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IMPROVEMENT OF PUNCHING SHEAR CAPACITY OF EXISTING FLAT PLATES BY USING SHEAR REINFORCEMENTS Md. Tusar Khandokar DEPARTMENT OF CIVIL ENGINEERING BANGLADESH UNIVERSITY OF ENGINEERING AND TECHNOLOGY December, 2015

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IMPROVEMENT OF PUNCHING SHEAR CAPACITY OF EXISTING

FLAT PLATES BY USING SHEAR REINFORCEMENTS

Md. Tusar Khandokar

DEPARTMENT OF CIVIL ENGINEERING

BANGLADESH UNIVERSITY OF ENGINEERING AND TECHNOLOGY

December, 2015

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IMPROVEMENT OF PUNCHING SHEAR CAPACITY OF EXISTING FLAT PLATES

BY USING SHEAR REINFORCEMENTS

A Thesis

by

Md. Tusar Khandokar

Submitted to the

Department of Civil Engineering,

Bangladesh University of Engineering and Technology (BUET), Dhaka

in partial fulfillment of the requirements for the degree

of

MASTER OF SCIENCE IN CIVIL ENGNEERING (STRUCTURAL)

DEPARTMENT OF CIVIL ENGINEERING

BANGLADESH UNIVERSITY OF ENGINEERING AND TECHNOLOGY

December, 2015

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DEDICATION

This thesis is dedicated to my parents and teachers

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ACKNOWLEDGEMENTS

First and foremost, I would like to admit the blessings of almighty, merciful, gracious Allah who

enables me to accomplish this thesis successfully.

I would like to take this opportunity to express my profound gratitude and deep regard to my

thesis supervisor Professor Dr. Raquib Ahsan, Department of Civil Engineering, Bangladesh

University of Engineering and Technology (BUET) for his exemplary guidance, quick response

and constant encouragement throughout the duration of the research. His valuable suggestions

and enthusiastic supervision were of immense help throughout my research work. Working

under him was an extremely knowledgeable experience for me.

I wish to express my gratitude and heartiest thanks to respected defence committee members

Prof. Dr. Abdul Muqtadir, Associate Prof. Dr. Mohammad Al Amin Siddique, Prof. Dr. Sharmin

Reza Chowdhury for their valuable advice and help in reviewing this thesis.

I would like to express my deep appreciation to Confidence Cement Limited and KSRM for their

material and technical support. It would not be possible to complete the thesis without their

assistance.

I would like to thank to all laboratory members for their advice and technical support throughout

the experimental program.

I pay my deepest homage to my family members. I am thankful to Ibrahim Hossain and Mst.

Nowrin Zakki for their unconditional help, inspire, blessings and great co-operation.

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ABSTRACT

As reinforced concrete flat plates do not contain beams, all the loads on slabs are transferred

directly to the columns. During an earthquake, the displacement-induced unbalanced moments

causes shear forces at the flat plate-column connections. Due to transfer of shear forces

combined with induced unbalanced moments between slab and column, brittle punching failure

can occur. Because of increase in applied loads and/or lack of consideration of seismic effects

during design or construction, a significant number of existing flat plates are currently required

to be strengthened against punching shear to avoid brittle punching failure. From literature

review, it is observed that use of U-stirrups as shear reinforcements with strong epoxy is very

convenient and effective in strengthening the punching shear capacities of flat plates.

Based on critical shear crack theory and structural mechanics, shear reinforcements have been

designed in the present study. Due to ease of accessibility and placement, U-stirrups are used for

retrofitting flat plate column connections.

In this experimental study, eight numbers half scale frame specimens were tested under lateral

cyclic loading to observe the punching capacity of flat plates. The test was loading control so

that the horizontal hydraulic jacks were used for imposing the cyclic loading. The specimens

were subjected to incremental cyclic loading provided by hydraulic jacks under constant axial or

gravity load and their load-deformation behavior was measured by dial gauges and video

extensometer. The behaviors of the strengthened flat plate column connection are compared to

the control models to observe improvement of punching shear capacity.

The joints without shear reinforcement underwent brittle failure under cyclic loading, but their

ductility increased with increased concrete strength. The joints with smaller flat plate thickness

strengthened with shear reinforcements showed equivalent load bearing capacity as compared to

that of greater plate thicknesses with enhanced ductile behavior. Due to use of shear

reinforcements, horizontal and vertical displacement capacities of flat plates under lateral loading

were increased compared to those of control specimen.

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TABLE OF CONTENTS

Page No.

DEDICATION ............................................................................................................................. iii

DECLARATION ............................................................................. Error! Bookmark not defined.

ACKNOWLEDGEMENTS .......................................................................................................... v

ABSTRACT.................................................................................................................................. vi

TABLE OF CONTENTS ........................................................................................................... vii

LIST OF FIGURES ....................................................................................................................... x

LIST OF TABLES ..................................................................................................................... xvi

NOTATIONS ........................................................................................................................... xviii

CHAPTER 1 ................................................................................................................................... 1

INTRODUCTION ......................................................................................................................... 1

1.1 General .............................................................................................................................. 1

1.2 Background of the Study................................................................................................... 1

1.3 Justification of the Study................................................................................................... 5

1.4 Objectives of the Research ................................................................................................ 6

1.5 Methodology ..................................................................................................................... 6

1.6 Scope of the Work............................................................................................................. 7

1.7 Organization of the Thesis ................................................................................................ 8

CHAPTER 2 ................................................................................................................................... 9

LITERATURE REVIEW ............................................................................................................. 9

2.1 General .............................................................................................................................. 9

2.2 Flat Plate ........................................................................................................................... 9

2.3 Shear Reinforcements ..................................................................................................... 10

2.4 Requirement of Shear Reinforcements for Lateral Loading in Flat Plates ..................... 12

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2.5 Retrofitting Strategy ........................................................................................................ 13

2.6 Guidelines for Use and Design of Shear Reinforcements in Flat Plates ......................... 14

2.6.1 Use of Shear Reinforcements .................................................................................. 14

2.6.2 Design of Shear Reinforcements to improve punching shear capacity ................... 16

2.6.3 Detailing of Shear Reinforcements in Plates ........................................................... 24

2.7 Cyclic Load ..................................................................................................................... 25

2.8 Literature Review of Earlier Research on Improvement of Punching Shear Capacity of

Flat Plate .................................................................................................................................... 26

2.9 Summary of Literature Review ....................................................................................... 32

CHAPTER 3 ................................................................................................................................. 33

MATERIAL PROPERTIES AND EXPERIMENTAL PROGRAM ..................................... 33

3.1 Introduction ..................................................................................................................... 33

3.2 Specimen Preparation ..................................................................................................... 33

3.2.1 Selection of Geometric Properties of Model Frames .............................................. 33

3.2.2 Material properties ................................................................................................... 40

3.3 Formation of Specimens ................................................................................................. 50

3.3.1 Base Beam and columns Construction .................................................................... 50

3.3.2 Flat Plate floor slab and Column top Construction ................................................. 52

3.3.3 Retrofitting Work ..................................................................................................... 53

3.4 Experimental Set Up, Testing Procedure, Data Acquisition ........................................... 59

CHAPTER 4 ................................................................................................................................. 62

ANALYSIS OF EXPERIMENTAL RESULTS AND DISCUSSIONS .................................. 62

4.1 Introduction ..................................................................................................................... 62

4.2 Test Set Up and Testing Procedure ................................................................................. 62

4.3 Failure Modes of Flat Plate ............................................................................................. 63

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4.4 Test Result of Specimen S-3-C-3 .................................................................................... 64

4.5 Test Result of Specimen S-4-C-3 .................................................................................... 66

4.6 Test Result of Specimen S-5-C-3 .................................................................................... 69

4.7 Test Result of Specimen S-5.5-C-3 (Control) ................................................................. 70

4.8 Test Result of Specimen S-3-C-4 .................................................................................... 73

4.9 Test Result of Specimen S-4-C-4 .................................................................................... 75

4.10 Test Result of Specimen S-5-C-4 .................................................................................... 77

4.11 Test Result of Specimen S-5.5-C-4 (Control) ................................................................. 79

4.12 Load-Deformation Response .......................................................................................... 80

CHAPTER 5 ................................................................................................................................. 98

SUMMARY, CONCLUSIONS AND RECOMMENDATIONS ............................................. 98

5.1 Summary ......................................................................................................................... 98

5.2 Conclusions ..................................................................................................................... 99

5.4 Recommendations for Further Study ............................................................................ 100

REFERENCES .......................................................................................................................... 101

APPENDIX-A ............................................................................................................................ 106

APPENDIX-B ............................................................................................................................. 125

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LIST OF FIGURES

Page No.

Figure 1.1: Comparison of the behavior and strength of two slabs with and without shear

reinforcement (Muttoni et al. 2008). ..................................................................................... 2

Figure 1.2: Reinforcing of existing slabs against punching shear: (a) concreting or installing

of steel-precast capital; (b) widening of column; (c) addition of upper concrete layer; (d)

addition of glued flexural reinforcement; (e) post installed shear reinforcement with

mechanical anchorage; and (f) bonded post-installed shear reinforcement (Ruiz et al., 2010).

.............................................................................................................................................. 3

Figure 1.3: Post-installed shear reinforcement: (a) typical cross section; (b) view of nut,

washers, and bar; (c) detail of anchor head; and (d) installing by drilling of inclined holes

(Ruiz et al., 2010). ................................................................................................................ 4

Figure 2.1: Conventional stirrup cages (adopted from Nilson et al. 2010) ........................... 11

Figure 2.2: Shear Studs (adopted from Nilson et al. 2010) ................................................. 11

Figure 2.3: Shearhead Reinforcement (Nilson et al. 2010) ................................................. 12

Figure 2.4: Location of critical and effective section in flat plates. (Song et al. 2012) ........ 13

Figure 2.5: Penetrating post-installed punching shear reinforcement (Muttoni et al. 2008) . 15

Figure 2.6: Post-installed punching shear reinforcement applied only from bottom side of

the slab(Muttoni et al. 2008) ............................................................................................... 15

Figure 2.7: Critical shear crack and punching shear cone (adopted from Muttoni et al. 2008)

............................................................................................................................................ 17

Figure 2.8: Comparison of failure criterion for slabs without shear reinforcement (Eq. (2.3))

to 99test results (Ruiz et al. 2010) ....................................................................................... 18

Figure 2.9: Calculation of strength and deformation capacity at failure according to the

CSCT (Ruiz et al. 2010) ...................................................................................................... 19

Figure 2.10: Effective depth and control perimeter outside the shear-reinforced zone as

function of the punching shear reinforcing system(Muttoni et. al. 2009).: (a) studs; (b)

stirrups; (c) bonded reinforcement with anchorage plates; and (d) shearheads (Ruiz et al.

