04 and ACI

318-08 respectively. Different from the CSA code, besides having a limit on the total shear resistance,

ACI also specifies the maximum shear that can be carried by the concrete and the stirrups separately, as

shown by Eq. (1-2) and Eq. (1-3).

Although previous research has shown that the shear provisions in ACI 318-08 is dangerously

unconservative for predicting members without stirrups (Collins et al. 2008), for members that already

contain more than minimum transverse reinforcements, however, it may be too conservative when

compared to CSA A23.3-04. Comparing the shear strength upper limits specified by both design codes, it

can be seen that they give similar results for low strength concrete, but for high strength concrete

structures, Eq. (1-4) from ACI results in much lower predictions than Eq. (1-1) from CSA, which is

expected since the controlling parameter in Eq. (1-4) is 'cf rather than fc′. An important issue with the

current ACI shear provisions is that they were developed based on the experimental data in the 1950’s and

1960’s (Xie, L. 2009) when the use of high strength concrete was very limited at that time. Hence, the

maximum value of Vn set by Eq. (1-4) was meant to apply for low strength and normal strength concrete

structures only (Russo et al, 2009). When applying to members constructed with high strength concrete,

Eq. (1-4) may become inadequate in predicting the actual shear capacity. Because the term 'cf could

significantly underestimate the shear that can be carried by transverse reinforcements, since stirrups

become more effective as the concrete strength increases (Cladera and Mari, 2005). Studies have also

shown that the shear strength of concrete beams could be increased further by putting more stirrups than

that allowed by Eq. (1-3) in ACI 318-08 (Lee and Hwang, 2010).

Lee and Hwang defined that a beam is under-reinforced in shear if the contribution of shear reinforcement

(ρt fyt) is less than the effective strength of concrete (vfc′), and the failure is triggered by yielding of the

shear reinforcement before crushing the concrete. When a beam is over-reinforced in shear, ρt fyt is greater

than vfc′, and failure occurs by web concrete crushing rather than yielding of shear reinforcement (Lee

and Hwang, 2010). In CSA A23.3-04, this reduction factor v is defined to be 0.25.

In the experiments done by Lee and Hwang, the shear behaviors of 18 RC beams were investigated. The

specimens were divided into four groups that differed by geometries and concrete strengths ranging from

2

26MPa to 84MPa, and the beams within each group had different shear reinforcement ratios ranging from

0.2% to 3%. All of their specimens failed after yielding of the stirrups despite some of the beams had

more than twice the maximum amount of shear reinforcement allowed by the ACI code, and the shear

strengths of these beams were also more than twice the values predicted by Eq. (1-4). The results from

Lee and Hwang’s experiments are summarized in Figure 1.1. It can be seen in Figure 1.1 that as the

concrete strength increases, the difference on the maximum allowed shear reinforcement ratio between

ACI and CSA also becomes greater, and some heavily shear reinforced specimens have reached strengths

far beyond the limit specified by Eq. (1-4).

Figure 1.1: Shear Strength as a Function of ρt fyt/ fc′ (Lee and Hwang, 2010)

(a) fc′ = 26.8MPa, (b) fc′ = 37.2MPa, (c) fc′ = 63MPa, (d) fc′ = 84.6MPa. The vertical lines in each

graph represent ρ t-max allowed by each code.

Besides testing the 18 RC beams, Lee and Hwang have also reviewed the failure mode of 178 RC beams

reported in a number of literatures. Based on all these results, they suggest that the maximum shear

reinforcement ratio can be as high as 0.2 fc′/ fyt before over-reinforced shear failure occurs, and the

maximum shear reinforcement limit in ACI 318-08 should be increased to account for high strength

concrete.

Although the research done by Lee and Hwang involved varying concrete strengths and shear

reinforcement ratios, all of their specimens had solid rectangular cross-sections, same shear span to depth

3

ratio (a/d = 3), and were tested under simply supported loading condition. Hence, their study is not

adequate to determine if ACI318-08 is also conservative for predicting the shear strengths of beams with

different geometry and loading conditions.

Compare to solid rectangular cross-section, beams constructed with I-sections can save materials and

have much less weight while maintaining most of the flexural capacity. This makes I-section a common

geometry used in many structural concrete members, such as transfer girders. However, one weakness of

I-beam is the significantly reduced shear strength, depending on the web width. To make I-section

structures not shear critical, the web shear reinforcement ratio is often expected to be much higher than

that of solid rectangular members. Therefore, the limit on maximum shear reinforcement ratio in

ACI318-08 could have a more negative influence on the application of I-section members in structures

that need to resist large shear forces. Although widely used in constructions, I-section is not preferred in

laboratory research for being much harder and more time consuming to build compare to solid rectangular

section. Thus, few experiments were conducted in the past with I-section specimens, and more data is

definitely needed to examine their shear behaviors.

The maximum shear reinforcement ratio suggested by Lee and Hwang is a function of fyt and fc′ only. It is

determined statistically based on the observed failure modes of 178 beams reported in previous literatures

and the 18 beams from their own experiment. However, one parameter that Lee and Hwang did not

include in their study was the shear span to depth ratio, which could have a large effect on the maximum

shear reinforcement ratio since stirrups become less effective as a/d ratio decreases. In the case of deep

beams when a/d is less than 2, shear transfers through arch action and the shear resistance will depend

primarily on the compressive strength of concrete. Transverse reinforcement has little influence on shear

strength except minimizing cracks widths and reducing deformations (Tuchscherer et al, 2011). Therefore

it is also necessary to have more experimental data on heavily shear reinforced beams covering a large

range of shear span to depth ratios.

Increasing the amount of shear reinforcement will make the structure more congested, which may become

a problem when casting the concrete. To ensure adequate consolidation in highly congested structures that

can not be easily reached by external vibrators, self-consolidating concrete is often used instead of normal

concrete because of its high fluidity. Compare to normal concrete, SCC has smaller amount of coarse

aggregates in order to achieve its workability. This fact will result in SCC having smoother cracked planes,

which can reduce the shear resistance of a member due to less aggregate interlock. Researches have

shown that with the same maximum coarse aggregate size, SCC that has lower coarse aggregate content

shows lower post-cracking shear resistance than normal concrete. By increasing the coarse aggregate size

from 12mm to 19mm, the pre-cracking strength of an SCC beam has decreased, but its ultimate shear

4

resistance has increased (Lachemi et al, 2005). Other studies had compared the shear performances of

SCC and conventional concrete on prestressed I-beams with varying a/d ratios. These beams were tested

under simply supported loading, and it was found that for concrete having the same compressive strength,

beams constructed with SCC had lower post-cracking stiffness and about 10% reduction in ultimate shear

resistance (Choulli et al, 2008). However, none of the past studies involved performing experiments on

SCC members that were heavily reinforced in shear.

1.2 Current Study This study will focus on some parameters that were not considered in experiments done in the past. The

shear behaviors of heavily reinforced I-beams constructed with high strength SCC will be examined. The

variables will be the transverse reinforcement ratio and the shear span-to-depth ratio. The primary

objective of this project is to show if using high strength concrete and more stirrups can bring up the shear

resistance of I-section beams above the upper limit specified by ACI 318-08. It is also expect to find out

what the maximum shear reinforcement ratio will be for the I-section beams before causing any

over-reinforced shear failures.

5

CHAPTER 2

Experimental Programme

2.1 Specimen Description

2.1.1 Specimen Design

This experimental Program involved destructive testing of six thin web I-section beams. Since the

objective was to study the shear behavior of these specimens, the loading condition was designed to

minimize the ratio of M/V so that shear strength would not be affected much by the flexural moment. This

was achieved through the anti-symmetric loading condition, which was used only among 8% of all past

shear tests (Collins et al., 2008). The anti-symmetric loading would result in a large shear force and zero

moment at mid-span of the beam. Therefore, the middle portion of a beam would be its test region. The

specimens and loading condition were designed as shown in Figure 2.1 below, which also includes the

expected deflected shape:

Figure 2.1: Sample View of the Specimen Geometry, Loading Condition, and Deflected Shape

The numerical labels in the Figure 2.1 indicate the following:

Region 1: This is the inner I-section located at the middle of each beam. It is also the test region where the

shear failure is expected to occur. The deflected shape of this region is expected to always have

double curvatures and a point of inflection at mid span.

Region 2: These are the two diaphragms that have the same width as the flanges and same thickness as the

6

load bearing plate. Instead of having a continuous I-section from Region 1 to 3, building two

diaphragms in between would prevent the flanges from collapsing under the two point loads P1.

Region 3: These are the two outer I-sections that have exactly the same cross sectional dimensions as

region 1, except they will always have more stirrups in order to ensure a much higher shear

resistance than the test region.

Region 4: These are the two solid rectangular blocks at the ends of each specimen that have the same

width as the flanges. There is also a 45o transition zone between region 3 and 4.

Note that for the rest of this thesis, phrases such as “shear force”, “reinforcement ratio”, “cracks”, etc.

all refer to the test region only, unless otherwise specified. The self weights of the specimens are

sufficiently small and thus will be ignored in all measurements and calculations.

The six beams were to be tested under the same loading condition. They were designed to have the same

cross sections but two different shear reinforcement ratios and three different shear span-to- depth ratios.

The longitudinal dimensions and reinforcement layouts were specifically chosen so that each beam would

fail in shear at its inner I-section. Details of beam geometries and reinforcements will be presented in

Section 2.12 and Section 2.13.

Ready-mixed self-consolidating concrete (SCC) with a specified 90-day strength of 70MPa was used for

designing all specimens. The actual concrete strength during the tests ranged between 86MPa and 88MPa,

which were typical for high strength concrete.

The name of each specimen was given by two characters that starting with a capital letter and ending with

a single digit number. The letter gives a qualitative description of the shear span-to-depth ratio, and the

number indicates the amount of shear reinforcement. For example: “M2” is the beam that has Medium

length (or Medium a/d ratio) and 2 times the amount of shear reinforcement allowed by ACI 318-08.

2.1.2 Specimen Dimensions

All six beams were designed with exactly the same cross sections. The specified height was h = 590 mm

and the width was bftop = bftop = 385 mm. The specified web thickness was bw = 80 mm. The only

geometric differences between the six beams were in the longitudinal dimensions. The beams were

divided into three groups with different lengths. Group L were the longest beams that had a shear span of

2220 mm. Group M were the medium length beams, and they had a shear span of 1278 mm. Group S

were the shortest beams with a shear span of 620 mm. The widths of load bearings were kept at a constant

of 150 mm for all beams, hence the thickness of all diaphragms was also 150 mm. The specified cross

7

sectional dimensions for the I-section part of each beam are shown in Figure 2.2.

Figure 2.2: Specified Cross Sectional Dimensions for the I-section of Each Beam (units: mm)

The specified longitudinal dimensions of Group L beams and their corresponding shear force and bending

moment diagrams are shown in Figure 2.3, and the ones for the other two groups are shown in Figure 2.4.

All shear force and bending moment diagrams are drawn by assuming the shear force in the test region

has a magnitude of V. Since every beam is symmetric about the mid-span, some of the dimensions are

only labeled on one half of the beam.

The specified dimensions of all beams are shown in Table 2.1. The as-built dimensions are shown in

Table 2.2 and were used in Chapter 5 for calculating the shear strength predictions using ACI and CSA

code.

8

L =

605

0

a =

222

0

V

1480

1162

525 67

8

150

2070

435

PW =

0.7

5VP E

= 1

.75V

RW =

1.7

5VR

E = 0

.75V

0.75

V0.

75V

S.F

.D (

kN)

B.M

.D (

kN*m

)

1.11

V

1.11

V

435

150

Fig

ure

2.3

: L

ongi

tud

inal

Dim

ensi

ons,

Sh

ear

For

ce D

iagr

am, a

nd

Ben

din

g M

omen

t D

iagr

am f

or G

rou

p L

Bea

ms

9

L =

358

2L

= 2

320

RW =

1.7

5VR

E = 0

.75V

PW =

0.7

5VPE

= 1

.75V

852

a =

127

8

150

608

317 46

911

28 V

0.75

VS

.F.D

(kN

)

B.M

.D (

kN*m

)

0.63

9V

0.75

V

0.63

9V

RE =

0.5

64V

PW =

0.5

64V

150

470

215 36

840

8

RW =

1.5

64V

PE =

1.5

64V

a =

620

550

V

S.F

.D (

kN)

B.M

.D (

kN*m

)

0.56

4V0.

564V

0.31

V

0.31

V

Fig

ure

2.4

: L

ongi

tud

inal

Dim

ensi

ons,

Sh

ear

For

ce D

iagr

am, a

nd

Ben

din

g M

omen

t D

iagr

am f

or G

rou

p M

(L

eft)

an

d G

rou

p S

(R

igh

t) B

eam

s

300

300

300

300

10

Table 2.1 Specified Dimensions of Beams

Specimen L1 L2 M1 M2 S1 S2

h (mm) 590

hftop (mm)

hftop (mm) 65

bftop (mm)

bfbot (mm) 385

bw (mm) 80

hw (mm) 390

d (mm) 551

As-top (mm2)

As-bot (mm2) 3150 3350 3050

Av (mm2) 100

s 101 51 101 51 101 51

ρy = Av / bws 1.238% 2.45% 1.238% 2.45% 1.238% 2.45%

ρy fyv (MPa) 5.57 11.03 5.57 11.03 5.57 11.03

Table 2.2 As-built Dimensions of Beams

Specimen L1 L2 M1 M2 S1 S2

h (mm) 592 594 592 591 590 592

hftop (mm) 68 69 67 68 67 66

hfbot (mm) 67 68 65 64 67 67

bftop (mm) 386 392 387 390 386 386

bfbot (mm) 387 388 385 388 386 385

bw (mm) 81 85 79 83 80 81

hw (mm) 391 392 391 391 390 391

d (mm) 551*

As-top (mm2)

As-bot (mm2) 3150 3350 3050

Av (mm2) 100

s 100 50 100 50 100 50

ρy = Av / bws

†

1.235% 2.35% 1.266% 2.41% 1.250% 2.48%

ρ f (MPa) 6.05 11.53 6.20 11.81 6.13 12.17 y yv

*) The as-built value of d for each beam could not be accurately determined since it depended on the

distance between the two layers of longitudinal reinforcements, and this distance could have large

variations depending on the stirrup lengths and the how tight the longitudinal rebars were tied to the

stirrups. For every beam, the position of top longitudinal reinforcement layer was lower than specified

11

due to self weight. Furthermore, even within the same reinforcement layer, every rebar had a different

height than others. While the specimen depths measured from the top surface to bottom rebar layer were

close to 551 mm, the ones measured from the bottom surface to top rebar layer were as many as 5 to 10

mm less than the specified value. For consistency, d will be taken as the specified value of 551 mm in all

calculations since it will give close approximations in predicted shear strength.

†) According to the as-built dimensions, every beam had a different shear reinforcement ratio, which was

very close to the specified value. Hence, for the ease of discussions, unless speaking about a particular

specimen, the specified shear reinforcement ratio shown in Table 2.1 will be used when referring to

several beams together.

2.1.3 Reinforcement Layout

The six specimens were designed to have two different transverse reinforcement ratios. Within each group,

one beam had the maximum amount of shear reinforcement allowed by ACI 318-08, and the other one

had twice the amount as the first beam. These ratios were initially calculated based on a specified concrete

strength of 70 MPa and stirrup yield strength of 450 MPa. Using the specified cross sectional dimensions

shown in Table 2.1, the maximum shear reinforcement ratio given by ACI 318-08 was 1.238%, which

was the quantity used when constructing the specimens. With a web width of 80 mm, the cross section of

every beam had only one single leg 10M stirrup in order to maintain adequate clear cover. The spacing of

stirrups for the specified 1.238% shear reinforcement was 101 mm, and the spacing was 51 mm for

doubling the amount of stirrups. The stirrups were more closely spaced in the outer I-sections of each

beam to ensure that the shear failure would first occur in the test region. In order to bring up the shear

reinforcement ratio, lots of stirrups were also put in the end blocks of each beam although they have much

higher shear resistance than the I-section parts. Stirrups at the two end blocks were scattered across the

entire width, and their spacing along each longitudinal bar was twice of that in the test region. The

reinforcement layout of every beam was symmetrical about the mid-span.

The longitudinal reinforcements in the two flanges of each beam were designed to provide sufficient

flexural capacity to prevent flexural failure from occurring before the beam fails in shear. The longitudinal

reinforcements for group M and group S beams were identical, which consisted of six 25M deformed bars

in each flange. Stronger longitudinal rebars were used for group L beams as they would be subjected to

higher bending moments. For specimen L1, each reinforcement layer contained four 25M deformed bars

and two 1″ Dywidag bars, which had specified yield strength of 800 MPa. For L2, six 1″ Dywidag bars

were used in each flange. A 10M longitudinal bar was put at the mid-height of each beam on the south

side of the stirrups to provide better crack control.

12

To hold together the six rebars within each layer of longitudinal reinforcements during caging, cross ties

were used for every beam. Since the reinforcement cages were very dense due to the high reinforcement

ratio in both longitudinal and transverse directions, small D4 wires were chosen for the cross ties and only

a few of them were placed at the two flanges in order to allow better flow of concrete during casting and

to maintain sufficient clear cover. This decision was later proved to be very mistaken, since the few

amount of cross ties were not able to reinforce the flanges from longitudinal splitting. This issue will be

discussed in detail in the next chapters.

The reinforcement details for the cross sections of each beam are shown in Figure 2.5, and the full

reinforcement drawings are shown from Figure 2.8 to Figure 2.11 that include both side view and top

view of the reinforcement layout. The top view shows the positions of D4 wires and also the detailed

arrangements of stirrups in the end blocks. Stirrups are also drawn to scale in the top view of every beam

instead of being represented by a single line.

The reinforcement cage for each beam was constructed separately in two parts. The upper part was a “T”

shaped cage that included the top layer of six longitudinal rebars, web stirrups, and one longitudinal bar at

the bottom that hang on the stirrups. The stirrups were always tied to the third longitudinal bar from south

side of the beam. The lower part of reinforcement cage contained the other five longitudinal rebars in the

bottom reinforcement layer. The entire cage was assembled by first putting its lower part at bottom of the

formwork, and then put the upper part on top. Stirrups for the end blocks were then slid into the beam

from the two ends. This method of assembly made the two diaphragms to be regions that have the lowest

transverse reinforcement ratio for each beam, because styrofoams that were used to create the outer

I-sections blocked the passages for sliding stirrups into the diaphragms.

13

10M

25M

25M

D4

10M

25M

25M

D4

1'' Dywidag

1'' Dywidag

10M

D4

1'' Dywidag

1'' Dywidag

63

56

61

69

57

1542

39 40

39

551

L1

Rebar positionsof all beams

L2

M1, M2, S1, S2

N S

Figure 2.5: Reinforcement Details at the Cross Sections for All Specimens

14

Upper reinforcement cage

Lower reinforcement cage

Figure 2.6: Typical Upper and Lower Reinforcement Cages

*Note that the 10M cross bar here was not a cross tie, it was simply used to hold the longitudinal

bars at the right positions when they were put into the formwork.

Places with white tapes are where the strain gauges were mounted.