2010) ................................................................................................................................... 19

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Figure 2.11: Influence of cracking on crushing shear strength: (a) detail of compression

struts nearthe support region; (b) development of flexural crack; (c) development of a shear

crack; and(d) development of delamination crack. (Ruiz F. and Muttoni A., 2010) ............ 21

Figure 3.1 Typical RC Flat Plate Frame Building 3D View ................................................ 34

Figure 3.2 Selection of interior Flat Plate-column Frame Plan View (All Dimensions are in

milimetres) .......................................................................................................................... 35

Figure 3.3: Selection of interior Flat Plate-column Frame Elevation ................................... 36

Figure 3.4: Typical Half Scaled Model Dimension ............................................................. 36

Figure 3.5: Placements of top and bottom bars of Flat Plate Floor Slab .............................. 38

Figure 3.6: Grain Size Distribution curve of fine aggregates ............................................... 42

Figure 3.7: Grain Size Distribution curve of coarse aggregates ........................................... 43

Figure 3.8.: Coarse Aggregate ............................................................................................. 44

Figure 3.9: Fine Aggregate ................................................................................................. 44

Figure 3.10: Concrete Mixing ............................................................................................. 45

Figure 3.11: Slump Test ...................................................................................................... 45

Figure 3.12: Concrete Cylinders are Stored in Water. ......................................................... 49

Figure 3.13. Compressive Strength Testing of Cylinders ................................................... 49

Figure 3.14: Formwork Ready for Base Beam and columns ............................................... 51

Figure 3.15: Concrete pouring into Formwork ................................................................... 51

Figure 3.16: Using Mechanical Vibrator ............................................................................ 51

Figure 3.17: Base Beams after column After Casting. ......................................................... 52

Figure 3.18: Base Beams and Columns Wrapped with Hessian for Curing. ......................... 52

Figure 3.19: Preparation of Flat Plate Formwork ................................................................ 52

Figure 3.20: Formwork Ready for Flat Plate Casting .......................................................... 52

Figure 3.21: Reinforcments arrangement ........................................................................... 53

Figure 3.22: Flat Plate after Casting .................................................................................... 53

Figure 3.23: Casted Column top and curing of Flat Plate ................................................. 53

Figure 3.24: Curing of Flat Plate and Column top ............................................................ 53

Figure 3.25: U-stirrups as Shear Reinforcements. ............................................................... 54

Figure 3.26: Ferro Scanner .................................................................................................. 55

Figure 3.27: Ink marked loaction of drilling and location of existing flat plate rebars ...... 55

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Figure 3.28: Drilling Machine ............................................................................................. 55

Figure 3.29: Drilling from soffit of the Plate using Drilling Machine ................................. 55

Figure 3.30: Hand Grinding Machine ................................................................................. 55

Figure 3.31: Removing clear cover using Hand Grinding Machine .................................... 55

Figure 3.32: Hammer and Chisel ........................................................................................ 56

Figure 3.33: Removing clear cover using Hammer and Chisel ............................................ 56

Figure 3.34: Round Brush ................................................................................................... 56

Figure 3.35: Cleaning borehole using Round Brush ............................................................ 56

Figure 3.36: Bore Holes washing by water spreading .......................................................... 56

Figure 3.37: Epoxy Adhesive Chemicals ............................................................................ 57

Figure 3.38: Epoxy ingredients .......................................................................................... 57

Figure 3.39: Epoxy Mixure ................................................................................................ 58

Figure 3.40: Application of Epoxy ..................................................................................... 58

Figure 3.41: Pushing Epoxy by Steel Bar ............................................................................ 58

Figure 3.42: After Application of Epoxy ............................................................................. 58

Figure 3.43: Inserting Shear Reinforcement into the Flat Plate .......................................... 59

Figure 3.44: Inserting Shear Reinforcement by Hammering ............................................... 59

Figure 3.45: After Inserting Shear Reinforcement .............................................................. 59

Figure 3.46: After Inserting Shear Reinforcement around the column ................................ 59

Figure 3.47: Micro Concrete Mixure .................................................................................. 59

Figure 3.48: Rebuilding Clear cover ................................................................................... 59

Figure 3.49: Schematic Diagram of Loading condition during test ..................................... 61

Figure 4.1: Dial Gauge-1 ..................................................................................................... 63

Figure 4.2: Dial Gauge-2 ..................................................................................................... 63

Figure 4.3: Initial State of Test Specimen ........................................................................... 64

Figure 4.4: Final crack pattern of specimen S-3-C-3 ........................................................... 65

Figure 4.5: Left side crack of flat plate ............................................................................... 65

Figure 4.6: Right side crack of flat plate ............................................................................. 65

Figure 4.7: Left side bottom crack view after 5 th Cycle ....................................................... 66

Figure 4.8: Right side bottom crack view after 5th Cycle .................................................... 66

Figure 4.9: Left top crack view after 5 th cycle .................................................................... 66

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Figure 4.10: Left side crack view after 5 th cycle .................................................................. 66

Figure 4.11: Final crack pattern of specimen S-4-C-3 ......................................................... 67

Figure 4.12: Left side of flat plate after 5 th cycle ................................................................ 67

Figure 4.13: Right side of flat plate after 5 th cycle .............................................................. 67

Figure 4.14: Left side flat plate bottom view after 5th cycle ................................................ 68

Figure 4.15: Right side flat plate bottom view after 5 th cycle .............................................. 68

Figure 4.16: Left side flat plate top view after 5 th cycle ...................................................... 68

Figure 4.17: Final crack pattern of specimen S-5-C-3 ......................................................... 69

Figure 4.18: Left side crack of flat plate ............................................................................ 70

Figure 4.19: Right side crack of flat plate .......................................................................... 70

Figure 4.20: Top crack view in left side of flat plate after 5 th cycle .................................... 70

Figure 4.21: Bottom crack view in right side of flat plate after 5 th cycle ............................. 70

Figure 4.22: Final crack pattern of specimen S-5.5-C-3(Control) ........................................ 71

Figure 4.23: Left side crack of flat plate ............................................................................ 72

Figure 4.24: Right side crack of flat plate .......................................................................... 72

Figure 4.25: Left side crack of flat plate after 5 th cycle ...................................................... 72

Figure 4.26: Right side crack of flat plate after 5 th cycle ..................................................... 72

Figure 4.27: Top crack view in flat plate after 5 th cycle ..................................................... 72

Figure 4.28: Right side crack of flat plate after 5 th cycle ..................................................... 72

Figure 4.29: Final crack pattern of specimen S-3-C-4 ......................................................... 73

Figure 4.30: Left side crack of flat plate ............................................................................ 74

Figure 4.31: Right side crack of flat plate .......................................................................... 74

Figure 4.32: Left side crack view after 5 th cycle .................................................................. 74

Figure 4.33: Right side crack view after 5th cycle ............................................................... 74

Figure 4.34: Left side top crack view after 5 th cycle ........................................................... 74

Figure 4.35: Right column bottom crack view after 5 th cycle .............................................. 74

Figure 4.36: Final crack pattern of specimen S-4-C-4 ......................................................... 75

Figure 4.37: Left side crack view of flat plate .................................................................... 76

Figure 4.38: Right side crack view of flat plate .................................................................. 76

Figure 4.39: Left side bottom crack view of flat plate after 5th cycle ................................. 76

Figure 4.40: Right side bottom crack view of flat plate after 5 th cycle ............................... 76

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Figure 4.41: Left side crack of flat plate ............................................................................ 76

Figure 4.42: Right side crack of flat plate .......................................................................... 76

Figure 4.43: Final crack pattern of specimen S-5-C-4 ......................................................... 77

Figure 4.44: Left side crack view of flat plate .................................................................... 78

Figure 4.45: Right side crack view of flat plate .................................................................. 78

Figure 4.46: Left side crack view of flat plate .................................................................... 78

Figure 4.47: Right side crack view of flat plate .................................................................. 78

Figure 4.48: Left bottom crack view of flat plate after 5 th cycle .......................................... 78

Figure 4.49: Right top crack view of flat plate after 5 th cycle .............................................. 78

Figure 4.50: Final crack pattern of specimen S-5.5-C-4 ...................................................... 79

Figure 4.51: Left side crack view of flat plate .................................................................... 80

Figure 4.52: Right side crack view of flat plate .................................................................. 80

Figure 4.53: Bottom crack view at left side of flat plate after 7th cycle ............................... 80

Figure 4.54: Right side crack view after 7 th cycle ............................................................... 80

Figure 4.55: Load- Lateral Deformation Response of Specimen S-3-C-3 ........................... 81

Figure 4.56: Load- Vertical Deformation Response of Specimen S-3-C-3 ......................... 82

Figure 4.57: Load- Lateral Deformation Response of Specimen S-4-C-3 ........................... 83

Figure 4.58: Load- Vertical Deformation Response of Specimen S-4-C-3 .......................... 83

Figure 4.59: Load-Deformation Response of Specimen S-5-C-3 ......................................... 84

Figure 4.60: Load- Vertical Deformation Response of Specimen S-5-C-3 ......................... 84

Figure 4.61: Load-Lateral Deformation Response of Specimen S-5.5-C-3 (Control) ......... 85

Figure 4.62: Load-Vertical Deformation Response of Specimen S-5.5-C-3 (Control) ........ 85

Figure 4.63: Load-Lateral Deformation Response of Specimen S-3-C-4 ............................ 85

Figure 4.64: Load-Vertical Deformation Response of Specimen S-3-C-4 .......................... 86

Figure 4.65: Load-Lateral Deformation Response of Specimen S-4-C-4 ........................... 86

Figure 4.66: Load-Vertical Deformation Response of Specimen S-4-C-4 .......................... 87

Figure 4.67: Load-Lateral Deformation Response of Specimen S-5-C-4 ............................ 87

Figure 4.68: Load-Vertical Deformation Response of Specimen S-5-C-4 .......................... 88

Figure 4.69: Load-Lateral Deformation Response of Specimen S-5.5-C-4(Control) .......... 88

Figure 4.70: Load-Vertical Deformation Response of Specimen S-5.5-C-4(Control) ......... 89

Figure 4.71: Summary Results of First Crack in Flat Plate .................................................. 92

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Figure 4.72: Summary Results of Second Crack in Flat Plate ............................................. 93

Figure 4.73: Summary Results of Very First Crack in Specimen ......................................... 93

Figure 4.74: Summary Results of Specimen Failure ............................................................ 93

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LIST OF TABLES

Page No.