StirrupsLongitudinal

Reinforcement

Cross Ties

North

South

Cross Ties

10M Cross Bar*

15

L2

M1

M2

S1 S2

Figure 2.7: Reinforcement Cages

16

L =

605

0

1480

1162

525 67

8

150

150

435

1110

1035

390

460

590

727

10

M@

10

11

0M

@1

011

0M

@75

6000

112

132

116

101

Top

Vie

w

Sid

e V

iew

4-2

5M

& 2

-1''

Dyw

ida

g

64

Fig

ure

2.8

: D

imen

sion

s an

d R

ein

forc

emen

t D

etai

ls f

or L

1

17

L =

605

0

1480

1162

525 67

8

150

150

435

1110

1035

390

460

590

727

Top

Vie

w

Sid

e V

iew

6000

7511

6

6-1

'' D

ywid

ag

2418

7

46

62

10M

@51

10M

@51

51

10M

@40

Fig

ure

2.9

: D

imen

sion

s an

d R

ein

forc

emen

t D

etai

ls f

or L

2

18

5176

L = 3582

852

150608317

469

150

564

639

390 460 300308590

10M@10110M@101 10M@75

129100 115 101

6-25M

3532

10M@51 10M@4010M@51

3532

60 90

87

26

6-25M

M1SideView

M1TopView

M2SideView

M2TopView

Figure 2.10: Dimensions and Reinforcement Details for M1 and M2

19

L = 2320

150 215

368408

550

150

300

107390 590460

10M@101 10M@7510M@101

75120103 101

65 14169

2270

2270

5156

10M@51 10M@51 10M@51

6-25M

6-25M

S1SideView

S1TopView

S2SideView

S2TopView

Figure 2.11: Dimensions and Reinforcement Details for S1 and S2

20

2.1.4 Formwork The formwork was constructed to allow all six specimens to be casted at once. The base was made by two

layers of interlacing plywood with four slots screwed onto it. Two of the slots were used for casting the

two long beams and the other two were built to cast the two medium and short beams. Each slot was

separated by a wall made of two layers of marine plywood with a 2” by 4” wood in between. Considering

that the formwork might be used for more than a single cast, marine plywood was chosen instead of

regular plywood in order to minimize the damages done by concrete during casting and curing. To prevent

the formwork from collapsing under the hydraulic pressure of unsettled concrete, its two sides were held

with diagonal struts spaced at 40 to 50 cm that were cut from 2” by 4” wood.

Another major component of the formwork was the styrofoams. They were used to create the I-sections

parts of all beams. The flange and web widths of each beam were designed such that when three layers of

styrofoams were pasted on each side of a casting slot, the middle gap in between was equal to the web

width. After cutting the tilted edges of styrofoams using a table saw, three styrofoam layers were pasted

together using normal spray glue to form a bundle, which was then wrapped around using adhesive

kitchen shelf paper to prevent it from falling apart during casting. The bundled styrofoams were attached

to the slot walls of formwork using standard construction glue. Each beam required six bundles to form its

inner I-section and the two outer I-sections, and before these styrofoams could be attached to the

formwork, the lower reinforcement cage must be put at bottom of the formwork first.

Figure 2.12: Formwork containing all Reinforcement Cages

21

Bundled Styrofoams Attached to the Slot Wall

Styrofoams for the long beams.

Small foam blocks used to

hold the bundled styrofoams

from sliding downwards

when the glue was not dried

Figure 2.13: Selected Pictures of Styrofoams

2.2 Material Properties 2.2.1 Concrete All specimens were casted at the same time using ready mixed high strength self consolidating concrete

with a specified strength of 70 MPa. Regular concrete could not be used because the poker vibrators were

not able to fit into the dense reinforcement cages. The casting process was finished in less than 90 minutes,

and the flowability of SCC did not have much decrease during that interval. Although SCC were meant

not be vibrated, it was still difficult for the air bubbles at the bottom flange to come out during casting.

Therefore, the casting of each beam was done in two steps by first pouring concrete only up to the mid

height of each beam, then filling up the rest. This allowed more time for the air bubbles to float up from

bottom of the beam.

The specimens were moist-cured using damp burlap. A thin layer of plastic sheet was covered on top of

the burlap to prevent moist loss. The moist curing lasted a week, and the formwork was then disassembled,

22

leaving the specimens in ambient environment. For every cured beam, lots of voids were found at the

surfaces that had contact with the styrofoam, including the web and the tapered inner flanges surfaces.

The largest of these voids had nearly 2cm diameter and more than 5mm depth, but they did not appear to

have any influence on the specimen behaviors during testing. There were few voids at parts of the beams

that had direct contact with the marine plywood such as the end blocks and two sides of the flanges. The

only concern was a noticeable honeycomb in the upper flange at the outer I-section of specimen S2. After

repaired using hydrostone that had strength of at least 40 MPa, the honeycomb region did not affect the

specimen behavior either.

The concrete strength was measured using standard cylinder compression test. Three or four cylinders

with 6″ diameter and 12″ height were tested each time to measure the concrete strength at a particular age.

The cylinder strengths were determined on 3 days and 7 days after the cast and also on the day after every

beam test, but the 28-day concrete strength was not available. The cylinder tests were performed using

three different equipments, and the loading rate was controlled at the standard 4.5 kN/s every time.

The stress-strain relationship of the concrete was only determined after all beams had been tested, but it

was reasonable to assume that Ec was almost constant throughout all six beam tests since the concrete

strengths had only slight changes between the first and last beam test. The concrete stress strain plot is

shown in Figure 2.14, and the detailed cylinder strength results are listed in Table 2.3.

Table 2.3 Concrete Compressive Strength

At Test (listed in chronological order of testing)

3-day 7-day M1 M2 S2 S1 L1 L2

Strength

(MPa) 44.3 62.6 86.0 86.2 85.0* 86.8 88.4 88.4

Ec (MPa) † — — 37700 37700 37500 37800 38100 38100

*) S2 was test after M2, so theoretically its concrete strength should be greater or equal to that of M2. The

cylinders for these two beams were not tested using the same equipment, which indicate the smaller

strength result for S2 might be due to the deviations between different equipments or the defects in

cylinders. Therefore, it is reasonable to assume that the concrete strength and Ec for S2 were equal to that

of M2.

†) Ec is computed using the equation Ec = 3320 'cf + 6900 for normal weight concrete (Collins and

Mitchell, 1997). Ec is measured to be 39500 MPa by averaging the slopes of the stress-strain plots for all

four cylinder tests, and it is sufficiently close to the calculated value for specimen L2.

23

0

20

40

60

80

100

0.0 0.5 1.0 1.5 2.0 2.5

Strain (mm/m)

Stress (MPa)

Figure 2.14: Stress Strain Relationship of One Cylinder Sample

Note that when measuring the stress strain relationship, the concrete cylinder was not tested to failure in order

to prevent damages to the equipment.

2.2.2 Reinforcement There were two types of longitudinal reinforcements used: the 25M deformed bar (As=500 mm2) and 1″

dywidag bar (As=550 mm2). The 25M bars had sudden decrease in elastic modulus before reaching the

yield plateau. The cause of this strange mechanical behavior is unknown, but it is reasonable to take fy

and εy as values corresponding to the start of yield plateau and calculate Es based on the stress-strain

relationship before the sudden decrease in stiffness.

There was only one type of reinforcement used for the stirrups, which was the 10M deformed bar

(As=100 mm2). However, these bars came in two separate shipments. For consistency, stirrups in the test

regions of all beams were cut from the bars that came from the first shipment only. Stirrups in other

regions of each specimen contained mixed bars from both shipments.

D4 wires (As≈30 mm2) were used for the flange cross ties. Breaking at small ultimate strain, the D4 wires

were much more brittle than other rebars.

The strength of reinforcement steel was determined through standard coupon test of 18″ long rebar

samples. For each type of reinforcement, the three coupon test samples gave consistent results. Therefore

24

the stress-strain relationship of only one sample is plotted in Figure 2.15 and Figure 2.16. The full plots

that include all test samples are shown in Appendix A. The results of coupon tests are summarized in

Table 2.4.

Table 2.4 Reinforcement Properties

Size db

(mm)

As

(mm2)

fy

(MPa)

fu

(MPa)

εy

(mε)

εu

(mε)

Es

(MPa)

D4 3 30 561 665 2.94 27 190931

10M (TR) 11.3 100 490 580 2.49 164 196540

10M (NTR) 11.3 100 500 611 2.50 161 200000

25M 25.2 500 460 583 3.13 130 191920

Dywidag 1 inch 550 966 — 4.74 — 203597

10M (Test Region)

0

100

200

300

400

500

600

0.00 0.05 0.10 0.15 0.20 0.25

Strain (mm/mm)

Str

ess

(MP

a)

10M (Non Test Region)

0

100

200

300

400

500

600

0.00 0.05 0.10 0.15 0.20

Strain (mm/mm)

Str

ess

(MP

a)

25M

0

100

200

300

400

500

600

0.00 0.05 0.10 0.15 0.20 0.25

Strain (mm/mm)

Str

ess

(MP

a)

25M (magnified plot)

0

100

200

300

400

500

600

0 2 4 6

Strain (mm/m)

Str

ess

(MP

a)

Drop in Es

8

Figure 2.15: Stress Strain Relationships of Reinforcement Steel (10M & 25M)

25

1" Dywidag

0

200

400

600

800

1000

1200

0 5 10 15 20 25 30

Strain (mm/m)

Str

ess

(MP

a)

D4

0

100

200

300

400

500

600

700

0 10 20 30 40 50

Strain (mm/m)

Str

ess

(MP

a)

Figure 2.16: Stress Strain Relationships of Reinforcement Steel (Dywidag & D4)

Note that the 1″ dywidag bars were not tested to failure due to the concern that instantly dropping the

applied force from more than 550 kN to zero could damage the coupon test equipment.

2.3 Test Setup All specimens were to be tested under downward monotonic loading using the Baldwin machine that had

1.2 million pound capacity. Since all beams were designed to have anti-symmetric loading, two point

loads and two reaction supports were required for each test. A spreader beam was used to distribute the

load from of Baldwin machine into two vertical point loads. The spreader beam was tightly clamped onto

the spherical head of Baldwin so that it did not need to be moved separately when switching specimens

between tests. There were two different spreader beams used among the six tests, one for M1, M2, S1,

and S2, and a larger one with higher flexural capacity was used for L1 and L2 because of a longer

distance between the two point loads. There was no load cells placed between the spreader beam and

specimen, because the point loads might exceed the maximum capacity of available load cells and cause

damage.

Every specimen had uneven surfaces due to the limited accuracy of casting. Therefore, a bag containing

plaster was placed between the beam and load/support bearing plate. The plaster was hardened several

minutes after mixing with water, but if they were not mixed properly, some water would be squeezed out

of the plaster bag under heavy load and cause rusting of the steel floor.

Since all beams were to be statically determinate, only the west reaction support was set up as a pin, the

26

east support and two point loads were all set up as rollers.

Lateral supports were not used in any of the experiments since the height to width ratio of all specimens

were small enough that the possibility of lateral buckling could be neglected. The detailed loading setup is

illustrated in Figure 2.17. Photos taken at both the north and south side of a specimen ready for test are

shown in Figure 2.18.

Spreader Beam

Roller Roller

RollerPin

Baldwin Head

Loading from Baldwin

West East

Figure 2.17: Illustration of Loading Setup

27

South Side

North Side (spreader beam was not lowered yet)

Figure 2.18: Typical Test Setup (M1)

28

2.4 Instrumentation 2.4.1 LVDTs The vertical deflection of each beam was continuously recorded by five vertical LVDTs with ±25 mm

measurement ranges that were centered at mid-width of the beam. Two of them were placed directly

under the two point loads (named WLD and ELD), the other three were placed at 1/4, 1/2, and 3/4

positions of the test region (named TCW, TC, and TCE). For specimens L1 and L2, four additional

vertical LVDTs were used to monitor displacements of the two reaction supports at two sides of the beam.

Each one of them was placed on top of an aluminum plate that was mounted on the beam at about 5 cm

above the support. No support LVDTs were used for the other four specimens since it was thought that the

LED targets mounted at the supports would provide the required displacement data, but in fact they did

not (to be explained in Section 2.4.5).

All vertical LVDTs were fixed to the steel floor using strong magnetic bases. For M1, M2, S1, and S2, the

shear deformation of test region was measured with two diagonal LVDTs installed on the flanges (named

TW-BE and TE-BW). They crossed each other at 90o at mid-span of the beam. There were four diagonal

cross LVDTs used for L1 because of a longer shear span. Two of them were installed at a quarter clear

span of test region from the west diaphragm, and the other two were at the same distance from east

diaphragm. Specimen L2 had no diagonal LVDTs at all because the external flange clamps would

intercept the LVDT passages.

2.4.2 Clinometers

Two clinometers were used for every test to measure rotations of the west reaction support. They were

mounted back to back on an aluminum plate, which was fixed on top of the west diaphragms centered at

mid-width. The two clinometers were most unstable among all instruments, and they produced completely

noisy data for L1 and M2. The detailed setups including all LVDTs and clinometers are shown in Figure

2.19.

29

TC

WT

CE

TC

ELD

WL

DT

CW

TC

ET

CE

LDW

LD

TC

WT

CE

TC

ELD

WL

D

SW

SE

Clin

om

eter

Clin

om

eter

Clin

om

eter

W-T

E-B

WW

-TW

-BE

E-T

E-B

WE

-TW

-BE

TE

-BW

TW

-BE

TE

-BW

TW

-BE

51

81

03

55

18

19

31

18

19

31

18

55

05

50

35

72

82

28

23

57

85

28

52

56

45

64

23

52

35

59

35

18

51

85

93

14

80

14

80

L1

S1

S2

M1

M2

Fig

ure

2.1

9: A

rran

gem

ents

of

LV

DT

s an

d C

lin

omet

ers

(N

ote

that

the

arra

ngem

ents

for

L2

are

the

sam

e as

thos

e fo

r L

1 ex

cept

hav

ing

no d

iago

nal L

VD

Ts)

30

2.4.3 Zurich Targets Electronic Zurich gauges with a precision of ±1μm were used in all experiments to measure deformations

at the specimen surfaces. For each beam, there were three rows of targets on the web, and the number of

columns was proportional to the shear span. Grids of 141 mm by 141 mm were used for web Zurich

targets on all beams. There were also targets mounted at one side of each flange. They covered through

the entire test region and extended to the outer I-sections so that more strain data could be obtained at the

extreme tension and compression faces of the beam. The spacing between flange Zurich targets was 141

mm for the two short beams and 200 mm for other four beams. The locations of flange Zurich targets

were an exception for Specimen L2. Instead of being mounted at the side faces, they were pasted onto the

tapered sections of flanges because the external clamps had blocked the pathways of these targets. All

Zurich targets were mounted on the north face of each beam and their positions were symmetrical about

the mid-span and mid-height.

21 3 4 5 6 7 98 10 11 12 13

1514 16 17 18 19 20 2221 23 24 25 26

2827 29 30 31 32 33 3534 36 37 38 39

41 4240 43 44 45 46 47 48 49 50 5554535251 56

72 7173 70 69 68 67 66 65 64 63 5859606162 57

41 4240 4344 45 46 47 48 49 50

5554535251

56

72 7173 7069 68 67 66 65 64 63

5859606162

57

6070

43 53

L1

L2

Grid Size:141mm × 141mm

Gauge Length inFlange: 200mm



21 3 4 5 6 7 98 10 11 12 13

1514 16 17 18 19 20 2221 23 24 25 26

2827 29 30 31 32 33 3534 36 37 38 39

Figure 2.20: Arrangement of Zurich Targets for L1 and L2

31

2322 25 26 27 28 29 30 31 32

4243 40 39 38 37 36 34 3341

98 10 11 12 13 14

1615 17 18 19 20 21

21 3 4 5 6 7

21 3

54 6

87 9

1110

12

14 1513 1816 17

2019 21 23 2422 27

25

26

35

24



M1M2



S1S2

Figure 2.21: Arrangement of Zurich Targets for M1, M2, S1 and S2

2.4.4 Strain Gauges Strain Gauges were mounted at both the top and bottom longitudinal reinforcements and also at the

stirrups. They were attached onto the smoothened rebar surfaces using ductile CNY glue that could allow

extra deformations after been dried. The amount of strain gauges depended on the lengths of shear span.

There were a total of 15 strain gauges used for each of the two long beams and 9 gauges for each medium

and short beam. Only stirrups located within the test regions were mounted with strain gauges at the mid

height. There was always one gauge mounted on the stirrup at mid-span and the others were positioned

symmetrically about this center stirrup. The strain gauges for longitudinal reinforcements were only

instrumented on one of the six rebars, and that was always the second bar from north at the top layer and

second bar from south at the bottom. For each longitudinal reinforcement layer, there were two strain

gauges mounted at locations of the two diaphragms, and the other gauges were distributed within the test

region. All strain gauge positions were identical for the two beams within each length group.

The strain gauges were named with a letter followed by a number, and the number was sequenced from

west to east. For example, “T3” indicated the third strain gauge at top longitudinal rebar counted from the

west and “B5” was the fifth bottom longitudinal gauge from west. The stirrups were denoted as “C”

instead of “S” in order to avoid confusions with names of the two short beams. The detailed layouts of

strain gauges are shown in Figure 2.22 and Figure 2.23 with the directions labeled. Note that these

figures do not include parts of specimens that did not have strain gauges.

32

T1 T2 T3 T4 T5

B1 B2 B3 B4 B5

C1 C2 C3

591 518 591518

C1 C2 C3 C4 C5

C5C4

429 303 303 429303303

423 306 306 423306306

Top

Bottom

EW

S

N

Elevation of L1

Elevation of L2

Figure 2.22: Strain Gauge Layout for L1 and L2

33

T1 T2 T3

B1 B2 B3

C1 C2 C3

C1 C2 C3

T1 T2 T3

B1 B2 B3

C1

C2

C3

C1

C2

C3

134 101 134101

133 102 133102

310 310

261 303 261303

258 306 258306

639 639

Top of M1 & M2 Top of S1 & S2

Bottom of M1 & M2 Bottom of S1 & S2 N

S

W E

Elevation of M1 Elevation of S1

Elevation of M2 Elevation of S2

Figure 2.23: Strain Gauge Layout for M1, M2, S1, and S2

34

2.4.5 Optical Scanner and LEDs Metris K-610 LED Optical Scanner was another device used to measure the surface strains of the beams.

It was able to determine the three-dimensional coordinates of LEDs with high accuracy and precision. The

LEDs targets were mounted on the north face of each beam, which was also the side where the Zurich

targets were located, and the sampling rate of 3D scanner was set to be 3Hz in all experiments. Three

stationary LEDs targets were required for each experiment to act as reference coordinates. In the first four

experiments, two of the reference LEDs were mounted on a Baldwin leg and the third was fixed on the

steel floor. In the last two experiments, all three reference LEDs were mounted on the floor.

The function of 3D scanner was limited by its small field of view and the number of available LEDs.

Although the LEDs were able to cover most part of the test regions for the medium and short beams, there

were only enough of them to be mounted on half the shear span for beam L1 and L2. Due to limited space,

the 3D scanner could not be placed far from the specimen. This reduced the detectable range of scanner as

the field of view was inversely proportional to the distance between scanner and the LEDs. In all cases,

the 3D scanner could only track one of the two support displacements within its field of view. Therefore,

displacement at the east support was always left unmeasured for being far from the test region. In order to

record LEDs positions at the test region of each specimen, the 3D scanner had to be oriented at an angle

towards the beam because the giant Baldwin leg would completely block the LED signals.

With plenty of other data obtained from other instruments, the 3D scanner data will not be used as a part

of experimental analysis except the support displacements measured for the two medium and short beams.

The arrangements of LED targets are shown in Figure 2.24. Note that numbers followed by letter “F”

indicate LEDs that were mounted on floor, and the ones ended with “B” were attached to the north

Baldwin leg. LED 14 for Specimen L2 was a special target located at top of the beam near the east side in

order to measure the out of plane deformation of flange.

35

1 2 3 4 5 6

7

1314 15 16 17

2221 20 19 18

23 F24 F25 F

23 F24 F 22 F

1315 16 17

14

21 2019

18

8 9 10 11 12

259 259

1 2 3 4 5 6

7 8 9 10 11 12

260 141

239 294 112

324 317 283 112

259 259

391

L1

L2

12 3

4

5 F 6 F

9 10 11 12 13

15 16 17

14

201918

21 F

23 2422 2526

27

12 3 4

5

6

11 12 13

1514 16

2120 22

1817 19

9 B 10 B

7 F8 F

7 B 8 B

282 282

117 117118118

282 282

212 141

235 71

M1M2

S1S2

Figure 2.24: Arrangement of LED Targets

36

2.5 Test Arrangement and Procedure Each of the six experiments was scheduled to last for one working day. The first thing to do on the day of

test was to zero instruments that included LVDTs, clinometers, and strain gauges. Two sets of Zurich

readings were also taken to represent initial state of the beam so that all the Zurich strains would be

calculated based on these readings. After calibrating all equipments, the Baldwin head with spreader beam

attached was then lowered to slightly touch the top of specimen without applying any force. The extra

constrains on the two load points and reaction supports were then removed so that only one pin and three

rollers remained.