Table 2.1: 𝐾𝑎𝑖 is a coefficient depending on the anchorage ................................................. 24

Table 3.1: Cross Section of Different Frame Components. ................................................. 37

Table 3.2: Group for Eight Frame Specimens. .................................................................... 39

Table 3.3: Detailing of Shear Reinforcements used in Flat Plate Column Connections

Retrofitting Work. ............................................................................................................... 40

Table 3.4: Physical properties of the fine aggregate (Sylhet Sand) according to ASTM

C128-88 .............................................................................................................................. 41

Table 3.5 Physical properties of the coarse aggregate (Stone Chips) according to ASTM

C128-88 .............................................................................................................................. 42

Table 3.6: Strength of Reinforcing Bars .............................................................................. 44

Table 3.7: Properties of Micro-concrete .............................................................................. 45

Table 3.8: Cylinder Strength for Targeted Strength 4000 psi for Base Beam and Column .. 46

Table 3.9: Cylinder Strength for Targeted Strength 3000 psi for Flat Plates. ...................... 47

Table 3.10: Cylinder Strength for Targeted Strength 27.59 MPa (4000 psi) for Flat Plates. 47

Table 3.11: Specifications using in designing punching shear reinforcements of flat plate . 49

Table 3.12: Theoretical punching shear capacity ................................................................. 50

Table 3.13: Loading History. .............................................................................................. 60

Table 4.1: Summary Results of Eight Specimens ................................................................ 90

Table 4.2: Summary of Maximum Horizontal and Vertical Displacement corresponding to

each cycle ........................................................................................................................... 94

Table 4.3: Summary of Maximum Lateral Deflection and Maximum Story Drift compared to

Allowable Minimum Story Drift as per ACI 352.1R ........................................................... 96

Table A.1: Load-Deflection Value for Specimen S-3-C-3 ................................................. 107

Table A.2: Load-Deflection Value for Specimen S-4-C-3 ................................................. 109

Table A.3: Load-Deflection Value for Specimen S-5-C-3 ................................................. 111

Table A.4: Load-Deflection Value for Specimen S-5.5-C-3 (Control) .............................. 113

Table A.5: Load-Deflection Value for Specimen S-3-C-4 ................................................. 115

Table A.6: Load-Deflection Value for Specimen S-4-C-4 ................................................. 117

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Table A.7: Load-Deflection Value for Specimen S-5-C-4 ................................................. 120

Table A.8: Load-Deflection Value for Specimen S-5.5-C-4 (Control) .............................. 122

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NOTATIONS

Asw = cross-sectional area of a shear reinforcement

Es = modulus of elasticity of reinforcement

V = shear force

Vcalc = calculated punching shear load

Vflex = shear force associated with flexural capacity of the slab

VR = punching shear strength

VR,c = concrete contribution to punching shear strength

V R,s = shear reinforcement contribution to punching shear strength

VR,crush = punching shear strength (governing crushing of concrete struts)

VR,in = punching shear strength (governing failure within shear-reinforced zone)

VR,out = punching shear strength (governing failure outside the shear-reinforced zone)

VSLS = shear force at time of strengthening

Vtest = measured punching shear load

b0 = perimeter of the critical section

b0,in = perimeter of the critical section (check of punching within the shear reinforced zone)

b0,out = perimeter of the critical section (check of punching shear outside the shear-reinforced

zone)

d = effective depth (distance from extreme compression fibre to the centroid of the longitudinal

tensile reinforcement)

db = diameter of a reinforcing bar

dinf = diameter of anchoring plate

dv = reduced effective depth

dg = maximum diameter of the aggregate

dg0 = reference aggregate size (16 mm (0.63 in))

fc = average compressive strength of concrete (measured on cylinder)

fy = yield strength of flexural reinforcement

fyw = yield strength of shear reinforcement

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h = vertical distance between the tip of the crack and the point where the shear reinforcement

crosses the critical shear crack

l= span of a slab, length

rs = distance between the column of a slab and the line of contraflexure of moments

s0 = horizontal distance between the border of the support region and first shear reinforcement

sv = horizontal distance between two adjacent reinforcements of same radius

wb = relative displacement of the lips of the critical shear crack parallel to shear reinforcement

α= angle between the critical shear crack and the soffit of the slab

β = angle between the shear reinforcement and the soffit of the slab

tb = bond strength

r = flexural reinforcement ratio

rw = shear reinforcement ratio

y= rotation of slab outside the column region

ycalc = calculated rotation at failure

yR = rotation of slab outside the column region at failure

ySLS = rotation of slab at time of strengthening

ytest = measured rotation at failure

ss = steel stress

VRd = design punching shear strength

VR,c,d = design concrete contribution to punching shear strength

VR,s,d = design shear reinforcement contribution to punching shear strength

VR,crush,d= design punching shear strength (governing crushing of concrete struts)

fck = characteristic compressive strength of concrete (measured on cylinder)

f’c = specified compressive strength of concrete (measured on cylinder)

fywd = design yield strength of shear reinforcement

gc = safety factor of concrete

gs = safety factor of steel

∅𝑐= concrete strength reduction factor

∅𝑠= steel strength reduction factor

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𝜏𝑏 ,𝑑 = design bond strength

ssd = steel stress for design

ss,el,d = design steel stress during elastic activation of shear reinforcement

ss,b,d = design maximum shear reinforcement stress due to bond failure

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1

CHAPTER 1

INTRODUCTION

1.1 General

Flat plate slab system is widely adopted by engineers as it provides many advantages. The

system can reduce the height of the building, provide more flexible spatial planning due to

absence of beams and further reduce the material cost (Widianto et al., 2006). However, the main

problem associated with flat plates is the brittle punching shear failure of such slab. Punching

shear failure is caused by the vertical shear and unbalanced moment borne by the slab-column

connection, which makes the flat-slab connections a weak link in the whole flat-slab structure,

and then leading to serious damage or even collapse. Unbalanced moments commonly occur in

buildings with flat slabs, caused by unequal spans or loading on either side of the column (Binici

et al., 2003). Due to the increase of applied loads and deficiencies during design or construction,

a number of existing flat slabs currently require strengthening against punching shear for safety

reasons or to comply with more stringent code requirements. There are some available

strengthening methods, however, not completely satisfactory, or they cannot be applied in many

cases (depending on the possibilities to enlarge column sizes or to intervene on the upper face of

slabs or availability of economic solution) (Ruiz et al., 2010).

1.2 Background of the Study

Punching shear reinforcement is increasingly used in flat slabs because of the significant

improvements introduced both in terms of strength and ductility. The enhancement on the

behavior of the slab is shown in Figure 1.1 with reference to two tests with same geometric and

mechanical characteristics, one containing shear reinforcement and the other not. The strength is

almost doubled for the test with shear reinforcement. Also, the deformation capacity is

significantly increased, being more than three times that of the member without shear

reinforcements (Ruiz et al., 2010). In general, strengthening slab-column connections involves

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installing external shear reinforcement and/or collars to increase the critical shear perimeter

(Widianto et al., 2006).

Figure 1.1: Comparison of the behavior and strength of two slabs with and without shear reinforcement (Muttoni et al., 2008).

Due to increase on strength and ductility of members, the vulnerability of the structure with

respect to accidental actions (earthquake, explosion, fire, impact etc.) and slab thickness are

reduced (Ruiz et al., 2010). During an earthquake, significant horizontal displacement of a flat

plate-column connection may occur, resulting in unbalanced moments that induce additional slab

shear stresses. Brittle punching failure can occur due to the transfer of shear forces combined

with unbalanced moments between slabs and columns. As a result, some flat plate structures

have collapsed by punching shear in past earthquakes (Berg and Stratta, 1964). Hueste and

Wight (1999) studied a building with a post-tensioned flat plate that experienced punching shear

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failures during the 1994 Northridge, earthquake. The displacement-induced unbalanced moments

and resulting shear forces at flat plate-column connections should be designed to prevent brittle

punching shear failure. Even when an independent lateral-force resisting system is provided, flat

plate-column connections should be designed to accommodate the moments and shear forces

associated with the displacements during earthquakes (ACI 421.2R-10, 2010). Some typical

solutions to strengthen against punching shear are shown in Figures 1.2(a) to 1.2(e). It comprises

enlargements of the support region (by the addition of column capitals or widening of the

columns strengthening of the flexural reinforcement (by casting a concrete topping or gluing

reinforcement or installing shear reinforcement. Those possibilities can, however, be impractical

in many situations, as they require accessing the upper face of the slab which is usually covered

by soil or floor, or enlarging the support region which is not always possible due to architecture

and space requirements. In this paper, the performance of an unusual solution, evolved from

previous works and overcoming previous problems, is investigated. The system (refer to Figures

1.2(f) and 1.3) consists of a series of inclined shear reinforcing bars, bonded within an existing

slab and installed by drilling holes only from the soffit of the slab (Ruiz et al.,2010).

Figure 1.2: Reinforcing of existing slabs against punching shear: (a) concreting or installing of

steel-precast capital; (b) widening of column; (c) addition of upper concrete layer; (d) addition of glued flexural reinforcement; (e) post installed shear reinforcement with mechanical anchorage;

and (f) bonded post-installed shear reinforcement (Ruiz et al., 2010).

Figure 1.3(a) shows a cross section of a member reinforced with the investigated system. It

consisted of bars installed into inclined holes (hammer-drilled at 45 degrees from the soffit of an

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existing slab [refer to Figure 1.3(d)]) and bonded by a high-performance epoxy adhesive. From

this analysis the critical shear crack theory described by the following:

Figure 1.3: Post-installed shear reinforcement: (a) typical cross section; (b) view of nut,

washers, and bar; (c) detail of anchor head; and (d) installing by drilling of inclined holes (Ruiz et al., 2010).

Inclined bonded bars are an effective way to reinforce existing slabs against

punching shear. This leads to economic solutions where only the soffit of the slab

has to be accessible.