The 3D scanner started recording data at the same time as the Baldwin started loading. The load rate was

controlled to be around 1kN/s in all tests, but this number always decreased drastically as the beam

approached its peak load. Each test had between 4-7 load stages. For all beams except L1, the increment

during load stages was around 250kN Baldwin force before reaching an applied load of 1000kN, and the

increment was halved after this point until failure. For L1, the increment was taken to around 200kN

Baldwin force. After reaching the end of a load stage, the applied load was reduced by around 10% for the

safety of manual measurements and to prevent excessive creep. Between load stages, updated crack traces

and Zurich readings were done, and the 3D scanner was stopped immediately after the 10% reduction in

load. However, the LVDTs, clinometers, and strain gauge readings were continuously recorded by the data

acquisition system at even between load stages. One set of readings were taken whenever there was a

10kN difference in Baldwin force or a 0.1 mm change in any of the LVDT measurements. For every test,

the loading was stopped immediately when the Load vs. Deflection (WLD & ELD LVDT) plot appeared

to flatten out as it might indicate a failure. A camcorder was mounted on a tripod to record the test, but

was stopped between load stages. Continuous fast photos at intervals of around 0.125s were taken when

the specimen appeared to be failing. Table 2.5 below shows the load stage information for all six beams.

Table 2.5 Shear Forces at the End of Each Load Stage (kN)

Specimen LS #1 LS #2 LS #3 LS #4 LS #5 LS #6 LS #7 ultimate

L1 80.6 159.5 239.5 305.1 − − − 320.3

L2 98.7 199.5 298.7 399.5 479.5 532.3 − 532.3

M1 109.1 200.1 301.1 401.4 450.5 − − 456.9

M2 101.0 201.6 303.2 399.3 450.5 501.8 531.7 531.7

S1 129.2 236.4 353.8 471.8 532 589.7 639.9 639.9

S2 123.0 236.6 353.8 469.2 589.7 649.9 677.5 677.5

37

CHAPTER 3

Experimental Observation

3.1 Overview All six beams failed in shear at their test regions. L1, M1, and S1 that contained roughly 1.238% shear

reinforcement showed under-reinforced shear failure. They failed gradually through opening up shear

cracks and crushing concrete in the web. L2 and M2 that had about 2.45% shear reinforcement, failed

abruptly by violent concrete crushing and spalling, which looked like brittle over-reinforced shear

failure. Despite having the same amount of stirrups as L2 and M2, S2 failed slowly, as it was a deep

beam and the shear force was carried primarily by compression strut, which appeared to have prevented

an abrupt failure from happening.

In general, doubling the amount of shear reinforcement did not improve the shear resistance as much as

expected, especially for S2, which had merely 5.8% increase in ultimate strength compared to S1. Table

3.1 below shows shear force and shear stress at first crack and ultimate loads.

Table 3.1 Summary of Test Results for Beams

Specimen Vcr-exp † (kN)

vcr-exp *(MPa)

Vu-exp

(kN) vu-exp *

(MPa)

L1 68.4 1.70 320.3 7.97

L2 70.4 1.67 532.3 12.63

M1 109.1 2.78 456.9 11.66

M2 94.6 2.30 531.7 12.92

S1 79 1.99 639.9 16.13

S2 123.0 3.08 677.5 16.97

*) vw

crcr db

Vv exp

exp

, and vw

uu db

Vv exp

exp

†) Vcr-exp is the shear force recorded with the first web-shear crack appeared within the test region. Note that the shear force above for each beam was calculated based on the total force exerted by the

Baldwin. Since there were no load cells attached to the spreader beam, the exact magnitudes of the two

point loads were unknown, but the test setup was sufficiently accurate that we can assume the actual

38

shear resistance was very close to the one listed in Table 3.1.

L1, L2, and M2 failed at the west half of their test regions at distances of 1.2 to 1.5 times dv from the

nearest support, while the failure of other three beams occurred roughly at the center. All beams had

more than sufficient flexural capacity. None of the beams had any major flexural cracks even at failure,

and the few flexural cracks developed on the flanges appeared to have little impact on the shear strength

of each specimen.

L1, L2, M1, and M2 showed sectional shear behavior, which were indicated by the almost parallel

cracks on the webs. For S1 and S2, although their small shear span to depth ratio should allow

strut-and-tie actions to dominate, the cracks were still mostly parallel, which was not expected.

The existence of two diaphragms in each beam had more influence on the behavior of the beam other

than simply holding the flanges under the point loads. They blocked the propagation of cracks from the

outer I-sections to the inner I-section so that the shear resistance of each beam was not affected by these

cracks. Furthermore, by greatly increasing the shear resistance at the load and support, the two

diaphragms could have reduced the length of disturbed regions, and thus making beam action to be the

governing mechanism for M1 and M2, which had a/d ratio as low as 2.32.

For every beam, two sides of the web looked different at failure, because the reinforcement layout was

highly unsymmetrical at the web cross section. As shown in Figure 2.5, the 10M longitudinal rebar at

mid-height of the beam was placed at south of the stirrups, which left only about 15 mm clear cover to

the south face of the web, while the clear cover at the north side was as thick as 42 mm. Therefore, every

beam was more damaged on the south side at failure with severe concrete spalling, but on the north side

there were only large diagonal shear cracks. For L1, L2, and M2, concrete spalled out along a distinct

horizontal crack on the south face of web. This crack was at the mid-height of the beam, which was

apparently a result of the weak plane caused by the 10M longitudinal rebar.

Except S1 and S2, all other four specimens had vertical shrinkage cracks before the tests. Some of the

cracks were through out the entire height of the beam. However, they seemed to have little effect on the

behaviors of the beams because neither flexural nor shear cracks were observed to have developed from

these shrinkage cracks in any of the six tests. Furthermore, for each test, the shrinkage crack widths had

unnoticeable changes at every load stage until failure.

One important observation for every test is that large longitudinal cracks were always developed at the

top and bottom faces of the flanges during middle load stages. This phenomenon could be caused by the

very lack of out of plane reinforcements in the flanges. Compare to ordinary flexural cracks, these

39

unexpected longitudinal cracks might have more detrimental effects on the shear resistance of each

beam since the confinement around the web region was reduced significantly due to damaged flanges.

3.2 Specimen Behavior The details of every specimen are discussed in this section. The descriptions will be primarily based on

measured cracks and other qualitative observations made during each experiment. Photos showing the

failure of each specimen and crack diagrams of selected load stages are also presented. All crack

diagrams are drawn on the south side of the specimen, because this was the side where the cracks

widths were measured. The cracks were marked in three different colors: black represents shear or

flexural cracks, green represents shrinkage cracks, and red indicates cracks that are especially discussed

in the text. Only crack diagrams for selected load stages are shown in this section, the detailed crack

traces of every load stage will be presented in the Appendix C.

3.2.1 L1

L1 had the longest shear span-to-depth ratio and a lower shear reinforcement ratio of 1.235%, it had the

lowest shear resistance among all six beams as expected. The beam had two 0.05 mm vertical shrinkage

cracks on both sides of the web, each located at roughly 43 cm from its closest diaphragm. The first

shear crack was in the west outer I-section when the shear force reached 32.8 kN. This crack was rather

random and unexpected since the outer I-section always had only 75% of the shear force in the test

region. Shortly after this crack, the first load stage was restarted due to the loosen LVDT under the west

cantilever. This restart had little effect on the specimen since the test region had no cracks yet.

The first web shear crack in the test region was formed at 68.4 kN. The first load stage was taken when

the shear force reached 80.6 kN. Three diagonal shear cracks were formed at Load Stage 1 in the test

region and they were all at roughly 45o. As shown in Figure 3.1, the crack near east diaphragm became

vertical below the mid-height, which might be caused by stress due to shrinkage and flexure.

A few more cracks were found in the second load stage, including two long diagonal cracks that

developed through the entire height of web at mid west of the test region. Many more new cracks were

formed during Load Stage 3, and the existing cracks from Load Stage 2 grew larger as expected. There

were a few small flexural cracks and longitudinal cracks developed on the flanges, but the beam still

maintained a linear load deflection response at the end of the third load stage. During Load Stage 4,

there were only a few new shear cracks formed and all of these new cracks were small and were

developed from the top and bottom of the web without extending much further. The shrinkage cracks

40

still had roughly the same widths as before, and they apparently had blocked the propagations of some

shear cracks, and thus might have beneficial effects on the shear strength. The longitudinal cracks were

significantly enlarged during Load Stage 4, and shortly after this final load stage, the beam reached its

ultimate shear resistance of 320.3 kN and started to fail.

0.05

0.05

0.05 0.050.05

Load Stage 1 V=80.6 kN 0.25 of ultimate

0.10.05 0.1

0.05

0.05

0.15

0.05

0.10.15

0.05

0.050.05


0.1 0.150.15

0.20.15

0.15

0.2

0.1

0.150.2

0.15

0.1

0.15

0.1

0.2

0.35


Figure 3.1: L1 Crack Diagrams for Selected Load Stages

As shown in Figure 3.2, after failure, the main longitudinal crack was about 5 mm wide and centered

roughly at mid-span. It also had large slip in the vertical direction, and the south side of upper flange

was less humped up and looked almost detached from rest of the flange. Among all six beams, L1 had

the most serious flange splitting. Based on the location of this longitudinal crack, if it was deep enough,

it could have entered the web region and even caused out of plane splitting of the web. Figure 3.2 shows

both sides of the beam after failure. Failure occurred primarily at the west half of test region along the

two diagonal cracks that were formed in Load Stage 2. The inclination of the critical crack on the west

was 38o and the one on the east was 33o.

41

South Side

North Side

Longitudinal Cracks at Top Flange W E

Figure 3.2: L1 after Failure

3.2.2 L2

L2 had the same shear span as L1 but had twice the amount of shear reinforcement. L2 was the last

specimen tested, and it had an ultimate shear resistance of 532.3 kN, which was 66% higher than that of

L1. Part of this large increase in strength was definitely contributed by the ten external clamps that were

used to reinforce the flanges. However, even with the external clamps, longitudinal cracks were still

developed during Load Stage 4 on the compression side of the two flanges. Fortunately, theses cracks

were much smaller than the ones in L1 and thus had much less detrimental effects.

The first shear crack in test region formed when shear force reached 70.4 kN, which was only slightly

higher than the 68.4 kN cracking strength of L1. The first load stage was taken at 98.7 kN. Two cracks at

the east of web near the mid-span had much larger angles than other cracks, but the one formed at top

half of the web soon developed into a large continuous shear crack during Load Stage 2. This crack

decreased its angle as it extended downwards until it was almost parallel to other shear cracks. The

stiffness of the beam appeared to be constant after the first crack and before the end of Load Stage 4

despite many new cracks were formed during this interval. L2 reached its peak load at the end of Load

42

Stage 6, but the beam still maintained very good integrity without any delaminations, and most of the

crack widths were also smaller than expected. Compare to L1, there were more shear cracks in L2 at its

last load stage. However, L2 had generally smaller crack widths than L1 did under similar shear forces.

While this difference was not apparent for Load Stages 1 and 2, the cracks widths of L2 at the end of

Load Stage 3 with a shear for of 298.7 kN were noticeably smaller than those of L1 at the end of Load

Stage 4 with V = 305.1 kN.

0.1

0.1

0.050.1

0.1

0.150.15


0.15

0.15

0.1

0.1

0.1 0.15

0.15

0.1

0.1 0.05

0.1

0.05

0.05

0.1

0.15

0.05

0.05

0.050.15

0.15

0.1


0.4

0.25

0.15

0.15

0.25 0.3

0.25

0.15

0.1 0.15

0.15

0.10.2

0.15

0.15

0.25

0.4

0.10.25

0.150.15

0.15

Load Stage 6 V=532.3 kN Peak load

Figure 3.3: L2 Crack Diagrams for Selected Load Stages

Shortly after the final load stage, L2 failed abruptly at the west half of the test region. As shown in

Figure 3.4, at the moment of failure, violent concrete spalling occurred along a horizontal line near the

mid-height. Although the two web shrinkage cracks had little change in widths from the first to last load

stage, the one near mid-span did open up at failure and became the east boundary of the failure region on

south side of the web. On the north side, however, the failure location extended beyond west of the

shrinkage crack, but the web was still less damaged. The two critical cracks on the south side appeared

to be in between the two shrinkage cracks, and they were first formed during Load Stage 3. The critical

crack on the north side was the one that crossed the west shrinkage crack at mid height. Inclinations of

all three cracks were around 33o.

43

t = −0.125 s

t = −0 s

t = 0.125 s

Figure 3.4: L2 during Failure

South Side

North Side

Figure 3.5: L2 after Failure

3.2.3 M1

M1 had a shear span to depth ratio of 2.32 and a shear reinforcement ratio that was the same as L1. M1

was the first beam tested, and it had an ultimate shear resistance of 456.9 kN, which was higher than the

shear strength of L1 as expected, but lower than that of L2. As displayed in Figure 3.6, cracks near the

two diaphragms were less inclined, while the ones closer to the mid-span had smaller angles and were

mostly parallel to each other. Therefore, M1 carried shear force primarily through beam action rather

44

than arch action.

0.15

0.1

0.10.1

0.15

0.1

Load stage 1 V=109.1 kN 0.24 of ultimate

0.2

0.1

0.15

0.15

0.1

0.1

0.15

0.1

0.10.1

0.2

0.15


0.3

0.2

0.15

0.2

0.250.25

0.45

0.25

0.45

0.2

0.250.15

0.3

0.25

0.55 0.2


Figure 3.6: M1 Crack Diagrams for Selected Load Stages

The first two shear cracks seemed to have formed simultaneously at around 109.1 kN in west of the test

region. This cracking strength was much higher than that of L1 and L2, but the initial crack widths were

also significantly larger. During the second load stage, more shear cracks were formed on the web at the

test region and some of them extended to the flanges. The diagonal shear crack formed at mid-span later

became the critical crack that initiated the failure of M1. More shear and flexural cracks developed

between the third and last load stage, and longitudinal cracks were formed in Load Stage 4 on both top

and bottom flanges.

M1 reached its peak load shortly after Load Stage 5 and started to fail gradually. The beam failed at its

mid-span, which was expected since it was very close to a distance of dv from the support. The failure

started from the top half of the web by opening up the critical crack, which was inclined at around 35o,

other cracks nearby also opened up shortly after. This result could be foreseen back in the last load stage

when the two web cracks at top mid-span had widths as large as 0.45 mm. Different from the two long

beams, M1 did not have concrete spalled out along a distinct horizontal crack along mid-height of the

web, although its south side was still more damaged than the north side.

45

South Side

North Side


Figure 3.7: M1 after Failure

3.2.4 M2

M2 had twice the amount of shear reinforcement of M1, but its ultimate shear resistance was 531.7 kN,

which was only 16.4% higher than M1. Despite the presence of longitudinal cracks that weakened the

beam, it could still be seen that doubling the amount of stirrups did not increase the shear strength as

much as expected.

The web shear cracks for M2 also looked parallel, although cracks near the two diaphragms had less

inclinations than the rest, the differences were not as obvious as in M1. However, there was one

exception, which was the diagonal crack located right at the mid-span. Formed at a shear force of around

94.6 kN, this was the first crack during the test, and it had an inclination of 56o. Having a much larger

angle than other cracks, the formation of this first crack could also have been contributed by stress due

to shrinkage other than shear stress. The benefit of having more stirrups on crack control is clearly

demonstrated by M2. Compare to M1, the crack widths of M2 at each load stage were noticeably

smaller (they can be compared easily since the same load stage number for these two beams

corresponded to almost the same shear force). Many more shear cracks are developed during the second

46

load stage. Tiny flexural cracks also appeared on two sides of the upper flange, but it was not until the

third load stage that some of these flexural cracks became visible on the top flange face. During Load

Stage 2, there was also a large shear crack formed at the east outer I-section that passed through a nearly

2 cm large void, but this did not affect the beam since the failure still ended up in the test region. The

first longitudinal crack was formed during Load Stage 4 at the top east flange and it had propagated to

the mid-span during Load Stage 7. A few more longitudinal cracks were also formed before at the end of

final load stage.

0.05


0.05

0.050.05

0.05

0.05

0.05

0.05

0.05

0.1


0.25 0.3

0.4 0.5

0.1

0.25

0.15

0.1

0.45

0.25

0.350.3

0.15

Load stage 7 V=531.7 kN Peak load

Figure 3.8: M2 Crack Diagrams for Selected Load Stages

t = −0.125 s t = 0 s t = 0.125 s

Figure 3.9: M2 during Failure

47

Abrupt failure shown in Figure 3.9 occurred shortly after Load Stage 7. Similar to the behavior of L2,

part of the web at west half of the test region was split along a horizontal line at mid height accompanied

by violent concrete spalling. By examining the north side of M2 after failure, it seemed that there were

two critical cracks, and one of them was actually the 56o crack formed during the first load stage. The

other critical crack at the west was formed during Load Stage 2, and it had an inclination of around 36o.

Compare to M1, the longitudinal cracks of M2 caused similar damages in the two flanges, but the crack

slips in vertical direction were much less compare to the ones in specimen L1.

South Side

North Side


Figure 3.10: M2 after Failure

3.2.5 S1

S1 was one of the two deep beams with a/d ratio of 1.125 and shear reinforcement ratio of 1.25%. The

beam had an ultimate shear resistance of 639.9 kN and it failed slowly like L1 and L2. Having a crack

pattern similar to that of M1, S1 also had more inclined parallel cracks near mid-span and two less

inclined cracks near the two diaphragms.

48

The exact cracking strength of S1 was not clearly known, because unlike other specimens, S1 did not

produce a very distinct sound when its first crack developed and this sound was mixed up with the noise

made by the Baldwin machine. The first crack might have occurred at around 79 kN since the beam had

a sudden increase in deflection at this load. The first load stage ended with a shear force of 129.2 kN,

and two cracks have already formed at the west half of test region. No crack was formed at the east half

until Load Stage 3, but the cracks started to distribute more evenly through out the web after this load

stage. The two discontinuous shear cracks at mid-span opened up greatly during Load Stage 7, with a

0.4 mm width, they were the largest shear cracks before failure. Delamination was also detected on

south face of the web at this final load stage.

0.10.05


0.05

0.20.2

0.15

0.1


0.150.1

0.3

0.4

0.40.25

0.2

0.25


Figure 3.11: S1 Crack Diagrams for Selected Load Stages The beam was not able to withstand higher load after Load Stage 7. Failure happened slowly through

crushing of the direct compression strut between the load and support. The inclination of compression

strut was around 42o. The south side of web had much more damages than the north side, but the bottom

flange on both sides appeared equally damaged as they both had large portions of concrete falling off.

The first longitudinal crack was formed early in Load Stage 3 at the top east flange, and multiple cracks

were developed afterwards on both flanges. Top of the east diaphragm was cracked under the point load

49

and thus allowed two of the longitudinal cracks extending to the flange at east outer I-section, which was

a never expected phenomenon. The longitudinal cracks were more concentrated near the load point or

support on both the top and bottom flanges. Therefore these cracks were most likely contributed by

stresses at the nodal regions of compression strut, since the two diaphragms should have provided the

flanges with much stronger confinement against longitudinal splitting compare to the long and medium

length beams.

South Side North Side

Bottom

W E

Top

W E

Figure 3.12: S1 after Failure

3.2.6 S2

S2 had the same a/d ratio as S1 but twice the amount of shear reinforcement. Despite being the strongest

beam among all specimens, it only had an ultimate shear resistance of 677.5 kN, which was only 5.8%

higher than S1. This tiny increase in shear strength could even by accounted as an error or deviation

within the normal range of tolerance. The differences on the crack widths between S1 and S2 were also

very small. This result showed that for deep beams with geometries and loading conditions similar to S2,

increasing the amount of shear reinforcement from 1.25% to 2.48% had almost no effect on the ultimate

shear resistance and crack widths.

The crack pattern of S2 was opposite from that of S1. Instead of having more inclined shear cracks near

the mid-span, S2 had more inclined cracks near the two diaphragms and one crack with the largest angle

formed at mid-span during Load Stage 1. This crack had an angle of 56o and was formed when the shear

50

forced reached 123 kN. Compare to S1, this cracking strength was much higher. During the second load

stage, two shear cracks were developed on each side of the central crack at inclinations of approximately

46o. The central crack opened up greatly during Load Stage 7 from 0.3 mm to 0.55 mm. Meanwhile,

delamination was also detected at south face of the web.

0.1


0.1

0.1

0.1

0.05


0.15

0.25 0.550.25

0.15

0.2

0.15

0.2

0.2


Figure 3.13: S2 Crack Diagrams for Selected Load Stages

Shear failure occurred soon after Load Stage 7. Unlike L2 and M2, S2 failed slowly despite having

roughly the same amount shear reinforcement. The failure of S2 also looked different than that of S1.

Rather than gradually crushing the compression strut and causing damages over a large area on the web,

S2 appeared to be failing along that 56o crack at mid span, which was formed back in Load Stage 1.

Although concrete spalling had also occurred at the top and bottom of web, it was apparently less severe

compare to S1. On north side of S2, the damages were more concentrated at top half of the web. The

first longitudinal crack was developed in Load Stage 4. The longitudinal cracks dealt significant

damages to the flanges within the region. Similar to S1, these damages were mostly near the load and

support and they appeared to be primarily caused by concrete crushing at nodal regions of the

compression strut. The inclination of this compression strut should be roughly between 46o and 56o.

Longitudinal cracks also extended to the top of east diaphragm and the bottom of west diaphragm, but

51

the damages were much less compare to the cracking on the east diaphragm of S1.

South Side North Side

Bottom

W E

Top

W E

Figure 3.14: S2 after Failure

52

CHAPTER 4

Evaluation of Test Results

This chapter focuses on the evaluation and analysis of the quantitative test data obtained from all the

instruments. The chapter will include: deflection and shear strain measured by the LVDTs, inclination of

reaction support measured by the clinometers, longitudinal and transverse strain gauge readings, and web

deformations at the test region for selected load stages calculated from the Zurich data. For the ease of

comparison, some of the test results are presented for all six beams together rather than for each specimen

separately.

4.1 LVDT Data

4.1.1 Deflection

The transverse displacements at five locations of each beam were measured by vertical LVDTs placed on

the floor. These displacements do not represent the actual deflection of the beam, because a large portion

of the displacements were contributed by the settlements of plasters at the two supports. The net

deflection could be easily calculated when the support displacements data were available. However, as

mentioned in Chapter 2, mistakes were made by not having LVDTs measuring the support displacements

during the first four experiments, and the 3D scanner was only able to track one of the two support

displacements on the north side of each specimen due to limited field of view. Therefore, except L1 and

L2, exact deflections of the other four specimens could never be known. Since the plasters always had

significant amount of settlements, instead of showing the total displacements measured by the five

vertical LVDTs, which apparently were not representative, a method was proposed to give a rough but

closer approximation to the actual deflection of each beam based on the available LED and LVDT data

from all six tests. The details of this method are explained in Appendix B. Figure 4.1 shows the

calculated deflections of all specimens at the end of each load stage. They are presented as a function of

the distance from mid-span, and the two locations that always have zero displacements on the graph are

the two reaction supports.

53

-2590 -1110 -518 0 518 1110 2590-10

-9

-8

-7

-6

-5

-4

-3

-2

-1

0

Distance From Mid-Span (mm)

De

flect

ion

(mm

)

L1

-2590 -1110 -518 0 518 1110

0

2590-12

-10

-8

-6

-4

-2


De

flect

ion

(mm

)

L2

1*

2

3

4

Ultimate

-1491 -639 -282 0 282 639 1491-6

-5

-4

-3

-2

-1

0


De

flect

ion

(m

m)

M1

-1491 -639 -282 0 282 639 1491-6

-5

-4

-3

-2

-1

0


De

flect

ion

(m

m)

M2

-860 -310 -118 0 118 310 860-4

-3.5

-3

-2.5

-2

-1.5

-1

-0.5

0


De

flect

ion

(mm

)

S1

-860 -310 -118 0 118 310 860-3.5

-3

-2.5

-2

-1.5

-1

-0.5

0


De

flect

ion

(mm

)

S2

Figure 4.1: Deflections of Beams

*The detailed load stage data can be found in Table 2.5 in Chapter 2. As each beam approached failure, stirrups at the failure location began to greatly elongate and the web

region started to bulge out in the transverse direction, making the beam no longer following the elastic

deflected shape. Thus, when reaching the ultimate load, it was reasonable for a beam to have greater

displacements near its mid-span than the one under the east point load. For specimen M1, the

54

displacement at 282 mm to the east of mid-span exceeded the one at east point load after Load Stage 4,

and kept to be the largest vertical displacement within the test region. Unlike M1 that failed at mid-span,

the failure location of M2 was mainly at west half of the test region. Hence, the maximum deflected point

of M2 at ultimate load was more towards the west compare to that of M1. Different from the two medium

beams, the two short beams always had their largest displacements under the east point load. This was

actually possible since the shear force in each short beam was primarily carried by the direct compression

strut between east load and west support, which could leave web regions near the mid-span not expanding

transversely as much compare to the medium beams. The deflections of L1 and L2 were mostly governed

by flexure and therefore were closer to the elastic deflected shape.

Under ideal conditions, displacements at the two point loads are expected to be equal due to symmetry.

For the long and medium beams, although displacements under the west load were always greater than the

ones under east load, the differences were within acceptable range. For S1 and S2, however,

displacements at the west were much less than the east.

For the medium and short beams, doubling the amount of shear reinforcement did not have much

influence on the deflections at ultimate load. The long beams were different as L2 had significantly larger

deflections at its ultimate load than L1, partly because without the external clamps, L1 failed very early

before reaching higher loads and greater deflections.

4.1.2 Shear Strain

Shear strains at the test regions were measured using cross LVDTs mounted on the top and bottom flanges.

These measurements were based on an assumption that the principal strains were aligned at 45o and 135o

to the horizontal axis, which would give reasonably close estimates to the actual results. The shear strain

data is not available for specimen L2 because the cross LVDTs were unable to be installed in the presence

of external flange clamps. Figure 4.2 and Figure 4.3 show the shear strains plotted as a function of shear

forces for each beam. Note that plots for S1 and S2 are not shown at the full range since the shear strains

kept increasing as these two beams failed slowly, and by the end of data acquisitions when the beams

were completely damaged, the measured values were too large that a portion of the them needed to be

excluded from the graphs in order to preserve details of the shear strain variations before ultimate loads.

55

L1

0

50

100

150

200

250

300

350

-1 1 3 5 7 9 11 13 15 17 19 21Shear Strain (mm/m)

V (

kN)

West

East

M1

0

100

200

300

400

500

-1 2 5 8 11 14 17 20 23 26Shear Strain (mm/m)

V (

kN)

M2

0

100

200

300

400

500

600

0 4 8 12 16 20 24 28Shear Strain (mm/m)

V (

kN)

S1

0

100

200

300

400

500

600

700

-1 2 5 8 11 14 17 20 23 26Shear Strain (mm/m)

V (

kN)

Figure 4.2: Shear Force vs. Shear Strain (L1, M1, M2, and S1)

56

S2

0

100

200

300

400

500

600

700

-1 2 5 8 11 14 17 20 23 26Shear Strain (mm/m)

V (

kN)

Figure 4.3: Shear Force vs. Shear Strain (S2)

Specimen L1 had two sets of shear strain readings measured at the each half of the clear span. The two

measurements were reasonably close to each other for the first three load stages. Shear strain at the east

half become much greater than the ones at west as the experiment was approaching Load Stage 4. After

reaching the ultimate load, shear strain at the west half increased drastically since this was where the

failure started to occur. As the load decreased, shear strain at the east half also started increasing at a

higher rate, which was expected since part of the upper flange in the east half of test region was also

damaged as the failure location expanded towards both sides. Unlike L1, shear strains were only

measured at the mid-span for each of the other four beams. Comparing the shear strains of M1 and M2 at

their ultimate loads, the one for M2 was 15.7% greater, which was reasonable. The shear strain difference

between S1 and S2 was completely unexpected, because S2 had larger strain than S1 at any given shear

force despite of having twice the amount of transverse reinforcements. Creep in shear trains occurred

mostly at late load stages and it seemed that they were not dependent upon the amount of stirrups or the

a/d ratios.

4.2 Strain Gauge Data

4.2.1 Longitudinal Strains

Strains in the longitudinal reinforcements measured by strain gauges at the end of each load stage are

shown in Figure 4.4 to Figure 4.6. Note that some data were missing due to damaged strain gauges. None

of the longitudinal reinforcements yielded since the beams were constructed with sufficient flexural

capacity. When reaching ultimate load, bond slip occurred to specimen L1 at the top reinforcement layer

near mid-span.

In ideal cases, the two sets of strain gauge readings for each specimen should be identical due to

57

symmetry. However, there were large differences between strains in the top and bottom longitudinal

reinforcements. Maximum tensile strains in the bottom longitudinal rebars were always larger than the

ones in the top, especially at late load stages. The available results indicate that all longitudinal bars tend

to have more positive strains than expected. For each beam, the strains at point of inflection were always

positive, and they were the largest strains at the bottom flange of the short beams. While plots for the

bottom longitudinal strains still look reasonable, the top east longitudinal strain of each beam kept

increasing at every load stage, which was exactly the opposite of what was expected to happen since the

top east strain gauge was located at the east diaphragm where the largest negative moment occurred. The

influence of shear reinforcement ratio on the longitudinal strains could not be concluded based on the

large fluctuations and randomness in strain gauge data.

-1110 -518 0 518 1110-200

0

200

400

600

800

1000

1200


Str

ain

-T ( )

L1

-1110 -518 0 518 1110-1000

-500

0

500

1000

1500


Str

ain

-B ( )

L1

ultimate

4

3

2

1

-1110 -518 0 518 1110-200

0

300

600

900

1200

1500


Str

ain

-T ( )

L2

-1110 -518 0 518 1110-1500

-1000

-500

0

500

1000

1500

2000


Stra

in-B

( )

L2

Figure 4.4: Longitudinal Strain (L1 and L2)

58

-639 0 639-200

0

300

600

900

1200


Str

ain

-T ( )

M1

-639 0 6390

300

600

900

1200

1500


Stra

in-B

( )

M1

-639 0 639-200

0

400

800

1200

1600


Str

ain

-T ( )

M2

-639 0 6390

400

800

1200

1600


Str

ain

-B ( )

M2

-310 0 3100

500

1000

1500

2000


Str

ain

-T ( )

S1

-310 0 310-400

0

400

800

1200


Stra

in-B

( )

S1

Figure 4.5: Longitudinal Strain (M1, M2, and S1)

59

-310 0 3100

400

800

1200

1600


Str

ain

-T ( )

S2

-310 0 3100

300

600

900

1200

1500


Str

ain

-B ( )

S2

Figure 4.6: Longitudinal Strain (S2)

4.2.2 Transverse Strains

Figure 4.6 shows the strains in the transverse reinforcements that were measured by strain gauges

mounted at the mid-height of the stirrups. Transverse strains of each beam at early load stages were

heavily dependent upon on the locations of web cracks, as strains were increased significantly when

regions near the strain gauges were crossed by cracks. At late load stages, the strains became more

consistent with the predictions as more cracks were distributed throughout the web.

The maximum transverse strains for specimens L1 and L2 were at west half of the test regions, which was

the location of failure. For the other four beams, maximum strains occurred at the middle stirrups during

late load stages, which were also reasonable since the beams were expected to fail at around the mid-span

according to the sectional shear predictions from both CSA A23.3-04 and ACI 318-08. Beam M2 was an

exception, despite having symmetrical strains about the mid-span, it eventually failed abruptly at west

half of the test region.

The available strain gauge data shows that none of the stirrups had yielded for L2, although data was

missing for the one at 612 mm west of mid-span, it was very possible that this stirrup had yielded. The

middle stirrups in M2 and S2 just reached the yield strain at ultimate loads. The results indicate that

over-reinforced shear failure occurred for these beams. For the other three beams that had half the amount

of shear reinforcements, the stirrups did yield before reaching the ultimate loads, but none of them had

ruptured.

60

-606 -303 0 303 6060

600

1200

1800

2400

3000


Str

ain

-C ( )

L1

-612 -306 0 306 6120

500

1000

1500

2000

2500


Str

ain

-C ( )

L2

1

ultimate

4

3

3

2

-303 0 3030

700

1400

2100

2800

3500


Str

ain

-C ( )

M1

-306 0 3060

600

1200

1800

2400

3000


Str

ain

-C ( )

M2

-101 0 101

0

700

1400

2100

2800

3500


Str

ain

-C ( )

S1

-102 0 102

0

500

1000

1500

2000

2500


Str

ain

-C ( )

S2

Figure 4.7: Transverse Strain

61

4.3 Zurich Data This section shows the Zurich data at selected load stages of each test. The load stage selections are the

same as those in Chapter 3 except that Load Stage 1 of each test is not be included. The data is presented

in two forms: the numerical strains measured directly by the electronic Zurich gauges and the two

dimensional web displaced shapes (scaled at 30x) at test regions computed using the method proposed by

Dr. Boyan Mihaylov. Each displaced shape shown here is computed as a reference to the initial state of

the specimen prior to loading. For each specimen, both the numerical strains and displaced shapes are

drawn on south side of the beam in order to be consistent with the orientation of crack trace diaphragms.

However, the actual Zurich data only represent measurements at the north face.

It is found that within each group of specimens, the horizontal Zurich strains on the two flanges were

generally smaller in the higher shear reinforced beam under similar shear forces. When comparing beams

with the same amount of stirrups, the flange Zurich strains appeared to be independent of the a/d ratios.

Opposite to what was expected from elastic beam actions, the absolute values of web horizontal surface

strains were usually much larger than the ones in flanges, indicating that deformations in the web regions

due to shear were larger than the ones due to flexure. At early load stages, the vertical Zurich strains were

apparently influenced by both the a/d ratios and shear reinforcement ratios. Under similar shear forces,

beams with more stirrups or smaller a/d ratios did have noticeably smaller vertical strains. However, these

were no longer effective as the specimens were approaching failure. At the final load stages, vertical

strains in the two long beams were much less than those in the other four beams, and despite of having

smaller shear forces, the two medium beams had larger vertical strains than the short beams did.

Although the Zurichs could only measure strains at concrete surface, they are expected to produce similar

results as the reinforcement strains measured at near locations. However, there were actually many

discrepancies between the Zurich strains at the strain gauge data. Unlike the longitudinal reinforcement

strains in which the largest measurements were always found at one of the two diaphragms, locations of

the largest horizontal Zurich strain on each of the two flanges appeared to be random. Vertical Zurich

strains were smaller than the stirrup strains at early load stages, but became much larger as the beams

were approaching failure. One thing that both flange Zurich strains and longitudinal reinforcement strains

had in common was that positive strain values were observed for each beam at regions near the point load

or the reaction support, which had maximum negative moment. This unexpected phenomenon could be

caused by the transverse expanding of the test region under shear force, which would possibly result in

stretching of the flanges.

62

4.3.1 L1

Unlike the top longitudinal reinforcement strains, the surface strains of L1 at top flange showed

reasonable changes from Load Stage 2 to 4. The most noticeable ones are the strains near east point load

that became more negative as the shear force increased instead of becoming more positive like the

reinforcement did. Surface strains at the bottom flange are exactly the opposite as they were all increasing

in the positive direction, even including ones above the west support. Based on the web displaced shapes,

it can be seen that the distributions of transverse Zurich strains and transverse reinforcement strains were

similar, although the two sets of measurement still had large differences in magnitudes.


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63

4.3.2 L2

For specimen L2, most of the Zurich strains at both top and bottom flanges became more positive after

Load Stage 3, and they had significantly different values compared to the longitudinal reinforcement

strains at the corresponding locations. As expected, most of the flange Zurich strains of L2 were smaller

than that of L1 at their last load stages, but the web surface strains for these two beams did not have much

difference. The web displaced shapes of L2 seem to be consistent with the distribution of stirrup strains as

the vertical Zurich strains at mid-span were apparently less than those at the two sides near locations of

the 2nd and 4th stirrup strain gauges. The vertical Zurich strains indicate that the damaged stirrup strain

gauge at 612 mm west of mid-span most likely had similar strains compared to the one at its east.


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282930313233343536373839

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-58.4-525-791-622

-524-86388.9-69.8-90.1-317

28.2

-169

-514

-492

-540

-609

-320

-713

-389

-726

27

409475292553604812613493

890404441049748131286724

766735862339374108

264681

5551031

456583

188284

6731876

1496890

175526

583533

1286717

4771109

1970-

5051110

1202

1773

781

1020

1828

1556

1632

1582

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1297

2237

1981

2561

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2250

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42 -4

61

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59 -7

53

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2680

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42

40

57

41

58

42

59

43

60

44

61

45

62

46

63

47

64

48

65

49

66

50

67

51

68

52

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53

70

54

71

55

72

56

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15785.5154

175 157

613

574

304

451

898

362

266

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925

720

1258

934

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-307

-397

-275

-245

-228

-68.7

-120 -173 -97.2

-50.7

3 6


12345678910111213

141516171819202122232425

282930313233343536373839

-227-914-950-380-952-665

-22.3-562-61.51387-11781207-7493368

-93810191224-877-292-190-112

-201

-497

-736

-67

26

27

664179830241967275999.7

8604232052926

17585232344789197

7821834

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2891097

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9

-631

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27

-6

25

-6

38

-7

64

-4

20

-4

19

-6

08

-7

32

-9

48

-6

36

-7

19

-7

17

-9

94

40

57

41

58

42

59

43

60

44

61

45

62

46

63

47

64

48

65

49

66

50

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68

52

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53

70

54

71

55

72

56

7371.8

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837 249

4051282

50.5 931

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1532

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799

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1268

775

914

897

1422

1316

1937

1586

-470

-421

-462

-359

-65.8-310

-459

-541

Figure 4.9: L2 Zurich Strains and Web Deformations at Selected Load Stages

64

4.3.3 M1

Zurich strains on the two flanges of M1 within the test region were getting more positive as the shear

force increased, even including ones at the negative moment regions, although their values are much less

compared to the longitudinal strain gauge readings. Different from the longitudinal reinforcement strains,

the largest surface strains on the top flange were near the mid-span rather than at one of the diaphragms at

Load Stage 5. While the vertical Zurich strains are less than the stirrup strains at Load Stage 2, but having

a higher rate of increase, they became much larger than the stirrup strains at Load Stage 5. The displaced

shapes of M1 are fairly symmetrical about the mid-span, which was also the location where failure

occurred.


1234567

89101314

161718192021

-95

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-245-1.65

151

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0

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177463491122645

5472052371265

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-8

2.8

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66

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38

-5

88

-5

86

22

33

23

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24

35

25

36

26

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98

95.1

257

318

546

220

393

395

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532

433

369

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20364018752161441854

169926897532672411

222513025874140

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4684

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29

7482

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8890

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98

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4349

1

50

4855

3121

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3

8809

4302

4904

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06

-8

80

22

33

23

34

24

35

25

36

26

37

27

38

28

39

29

40

30

41

31

42

32

43

9.83

262

566

334

928

966

1019

811

1191

489

670

578

1019

838

988

678

1070

1051

-182

-220

Figure 4.10: M1 Zurich Strains and Web Deformations at Selected Load Stages

4.3.4 M2

M2 had noticeably smaller Zurich strains than M1 at Load Stage 2 (the shear forces were almost the

same). However, at their final load stages, the Zurich strains of M2 were slightly larger overall. Similar to

M1, the stirrups strains of M2 were greater than its vertical Zurich strains at Load Stage 2 but were

smaller than those at Load Stage 7. The beam failed at west half of the test region, and this is confirmed

by the web displaced shape at Load Stage 7, which shows maximum deformation at the west side of

65

mid-span.