The shear failure of slabs reinforced with this system can develop by crushing

concrete struts, punching within the shear reinforced zone, and punching outside

the shear reinforced zone. For slabs with low flexural reinforcement ratios, the

development of a plastic mechanism is also possible if sufficient shear

reinforcement is provided.

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A consistent design concept based on the critical shear crack is provided for this

system. It accounts for the various failure modes and allows considering (amongst

others) the influence of bond, anchorage dimensions, and rotations of the slab on

the strength of the member at the time of reinforcing.

Based on this theory, it is shown that to enhance efficiency of such a system, high

bond strength between the bars and the slab is required. Also, using inclined bars

helps developing their strength as bond and anchorage lengths increase.

1.3 Justification of the Study

Most of the RC buildings in Bangladesh including industrial buildings were constructed without

seismic detailing in the Flat Plate slabs before or even after the inception of BNBC (1993).

Those were designed considering only gravity loads. However, Bangladesh is in severe risk of

earthquake. Change in the building occupancy as residential buildings to commercial and

industrial buildings is very common in Bangladesh. Increase of number of floors without proper

design or analysis is also an important issue. These buildings are vulnerable to seismic hazard

and need to be strengthened. Conventional retrofitting methods are sometimes difficult due to the

nature of occupancy, importance of the structure, economic value of the non-operational period

and cost of the man and materials. Many buildings especially industrial ones using flat plate slab

are under the risk of punching failure. Thus most economic and available retrofitting solution is

needed urgently. Using shear reinforcement of conventional inclined stirrup with strong epoxy

could be the economic and easily available solution to retrofit. Several alternatives to increase

shear capacity at the critical section include (i) steel bars grouted into 45-degree inclined drilled

holes (Hassanzadeh and Sundqvist 1998), (ii) bolts to act as shear reinforcement (El-Salakawy et

al. 2003), and (iii) carbon fiber reinforced polymers (CFRP) stirrups (Binici, 2003). The shear

perimeter has been increased by (i) installing column capital using reinforced concrete, (ii)

attaching steel collars (Hassanzadeh and Sundqvist, 1998), and (iii) sandwiching the slab

between steel plates connected by through bolts (Ebead and Marzouk, 2002). The flexural

strength of a connection has been increased by applying CFRP on the slab surface thereby

increasing the shear strength of the connection (Harajli and Soudki, 2003). The efficiency of

CFRP is highly dependent on the ability to prevent an early delamination (Ebead and Marzouk,

2004). Song et al. (2012) conducted research on effective punching shear and moment capacity

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of prefabricated flat plate using shear reinforcements as vertical stirrups, studs and bands but that

was not retrofitting design. An effective flat plate retrofitting related research was done by Ruiz

et al. (2010). They tested strengthening analysis of flat plate using post-installed shear

reinforcement by considering punching effect due to vertical loading only. They used inclined

bounded shear reinforcements with bolting. They also showed the design of punching shear

reinforcements using critical shear crack theory. Widianto et al. (2006) conducted research on

the rehabilitation of earthquake-damaged reinforced concrete flat-plate slab-column connections

for two-way shear using CFRP. This study attempted to access improvement of punching shear

of the interior flat plate column joints considering column strip. It also attempted to increase the

shear strength of the joints by post installing shear reinforcements as stirrup into the flat plate.

Use of shear reinforcements in Bangladesh is relatively easy and economic. In the present study,

punching effect of flat slabs strengthened with shear reinforcements due to lateral loading in

addition to vertical loading is investigated. The outcome of the study ensure the effect of

earthquake on flat plate as easy, available and economic way of retrofitting flat plate using shear

reinforcement. The research will also facilitate in developing methods of determining strength of

retrofitted joints and identify suitable procedures to retrofit interior flat plate by shear

reinforcements.

1.4 Objectives of the Research

The main objective of this thesis is to conduct experiments on six frames with post install shear

reinforcements and two frames without shear reinforcements by two different concrete strengths

to interpret experimental findings.

The objective of the investigation is as follows –

To measure the change in punching shear capacity due to use of different amount of shear

reinforcements for various concrete strengths and slab thicknesses of flat plate for lateral

loading.

1.5 Methodology

To investigate the improvement of punching shear capacity of flat plates for lateral loading with

varying flat plate thickness and concrete strengths, cyclic static incremental horizontal load were

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provided to test the frames with sustained vertical load. The specimens were retrofitted by using

shear reinforcements as stirrups and tested for lateral loading. Half scale RC model frames were

prepared, integral with a heavily reinforced concrete base. Frames were of 1000mm height and

2520mm span. To investigate the improvement of punching shear capacity of reinforced concrete

frame with varying concrete strengths and thicknesses of flat plates following parameters were

considered:

Different types of flat plate thickness (75 mm, 100 mm, 125 mm, 140mm).

Two types of concrete strengths ( 20.69 MPa, 27.59 MPa )

A total of 8 (eight) frames were constructed for the study:

Four frames were constructed with different plate thickness (75 mm, 100 mm, 125

mm, 140mm) for the concrete strength 20.69MPa. Among them three were

retrofitted using shear reinforcements as stirrups and other one without retrofitting

used as control frame specimen.

Four frames were constructed with different plate thickness (75 mm, 100 mm, 125

mm, 140mm) for the concrete strength 27.59MPa. Among them three were

retrofitted using shear reinforcements as stirrups and other one without retrofitting

used as controlled frame model.

Clear cover from bottom side of specimens was removed and holes were drilled at

45° to longitudinal bars.

Vertical shear reinforcement (U-stirrups) were placed through those drilled holes

from flat slab soffit surrounding the column face and they were bounded by

strong adhesive glue named Epoxy and clear cover was rebuilt by micro-

concrete.

Finally, the load deflection curves were compared for the considered different frames with

retrofitted and without retrofitted.

1.6 Scope of the Work

The outcome of this study may be helpful in retrofitting design of existing flat plates floor slab

building to eliminate the punching failure possibilities. It will be possible to make

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recommendations about effects of existing flat plate thickness on punching shear capacity in

relation to concrete strengths using experimental investigations.

1.7 Organization of the Thesis

Apart from this chapter, the remainder of the thesis has been divided into four chapters. Chapter

2 presents literature review concerning earlier research. It includes use of shear reinforcements in

flat plates, cyclic load and its effect on reinforced concrete structure. Chapter 3 presents the step

by step construction procedure of frame specimens and adopted procedure for testing under

cyclic loading in detail. It includes the details of the specimen dimensions, material properties,

casting procedures, workability observations, test setups, and test instrumentation. Chapter 4

presents the results from the experimental program of this research. Also summarize the

improvement of the punching shear capacity of the frames and the comparison of the responses

using shear reinforcements. Chapter 5 presents the final conclusions, which can be drawn out

from this research and also provides recommendations for future study.

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CHAPTER 2

LITERATURE REVIEW

2.1 General

This chapter discusses the flat plate, punching shear capacity of the flat plate structure, shear

reinforcements, types of shear reinforcements, design and detailing of shear reinforcements, the

effects of shear reinforcement on punching shear behavior under seismic condition, punching

shear resisting mechanism in flat plate column connection and cyclic load. In this chapter, pros

and cons of various retrofitting strategy are also highlighted. Post-install shear reinforcement as

U-stirrup draws attention of the designers as a retrofitting material due to its economical, easily

availability and easy placement methods. Many researchers worked on punching shear capacity

of the flat plate structures using various types of shear reinforcements and also evaluated their

punching behavior on flat plate under seismic conditions. Since no previous study on post-install

shear reinforcement for lateral loading has been made. The pre-install shear reinforcement for

lateral loading and post-install shear reinforcement for vertical loading on flat plates had been

done which will be mentioned. Outcome of some of the researches are also discussed in this

chapter.

2.2 Flat Plate

Flat plate is one of the most common floor systems for large span commercial buildings. The

advantages of a flat-Plate floor system are numerous. It provides architectural flexibility, more

clear space, less building height, easier form work, and, consequently, shorter construction time.

Low floor to floor heights reduce the total building height, thus reducing lateral loads, cost of

building cladding, cost of vertical mechanical and electrical lines, and air conditioning/heating

costs. For vertical loads, the structural performance and design of flat plates are well established.

Under lateral loads, many aspects of the behavior of flat plates are uncertain. A serious problem

that can arise in flat plates is brittle punching shear failure due to poor transfer capacity of

shearing forces and unbalanced moments between slabs and columns. In seismic zones, a

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structure can be subjected to strong ground motions and for economical design a structure is

considered to undergo deformations in the inelastic range. Therefore in addition to strength

requirement, slab-column connections must undergo these inelastic deformations without

premature punching or shear failure. In other words slab column connections must have adequate

ductility.

2.3 Shear Reinforcements

Two kinds of shear may be critical in the design of flat plates. The first is the familiar beam-type

shear leading to diagonal tension failure. A potential diagonal crack extends in a plane across the

entire width of the slab. So the design strength must be at least equal to the required strength at

factored loads. Alternatively, failure may occur by punching shear, with the potential diagonal

crack following the surface of a truncated cone or pyramid around the column. The critical

section for shear is taken perpendicular to the plane of the slab and a distance of half of the

effective depth from the periphery of the support. Thus for preventing shear failure additional

reinforcement may be provided to be known as shear reinforcement. There are different type of

shear reinforcements which are discussed below.

Conventional stirrup cages

Conventional stirrup cages require large diameter longitudinal bars as anchors. These usually

interfere with the column reinforcement making the cages hard to install. A stirrup cage with

longitudinal rebar in both directions is difficult to place and interferes with the column

reinforcement (Figure 2.1).The first critical section for shear design in the slab is taken at d/2

from the column face as usual. Using stirrups it is extended outward from the column in four

directions for the typical interior case (three or two directions for exterior or corner columns,

respectively), until the concrete alone can carry the shear, with 𝑉𝑐 = 4 𝑓𝑐′𝑏0𝑑 at the second

critical section. Within the region adjacent to the column, where shear resistance is provided by a

combination of concrete and steel, the nominal shear strength 𝑉𝑛 must not exceed 6 𝑓𝑐′𝑏0𝑑,

according to ACI Code 318-08(11.12.3).

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Shear studs reinforcements

This shear reinforcement consists of large-head studs welded to steel strips (Figure 2.1 to 2.2).

The steel strip is positioned with bar chairs and fastened to the form by nails driven through

holes in the steel strip. The chairs provide the required concrete cover and the nails anchor the

strip to prevent movement during construction. These studded steel strips have been designed to

be more effective than conventional shear reinforcement. Conventional shear reinforcement is

not fully effective because the stirrups can’t be adequately anchored into the concrete. In thin

slabs this ineffective anchorage increases the shear crack width and the shear reinforcement

never yields. The ACI Building Code, recognizing these limitations, requires a conservative

design recognizing these limitations requires a conservative design. The dimensions of the

studded steel strips (Figure 2.2) have been set to provide full anchorage and to ensure that at

ultimate load the steel studs yield. To achieve complete anchorage and yield at ultimate load, the

yield strength of the stud material is specified between 40,000 and 60,000 psi.

Figure 2.1: Conventional stirrup cages (adopted from Nilson et al., 2010)

Figure 2.2: Shear Studs (adopted from Nilson et al., 2010)

Shearhead Reinforcements

The shearhead reinforcement shown in figure 2.3. It serves to increase the effective perimeter 𝑏0

of the critical section for shear. In addition it may contribute to the negative bending resistance

of the slab. The reinforcement shown in figure 2.3 is particularly suited for use with concrete

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columns. It consists of short lengths of I or wide flange beams, cut and welded at the crossing

point so that the arms are continuous through the column. Normal negative slab reinforcement

passes over the top of the structural steel, while bottom bars are stopped short of the shearhead.

Column bars pass vertically at the corners of the column.

Figure 2.3: Shearhead Reinforcement (Nilson et al., 2010)

2.4 Requirement of Shear Reinforcements for Lateral Loading in Flat Plates

Due to a series of factors not only the fire (which in fact was not very significant) but also

overloading of the structure (larger ground cover than expected), too coarse approaches on the

check of the punching shear strength (some of them in agreement to the codes applied at the time

the garage was designed), and deficiencies in the construction. In addition, the thickness of the

slab, large reinforcement ratio, and the fact that the slab did not have transverse reinforcement

severely limited the deformation capacity of the structure. As a consequence, once the slab

punched around one column, the progressive and sudden collapse of the structure could not be

avoided.

Flat plate structures are commonly used in moderate and low seismic zones as lateral force

resisting systems whereas they are coupled with shear walls or moment resisting frames in high

seismic zones. Because reinforced concrete flat plate structures do not contain beams, they are

able to transfer all the loads acting on slabs directly to the columns. The ductility of these

systems is generally limited by the deformation capacity of the slab-column connections.

Punching shear failure is the governing failure mode in the presence of pronounced gravity and

lateral load combinations. The ductility of the slab-column connections can be enhanced with the

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use of shear reinforcement for new construction and the risk of punching shear failure can be

highly reduced when the connection is designed and detailed properly. At the time when the

loads are transferred, all moments that are generated by the delivery load and critical sections

that resist the moment (Figure 2.4) also converge on the slabs near the columns. When a moment

is caused by a delivery load, it is an unbalanced moment that occurs because of a direct shear

moment originating from a vertical load and eccentricity and to the lateral load of a vertical load.

Figure 2.4: Location of critical and effective section in flat plates. (Song et al., 2012)

2.5 Retrofitting Strategy

There are many methods available to strengthen the flat plates against punching shear failure

however some of them are not completely satisfactory. They cannot be applied in many cases

(depending on the possibilities to enlarge column sizes or to intervene on the upper face of

slabs). An innovative system for strengthening slabs against punching shear and overcoming

most of difficulties of existing method is described. It consists of inclined shear reinforcement

installed within existing slabs by drilling holes only from soffit of the slab and by bonding it with

high-performance adhesive.

Dimensioning of such reinforcement can be performed according to available models and codes

of practice. However, there is currently no general agreement on the interaction between the

concrete and shear reinforcement contributions to the shear strength. Thus, different codes

propose different models.

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Existing slabs of cured concrete can also be strengthened: by increasing the size of the slab or the

column, by adding tensile reinforcement e.g. as glued laminates or by adding post-installed shear

reinforcement. Obvious advantages of the latter method are that the original geometry can be

maintained, that the installation work can be carried out from the lower side of the slab and that

the intervention remains invisible.

Post-installed punching shear reinforcements can be applied in two ways: if both the lower and

the upper side of the slab are accessible for work simultaneously, then holes can be drilled

through the slab. Steel bars can then be introduced through the holes and be prestressed against

the slab by tightening nuts on both sides. An appropriate mortar is then injected into the annular

gap through an injector washer. Thus the steel rods cannot move under shear load and water

cannot penetrate into the annular gap.

2.6 Guidelines for Use and Design of Shear Reinforcements in Flat Plates

2.6.1 Use of Shear Reinforcements

The method for the design and construction of externally shear reinforcements as vertical stirrups

for strengthening flat plate column connections against punching failure is carried out using

Critical shear crack theory, ACI 318-08, ACI 421.1R-08 and ACI 441.2R-10. Design theory is

based on a physical model allowing to calculate the strength and deformation capacity of

members failing in punching shear.

The safety against punching shear of existing concrete slabs is basically determined on the basis

of the geometry and the reinforcement of the slab and the column. Such data can be taken from

construction drawings if available or they are evaluated in situ by taking out concrete cores and

seeking the existing reinforcement.

Such methods which include working from the upper side of the slab also have certain

drawbacks: The cover of the slab has to be removed (earth, tiles etc). Moreover the

waterproofing system is penetrated and has to be repaired properly after installation of the

reinforcement.

As often the upper side is not accessible for work or is accessible only with a high effort, a

method has been developed to apply punching shear reinforcement only from the lower side of

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the slab. Vertical U-Stirrups anchors are bonded into drill holes inclined towards the column by

means of an appropriate adhesive mortar like micro concrete. The drilled holes should protrude

until at least the level just below the lowest layer of the upper (tensile) reinforcements, but

preferably to the centre of the tensile reinforcement. As the effectiveness of punching shear

reinforcement strongly depends on the quality of its anchorage is carried out with U-stirrups.

Figure 2.5: Penetrating post-installed punching shear reinforcement (Muttoni et al., 2008)

As penetrating reinforcement according to figure 2.5 can be designed like cast-in-place punching

shear reinforcements on the safe side. According to figure 2.6 post-installed punching shear

reinforcement applied only from the lower side of the slab.

Figure 2.6: Post-installed punching shear reinforcement applied only from bottom side of the slab (Muttoni et al., 2008)

U-stirrups anchors in combination with high adhesive glue Epoxy are used to install punching

shear reinforcement into already hardened concrete slabs.

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Inclined holes are hammer drilled into the concrete slab under an angle of 45°and in the direction

towards the column. The length of the drilled holes should be such that they reach at least the

lowest level of the upper (tensile) reinforcement, but preferably, the holes should end at the level

between the tensile reinforcements in the two directions.

Adhesive epoxy is injected into the drilled holes and the U-stirrups anchors are set into the epoxy

filled holes. The tension anchor consists of a reinforcement bar of diameter 8mm in the upper

part.

After inserting epoxy adhesive within 10 minute through drilled holes U-stirrups are installed

from soffit of the slab by hammering. The epoxy provided such amount that it come out from

holes during installing U-stirrups.

The anchor bar can be installed on the concrete surface inclined at 45°or be embedded in an

enlarged part of the drilled hole. The embedded anchorage has the advantage that it can be

covered with a high adhesive epoxy and is not visible after the installation.

After installing U-stirrups through drilled holes with high adhesive epoxy micro concrete is used

to fill the bottom surface of the slab to smoothen.

2.6.2 Design of Shear Reinforcements to improve punching shear capacity

2.6.2.1 The Critical Shear Crack Theory

The critical shear crack theory was first developed for flat slabs without transverse reinforcement

failing in punching shear and it was later extended to beams without stirrups and slabs with shear

reinforcement (Ruiz et. al., 2010). The theory proposes that the shear load that can be carried by

members without shear reinforcement is a function of the opening and of the roughness of a

critical shear (Muttoni et. al., 2008). 𝑉𝑅

𝑏0𝑑= 𝑓𝑐𝑓 𝑤, 𝑑𝑔 …………………………………………………………………………………………………………………….2.1

where VR is the shear strength, b0 is a control perimeter (set at d/2 of the border of the support

region for punching shear), d is the effective depth of the member, fc is the compressive strength

of the concrete, w is the width of the shear critical crack and dg is the maximum size of the

aggregate (accounting for the roughness of the lips of the cracks).For two-way slabs, the opening

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of the critical shear can be correlated in an effective way to the rotation of the slab (𝜓) times the

effective depth of the member (d), as figure 2.7:

𝑤 ∞ 𝜓. 𝑑………………………………………………………………………….………………………………………………………..2.2

Figure 2.7: Critical shear crack and punching shear cone (Muttoni et al., 2008)

The following failure criterion was proposed for punching shear failures in slabs without

transverse reinforcement: 𝑉𝑅

𝑏0𝑑 𝑓𝑐=

3 4

1+15Ψ .d

𝑑𝑔𝑜 +𝑑𝑔

𝑺𝑰 − 𝒖𝒏𝒊𝒕𝒔: 𝑴𝑷𝒂, 𝒎𝒎 .........................................................................................2.3

where dg0 is a reference aggregate size (equal to 16 mm). This failure criterion reduces the

maximum shear force that can be carried as deformations (rotations) increase. This is logical

since wider cracks reduce the ability of concrete to transfer shear. Figure 2.8 compares the

failure criterion of Eq. (2.3) to 99 test results available in the scientific literature showing good

agreement (Muttoni et. al., 2008).

Such punching shear criterion can be used to calculate the strength and ductility of slabs failing

in punching shear by considering a suitable load-rotation relationship for the slab as figure 2.9. A

design expression for this relationship has been proposed by Muttoni considering a number of

simplifications from a more general theoretically-derived expression:

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𝛹𝑑 = 1.5 𝑟𝑠

𝑑

𝑓𝑦

𝐸𝑠

𝑉𝑑

𝑉𝑓𝑙𝑒𝑥

32

………………………………………………………………………………….2.4

Where 𝑟𝑠 =distance from column edge to line of contraflexure for bending moments [mm], for

Figure 2.8: Comparison of failure criterion for slabs without shear reinforcement (Eq. (2.3)) to

99test results (Ruiz et al., 2010) rectangular slabs; 𝑟𝑠 = 0.22𝑙.