1234567

891011121314

15161718192021

-249

-323-204

38

-76.57

-3

02

-2

438355472322222

4921063624152

28138.3328403299416

558182

920618

8556

167

923736

430849

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849

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04

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-7

35

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70

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19521560

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2641

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5

7780

3513

5598

4279

8

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19

-9

09

-8

12

22

33

23

34

24

35

25

36

26

37

27

38

28

39

29

40

30

41

31

42

32

43256

163

360

2220

1797

1045

1185

730

1086

580

708

934

445

607

989

529

688

-249

-388

-457

Figure 4.11: M2 Zurich Strains and Web Deformations at Selected Load Stages

4.3.5 S1

All horizontal strains on the flanges became positive after Load Stage 2, except the one between Zurich

targets 13 and 14. Zurich strains on the top flange showed similar distribution as the available longitudinal

strain gauge data, but the ones at bottom flange above the west reaction support were completely different

than the longitudinal reinforcement strains at that location. At the end of Load Stage 3, the vertical surface

strains were very different from the stirrups strains, but they showed similar distributions at later load

stages. With only three columns of Zurich targets in the web, the displaced shapes look symmetrical about

the mid-span as no significant deformations occurred on either half of the test region. Therefore, unlike

the long and medium beams, displaced shapes of S1 do not effectively reveal the location at which failure

would occur.

7

2009

-2

44

1283

1402

-3

95

1207

-418

22

33

23

34

24

35

25

36

26

37

27

38

28

39

29

40

30

41

31

42

32

43

0

40.5

13.3

10.2

21.5

165

132

269

392

343

460

248

83.1

370

187

68

-10

-89.8

-167-13.2

-49.8

66


123

456

789 -235

-16

4

-6

31 -5

32

-6

82

-8

92

1788706

11401489

1791

1507

1616

181

1

1097

123

0

3556

3083

1868

3752

10

19

11

20

12

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13

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14

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24

16

25

17

26

18

27

529

482

400

185

869

259

509

269

104

352

206

1117

229

168

687

85.9


123

456

89

-8

57

-6

57

-8

02

-1

579

7

30761827

31723838

11261856

4384

993

4391

3638

2316

3994

8003

6586

5104

8181

10

19

11

20

12

21

13

22

14

23

15

24

16

25

17

26

18

27

1478

1102

3015

651

4070

9431209

31.8

1123

174

1875

245

689

1232

96.5

-228

Figure 4.12: S1 Zurich Strains and Web Deformations at Selected Load Stages

4.3.6 S2

The horizontal Zurich strains at both flanges were similar to the longitudinal reinforcement strains at the

end of Load Stage 2. At Load Stage 7, however, Zurich strains at the bottom flange were much smaller

than the strain gauge measurements. S2 and S1 had similar strains on the flanges when they were both at

Load Stage 7, except the ones under east point load that were much smaller in S2. The vertical Zurich

strains of S2 were generally consistent with the strain distributions in stirrups, but at late load stages, the

surface strain became much larger than the stirrup strain at mid-span. There was a very large transverse

strain between targets number 2 and 5 at Load Stage 7, which is clearly shown by the web displaced shape.

This is consistent with the result of the experiment since top half of the web had more damage than the

bottom half at failure.


123

456

89

-180

-89

-43.1

-4

0

7

981

4851201

1066

44259.2

1644407

489

0

2244

1660

624

-3

57

-4

03

-7

22

2267

10

19

11

20

12

21

13

22

14

23

15

24

16

25

17

26

18

27 18.7150

239

317

341

203

262

437

238

405

163173 -30.8-31.9

-31.9-60


123

456

89

-88.6

-9

34

-6

97

-5

80

-3

692

7

1321

28072355

11821743

3007613

77072309

6603470

7698

6663

3822

8416

10

19

11

20

12

21

13

22

14

23

15

24

16

25

17

26

18

27 633

255

467

1175

363

1139

249

948

1411

964

1218

1223

1945

647

120

-211

Figure 4.13: S2 Zurich Strains and Web Deformations at Selected Load Stages

67

4.4 Clinometer Data Each specimen had two clinometers mounted at the top center of west diaphragm in order to continuously

track the inclination of west reaction support. Clinometers were the least stable instrument used in the

experiments because the recorded data always contained lots of noise. The measurements for specimen L1

and M2 were completely governed by noise that made them useless for experimental analysis. For the

other four specimens, the inclinations are plotted as functions of the shear forces shown in Figure 4.14.

Rotations are obtained by averaging the readings from the two clinometers. Similar to the settings used

for shear strain graphs, the inclination plots do not include the full range of data on the x-axis in order to

preserve more details for parts of the plots before the ultimate loads. Note that negative rotation indicates

the inclination was towards the east.

L2

0

100

200

300

400

500

600

-0.05 0.05 0.15 0.25 0.35 0.45 0.55

Inclination (degrees)

V (

kN)

M1

0

100

200

300

400

500

0 0.1 0.2 0.3 0.4 0.5 0.6


V (

kN)

S1

0

100

200

300

400

500

600

700

-0.05 0 0.05 0.1 0.15 0.2 0.25 0.3


V (

kN)

S2

0

100

200

300

400

500

600

700

800

-0.05 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4


V (

kN)

Figure 4.14: Inclinations at West Reaction Support

Rotation of west reaction support mainly depended upon the magnitude of loading and flexural behavior

of each beam. The two specimens within each group had the same geometry and loading conditions, thus

before cracking, they were expected to have the same support inclinations under equal shear forces

68

regardless of the difference in the amount of shear reinforcements. However, flexural properties of the

specimens were actually affected by the cracks, which would cause the rotations to be less predictable.

The plots showed large differences in the west support rotations of S1 and S2. While S1 had larger

inclinations than S2 at early load stages, it had a significant decrease in rotation after Load Stage 5. This

decrease also occurred on specimen L2 and M1. L2 also had a rapid increase in the support rotation

during Load Stage 4, but there were not much increase in the crack widths and number of cracks between

Load Stage 3 and 4. Based on the available data, M1 was the only one that did not have negative

inclinations.

69

CHAPTER 5

Comparison of Experimental and Analytical Results

This Chapter provides comparisons between the experimental and predicted results. Shear strengths of the

six specimens were calculated using equations from the ACI code and CSA code. Everything used in the

calculations are as-built values that include the measured specimen dimensions shown in Table 2.2 and

the measured material properties listed in Table 2.3 and Table 2.4.

5.1 ACI Code The shear provisions from Chapter 11 of ACI 318-08 are used to calculate the shear strengths of the six

specimens. Since none of the beams was prestressed, according to the loading condition, the maximum

factored shear force Vu would occur inside the test region at a distance d from the edge of either one of

the diaphragms. All equations in this section have lb/in units.

Eq. (11-2) of ACI code defines the nominal shear strength of a beam to be the sum of strengths provided

by concrete and shear reinforcement separately:

Vn = Vc + Vs (5-1)

The shear strength contributed by concrete alone is given by Eq. (11-5) of the code:

Vc = (1.9 'cf +2500 wu

u

M

dV) dbw 3.5 'cf dbw (5-2)

Where w = db

A

w

s , and u

u

M

dV 1

According to Eq. (11-15) of the code, the shear strength provided by the stirrups is calculated as

following:

Vs = s

dfA ytv 8 'cf dbw (5-3)

In accordance with Clause 11.7.3, the maximum allowed shear strength of deep beams is given by:

Vn 10 'cf d bw (5-4)

As stated by Clause 11.1.2 of ACI 318-08, the concrete strength is limited by 'cf 100 psi for

calculating Vs and Vn, but according to Clause 11.1.2.1, this limit can be exceeded when computing Vc

alone, since the beams already contain more than minimum amount of web reinforcement. The maximum

70

yield strength of shear reinforcement can not exceed 60000 psi according to Clause 11.4.2, but for these

six beams it is reasonable to ignore this limit and use the actual measured values in calculations. The

shear strength is computed through iterative process by assuming a value of Vu for each new iteration

until Vu and Vn are equal.

5.2 CSA Code For CSA predictions, equations from Chapter 11 of CSA A23.3-04 are used. Based on the reinforcement

layout of the six beams, the critical section is taken at a distance dv from face of the support instead of d

as in ACI code. All equations in this section have N/mm units.

In CSA A23.3-04, the shear resistance is also obtained by summing the strengths provided by concrete

and shear reinforcement together:

Vr = Vc + Vs (5-5)

The shear strength provided by concrete is given is give by Eq. (11-6) of the code:

Vc = 'cf vwdb (5-6)

The shear strength provided by transverse reinforcement is given by Eq. (11-7) of the code:

Vs = cots

dfA vytv

(5-7)

The parameters β and θ used in the above equations are determined as the following:

)1000(

1300

)1(

40.0

zex s

(5-8)

ss

fvfx AE

VdM

2

/ , where f

v

f Vd

M (5-9)

g

zze a15

ss

35 = 300 mm for all six beams

x 700029 (5-10)

Clause 11.3.3 of the code specifies an upper limit to the shear strength of any reinforced concrete

member:

Vr 0.25fc′ vwdb (5-11)

In CSA A23.3-04, there is no limit on the reinforcement yield strength, but for concrete,

'cf 8 MPa

must be applied when determining Vc. The value of Vr is computed through iterative process by assuming

a value of Vf in each iteration until both quantities are equal.

71

The above equations are the general method for calculating the shear strength based on sectional shear

model. Although it was observed that the two short beams were governed primarily by strut-and-tie

ctions, only the sectional model was used in to predict their shear strengths for consistency.

he experimental and predicted shear strengths are shown in Table 5.1 below.

Table 5.1 Shear Str Predictions (kN)

Sp

a

5.3 Predicted Results T

ength

ecimens L1 L2 M1 M2 S1 S2

Vu-exp 320.3 532.3 456.9 531.7 639.9 677.5

ACI 307.7 322.9 300.1 315.3 303.9 305.8

CSA 421.0 704.1 418.9 684.7 419.5 683.6

Exp/ACI 1.04 1.65 1.52 1.69 2.11 2.22

EXP/CSA 0.76 0.76 1.09 0.78 1.53 0.99

For every beam, the shear strength predicted by ACI code was limited by Eq. (5-4), indicating that ACI is

too conservative on the maximum allowed concrete strength and shear reinforcement ratio. None of the

CSA predictions exceeded the limit of Eq. (5-11), and the CSA code significantly over-estimated the shear

strengths of L1, L2 and M2, but it gave close predictions for M1 and S2. The anti-symmetric loading

conditions enabled the predictions from both codes to be almost independent of the a/d ratios, as the

alculated shear strengths are very similar for beams with the same reinforcement ratios.

ent ratio did not

rease the shear resistance much, especially for the short beams.

c

Eq. (5-3) and Eq. (5-7) show that both ACI and CSA assume an almost linear correlation between Vs and

the shear reinforcement ratio, which indicate that doubling the amount of stirrups would significantly

increase the shear strength, since concrete itself only had minor contributions when a beam is heavily

reinforced in shear. This disagrees with the test results as doubling the shear reinforcem

inc

72

CHAPTER 6

Conclusions and Recommendations

6.1 Conclusions The objective of this study was to find out the shear strength upper limit of heavily shear reinforced high

strength concrete beams and the maximum amount of transverse reinforcement that could be put into a

beam before over-reinforced shear failure would occur. Through the destructive testing of six I-beams

with three different shear span-to-depth ratios and two different shear reinforcement ratios, it was found

that the shear provision of ACI 318-08 was too conservative for high strength concrete members and the

limit on concrete strength and transverse reinforcement ratio should be increased. However, the sectional

model in CSA A23.3-04 over-estimated the ultimate shear resistance of the three beams that contained

roughly twice the maximum amount of stirrups allowed by ACI code. In general, none of the two current

concrete codes was able to give close predictions to all six experiments.

The more detailed conclusions are listed as below:

1). Increasing the transverse reinforcement ratio from 1.238% to 2.45% did not double the ultimate shear

resistances, and the percentage of strength gain diminished as the a/d ratio decreased. S2 had only

5.8% higher shear strength than S1, indicating that for deep beams with I-sections, putting more shear

reinforcement beyond the maximum allowed by ACI code would have little effect on improving the

shear strength.

2). Since the two short beams both had more than twice the shear resistance predicted by the ACI code,

the shear strength upper limit described by Eq. (5-4) should be increased. It is reasonable to raise the

concrete strength limit and increase the coefficient from 10 to a larger number. For slender beams, the

maximum allowed shear reinforcement ratio in ACI code could be doubled, but Eq. (5-3) would also

need to be modified since Vs would not increase linearly with further increase of shear reinforcement

ratio.

3). Specimen L1, M1, and S1 with lower shear reinforcement ratios had under-reinforced shear failures

through yielding of the stirrups at the failure locations. The other three beams that had more stirrups

showed over-reinforced shear failures since their stirrups were just starting to yield at the peak loads.

Among them, L2 and M2 failed abruptly, but S2 had a slower failure since its shear force was carried

directly through the diagonal compression strut and its web region received greater confining forces

from the flange diaphragms due to smaller a/d ratio.

4). According to strain gauge data and qualitative observations, the maximum transverse reinforcement

73

ratio should be around 2.45% for high strength concrete beams as it appeared to be the point where

over-reinforced shear failure started to occur. This ratio is equal to 0.138 fc′/ fyt, which is much less

than the 0.2 fc′/ fyt suggested in other studies (Lee and Hwang, 2010), although the latter was obtained

by testing beams with solid rectangular sections instead of I-sections.

5). For every specimen, the web surface at north side appeared very differently from the one at south side

after failure. The south face was always much more damaged than north face because the 10M

longitudinal rebar at mid-height of each beam resulted in much less concrete cover for the south web

surface, making it easily delaminated. Although this rebar helped crack width control, it weakened the

shear resistance of the web in a way that was predicted by neither ACI nor CSA code.

6). The lack of out of plane reinforcements in the two flanges caused longitudinal flange splitting during

every test. This problem was especially serious for specimen L1, which had a very large crack in the

middle of the top flange and eventually failed at a shear force much lower than expected. The external

flange clamps allowed L2 to have much fewer and smaller longitudinal cracks than L1, and reach

shear strength as high as that of M2. Therefore, flange cracking did affect the shear resistance of the

beams and this effect became smaller as a/d ratio decreased because of stronger constraints from the

two diaphragms.

7). Existence of the two diaphragms likely reduced the length of disturbed regions by spreading large

portions of the point loads outside the web and thus made each beam showing more sectional shear

behavior than expected. This was demonstrated by the parallel cracks that appeared on the two

medium and even the short beams, although the anti-symmetric loading condition would also result in

more parallel cracks due to zero moment at mid-span.

8). Measurements from both stirrup strain gauges and Zurich gauges showed that at similar shear forces,

increasing the shear reinforcement ratio or decreasing the a/d ratio would result in smaller transverse

strains. However, variations in these two parameters did not have apparent influences on other

deformations such as shear strains and longitudinal strains.

6.2 Recommendations for Future Work Despite the popularity of I-sections members in a wide variety of constructions, not many studies were

performed on examining the shear behaviors of I-beams with high transverse reinforcement ratios. The six

tests in this study only provided limited data for this topic, and more experiments are required for better

understanding of the shear behaviors of I-beams so that more accurate shear strength predictions can be

developed. The following future researches are recommended:

1). Every specimen in this project suffered longitudinal flange splitting for not having enough cross ties

74

in the flanges. Unlike solid rectangular beams, the shear flow in an I-section is not in a uniform

direction and will produce out of plane tension in the flanges that can cause them to split if not

enough cross ties were available. Therefore, it is important to test some specimens that are strongly

reinforced in the out of plane direction in order to prevent longitudinal cracking of the flanges at high

shear forces. By comparing with the results from this thesis, the effects of longitudinal cracking on

the ultimate shear strengths could be clearly shown.

2). The anti-symmetric loading condition used in this study provided each specimen with a very low

moment-to-shear force ratio at its critical section within the test region, which was ideal for analyzing

the behavior of a beam under almost pure shear. However, this loading condition made both

predictions from ACI and CSA code nearly independent of the a/d ratios, and the predicted results for

all three groups of beams were all roughly the same. Thus, more similar specimens should be tested

under different loading conditions to examine how their shear strengths will be affected. If possible,

slender I-section beams with a/d ratios much larger than that of L1 should also be tested.

3). Having different concrete covers at two faces of the web would not be a problem if a beam is lightly

reinforced in shear. However, when the beam contains lots of web reinforcements, a week plane is

created, and if one side of the web has much less clear cover than the other, it will fail earlier. Hence,

further experiments on thin web I-section beams should ensure that both sides of the web have similar

concrete clear covers. The six tests from this project should be repeated by simply removing the 10M

longitudinal rebar at mid-height to give each beam additional 11 mm concrete cover at south face of

the web. Although the north face still has more clear cover, the beams should be expected to have

higher ultimate shear strengths, especially for the ones with more stirrups.

75

References Canadian Standards Association (2004). A23.3-04, Design of Concrete Structures. Missisauga, Ontario.

Committee 318, A. C. I. (2008). Building Code Requirements for Structural Concrete (ACI

318-08) and Commentary. American Concrete Institute, Farmington Hills, MI.

Choulli, Y., Mari, A. R., and Cladera, A. (2008). Shear Behaviour of Full-Scale Prestressed I-Beams Made

with Self Compacting Concrete. Materials and Structures, 41, pp. 131-141.

Cladera, A., and Mari, A. R. (2005). Experimental Study on High-Strength Beams Failing in Shear.

Engineering Structures, 27, pp. 1519-1527.

Collins, M. P., Bentz, E. C., and Sherwood, E. G. (2008). Where is Shear Reinforcement

Required? Review of Research Results and Design Procedures. ACI Structural Journal, 105(5), pp.

590-600.

Collins, M. P., and Mitchell, D. (1997) Prestressed Concrete Structures, Response Publications, Toronto and Montreal, Canada.

Lachemi, M., Hossain, K. M. A., and Lambros, V. (2005). Shear Resistance of Self-Consolidating

Concrete Beams—Experimental Investigations. Canadian Journal of Civil Engineering, 32, pp.

1103-1113.

Lee, J. Y., and Hwang, H. B. (2010). Maximum Shear Reinforcement of Reinforced Concrete Beams. ACI

Structural Journal, 107(5), pp. 580-588.

Russo, G., Venir, R., and Pauletta, M. (2009). Reinforced Concrete Deep Beams—Shear Strength Model

and Design Formula. ACI Structural Journal, 102(3), pp. 429-437.

Tuchscherer, R., Birrcher, D., Huizinga, M., and Bayrak, O. (2011). Distribution of Stirrups across Web of

Deep Beams. ACI Structural Journal, 108(1), pp. 108-115.

Xie, L. (2009). The Influence of Axial Load and Prestress on The Shear Strength of Web-Shear Critical

Reinforced Concrete Elements. Ph.D. thesis, University of Toronto.

76

APPENDIX A

Material Properties

The detailed material properties are summarized in this appendix. These include the concrete

strength test results and the coupon test results of all steel reinforcements.

A.1 Concrete Properties Traditional slump flow method was used to measure the concrete workability. The workability of

the ready-mix SCC used in this test was acceptable. Diameter of the slump flow was measured to

be 590 mm, and this was reached in 3.5 seconds. There were no additional admixtures added to

the concrete before casting. The stress strain behavior of the concrete tested on the 148 day after

casting is shown in Figure A.1.

90

80

Cylinder #170 Cylinder #2

Cylinder #360

Figure A.1: Compressive Stress-Strain Curves for Concrete Cylinders

0

10

20

30

40

50

0.0 0.5 1.0 1.5 2.0 2.5

Cylinder #4

Stress (MPa)

Strain (×10-³)

77

The concrete strength was tested using three different equipments. The detailed test results are tabulated in table A.1 in chronological order.