𝑓𝑦𝑑 =design yield strength of horizontal slab reinforcement [N/mm2]

𝐸𝑠 =Young’s modulus of steel [N/mm2]

𝑉𝑑 = Column load [kN]

𝑉𝑓𝑙𝑒𝑥 = Design load required to develop flexural strength of the slab [kN]

2.6.2.2 Applications of the Critical Shear Crack Theory to Punching of Shear-

Reinforced Slabs

The Critical shear crack theory can be used to calculate the punching shear strength of the

various failure modes previously described (Figure 2.10). In this section, the way it allows

accounting for the particularities of each punching shear reinforcing system will be discussed.

With respect to the effective depth of the slab (dv), it accounts for the fact that the punching shear

crack develops around the shear reinforcement (Figure 2.10c). This value is thus dependent on

the type and geometry of the shear reinforcement, as shown in Figure 2.10 for various cases.

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This approach provides very good agreement to test results. Taking advantage of the fact that the

deformation (rotation) of the slab is the key parameter governing the amount of shear carried by

concrete, the theory has also been extended to flat slabs with shear reinforcement (Muttoni et. al.,

2009).

Figure 2.9: Calculation of strength and deformation capacity at failure according to the CSCT

(Ruiz et al., 2010)

Figure 2.10: Effective depth and control perimeter outside the shear-reinforced zone as function

of the punching shear reinforcing system(Muttoni et. al., 2009).: (a) studs; (b) stirrups; (c) bonded reinforcement with anchorage plates; and (d) shearheads (Ruiz et al., 2010)

This can be done by considering that as the rotations of the slab increase, the shear cracks open

(according to Eq. (2.2)), progressively activating the shear reinforcements, see Figure 2.10a.

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The shear reinforcement develops thus tensile stresses depending on the opening of the critical

shear crack and on the shear reinforcement bond conditions, as figure 2.11b. This allows

adapting the model to the particularities of each shear reinforcing system (applications for

smooth and deformed bars can be found in Ruiz F. and Muttoni A., 2008).

For low or moderate rotations, shear reinforcement remains elastic and follows thus an activation

phase where its tensile stress increases with rotations (Profile A of Figure 2.11b, point A in

Figure 2.10d). This phase ends when the steel reinforcement yields (point B of Figure 2.10b),

leading to the maximum contribution of such reinforcement. The sum of all vertical components

of shear reinforcements (Figure 2.10c) allows determining the shear carried by the transverse

reinforcement (Figure 2.10d). It can be noted that when all shear reinforcements reach their yield

strength (or anchorage strength in some cases) the contribution of shear reinforcement remains

constant even if rotations increase (Point C in Figure 2.10d).

The total shear strength can finally be calculated by intersecting the failure criterion (accounting

for concrete and shear reinforcement contributions) with the load-rotation relationship of the

slab, as point D in Figure 2.10d. It is interesting to note that, with respect to the shear strength of

members without transverse reinforcement (value Vc0 in Figure 2.10d), the total shear strength is

increased by adding a shear reinforcement, although concrete contribution at failure diminishes

as the developed rotations are larger (Vc<Vc0).

2.6.2.3 Crushing Shear Failure

Crushing shear strength depends on the compressive strength of concrete near the column region.

This strength is mainly influenced by the concrete compressive strength and by the state of

transverse strains of concrete. According to figure 2.11, compression struts may be disturbed by

the presence of transverse cracking. Such cracks may be originated by bending of the slab

(Figure 2.11b, whose width is controlled by the flexural reinforcement), by shear (Figure 2.11c,

whose width is controlled by the transverse reinforcement as previously discussed) or by

delamination of the core (Figure 2.11d).

The actual crushing strength depends thus not only on the geometry of the slab and on its

mechanical and material properties, but it is also significantly influenced by the type shear

reinforcement used. This is justified because the position, development and opening of the cracks

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affecting the compression struts is strongly influenced by the shear reinforcing system. As a

consequence, detailing rules (arrangement and angle of reinforcement, sizes of anchorages etc.)

have a significant influence on the crushing shear strength of a shear reinforcing system.

Figure 2.11: Influence of cracking on crushing shear strength: (a) detail of compression struts nearthe support region; (b) development of flexural crack; (c) development of a shear crack;

and(d) development of delamination crack. (Ruiz F. and Muttoni A., 2010) Even if shear reinforcement is provided, the codes usually define a maximum possible punching

shear strength accounting for failure of the compression zone of the slab near the column. On the

other hand’s side, the specific design concept for reinforcement defines a maximum resistance

that can be achieved with this method. This value should not be exceeded even if 𝑉𝑅𝑑 ,𝑚𝑎𝑥 ,𝑐𝑜𝑑𝑒 is

higher.

If the column load 𝑉𝑑 is higher than the punching shear resistance of the slab without shear

reinforcement, 𝑉𝑅𝑑 ,𝑐𝑐 then the slab should be strengthened.

The design model for strengthening is based on the critical shear crack theory with the following

assumptions:

The punching shear strength of the strengthened slab is the sum of a contribution by the cracked

concrete and another contribution by the steel reinforcement. In order to activate the

reinforcement, the opening of the shear crack is initiated. The opening of the punching shear

crack and the maximum aggregate size of the concrete influence the remaining shear resistance

of the concrete slab.

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The opening of the punching shear crack is represented by the rotation of the slab (Figure 2.11).

The line failure criterion shows how the punching shear resistance decreases with increasing

rotation of the slab, i.e. with increasing opening of the shear crack.

The remaining shear strength considering a rotation 𝛹𝑑 of the slab is:

𝑉𝑅𝑐 ,𝑑= 2.Ƞ𝑡 . 𝑓𝑐𝑘

4.5 1+20𝛹𝑑 .𝑑

𝑑𝑔+16

. 𝑑. 𝑢′………………………………………………………………………………..2.5

where 𝑉𝑅𝑐 ,𝑑= concrete contribution to the punching shear resistance [N]

Ƞ𝑡 =factor for long term effects

𝑓𝑐𝑘 =characteristic compressive strength of concrete on cylinder [N/mm2]

𝑑𝑔 =maximum diameter of concrete aggregates [mm]

𝑑 = effective depth [mm]

𝑢′= critical section at d/2 from column edge [mm]

The rotation of the slab under load 𝑉𝑑[kN] is evaluated by

𝛹𝑑 = 1.5 𝑟𝑠

𝑑

𝑓𝑦𝑑

𝐸𝑠

𝑉𝑑

𝑉𝑓𝑙𝑒𝑥

32

……………………………………………………….………………………..2.6

where 𝑟𝑠 =distance from column edge to line of contraflexure for bending moments [mm], for

rectangular slabs;𝑟𝑠 = 0.22𝑙.

𝑓𝑦𝑑 =design yield strength of horizontal slab reinforcement [N/mm2]

𝐸𝑠 =Young’s modulus of steel [N/mm2]

𝑉𝑑 =column load [kN]

𝑉𝑓𝑙𝑒𝑥 =design load required to develop flexural strength of the slab [kN]

where 𝑉𝑓𝑙𝑒𝑥 = 𝑎. 𝑚𝑅𝑑 is an approximation of the column force at which the flexural resistance of

the slab is reached, where 𝑚𝑅𝑑 the bending resistance of the slab is and is a constant depending

on the position of the column. The smallest value of 𝑉𝑓𝑙𝑒𝑥 resulting from the different checks has

to be considered:

Interior columns: a=8check upper reinforcement in both directions

Edge columns: a=4check upper reinforcement parallel to edge

a=8check upper and lower reinforcement perpendicular to edge

Corner columns: a=2check upper and lower reinforcement in both directions

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The design model uses a critical shear perimeter at a distance of1/2 times the effective depth of

the slab. The shear perimeter u′ will be multiplied by 𝐾𝑒which a reduction factor is taking into

account for irregular distribution of the shear force around the column.

u′=u0.Ke ; Ke=1/ (1+ (e/b))……………………………………………………………..………………………………………2.7

If the column connection takes up a bending moment 𝑀𝐷 , then the irregular distribution of the

shear force is taken into account by 𝐾𝑒=1/(1+(e/b)) where e is [𝑀𝐷/𝑉𝐷] and b is the diameter od a

circle with the same area as is inside the critical shaer perimeter at ½ times the effective depth of

the slab. For internal columns with regular spacing 𝐾𝑒=0.9 can be assumed.

If column load 𝑉𝐷is not higher than the maximum possible resistance of the strengthed slab;

𝑉𝑅𝑑 ,𝑚𝑎𝑥 [𝑁] =5.2.Ƞ𝑡 . 𝑓𝑐𝑘

4.5 1+20𝛹 𝑉𝑅𝑑 ,𝑚𝑎𝑥

𝑑𝑔+16

𝑑. 𝑢′…………………………………………………………………………………………2.8

𝛹 𝑉𝑅𝑑 ,𝑚𝑎𝑥 is evaluated with equation (2) using 𝑉𝑅𝑑 ,𝑚𝑎𝑥 instead of𝑉𝑑 . The shear force which has

to be taken up by the strengthening anchors is then:

𝑉𝑅𝑑 ′ 𝑠,𝑟𝑒𝑞 = 𝑉𝑑 − 𝑉𝑅𝑑 ,𝑐 ≥ 0.2𝑉𝑑

𝑉𝑅𝑑 ,𝑐 is calculated using the rotation according to formula (2) with parameter 𝑉𝑑 .

The shear reinforcement is designed satisfying the following condition:

𝑉𝑠,𝑑 ≤ 𝑁𝑠𝑖 ,𝑑 sin 𝛽𝑖𝑘𝑒

𝑛

𝑖=1

where 𝑁𝑠𝑖 ,𝑑 is the factored strength of the shear reinforcement and 𝛽𝑖 is the angle of the shear

reinforcement.

The design strength of the U-stirrups tension bar is equal to the minimum of the following

values:

𝑁𝑠𝑖 ,𝑑 = 𝑚𝑖𝑛 𝑁𝑠𝑖 ,𝑒𝑙 ,𝑑𝑁𝑠𝑖 ,𝑝𝑙 ,𝑑𝑁𝑠𝑖 ,𝑏 ,𝑑

where 𝑁𝑠𝑖 ,𝑒𝑙 ,𝑑 is the force angle of the shear reinforcement that can be activated assuming an

elastic behavior of the bar. This value, according for the rotation of the slab at SLS results:

𝑁𝑠𝑖 ,𝑒𝑙 ,𝑑 = 𝐾𝑎𝑖 ∆𝜓𝑑𝑕𝑖 sin(𝛼 + 𝛽𝑖) [MN] ……………………………………………………….…2.9

where 𝛼 is the angle of the critical shear crack (normally set to 45°). In the standard case of

reinforcements set under 𝛽𝑖 = 45° the value of sin(𝛼 + 𝛽𝑖) = 1.0. 𝑕𝑖 is the height at decisive

rotation of the structure to be reinforced; ∆Ψ𝑑 = Ψ𝑑 + Ψ𝑆𝐿𝑆 .