Table A.1: Concrete Cylinder Compressive Strengths

Specimen Cylinder fc′ (MPa) Age at cylinder testing (days)

Age of specimen at testing (days)

1 44.2 2 44.5

— 3 44.1

3

—

1 63.9 2 61.0

— 3 62.9

7

—

1 86.9 2 85.1

M1

3 85.9

52

51

1 86.9 2 86.2

M2

3 85.6

64

63

1 89.2 2 84.8 3 84.5

S2

4 81.4

71

71

1 88.2 2 88.5 3 84.5

S1

4 85.9

85

84

1 88.8 2 88.8 3 87.9

L1, L2

4 88.2

129

127 (L1)

143 (L2)

78

A.2 Steel Reinforcement Properties The results of all tensile coupon tests are provided through Figures A.2 to Figures A.6.

0

100

200

300

400

500

600

700

0.00 0.05 0.10 0.15 0.20 0.25 0.30

Strain

Stress (MPa)

Figure A.2: Stress Strain Relationship of 25M Deformed steel bar

0

200

400

600

800

1000

1200

0 5 10 15 20 25 30

Strain (mm/m)

Stress (MPa)

Figure A.3: Stress Strain Relationship of 1″ Dywidag bar

79

0

100

200

300

400

500

600

700

0.00 0.05 0.10 0.15 0.20 0.25

Strain

Stress (MPa)

Figure A.4: Stress Strain Relationship of 10M Deformed Bar used in Test Region

0

100

200

300

400

500

600

700

0.00 0.05 0.10 0.15 0.20

Strain

Stress (MPa)

Figure A.5: Stress Strain Relationship of 10M Deformed Bar used in Non Test Region

80

0

100

200

300

400

500

600

700

0 10 20 30 40 5

Strain (mm/m)

Stress (MPa)

0

Figure A.6: Stress Strain Relationship of D4 wire

81

APPENDIX B

Method for Estimating the Vertical Displacement

This appendix explains the detailed method used to obtain the vertical deflections for specimens

M1, M2, S1 and S2 shown in Figure 4.1 in Chapter 4.

Due to the mistakes of not having LVDTs measuring the support displacements in the first four

experiments, the actual vertical deflections of the two medium beams and two short beams could

not be determined using the existing LVDT data along. In order to calculate the support

displacements, the 3D scanner data was used.

As shown in Figure 2.24, Specimens S1 and S2 both had two LED targets mounted on the west

diaphragm with one LED at the top and the other one at the bottom. This bottom target provided

an estimation of the displacement for the west support. It was just an estimation was because the

LED target was only at north side of the beam, where for specimens L1 and L2, the displacement

at each support was measured by two LVDTs with one placed at each side of the beam. Based on

data from the two long beams, there was indeed a large difference between the support

displacements measured at the two sides. Furthermore, the LED data was not available between

load stages, so the support displacements between load stages were generated using linear

interpolation based on the LED measurements from the end of previous load stage and the start of

next load stage.

Unlike the two short beams, M1 and M2 only had one LED target on the west diaphragm, and it

was mounted at the top since the 3D scanner was not able to detect a target at the bottom. Data

from the two LED targets mounted on the east diaphragms of these two beams showed that there

was negligible amount of compression in the east diaphragm throughout the experiments.

Therefore, this LED at the top of west diaphragm was able to provide an estimated displacement

data for the west support except that it was also affected by rotation of the diaphragm compare to

the bottom LED. For both M1 and M2, this rotation resulted in smaller vertical displacement

measured by the top LED at the last load stages. To account for this, the support displacement

was taken to be the last measurement before it started to drastically decrease, and then kept

constant until the loading stopped. This adjustment was based on assuming that the support

displacement was contributed primarily by the settlement of plaster, which was not ductile. This

assumption was reasonable because the maximum vertical movement of the floor was only

82

around 0.2 mm, less than 10% of the total support displacement.

Calculating the net deflection of a beam requires the vertical displacements at both supports.

However, due to the limit on field of view, the 3D scanner was only able to capture the LED

position at the west support, leaving the east support displacement completely unknown for these

four beams. Therefore, displacement at the east support must be estimated based on the data that

is already available. This is achieved through the following steps:

1. Plot all the available support displacements as a function of the corresponding reaction force.

This include the displacements recorded by the LVDTs at both east and west supports for the

two long beams and the ones measured by LEDs at the west support for the other four beams.

2. Assume the supports had a linear load-deflection relationship and draw a line of best fit for all

data on the plot.

3. Use this line of best fit to calculate the expected displacement at the east support.

Figure B.1 on the next page shows the available support displacement data for all six beams.

Note that displacement at the west support of L2 was not taken into account when producing the

line of best fit because the plaster at that support was more fluid than the others, and resulted in

large settlement at early load stages.

83

0

200

400

600

800

1000

0 1 2 3 4 5

Support Displacement (mm)

6

L1 West supportL1 East supportL2 West supportL2 East supportM1 West supportM2 West supportS1 West supportS2 West support

Reaction Force (kN)

Figure B.1: Support Displacement as a Function of Reaction Force

The line of best fit in the Figure above has a slope of approximately 240 kN/mm, which is the

number used to calculated the east support displacements for M1, M2, S1, and S2. Note that this

method only yields a very rough estimation of the displacement at east support, and the LED

target alone could not accurately track the displacement at west support either. Hence, the net

deflections calculated for these four beams were not accurate, but at least they gave closer

representations of the actual deflections compare to the ones measured directly by the vertical

LVDTs underneath the beams.

84

APPENDIX C

Test Results

This Appendix contains the results from all six experiments. These include all the crack diagrams,

load-displacement and shear strain plots, Zurich data, and load stage data.

The load-displacement graphs for M1, S1, S2, and L1 do not include the full ranges of

displacements because these four beams all had slow failures and the increasing damages in the

test region made the LVDT readings no longer accurate as the beams were failing. Same things

also apply for the shear strain plots.

The Zurich data will include displaced shape diagrams and numerical Zurich strains. The

displaced shape diagrams were drawn using the MATLAB script provided by Dr. Boyan

Mihaylov. Although the Zurich targets and crack traces were on two different sides of the web,

the displaced shape diagrams produced by Zurich readings are drawn in the same orientation as

the crack trace diagrams since they are placed adjacent to each other for each of comparison. The

displaced shape diagrams are only shown for the web region of each beam, since Zurich grids in

the flanges had readings in the horizontal direction only, which made it impossible to construct

two dimensional displaced shapes.

The numerical Zurich strain data are also provided for every load stage of each beam. All strains

are calculated based on the initial Zurich readings before starting the experiment. All negative

strains were labeled in red color, and others are labeled in blue. These numerical strains are

displayed in the same orientation as the crack trace diagrams.

The load stage data for each specimen is summarized in a table that includes selected readings

from the LVDTs, strain gauges, and clinometer. Numbers listed for the five vertical LVDTs placed

at bottom of the beam are the net deflections that have already taken into the account of the

support displacements. Note that for beams M1, M2, S1, and S2, the displacement of west

support was measured by the 3D scanner, and the one of east support was calculated using the

method shown in Appendix B.

85

C.1 L1

0

50

100

150

200

250

300

350

0 2 4 6 8 10 12

Displacement (mm)

V (kN)

14

ELD

WLD

TC

TCE

TCW

Figure C.1: Net Displacement of L1 Measured by Five Vertical LVDTs

0

50

100

150

200

250

300

350

-1 1 3 5 7 9

Shear Strain (mm/m)

V (kN)

11

West

East

Figure C.2: Shear Strain of L1 Measured by the Cross LVDTs

86

Cro

ss L

VD

Ts

Ver

tica

l LV

DT

s C

lino

met

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Net

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t D

set

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t γ–

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TC

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gm

Rot

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n

B3

C3

T3

Loa

d

Sta

ge

(#)

(h:m

m:s

s)

(kN

) (με)

(με)

(m

m)

(mm

)(m

m)

(mm

)(m

m)

(mm

) (m

m)

(deg

rees

) (με)

)(με

(με)

0 in

itia

lize

0

0 0

0 0

0 0

0 0

0 0

0 0

0

31

0:00

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6.9

6 2

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15

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0.57

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0.

24

0.25

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65

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16

13

20

114

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50

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0.

96

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0.

34

0.23

44

46

45

1

(res

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125

0:55

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73.8

36

3 51

2 1.

29

0.24

0.

47

0.85

0.

96

0.29

0.

34

0.15

45

47

47

190

1:07

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159.

5 14

89

1475

3.

15

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1.

52

2.39

2.

68

0.71

0.

49

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16

7 64

23

7 2

207

1:25

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145.

8 15

08

1516

3.

01

0.64

1.

42

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55

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0.

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5 73

23

7

268

1:37

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239.

5 29

62

2810

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20

1.59

3.

02

4.38

4.

69

1.60

0.

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33

1 14

02

367

3

296

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213.

9 29

11

2801

4.

92

1.51

2.

85

4.11

4.

45

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0.

65

0.31

31

3 13

57

354

358

3:10

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305.

1 36

47

4544

7.

09

2.25

4.

19

6.04

6.

43

2.19

0.

76

0.42

47

8 19

22

464

4

375

3:50

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274.

7 35

85

4607

6.

86

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06

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0.

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fail

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415

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Tab

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Loa

d S

tage

Dat

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pec

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L1

87

Loa

d St

age

1

V=

80.6

kN

0.25

of

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mat

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0.05

0.0

5

0.0

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05

0.0

5

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spla

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shap

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scal

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plac

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t bet

wee

n lo

ad s

tage

s (s

cale

d 40

x) 1—

2

Loa

d St

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2

V=

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5 kN

0.

50 o

f ul

tim

ate

0.1

0.0

50.

10.

05

0.0

5

0.1

5

0.0

5

0.1

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Fig

ure

C.3

: L

1 C

rack

Tra

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and

Zu

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Dis

pla

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Sh

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88

Loa

d St

age

3

V=

239.

5 kN

0.

75 o

f ul

tim

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0.1

50

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150.

15

0.1

0.2

0.1

0.1

50

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5

0.1

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Abs

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spla

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shap

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scal

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cale

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x) 3—

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L

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V

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5.1

kN

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of

ulti

mat

e

0.1

0.1

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15

0.2

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0.1

5

0.2

0.1

0.1

50

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0.1

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Fig

ure

C.4

: L

1 C

rack

Tra

ces

and

Zu

rich

Dis

pla

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apes

89

F

ailu

re

V

=32

0.3

kN

Fig

ure

C.5

: L

1 C

rack

Tra

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at F

ailu

re

90

L

oad

Stag

e 1

V

=80

.6 k

N

0

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of u

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12 15

1617

1819

2021

2223

2425

2829

3031

3233

3536

3738

39

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-96.8

-124

-45

-249

-288

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-102

-47

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-237

-149

-204

-207

-0.709

-16.9

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-72.8

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68.2

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36.8

23.7

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4

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1.06

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7

-8

8.7

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8

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8.6

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6.6

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54

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68

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0.6

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4

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2.5

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6.1

-2

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10

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33

-6

0.7

34

56

78

910

1112

13

1426

2734

107

706

50.3

692

610

497

19.8

936

55.5

238

66.5 383

4.59 -

480 71.7

590

- 138

46.6 234

- 313

74.1

520 8.8

596

147 211

48.5 -

534

731

13.5

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3

48.5

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3

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53.5

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47

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48 65

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66

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67

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68

52

69

53

70

54

71

55

72

56

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3.5

83.3

80.6

113

168

41.5

225

141

298

97.6

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405

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17.3

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362

248

158

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515

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1516

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26

2829

3031

3233

3436

3738

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6

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7

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80

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38

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86

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35

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82

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21

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69

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8.6

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02

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20

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2.9

78

910

1113

1423

2735

244

513

389

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999

965

958

806

711

46621

234

748

724

466

480

729

85.7

57.7

774 1280

127 1063

1142 1168

18 1567

21.1 703

164

1092 65.2

627 1544

1756 933

1301 1392

1.42 1076

104

553 10.3

788

541

849

742

1523

1192

2515

1115

814

233

7

900

214

8

122

1

350

964

4.5

807

211

8

204

3

600

40

57

41

58

42

59

43

60

44

61

45

62

46

63

47

64

48 65

49

66

50

67

51

68

52

69

53

70

54

71

55

72

56

73

10.3

127

15.8

161

350

275

488

389

383

217

603

922

741

368

451

719

468

388

656

937

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-197

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Fig

ure

C.6

: L

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uri

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for

Loa

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Loa

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3

V=

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0.75

of

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12

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56

78

910

1112

13

1415

21

2324

26

28

2930

32

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3637

38

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55 -

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32

207

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1617

18

19

2022

25

2731

3335

114

166

179

375

354

33.3

1454

70.5

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1200

1638

385

944

661

516

1140

565

1321

1102

180

448

91.2

612

351

138

1086

1396 1575

-2 1761

1802 1976

1256 1876

1458 1e+003

754 2047

1708 1654

698 1956

1841 1570

2506 1801

1861 1526

524 2131

635 371

1645

1370

2380

91

.6

14

47

2321

1526

2234

1335

3857

2691

2775

2024

51

5

193

2

302

3

33

1

8

242

2

99

.2

168

0

59

2

32

1

5

52

7

0

275

6

249

6

40

57

41

58

42

59

43

60

44

61

45

62

46

63

47

64

48 65

49

66

50

67

51

68

52

69

53

70

54

71

55

72

56

73

50.8

241

181

390

179

574

505

818

691

717

419

870

1278

1097

513

677

1069

787

633

981

1173

-159

-244

-316

-228

-139

-148

-144

-171

-142

-137

-41.3

Loa

d St

age

4

V=

305.

1 kN

0

.95

of u

ltim

ate

12

34

56

78

910

1112

13

1415

21

2324

26

28

2930

32

34

3637

38

39

-45.9

-236

-545

-736

-354

-427

-679

8

-441

-126

-466

-68.3

-13.

5

-371

-12.

5

-110

-168

-357

-89.

1

-230

-220

-2

0

-3

09

-1

04

-1

19

-4

2

3

-1

89

3

-2

10

2

-3

84

-4

06

4

1617

18

19

2022

25

2731

3335

158

50.2

110

10.3

328

2236

1208

949

2068

2179

136

1083

452

314

5.1

2226

1616

1978

1925

980

286

898

694

230

1590

1726 2231

530 2427

3166 3221

1928 2375

2871 1227

1572 2795

2593 2392

603 2715

2744 2500

4316 2488

4474 1900

1708 2859

1322 1230

2596

2179

2880

36

8

20

43

3144

96

.6

22

60

2255

16

6

18

07

5489

5530

5269

3850

46

68

28

07

42

31

12

7

15

65

30

05

28

8

21

84

35

7

61

3

15

33

32

6

59

2

40

86

13

6

40

57

41

58

42

59

43

60

44

61

45

62

46

63

47

64

48 65

49

66

50

67

51

68

52

69

53

70

54

71

55

72

56

73

127

141

265

229

289

414

206

707

904

727

26891

1109

24933

1406

747

809

808

2030

1207

1153

752

1692

922

1201

954

1722

-332

-417

-258

-217

-268

-23.8

Fig

ure

C.7

: L

1 N

um

eric

al Z

uri

ch S

trai

ns

for

Loa

d S

tage

3—

4 (u

nit

s: με)

92

C.2 L2

0

100

200

300

400

500

600

0 5 10 15 20 25 30

Displacement (mm)

V (kN)

WLD

TCW

TC

TCE

ELD

Figure C.8: Net Displacement of L2 Measured by Five Vertical LVDTs

There is no shear strain measured for L2 because the cross LVDTs were not able to be mounted in

the presence of external clamps on the flanges.

93

Ver

tica

l LV

DT

s C

lino

met

erSt

rain

Gau

ges

Net

Dis

plac

emen

t of

Bea

m

Sup

port

Dis

plac

emen

tD

set

T

ime

V

WL

D

TC

W

TC

T

CE

E

LD

W

est

Eas

t

Wes

t

Dia

phra

gm

Rot

atio

n

B3

C3

T3

(#)

(h:m

m:s

s)

(kN

) (m

m)

(mm

) (m

m)

(mm

) (m

m)

(mm

) (m

m)

(deg

rees

)(με)

(με)

(με)

Loa

d

Stag

e

0 in

itia

lize

0

0 0

0 0

0 0

0 0

0 0

0

12

0:00

:00

7.5

0.

11

0.06

0.

03

0.06

0.

05

0.12

0.

21

-0.0

06

2 3

1

85

0:13

:32

98.7

1.

53

0.50

0.

80

1.14

1.

23

1.21

0.

50

-0.0

07

32

36

147

1

97

0:42

:22

85.9

1.

49

0.63

0.

80

1.10

1.

17

1.53

0.

50

-0.0

16

32

34

144

176

0:57

:00

199.

5

3.55

1.

11

2.04

2.

89

3.13

2.

88

0.67

0.

012

27

9 66

4 34

0 2

199

2:09

:20

173.

1

3.37

1.

08

1.92

2.

72

2.92

3.

40

0.67

0.

002

26

4 63

9 31

8

282

2:23

:23

298.

7

5.51

1.

74

3.13

4.

60

4.99

3.

61

0.81

0.

013

39

7 97

1 50

3 3

298

2:45

:23

265.

9

5.14

1.

59

2.89

4.

22

4.64

3.

79

0.81

0.

010

37

2 93

6 48

0

384

2:57

:13

399.

5

7.58

2.

35

4.35

6.

40

7.01

3.

94

0.99

0.

18

514

1379

62

8 4

397

3:25

:13

353.

9

7.17

2.

26

4.07

5.

96

6.53

4.

03

1.09

0.

15

477

1296

58

8

482

3:35

:23

479.

5

9.96

3.

24

5.86

8.

35

8.99

4.

10

1.98

0.

17

687

1679

72

0 5

498

3:58

:29

421.

9

9.30

3.

00

5.41

7.

73

8.32

4.

21

2.27

0.

16

634

1551

66

3

593

4:09

:43

532.

3

12.0

0 4.

28

7.55

10

.33

10.8

2 4.

25

2.53

0.

19

907

1859

80

0

6

ulti

mat

e

613

4:40

:26

471.

5

11.5

3 4.

16

7.33

9.

89

10.2

6 4.

31

2.72

0.

19

852

1719

70

3 on

set t

o

fail

ure

673

4:48

:57

207.

5

21.5

5 28

.91

28.7

8 24

.67

18.8

6 3.

93

2.42

0.

60

489

641

-485

ab

rupt

fail

ure

Tab

le C

.2:

Loa

d S

tage

Dat

a fo

r S

pec

imen

L2

94

Loa

d St

age

1

V=

98.7

kN

0.1

9 of

ult

imat

e

0.1

0.1

0.0

50.

1

0.1

0.1

50.

15

0—1

Abs

olut

e di

spla

ced

shap

es (

scal

ed 3

0x)

Dis

plac

emen

t bet

wee

n lo

ad s

tage

s (s

cale

d 40

x) 1—

2

L

oad

Stag

e 2

V

=19

9.5

kN

0.3

7 of

ult

imat

e

0.1

0.15

0.1

0.1

0.1

0.1

5

0.1 0.1

0.1

0.1

0.0

5 0.1

0.1

0.05

0.1

0.0

5

0—2

2—3

F

igu

re C

.9:

L2

Cra

ck T

race

s an

d Z

uri

ch D

isp

lace

d S

hap

es

95

Loa

d St

age

3

V=

298.

7 kN

0

.56

of u

ltim

ate

0.1

5

0.1

5

0.1

0.1

0.1

0.1

5

0.1

5

0.1

0.1

0.0

5 0.1

0.0

50.0

5

0.1

0.1

5

0.0

5

0.0

5

0.05

0.1

5

0.1

5

0.1

0—3

Abs

olut

e di

spla

ced

shap

es (

scal

ed 3

0x)

Dis

plac

emen

t bet

wee

n lo

ad s

tage

s (s

cale

d 40

x) 3—

4

L

oad

Stag

e 4

V

=39

9.5

kN

0.7

5 of

ult

imat

e

0.3

0.1

5

0.1

0.1

5 0.2

0.3

0.2

5

0.1

0.1

0.05 0.1

5

0.1

0.1

0.2

0.1

5

0.0

5

0.25

0.2

50

.15

0.1

5

0.1

0—4

4—5

F

igu

re C

.10:

L2

Cra

ck T

race

s an

d Z

uri

ch D

isp

lace

d S

hap

es

96

Loa

d St

age

5

V=

479.