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𝑉𝑆𝐿𝑆is the column load acting while the strengthening work is carried out. Therefore, equation

(2), in the case of interior columns, becomes:

∆𝛹𝑑 = 1.5 𝑟𝑠

𝑑

𝑓𝑦𝑑

𝐸𝑠

𝑉𝑑

8𝑚𝑅𝑑

32

− 𝑉𝑆𝐿𝑆

8𝑚𝑅𝑑

32

……………………………………………………2.10

𝐓𝐚𝐛𝐥𝐞 𝟐. 𝟏: 𝑲𝒂𝒊 is a coefficient depending on the anchorage

Diameter[mm] 16 20

𝐾𝑎𝑖 2.62 𝑓𝑐𝑐 ,𝑘[𝑁 𝑚𝑚2 ]

25

0.5

3.67 𝑓𝑐𝑐 ,𝑘[𝑁 𝑚𝑚2 ]

25

0.5

Table 2.1: anchorage factors (𝑓𝑐𝑐 ,𝑘 =characteristic cube strength of concrete)

𝑁𝑠𝑖 ,𝑝𝑙 ,𝑑 is the plastic resistance of the reinforcement bar, its value is:

𝑁𝑠𝑖 ,𝑝𝑙 ,𝑑 = 𝐴𝑠𝑡 . 𝑓𝑦𝑑 ……………………………………………………………………………..…………2.11

𝑁𝑠𝑖 ,𝑝𝑙 ,𝑑 is the upper limit of the resistance due to the bond strength. It is assumed that the bar is

bonded between the point where it cuts the shear crack and its upper end.

𝑁𝑠𝑖 ,𝑏 ,𝑑 = 𝜏𝑏𝑑 . 𝑑𝑏 . 𝜋. 𝑙𝑏 ,𝑠𝑢𝑝 ,𝑖………………………………………………………………………………2.12

The design value of the bond strength is evaluated as 𝜏𝑏𝑑 = 𝜏𝑏𝑑° . 𝑓𝐵,𝑁

Where 𝜏𝑏𝑑° is the design strength in a concrete of class C20/25 and 𝑓𝐵,𝑁 takes into account the

effective concrete strength. The values are given 2. 𝑓𝑐𝑐 ,𝑘 should not be considered higher than 60

N/mm2.

Bond Strength 𝜏𝑏𝑑° = 2.00 𝑁 𝑚𝑚2

Influence of concrete strength: 𝑓𝐵 ,𝑁=

𝑓𝑐𝑐 ,𝑘 [𝑁

𝑚𝑚 2]

25

0.1

[25MPa ≤ 𝑓𝑐𝑐 ,𝑘 ≤ 60MPa]

2.6.3 Detailing of Shear Reinforcements in Plates

In order obtain a good detailing, the following constructive rules should be followed when

designing punching shear reinforcement as Vertical U-stirrups.

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Number of radii

The tension U-stirrups anchors are placed along a series of redials where the angle

between tem has to be lower or equal than 45°.𝛼𝑕 ≤ 45°

Number of reinforcement in a radial

At least one vertical U-stirrup should be placed at each radial

Distance between reinforcements and column

The distance of the first anchorage to the border of the column should be lower than or

equal to 0.75d where d is the average effective depth of the structure to be

strengthened, 𝑑 = 𝑑𝑥 + 𝑑𝑦

2 : 𝑆0 ≤ 0.75𝑑

If a very small value is selected, then the capacity of the first reinforcement bar may be

strongly reduced. The presented design concept takes this into account. Moreover a small

distance may lead to difficulties if there is dense column reinforcement.

Axial distance

The minimal distance between axes of one stirrup to another has to be greater than 3

times of the bored hole.

Direction of the drilled holes

The direction of the drilled holes should be an angle 45° compared to the slab surface and

towards the column:

𝛽𝑖 = 45°

Length of the drilled holes

The height at which a U-stirrups anchor should be bonded is equal to d:

𝑕0 = 𝑑

2.7 Cyclic Load

Cyclic loading is ―generated‖ by earthquakes which are one of the most dangerous and

destructive forms of natural hazard. Cyclic loading can be grouped into two categories; low-

cycle load, or a load history involving few cycles but having very large bond stress ranges. This

group of loading is very common to seismic and high wind loadings. The second group relates to

high-cycle or otherwise known as fatigue loading. The load history in this case includes many

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cycles but at a low bond stress range. Offshore structures and bridge members are repeatedly

subjected to such kind of load.

2.8 Literature Review of Earlier Research on Improvement of Punching Shear Capacity

of Flat Plate

Kang et al. (2004)

Kang et al. (2004) presented research study was undertaken to assess performance of flat plate

systems constructed with slab shear reinforcement under dynamic loads. The research program

consisted of shake table tests and accompanying analytical studies of two, approximately one-

third scale, two-story, two-bay, slab-column frames. One specimen was constructed with

reinforced concrete (RC) slab, whereas the other specimen consisted of post-tensioned (PT) slab.

The shear capacity of the slab-column connections was enhanced by the use of stud-rails for both

specimens. Good agreement between analytical and experimental results was achieved by using

an innovative modeling approach. Test results for drift ratios at punching failure versus gravity

shear ratios on the slab critical section were evaluated to assess trends for slabs with and without

shear reinforcement, as well as new provisions adopted for ACI 318-05. Results for the shake

table tests conducted indicate substantially less drift capacity than for prior tests of isolated

connections, possibly due to the lower strain demands on the shear reinforcement and the

rotation of the slab-column connection due to the apparent loss of interface shear capacity. The

relationship between drift and gravity shear ratio adopted in the new ACI provisions is

essentially a lower bound estimate of when punching will occur for RC specimens without shear

reinforcement, as well as the shake table tests conducted as part of this study.

Stark et al. (2004)

Stark et al. (2004) provided an alternative method for upgrading existing flat plate building

connections that were designed to carry gravity loads and that are subjected to lateral

deformation reversals. Some slab-column connections specimens were tested under constant

gravity shear and lateral displacements were applied in reversed cyclic manner which were

upgraded by externally installed CFRP stirrups in two different patterns. Test specimens were

modeled from a typical interior connection of a four-story prototype structure which was a flat-

plate concrete building, designed for office occupancy in a moderate seismic zone. From test

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result it was showed that punching shear failure occurred for the control specimens at a lateral

drift-ratio of about 2.3% but upgraded specimens had significant flexural yielding and sustained

deformations up to a drift ratio of about 8% without significant losses of strength. Punching

failure was not observed in the upgraded specimens.

Widianto et al. (2006)

Widianto et. al., (2006) presented rehabilitation technique of earthquake-damaged reinforced

concrete flat-plate slab-column connections for two-way shear against punching shear failure.

Two methods for strengthening earthquake-damaged connections with 0.5% top reinforcement

ratio were developed: (i) installation of the external CFRP stirrups and (ii) application of well

anchored CFRP sheets on the tension surface of the slab. Experimental research on 2/3-scale

slab-column connections was conducted to quantify the effects of earthquake-damage and low

reinforcement ratios on the punching shear strength, and to study the efficiency of various

rehabilitation techniques. Test results showed that connections with about 0.5 % top

reinforcement ratio within the (c+3h) region, which is typical in the older flat plate structures,

had about two-third of the two-way shear capacity estimated using ACI 318-05 expressions.

Installing external carbon fiber reinforced polymer (CFRP) stirrups and applying well-anchored

CFRP sheets on the tension surface of the slab were effective in increasing the punching shear

strength of the earthquake-damaged connections. In addition to increasing the punching shear

strength of the slab-column connection, the rehabilitation methods developed in this study also

improved the residual capacity after punching shear failure.

Binici (2007)

Binici (2007) also used a strengthening technique as using new economical and easy way to

install CFRP to enhance punching shear strength of reinforced slab-column connections. Four

test specimens that were simply supported along four edges with corners free to lift up,

representing the interior slab-column connection were tested. Self-manufactured CFRP dowels

were placed around the column stubs of the flat-plate specimens as vertical shear reinforcement.

As a result of experiments, it was observed that the vertical load carrying capacities of the

strengthened specimens were increased. The ultimate load capacities and failure modes of the

test specimens were compared with the ACI318-05 provisions. The test results show that the

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proposed FRP retrofit technique can be used successfully to enhance punching shear capacity of

slab-column connections.

Cueva & Robertson (2008)

Cueva & Robertson (2008) presented an experimental program designed to compute

effectiveness of the use of Carbon Fiber Reinforced Polymer (CFRP) studs as a viable

retrofitting method/device to help increase the punching shear capacity and ductility of concrete

flat slabs (at their slab-column connections) during a cyclic loading event such as an earthquake.

The layout of the CFRP studs was determined using the standards set in the ACI 318-05 Code.

Two scaled specimens, a control slab (without studs) and an experimental slab (with studs), of a

typical slab-column connection in a flat slab building were subjected to several cycles of quasi-

static reverse-cyclic loads from a hydraulic ram until either punching occurred or the limit of the

hydraulic testing apparatus was reached. The results showed that the CFRP studs were able to

increase the retrofitted slab’s punching shear capacity and ductility by reaching the capacity of

the testing apparatus at 10 percent drift without punching shear failure, compared to the control

slab which experienced a sudden punching shear failure at 2.9 percent lateral drift.

Mirzaei (2008)

Mirzaei (2008) analyzed 24 flat slabs to investigate the post punching behavior of reinforced

slab-column connections with various flexural reinforcement layouts are introduced and

compared. The first series investigated the effect of available tensile reinforcement in the

negative moment area over the column on the post punching behavior of flat slabs. The second

series consisted of eight specimens. Four specimens to investigate the effect of additional straight

bars placing on the compression side of the slabs passing through the column and the other four

specimens included bent-up bars to investigate the effect of additional bars acting as shear

reinforcement without sufficient anchorage length. The third series consisted of twelve

specimens: Four specimens included bent-up bars with a sufficient anchorage length, two

specimens included straight compressive reinforcement, two had only tensile reinforcement, and

the last four included both tensile reinforcement and straight reinforcing bars passing through the

column on the compression side of the slab. It was generally observed that after the punching

shear strength has been reached, the load decreases rapidly. Then it started increasing with

further deflection. At this stage, because of the large strains at the slab top surface, cracks

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propagate through the slab and yielding of reinforcement spreads throughout the slab. The load

was carried by the reinforcement acting as a tensile membrane and with further deflection, the

load carried increases until the reinforcement start to fracture.