5 kN

0

.90

of u

ltim

ate

0.4

0.2

0.15

0.15 0

.25

0.3

0.2

5 0.1

0.1

0.15

0.15

0.1

0.1

0.2

0.15

0.1

0.25

0.3

0.1

50.

15

0.1

0—5

Abs

olut

e di

spla

ced

shap

es (

scal

ed 3

0x)

Dis

plac

emen

t bet

wee

n lo

ad s

tage

s (s

cale

d 40

x) 5—

6

L

oad

Stag

e 6

V

=53

2.3

kN

P

eak

load

0.4

0.25

0.15

0.15 0

.25

0.3

0.2

5 0.1

5

0.1

0.1

5 0.1

5

0.1

0.2

0.15

0.1

5

0.2

5

0.4

0.1

0.2

5

0.1

50

.15

0.1

5

0—6

Fig

ure

C.1

1: L

2 C

rack

Tra

ces

and

Zu

rich

Dis

pla

ced

Sh

apes

97

F

ailu

re

V

=53

2.3

kN

Fig

ure

C.1

2: L

2 C

rack

Tra

ces

at F

ailu

re

98

L

oad

Stag

e 1

V

=98

.7 k

N

0

.19

of u

ltim

ate

12

34

56

78

910

1112

13

14

15

1617

1920

22

2425

28

2930

3132

33

34

35

36

3738

39

-50.5

-132

-55.2

-150

-61

-123

-80.3

-237

-202

-349

-198

-100

-96.8

-278

-155

-250

-140

-194

-1.06

-190

-58.3

-293

-48.7 -153

-8.89

-338 -211

-92.1

-124 6.7

-192

-57.1

-173

-2

77

-229

-130

-168

-458

-152

-307

-198

-2

56

-263

-371

-1

31

-1

08

-2

7.3

-1

68

-2

16

-2

33

-1

79

-1

85

-2

80

-1

31

-2

40

-9

.51

-1

55

-3

72

1821

23

26

27

547

59.4

198

11.3

487

240

643

398

336

821

373

481

615

8.86

184

19 417

25.7

125

30.5 221

63.7 29.7

15.3 4.61

116

-7

329 83

658

409

2.02

26.

5

0.752

622

119

97.7

86.9

305

83.4

641

662

590

630

53.

4

627

626

119

126

249

135

721

109

5

40

57

41

58

42

59

43

60

44

61

45

62

46

63

47

64

48

65

49

66

50

67

51

68

52

69

53

70

54

71

55

72

56

73

72.3

97256

97

52.8

61.1

178

94

216

109

314

164

399

225

-80.5

-97.8

-89.1

-60.8

-130

-167

-72.1

-94.1

-120

-177

-190

-48.9

-73.4

-41.7

-75.3

-127

-13.3

-31.5

Loa

d St

age

2

V=

199.

5 kN

0

.37

of u

ltim

ate

12

3 1617

1920

2122

25

2829

3031

3233

3435

36

3738

39

-219

-332

-141

-350

-225

-362

-658

-311

-114

-681

-351

-137

-392

-67.7

-598

-166

-106

-111

-36.8

-400

97.3

-378

-232

-418

-443

-8

.82

-360

-441

-317

-669

-339

-636

-279

-370

-410

-604

-2

03

-2

60

-1

24

-3

13

-3

8.9

-3

82

-3

85

-5

81

-3

82

-4

87

-3

67

-7

02

45

67

89

10

1112

13

14

1518

23

2426

27

532

256

141

234

562

213

350

409

454

844

660

605

747

494

443

509

323

126

79.7

289 740

-31.4 832

171

185

447 1165

1086 771

204 490

359 621

993 576

682

468 -

441

610

724

230

1482

1276

1329

1193

1204

1054

896

1183

1133

17

79

10

03

24

4

10

81

11

77

12

12

12

75

64

3

15

39

63

3

83

2

17

49

40

57

41

58

42

59

43

60

44

61

45

62

46

63

47

64

48 65

49

66

50

67

51

68

52

69

53

70

54

71

55

72

56

73

108

26.5

109

24.2

32.5

225

30.5

122

308

636

182

80.6

300

367

177

401

192

601

401

815

478

-150

-210

-247

-231

-219

-195

-96.6

-78.5

-74

-116

-48.6

Fig

ure

C.1

3: L

2 N

um

eric

al Z

uri

ch S

trai

ns

for

Loa

d S

tage

s 1—

2 (u

nit

s: με)

99

L

oad

Stag

e 3

V

=29

8.7

kN

0.5

6 of

ult

imat

e

12

34

56

78

910

1112

13

14

15

1617

1920

22

2425

28

2930

3132

33

34

35

36

3738

39

-733

-235

-422

-45.6

-58.4

-525

-791

-622

-524

-863

-69.8

-90.1

-317

-169

-514

-492

-540

-609

-320

-713

-389

-778

-442

-46

1

-3

59

-753

-4

20

-5

07

-2

05

-2

85

-2

7.3

-4

66

-4

15

-6

79

-4

17

-5

10

-5

50

-8

42

1821

23

26

27

409

475

292

553

604

812

613

493

890

40444

104

974

813

1286

724

766

735

862

339

374

108

88.9

264 681

555 1031

456 583

188 284

673 1876

1496 890

175 526

583 533

1286 717

477 1109

1970 -28.2

505 1110

1202

1773

781

1020

1828

1556

1632

1582

1297

2237

1981

256

1

1493

225

0

163

5

144

2

150

6

166

5

173

4

163

4

701

211

6

992

184

8

268

0

40

57

41

58

42

59

43

60

44

61

45

62

46

63

47

64

48

65

49

66

50

67

51

68

52

69

53

70

54

71

55

72

56

73

157

85.5

154

175

157

613

574

304

451

898

362

266

674

566

331

572

482

925

720

1258

934

-309

-307

-397

-275

-245

-228

-68.7

-120

-173

-97.2

-50.7

Loa

d St

age

4

V=

399.

5 kN

0

.75

of u

ltim

ate

12

34

56

78

910

1112

13

14

1516

1719

2022

25

2829

3031

3233

3435

36

3738

39

-481

-7.08

-694

-392

-404

1-1082

-658

1

-810

-677

7-29.7

-205

-764

-91

2

-93

2

-111

1

-66

8

-11

08

-790

-69

1

-505

-403

-42

1

-71

6

-5

24

-6

60

-4

38

-4

01

-2

81

-5

15

2

-4

72

-6

98

-4

54

-6

12

1821

23

2426

27

101

775

549

685

980

968

1076

353

1107

106

529

493

431

163

1027

422

1382

961

884

1220

704

584

498

260

112

0.3

740 703

1243 1092

863 1166

551 857

1030 2784

2142 1370

496 1068

1093 845

1689 992

1064 1577

2758 93

1216 1701

1991

2338

1409

1623

2352

2212

2249

2473

1750

3255

2953

3939

2433

27

42

23

72

25

33

22

51

24

75

17

4

22

27

92

3

26

18

11

91

43

0

37

99

-6

22

2

-8

67

40

57

41

58

42

59

43

60

44

61

45

62

46

63

47

64

48 65

49

66

50

67

51

68

52

69

53

70

54

71

55

72

56

73

129

114

319

82.2

68.2

788

891

533

270

1158

405

425

778

774

334

729

497

1165

818

1617

1068

-377

-413

-412

-311

-240

-152

-93.1

-175

-423

-200

-6.35

Fig

ure

C.1

4: L

2 N

um

eric

al Z

uri

ch S

trai

ns

for

Loa

d S

tage

3—

4 (u

nit

s: με)

100

L

oad

Stag

e 5

V

=47

9.5

kN

0.9

0 of

ult

imat

e

12

34

56

78

910

1112

13

14

15

1617

1920

22

2425

28

2930

3132

33

34

35

36

3738

39

-642

-253

-1043

-741

-681

-1552

-422

-1066

-941

-105

-77.4

-159

-53.1

-402

-715

-770

-79

9

-974

-28

6

-78

6

-582

-11

22

-551

-72

7

-65

9

-925

-7

40

-7

76

-7

08

-5

70

-4

50

-7

54

-3

91

-9

73

-7

20

-8

182

-7

98

-1

137

1821

23

26

27

203

327

756

1215

1998

1296

1964

417

966

6.72

453

241

244

1243

1302

1635

1574

1318

864

1278

769

579

772

341

761 1285

1373 1370

1036 1481

343 1020

1164 2812

3113 1160

763 1723

1650 1587

2146 1230

1620 1634

4064

2530 2080

2710

2604

1784

1780

2389

2992

2719

3097

2205

4609

3968

5616

2916

33

41

28

28

32

15

23

84

28

80

30

35

32

26

14

15

31

26

1

33

27

79

46

68

40

57

41

58

42

59

43

60

44

61

45

62

46

63

47

64

48

65

49

66

50

67

51

68

52

69

53

70

54

71

55

72

56

73

48.3

418

525

103

378

515

287

501

720

1638

627

193

1376

720

583

1042

987

615

1029

801

1484

1155

1967

1472

-430

-210

-422

-152

-243

-8.56

-94.7

-83.5

Loa

d St

age

6

V=

532.

3 kN

Pea

k lo

ad

12

34

56

78

910

1112

13

14

1516

1719

2021

2225

2829

3031

3233

3435

36

3738

39

-227

-914

-950

-380

-952

-665

-22.3

-562

-61.5

1-1178

-749

2

-938

1-877

-292

-190

-112

-201

-497

-736

-677

-793

-107

0

-293

-689

-654

-135

9

-631

-495

-503

-627

-6

25

-6

38

-7

64

-4

20

-4

19

-6

08

-7

32

-9

48

-6

36

-7

19

-7

17

-9

94

1823

2426

27

664

1798

3024

1967

2759

99.7

860

423

205

387

1207

926

3368

1758

523

2344

1019

789

224

197

782 1834

1531 1642

1131 2074

289 1097

1430 4073

3409 2394

943 2192

2241 1667

2982 2010

3483 1741

5778

4260 2500

3662

2654

2024

1791

2331

2699

3152

4386

3579

6678

6325

8661

4617

377

6

302

2

377

3

256

6

348

5

370

5

372

2

182

6

382

0

146

8

356

9

620

8

40

57

41

58

42

59

43

60

44

61

45

62

46

63

47

64

48 65

49

66

50

67

51

68

52

69

53

70

54

71

55

72

56

7371.8

473

837

249

405

1282

50.5

931

1432

1787

397

129

1532

1131

799

1002

1268

775

914

897

1422

1316

1937

1586

-470

-421

-462

-359

-65.8

-310

-459

-541

Fig

ure

C.1

4: L

2 N

um

eric

al Z

uri

ch S

trai

ns

(un

its:

με)

Loa

d S

tage

5—

6

101

C.3 M1

0

100

200

300

400

500

0 1 2 3 4 5 6 7

Displacement (mm)

V (kN)

8

WLD

TCW

TC

TCE

ELD

Figure C.15: Net Displacement of M1 Computed Based on Vertical LVDT Data

0.0

100.0

200.0

300.0

400.0

500.0

-1 1 3 5 7 9

Shear Strain (mm/m)

V (kN)

11

Figure C.16: Shear Strain of M1 Measured by the Cross LVDTs

102

Cro

ss L

VD

Ts

Ver

tica

l LV

DT

s 3D

Sca

nner

C

lino

met

erS

trai

n G

auge

s

Net

Dis

plac

emen

t of

Bea

m

Sup

port

Dis

plac

emen

tD

set

Tim

e V

γ

– C

ente

r W

LD

T

CW

T

C

TC

E

EL

D

Wes

t E

ast

Wes

t

Dia

phra

gm

Rot

atio

n

B2

C2

T2

(#)

(h:m

m:s

s)

(kN

) (με)

(m

m)

(mm

) (m

m)

(mm

) (m

m)

(mm

) (m

m)

(deg

rees

)(με)

)(με

(με)

Loa

d

Stag

e

0 in

itia

lize

0

0 0

0 0

0 0

0 0

0 0

0 0

6 0:

00:0

0 2.

6 5

0.13

0.

02

0.05

0.

03

0.10

0.

09

0.01

0.

000

1 0

4

33

0:17

:06

109.

1 39

0 0.

57

0.29

0.

41

0.47

0.

57

0.47

0.

34

0.03

7 23

35

52

1

42

0:38

:04

96.9

57

4 0.

67

0.33

0.

49

0.51

0.

60

0.46

0.

30

0.04

0 55

17

16

4

118

0:53

:23

200.

1 17

65

1.43

0.

57

0.87

1.

19

1.27

0.

95

0.62

0.

080

458

1255

293

2

133

1:17

:15

180.

0 17

00

1.42

0.

61

0.88

1.

20

1.27

1.

08

0.56

0.

045

440

1188

283

272

1:32

:45

301.

1 28

96

2.40

0.

99

1.61

2.

13

2.15

1.

81

0.93

0.

12

688

1928

403

3

295

1:55

:41

269

2781

2.

38

1.02

1.

61

2.07

2.

14

1.95

0.

83

0.12

65

818

3538

5

431

2:08

:19

401.

4 43

87

3.83

1.

82

2.71

3.

35

3.20

2.

17

1.24

0.

19

988

2835

510

4

461

3:40

:26

365.

1 44

00

3.69

1.

87

2.70

3.

34

3.23

2.

52

1.13

0.

19

930

2698

475

513

3:45

:58

450.

5 56

55

4.80

2.

69

3.89

4.

48

4.14

2.

57

1.40

0.

25

1113

3250

610

5

535

4:07

:49

401.

4 55

91

4.66

2.

76

3.92

4.

43

4.12

2.

59

1.24

0.

23

1048

3025

570

onse

t to

fail

ure

580

4:13

:25

456.

9 64

94

5.58

3.

47

4.81

5.

27

4.70

2.

47

1.42

0.

27

1200

3350

613

ulti

mat

e

Tab

le C

.3:

Loa

d S

tage

Dat

a fo

r S

pec

imen

M1

103

0.1

5

0.1

0.1

0.1

0.15

0.1

Loa

d st

age

1 V

=10

9.1

kN

0.24

of

ulti

mat

e

0—

1

1—2

Dis

plac

emen

t bet

wee

n

load

sta

ges

(sca

led

50x)

Abs

olut

e di

spla

ced

shap

es (

scal

ed 3

0x)

0.2

0.10.1

5

0.1

5

0.1

0.1

0.1

5

0.1

0.1

0.1

0.2

0.1

5

Loa

d st

age

2 V

=20

0.1

kN

0.44

of

ulti

mat

e

0—

2

2—3

0.2

0.2

0.1

0.15

0.15

0.2

0.15

0.2

0.1

5

0.1

5

0.1

50

.1

0.2

0.15

Loa

d st

age

3 V

=30

1.1

kN

0.66

of

ulti

mat

e

0—

3

Fig

ure

C.1

7: M

1 C

rack

Tra

ces

and

Zu

rich

Dis

pla

ced

Sh

apes

104

3—4

Dis

plac

emen

t bet

wee

n

load

sta

ges

(sca

led

50x)

Abs

olut

e di

spla

ced

shap

es (

scal

ed 3

0x)

0.25

0.2

0.1

0.1

5

0.2

50.

25

0.2

0.2

50.3

0.2

0.2

0.1

5

0.2

50.1

5

0.2

Loa

d st

age

4 V

=40

1.4

kN

0.88

of

ulti

mat

e

0—

4

4—5

0.3

0.2

0.1

50.2

0.2

50

.25

0.4

5

0.2

50.4

5

0.2

0.25

0.1

5

0.3

0.2

5

0.5

50

.2

Loa

d st

age

5 V

=45

0.5

kN

0.99

of

ulti

mat

e

0—

5

Fai

lure

V

=45

6.9

kN

Fig

ure

C.1

8: M

1 C

rack

Tra

ces

and

Zu

rich

Dis

pla

ced

Sh

apes

105


1234567

891011121314

15161718192021

-29.9-78.2-110

-89.6-99.2-179-204

-17.9-10.9-110-127

-25

-35

-1

99

-1

51

-1

31

-2

02

-2

02

15

7

-4

3.6

-117

-47.5

-1

65

-68.7

-8

8.3

-107

-1

85

-128

-2

79

59658.5615

72.91604

12.57.8

348

95.471.1

85.50.70

7

13.711.6

85754.2

994

8.51347

97.6

229

45.2

818

972

-

1699

1

42

1546

22

33

23

34

24

35

25

36

26

37

27

38

28

39

29

40

30

41

31

42

32

43

116067.221175.529.574.6

23.3-227

-59.2

-91.6

-47.3

-117 -147 -125 -116 -88.1 -13.2 -32

-7


1234567

8910

161718192021

-95

-306-444

-245-1.65

-151

-290

346

-1

42

-6

6.3

-113

-166

-3

12

-8

2.8

-6

66

-4

38

-5

88

-5

86

11121314

15

177463491122645

5472052371265

975275241138

68776

0

28.3

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998

2287

2099

926

1240

173

-143

1

738

815

1

36

1638

2

9.7

2607

2035

1984

1790

867

839

819

1576

2539

22

33

23

34

24

35

25

36

26

37

27

38

28

39

29

40

30

41

31

42

32

43

52.7

35

98

95.1

257

318

546

220

393

395

447

532

433

369

383

593

-177

-105

-149

-133


1234567

89101114

161718192021

-344

-274

.6

-4

23

-1

51

-5

2.4

-1

27

-4

93

-4

44

-8

6.8

-6

36

-5

30

-7

71

-6

93

1123

15

739334461665393602

10334984913802014

1196705814239382

908

1290

1469

1541

3045

1683

3062

1652

2907

1636

2060

1044

-5428

68

2412

2382

4

7.4

3526

3644

2974

2809

2583

1435

2559

2553

2175

3554

22

33

23

34

24

35

25

36

26

37

27

38

28

39

29

40

30

41

31

42

32

43121

109

241

51.5

277

208

434

231

370

217

742

-253

-241

-852

-591

-482

-372

-560

-166

-293

Figure C.19: M1 Numerical Zurich Strains for Load Stages 1—3 (units: με)

106


1234567

891213

1617181920

-147

111

-7

09

-3

02

-9

0.5

-9

8.2

-7

69

-2

71

-7

8.3

-8

47

-7

00

-9

27

-8

24

101114

1521

14382349011286409644

169010926494992246

18446791003196911724.1

1293

2230

2587

2775

4556

2558

4712

2959

4321

2487

2851

1384

-3688

4028

3904

2

90

5608

5623

4090

3453

4233

2920

4183

4462

2843

4254

22

33

23

34

24

35

25

36

26

37

27

38

28

39

29

40

30

41

31

42

32

43

142

616

277

550

627

410

318

444

593

730

499

588

672

930

-665

-338

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-5.5


1234567

891011121314

15161718192021

-427

-727-228

31

314

-767

-53.

4-9

42

-1

79

-8

63

-6

33

-9

06

-8

80

20364018752161441854

169926897532672411

222513025874140

14172684

41153387

10742208

8614570

5596145

33121653

-37468

5535

2

29

7482

2

089

9707

8890

3

98

4706

4349

1

50

4855

3121

6034

8809

4302

4904

22

33

23

34

24

35

25

36

26

37

27

38

28

39

29

40

30

41

31

42

32

43

9.83

262

566

334

928

966

1019

811

1191

489

670

578

1019

838

988

678

1070

1051

-182

-220

Figure C.20: M1 Numerical Zurich Strains for Load Stages 4—5 (units: με)

107

C.4 M2

0

100

200

300

400

500

600

0 2 4 6 8 10 12 14 16 1

Displacement (mm)

V (kN)

8

WLD

TCW

TC

TCE

ELD

Figure C.21: Net Displacement of M2 Computed Based on Vertical LVDT Data

0

100

200

300

400

500

600

0 5 10 15 20 25 30

Shear Strain (mm/m)

V (kN)

Figure C.22: Shear Strain of M2 Measured by the Cross LVDTs

108

Cro

ss L

VD

Ts

Ver

tica

l LV

DT

s 3D

Sca

nner

C

lino

met

erS

trai

n G

auge

s

Net

Dis

plac

emen

t of

Bea

m

Sup

port

Dis

plac

emen

tD

set

Tim

e V

γ

– C

ente

r W

LD

T

CW

T

C

TC

E

EL

D

Wes

t E

ast

Wes

t

Dia

phra

gm

Rot

atio

n

B2

C2

T2

(#)

(h:m

m:s

s)

(kN

) (με)

(m

m)

(mm

) (m

m)

(mm

) (m

m)

(mm

) (m

m)

(deg

rees

)(με)

)(με

(με)

Loa

d

Stag

e

0 in

itia

lize

0

0 0

0 0

0 0

0 0

0 0

0 0

5 0:

00:0

0 4.

3 17

1 0.

19

0.16

0.

13

0.20

0.

17

0.01

2 0.

013

0.12

6

-3

-7

52

0:05

:55

101.

0 38

0 0.

40

0.21

0.

29

0.40

0.

35

0.35

0.

31

0.13

73

60

029

1

62

0:32

:12

89.3

34

5 0.

40

0.19

0.

30

0.42

0.

40

0.38

0.

28

0.88

83

59

534

153

0:45

:17

201.

6 12

00

1.42

0.

64

0.89

1.

20

1.18

0.

61

0.62

0.

12

221

1058

290

2

164

1:08

:13

173.

2 96

6 1.

23

0.56

0.

81

1.13

1.

12

0.73

0.

54

0.08

21

410

1328

0

247

1:16

:34

303.

2 19

92

2.01

0.

80

1.20

1.

67

1.70

1.

29

0.94

0.

24

365

1410

490

3

270

2:19

:17

271.

2 18

64

2.08

0.

89

1.27

1.

70

1.70

1.

43

0.84

0.

70

353

1360

470

345

2:28

:35

399.

3 32

49

3.04

1.

25

1.91

2.

50

2.44

1.

69

1.24

0.

53

665

1968

650

4

359

2:45

:01

354.

4 30

30

2.82

1.

21

1.82

2.

42

2.39

1.

79

1.10

0.

20

633

1870

608

413

2:52

:26

450.

5 43

29

3.64

1.

85

2.72

3.

24

3.09

1.

92

1.40

0.

04

845

2160

705

5

443

3:08

:16

405.

7 40

44

3.44

1.

84

2.71

3.

15

3.02

1.

97

1.26

0.

45

795

2058

663

521

3:17

:11

501.

8 54

52

4.43

2.

59

3.84

4.

06

3.79

2.

05

1.56

0.

39

853

2320

743

6

537

3:32

:15

452.

7 52

08

4.23

2.

59

3.79

3.

96

3.70

2.

08

1.40

0.

44

813

2240

705

616

3:40

:08

531.

7 75

14

5.78

4.

36

5.74

5.

52

4.87

2.

04

1.65

0.

25

973

2543

698

7

ulti

mat

e

641

3:54

:06

476.

2 75

18

5.65

4.

44

5.76

5.

56

4.86

2.

03

1.48

0.

42

918

2400

620

onse

t to

fail

ure

696

3:57

:58

162.

3 27

444

11.3

3 12

.07

17.5

4 15

.30

11.3

0 1.

85

0.50

0.

71

1553

895

-194

8ab

rupt

fail

ure

Tab

le C

.4:

Loa

d S

tage

Dat

a fo

r S

pec

imen

M2

109

0.0

5

Loa

d st

age

1 V

=10

1.0

kN

0.19

of

ulti

mat

e

0—

1

1—2

Dis

plac

emen

t bet

wee

n

load

sta

ges

(sca

led

50x)

Abs

olut

e di

spla

ced

shap

es (

scal

ed 3

0x)

0.0

5 0.0

50.

05

0.0

5

0.0

5

0.0

5

0.0

5 0.0

5

0.1

Loa

d st

age

2 V

=20

1.6

kN

0.38

of

ulti

mat

e

0—

2

2—3

0.0

5

0.05

0.1

0.1

0.1

5

0.0

5

0.1

0.1

0.05

Loa

d st

age

3 V

=30

3.2

kN

0.57

of

ulti

mat

e

0—

3

Fig

ure

C.2

3: M

2 C

rack

Tra

ces

and

Zu

rich

Dis

pla

ced

Sh

apes

110

3—4

Dis

plac

emen

t bet

wee

n

load

sta

ges

(sca

led

50x)

Abs

olut

e di

spla

ced

shap

es (

scal

ed 3

0x)

0.1

0.1 0.

10

.15

0.1

0.1

5

0.1

0.05

0.15

0.1

0.0

5

Loa

d st

age

4 V

=39

9.3

kN

0.75

of

ulti

mat

e

0—

4

4—5

0.15

0.1

5 0.15

0.25

0.1

0.2

0.15

0.1

0.2

0.15

0.15

0.1

Loa

d st

age

5 V

=45

0.5

kN

0.85

of

ulti

mat

e

0—

5

5—6

Fig

ure

C.2

4: M

2 C

rack

Tra

ces

and

Zu

rich

Dis

pla

ced

Sh

apes

111

0.2

50

.2 0.2

0.4

0.1

0.2

5

0.15

0.1

0.25

0.25

0.2

0.2

5 0.1

5

Loa

d st

age

6 V

=50

1.8

kN

0.94

of

ulti

mat

e

0—

6

6—7

Dis

plac

emen

t bet

wee

n

load

sta

ges

(sca

led

50x)

Abs

olut

e di

spla

ced

shap

es (

scal

ed 3

0x)

0.2

50

.3 0.4

0.5

0.1

0.25

0.15

0.1

0.4

5

0.2

5

0.3

50.

3

0.15

Loa

d st

age

7 V

=53

1.7

kN

Pea

k lo

ad

0—

7

Fai

lure

V

=53

1.7

kN

Fig

ure

C.2

5: M

2 C

rack

Tra

ces

and

Zu

rich

Dis

pla

ced

Sh

apes

112

Figure C.26: M2 Numerical Zurich Strains for Load Stage 1—4 (units: με)

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113


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Figure C.27: M2 Numerical Zurich Strains for Load Stage 5—7 (units: με)

114

C.5 S1

0

100

200

300

400

500

600

700

-0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5

Displacement (mm)

V (kN)

WLD

TCW

TC

TCE

ELD

Figure C.28: Net Displacement of S1 Computed Based on Vertical LVDT Data

0

100

200

300

400

500

600

700

-1 1 3 5 7 9 11 13

Shear Strain (mm/m)

V (kN)

15

Figure C.29: Shear Strain of S1 Measured by the Cross LVDTs

115

Cro

ss L

VD

Ts

Ver

tica

l LV

DT

s 3D

Sca

nner

C

lino

met

erS

trai

n G

auge

s

Net

Dis

plac

emen

t of

Bea

m

Sup

port

Dis

plac

emen

tD

set

Tim

e V

γ

– C

ente

r W

LD

T

CW

T

C

TC

E

EL

D

Wes

t E

ast

Wes

t

Dia

phra

gm

Rot

atio

n

B2

C2

T2

(#)

(h:m

m:s

s)

(kN

) (με)

(m

m)

(mm

) (m

m)

(mm

) (m

m)

(mm

) (m

m)

(deg

rees

)(με)

)(με

(με)

Loa

d

Stag

e

0 in

itia

lize

0

0 0

0 0

0 0

0 0

0 0

0 0

11

0:00

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012

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008

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11

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007

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55

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2 65

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14

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33

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0 84

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17

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145

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4 0.

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56

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71

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55

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048

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82

153

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0 72

0 0.

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57

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049

029

3

231

1:02

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353.

8 18

93

1.12

0.

78

1.05

1.

23

1.24

2.

07

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0.

094

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1398

408

3

240

1:15

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316.

2 18

42

1.05

0.

78

1.05

1.

22

1.29

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32

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0.

10

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1378

390

349

1:28

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471.

8 32

20

1.70

1.

20

1.55

1.

79

1.84

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60

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12

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2380

428

4

360

1:45

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1 31

61

1.65

1.

25

1.60

1.

88

1.94

2.

70

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12

763

2350

418

396

1:50

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0 39

70

1.94

1.

52

1.94

2.

28

2.45

2.

76

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0.

11

878

2755

468

5

409

1:59

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2 38

10

1.80

1.

55

1.98

2.

35

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2.

73

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10

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2575

448

488

2:04

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7 48

81

2.23

1.

82

2.29

2.

70

2.94

2.

80

1.37

0.

11

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2953

535

6

502

2:13

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9 46

96

2.02

1.

82

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2.

79

3.04

2.

79

1.20

0.

10

923

2728

488

641

2:20

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639.

9 63

64

2.50

2.

12

2.71

3.

32

3.54

2.

90

1.49

0.

13

1115

3100

408

7

ulti

mat

e

656

2:29

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557.

1 63

47

2.33

2.

14

2.77

3.

42

3.66

2.

89

1.30

0.

13

1035

2865

370

onse

t to

fail

ure

Tab

le C

.5:

Loa

d S

tage

Dat

a fo

r S

pec

imen

S1

116

0.10.05

Load stage 1V=129.2 kN0.20 of ultimate

0—1

1—2

Displacement between

load stages (scaled 50x)

Absolute displaced

Shapes (scaled 30x)

0.150.15

0.05


0—2

2—3

0.05

0.20.2

0.15

0.1


0—3

3—4

0.05 0.05

0.2

0.1

0.20.15

0.1


0—4

4—5

Figure C.30: S1 Crack Traces and Zurich Displaced Shapes

117

0.10.1

0.25

0.1

0.20.15

0.15


0—5

5—6



Absolute displaced

Shapes (scaled 30x)

0.10.1

0.3

0.1

0.250.2

0.15


0—6

6—7

0.150.1

0.3

0.4

0.40.25

0.2

0.25

Load stage 7V=639.9 kNPeak load

0—7

Failure V=639.9 kN


118




123

456

89

-90-119

-147

-112

-1

98

-2

90

-2

37

-9

1.3

7

14.8937

49.9495

39.7

121

76196.8

27.3

1007

156

196

10

19

11

20

12

21

13

22

14

23

15

24

16

25

17

26

18

27

50.3

43.6

52.5

32.3

152

7.8

92.771.5

53.9

119

37311.7

180

39.2 -5.32

-65.3

123

45

7

1169656

1253

1082

84481

0

1453

2565

118

1682

6

89

-276

-116-46.3

-109

-118

-53.5

-496

-4

01

-3

64

-3

15

10

19

11

20

12

21

13

22

14

23

15

24

16

25

17

26

18

27 69.1159

443

111

229

256

166

162

229

619

46.3

39.3

439

115

-153-70.9

123

4

7

1788706

11401489

1791

1507

16161811

10971230

3556

3083

1868

3752

56

89 -235

-164

-6

31

-5

32

-6

82

-8

92

10

19

11

20

12

21

13

22

14

23

15

24

16

25

17

26

18

27

529

482

400

185

869

259

509

269

104

352

206

1117

229

168

687

85.9

123

456

7

2335986

21691855

5451511

244

065

6

219

1292

1

137

2262

8

5228

3882

3704

5133

89

-7

15 -5

85

-8

88

-9

49

10

19

11

20

12

21

13

22

14

23

15

24

16

25

17

26

18

27

1238

603

661

346

1143

476

739

336

345

629

192

1369

234

452

913

118


Figure C.32: S1 Numerical Zurich Strains for Load Stages 1—4 (units: με)

119



123

456

789

-8

22 -5

83

-9

25

-1

086

27361033

26121964

5801409

2628369

23153191

16692893

6077

4297

4290

5874

10

19

11

20

12

21

13

22

14

23

15

24

16

25

17

26

18

27

1848

800

935

389

1434

616

672

408

253

741

78.2

1620

182

499

986

78.1

123

46

7

28811433

31382430

90116092770

527

26673196

20233129

6478

4744

5

89

-9

05

-5

73

4711

6263

-787

-1

247

10

19

11

20

12

21

13

22

14

23

15

24

16

25

17

26

18

27

2001

968

1486

457

2607

776758

291

813

83.9

1385

153

374

1034

12.4

-76.4


123

46

7

30761827

31723838

11261856

4384

993

4391

3638

2316

3994

8003

6586

5104

8181

5

89

-8

57

-6

57

-8

02

-1

579

10

19

11

20

12

21

13

22

14

23

15

24

16

25

17

26

18

27

1478

1102

3015

651

4070

9431209

31.8

1123

174

1875

245

689

1232

96.5

-228


120

C.6 S2

0

100

200

300

400

500

600

700

0 1 2 3 4 5 6

Displacement (mm)

V (kN)

WLD

TCW

TC

TCE

ELD

Figure C.34: Net Displacement of S2 Computed Based on Vertical LVDT Data

0

100

200

300

400

500

600

700

-1 1 3 5 7 9 11 13 15 17

Shear Strain (mm/m)

V (kN)

19

Figure C.35: Shear Strain of S2 Measured by the Cross LVDTs

121

Cro

ss L

VD

Ts

Ver

tica

l LV

DT

s 3D

Sca

nner

C

lino

met

erS

trai

n G

auge

s

Net

Dis

plac

emen

t of

Bea

m

Sup

port

Dis

plac

emen

tD

set

Tim

e V

γ

– C

ente

r W

LD

T

CW

TC

T

CE

E

LD

Wes

t E

ast

Wes

t

Dia

phra

gm

Rot

atio

n

B2

C2

T2

(#)

(h:m

m:s

s)

(kN

) (με)

(m

m)

(mm

)(m

m)

(mm

)(m

m)

(mm

) (m

m)

(deg

rees

)(με)

)(με

(με)

Loa

d

Stag

e

0 in

itia

lize

0

0 0

0 0

0 0

0 0

0 0

0 0

11

0:00

:00

4.3

-30

0.39

-0

.007

-0.0

07-0

.008

-0.0

080.

007

0.01

0 0.

007

-3

1 -4

24

0:03

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50.2

37

0.

43

0.29

0.

32

0.33

0.

35

0.01

2 0.

12

-0.0

02

-3

3 -8

1

32

0:08

:00

9.0

-26

0.30

0.

08

0.13

0.

13

0.16

0.

07

0.02

0.

000

-2

1 -5

65

0:13

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123.

0 42

9 0.

17

0.20

0.

35

0.45

0.

53

0.51

0.

29

-0.0

10

79

688

52

1

(res

tart

)

75

0:29

:30

115.

4 42

4 0.

14

0.21

0.

36

0.47

0.

56

0.56

0.

27

-0.0

20

88

665

60

156

0:36

:35

236.

6 11

62

0.13

0.

27

0.55

0.

76

0.77

1.

22

0.55

-0

.002

23

210

8814

82

165

0:53

:20

219.

3 11

21

0.03

0.

22

0.51

0.

73

0.80

1.

33

0.51

-0

.009

22

810

1814

9

235

1:01

:30

353.

8 22

79

0.27

0.

37

0.76

1.

07

1.08

2.

13

0.82

0.

030

410

1410

245

3

251

1:19

:24

306.

1 21

49

0.14

0.

35

0.73

1.

07

1.15

2.

32

0.71

0.

034

390

1300

235

330

1:26

:13

469.

2 38

19

0.82

0.

72

1.17

1.

64

1.67

3.

38

1.09

0.

083

738

1708

343

4

352

1:43

:50

414.

0 37

39

0.71

0.

73

1.20

1.

67

1.79

3.

65

0.96

0.

088

708

1578

323

487

1:52

:17

589.

7 55

27

1.22

1.

17

1.74

2.

37

2.49

4.

08

1.37

0.

11

963

2050

440

5

502

2:08

:25

516.

9 54

76

1.06

1.

17

1.75

2.

40

2.60

4.

26

1.20

0.

10

910

1870

413

596

2:15

:30

649.

9 68

91

1.47

1.

40

2.05

2.

78

2.90

4.

50

1.51

0.

13

1080

2258

510

6

608

2:26

:56

572.

1 67

73

1.30

1.

43

2.05

2.

78

2.97

4.

57

1.33

0.

13

1045

2073

485

676

2:31

:01

677.

5 82

90

1.63

1.

64

2.32

3.

11

3.22

4.

82

1.58

0.

16

1298

2500

555

7

ulti

mat

e

708

2:47

:24

602.

2 91

82

1.73

2.

02

2.61

3.

44

3.53

4.

90

1.40

0.

18

1383

2563

453

onse

t to

fail

ure

Tab

le C

.6:

Loa

d S

tage

Dat

a fo

r S

pec

imen

S2

122

0.1


0—1

1—2



Absolute displaced

Shapes (scaled 30x)

0.1

0.1

0.1

0.05


0—2

2—3

0.15

0.15

0.05

0.150.1

0.1

0.15


0—3

3—4

0.1

0.15 0.2

0.15

0.1

0.15

0.1

0.15

0.1


0—4

4—5


123

0.15

0.250.3

0.2

0.1

0.15

0.1

0.15

0.15


0—5

5—6



Absolute displaced

Shapes (scaled 30x)

0.15

0.25 0.30.2

0.1

0.15

0.1

0.2

0.2


0—6

6—7

0.15

0.25 0.550.25

0.15

0.2

0.15

0.2

0.2

Load stage 7V=677.5 kNPeak load

0—7

Failure V=677.5 kN


124




123

45

89

-60.9

-22.3

-9.57

-71.

5

-107

-133

-2

30 -1

90

-1

06

-48.8

-2

42

6

7

675

798

599

65.6

7670

781

843

799

10

19

11

20

12

21

13

22

14

23

15

24

16

25

17

26

18

27

2.47

20.8

53.2

135

61.4

168

238

40.6

208

310

81.6

90.7

37.9

26.940.3

-1.77

123

456

7

981

4851201

1066

442

59.2

1644

407

489

89

-180

-89

-43.1

-4

00

2244

1660

624

2267

-3

57

-4

03

-7

22

10

19

11

20

12

21

13

22

14

23

15

24

16

25

17

26

18

27 18.7150

239

317

341

203

262

437

238

405

163173 -30.8-31.9

-31.9-60

123

46

7

1202

8411621

1751041

94820

1

246965

6

1140

3309

2400

1165

5

89

-237

-145

-5

67

-4

82

-4

99

-1

1

3263

28

10

19

11

20

12

21

13

22

14

23

15

24

16

25

17

26

18

27 190274

391

527

360

210

315

613

444

401

380

334

219

11.3

-81.6-16.3


123

456

7

110380

11721819

339933

1440390

31871231

1977

4078

89

-56.5

-7

01

3131

1935

-653

-6

51

4309

-165

0

10

19

11

20

12

21

13

22

14

23

15

24

16

25

17

26

18

27 458

177

304

632

516

575

175

307

1016

477

529

621

801

268 -109

-5.65


125



123

456

789

-6

96 -6

86

-6

01

-1

807

741775

17001840

423941

2056

333

3948

1573

343

2654

4983

4146

2456

5265

10

19

11

20

12

21

13

22

14

23

15

24

16

25

17

26

18

27 574

340

454

895

500

795

247

304

1271

651

646

842

1016

404

484

-95.8

123

46

7

5621193

19421941

9399832317

218

44231633

6142590

5446

4723

2990

5

89

-9

14

-6

82

-7

59

-2

2

5851

75

10

19

11

20

12

21

13

22

14

23

15

24

16

25

17

26

18

27 609

360

485

1044

406

926

232

494

1276

870

831

1011

1799

453

516

-152


123

456

7

1321

28072355

11821743

3007

613

7707

2309

660347

0

7698

6663

3822

8416

89

-88.6

-9

34

-6

97

-5

80

-3

692

10

19

11

20

12

21

13

22

14

23

15

24

16

25

17

26

18

27 633

255

467

1175

363

1139

249

948

1411

964

1218

1223

1945

647

120

-211


126

Shear Resistance of High Strength Concrete I-Beams with ... · Shear Resistance of High Strength...

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Transcript of Shear Resistance of High Strength Concrete I-Beams with ... · Shear Resistance of High Strength...