Ruiz et al. (2009)

Ruiz et al. (2010) established an innovative system for strengthening of flat slabs against

punching shear using post-installed shear reinforcement as the combine use of nut, washers and

bars. They tested 12 full-size slabs models, strengthened by using inclined shear reinforcements

installed within existing slabs by drilling holes only from the soffit of the slab and by bonding it

with high-performance epoxy adhesive. The results show that such reinforcements are an

efficient way to increase both the strength and deformation capacity of flat slabs. Finally the

design of the reinforcement based on the critical shear-crack theory (CSCT) is presented.

Ruiz et al. (2010)

Ruiz et al. (2010) studied about performance and design of punching shear reinforcing systems

of Flat slabs. They explained critical shear crack theory with respect to the design of punching

shear reinforcing systems. They tasted full scale slabs with same flexural and shear reinforcing

ratio but with different punching shear reinforcing systems. The experimental results confirm

that the strength and deformation capacity are strongly influenced by the characteristics of the

shear reinforcing system. The results for the various systems are finally investigated within the

frame of the critical shear crack theory, leading to a series of recommendations for design.

Song et al. (2012)

Song et al. (2012) tested total of four flat plate interior joints were subjected to gravity and cyclic

lateral loads. Three 2/3 scale isolated interior flat slab-column connections that include three

types of shear reinforcements (stirrups, headed shear stud and shear bands) are used to observe

effective punching shear and moment capacity of flat plate-column connection for lateral

loading. It is showed that the flexural failure mode appears in most specimens while the

maximum unbalanced moment and energy absorbing capacity increases effectively, with the

exception of an unreinforced standard specimen. Finally, the results of the experiments, as well

as those of experiments previously carried out by researchers, are applied to the eccentricity

shear stress model presented in ACI 318-08. The failure mode is therefore defined in this study

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by considering the upper limits for punching shear and unbalanced moment. In addition, an

intensity factor is proposed for effective widths of slabs that carry an unbalanced moment

delivered by bending.

Ferreira et al. (2012)

Ferreira et al. (2012) tested 12 slabs to evaluate the accuracies of the design methods using

comparisons between experimental and calculated strengths for punching of reinforced concrete

flat slabs with double-headed shear reinforcement. 11 slabs contained double-headed studs as

shear reinforcement, were tested supported by central column and loaded concentrically. Their

behavior is described in terms of deflections, rotations, strains of the concrete close to the

column, strains of the flexural reinforcement across the slab width, and strains of the studs. All

failures were by punching, in most cases within the shear reinforced region. The treatments of

punching resistance in ACI 318, Eurocode 2 (EC2), and the critical shear crack theory (CSCT)

are described, and their predictions are compared with the results of the present tests and 39

others from the literature. The accuracy of predictions improves from ACI 318 to EC2 to

CSCT—that is, with increasing complexity. However, the CSCT assumptions about behavior are

not well supported by the experimental observations.

Rha et al. (2013)

Rha et al. (2013) demonstrate gravity and lateral load-carrying capacities of reinforced concrete

flat plate systems. Total of five half-scale reinforced concrete slab-column frame specimens were

tested under gravity loads or combined gravity and lateral loads. Each specimen represented a

complete story of a two-bay by two-bay moment frame, in which a continuous flat plate system

was used with nine columns assumed isolated at inflection points between floors. The tested

variables were slab reinforcement ratio and loading history (monotonic versus reversed cyclic).

The tests showed that consecutive punching failures at the slab column connections induced

transient drops in the applied load, but the load-carrying capacity of the entire system was

recovered and maintained until the system completely collapsed. The amount of top and bottom

slab bars and loading history affected the punching shear capacity as well as the gravity or lateral

load carrying capacity, stiffness, and ductility. Finally, the ACI 318-11 punching shear

provisions were evaluated based on the test results and proved to be conservative for the tested

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continuous flat plate systems. The test results are important in that the test replicated real

boundary conditions of inter-story flat plate systems and monitored the direct shear and

unbalanced moment at each connection of the continuous systems.

Khaleel et al. (2013)

Khaleel et al. (2013) tested 4 half-scale two-way slab-column interior connections which were

constructed and tested under punching shear caused by centric vertical load. It is carried out to

determine the efficiency of using Fiber Reinforced Polymers (FRP) to strengthen the slab-

column connections subjected to punching shear. The use of steel links, external stirrups made

from glass specimen Fiber Reinforced Polymer (GFRP) and external stirrups made from Carbon

Fiber Reinforced Polymer (CFRP) for strengthening the flat slabs against punching shear was

considered as a new application. The experimental results showed a noticeable increase in

punching shear resistance and flexural stiffness for the strengthened specimens compared to

control specimen. Also, the strengthened tested slabs showed a relative ductility enhancement.

Finally, equations for punching shear strength prediction of slab-column connections

strengthened using different materials (Steel, GFRP & CFRP) were applied and compared with

the experimental results.

Askar (2015)

Askar (2015) conducted some tests of repairing damaged flat plates by using vertical studs with

different arrangements through holes drilled in the plates to assess the efficiency of the suggested

repairing system and to investigate the slabs load carrying capacity, deformation characteristics

and cracking behavior. As per different codes and critical shear crack theory theoretical results, a

series of 8 specimens tested were done considering the shear reinforcement volume and concrete

compressive strength as two parameters of investigations. It is found that using the proposed

system on repairing damaged flat plates due to punching shear is very efficient to regain strength,

deformation capacity and ductility.

Moreno et al. (2015)

Moreno et al. (2015) used a strengthening technique of flat slabs-column connection. To

investigate the strengthening practice of existing flat slabs against punching shear failure, the

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experimental programme carried out using carbon fibre reinforced polymers (CFRP) and shear

reinforcements. Four normal strength concrete slabs (1100mmx1100mmx100mm) with and

without shear reinforcement, submitted to punching under a concentrated load. Moreover, the

near surface mounted technique has also been tested within current experimental work. Finally, a

fourth specimen servedas reference. The effects of shear reinforcement and of the carbon fibre

reinforced polymers enhancing punching shear capacity are observed.

2.9 Summary of Literature Review

Punching shear failures in flat plates are usually sudden and catastrophic because reinforced

concrete flat plate structures do not contain beams. During an earthquake, significant horizontal

displacement of a flat plate-column connection may occur, resulting in unbalanced moments that

induce additional slab shear stresses. As a result, some flat plate structures have collapsed by

punching shear in past earthquakes. Many researchers worked on strengthening the existing RC

flat plate column connections using different types of shear reinforcements, carbon fiber

reinforced polymers (CFRP) stirrups, bolts to act as shear reinforcement, Strengthening anchor

Hilti HZA-P and vertical studs but using post-installed inclined U-stirrups for strengthening flat

plate column connection for lateral cyclic loading is still not used as a research topic.

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CHAPTER 3

MATERIAL PROPERTIES AND EXPERIMENTAL PROGRAM

3.1 Introduction

This chapter presents the experimental program of the present research consisting of specimen

preparation of half scale models of concrete frames. To investigate the improvement of punching

shear capacity using post-installed shear reinforcements in existing flat plate column connections

for lateral loading, eight reinforced concrete frames with different slab thicknesses and concrete

strengths have been tested. The material properties and experimental program are discussed

below.

3.2 Specimen Preparation

3.2.1 Selection of Geometric Properties of Model Frames

A typical full scale four storied flat plate column frame RC Building as shown in figure 3.1 was

analyzed as per BNBC. To identify the effect of seismic loading on flat plate with shear

reinforcement a one bay frame of the bottom story of a four storied building structure was

selected for the experimental program as shown in figure 3.1 to 3.3. The size of the flat plate and

columns connections frame has been taken from the analysis. Considering total cost and the

existing laboratory facilities half scale specimen has been finally selected to make the

investigation more convenient. Considering column strip from flat plate panel, equivalent flat

plate column frame selected as specimen giving details as shown in figure 3.4 to 3.5. Moreover

the dimensions of the as built specimens are shown in figure 3.4.

Two vertical point loads on two column and uniform dead loads on plates were applied to get the

effect of sustained gravity load along with a horizontal incremental static repeated loading for

seismic effect. All frames had the span length of 2520mm and height of 1000mm. Figure 3.4

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Figure 3.1 Typical RC Flat Plate Frame Building 3D View

shows the layout and dimensions of the frames and the structural elements. Detail geometry and

reinforcement of a Flat plate frame is shown in Figure 3.5 and cross sectional details of columns

and base beam are presented in table 3.1.

Frames were constructed in two groups mainly based on flat plate thickness and presence of

shear reinforcements through retrofitting, categorized in table 3.2.

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Figure 3.2 Selection of interior Flat Plate-column Frame Plan View (All Dimensions are in

milimetres)

The variations in flat plate thicknesses were 75 mm, 100 mm, 125 mm and 140 mm. For

introducing more variations in frames two types of concrete strength were used, such as 20.69

MPa and 27.59 MPa and lastly two control frame were prepared without retrofitting for

comparing with the results of frames with retrofitting using shear reinforcements.

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Figure 3.3: Selection of interior Flat Plate-column Frame Elevation

400mm Flat Plate Floor slab 400mm

300 mm

Column 2520m

1000 mm

Base Beam

2400 mm

Figure 3.4: Typical Half Scaled Model Dimension

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Table 3.1: Cross Section of Different Frame Components.

Frame Part Cross Section Reinforcement Details

Base Beam

Base Beam B x D = 250 mm x 200 mm Main bar: top 8-R12 bottom 8-R12 Stirrup: R8 @100mm with 135 degree hook Clear Cover= 20mm L = 6d

Column (Two columns are symmetric)

Column B x D = 190.5 mm x 190.5 mm Main bar: 8-R10 Hoop: R8 @150mm with 135 degree hook, L = 6d Clear Cover= 20mm

Typical model:

Group A: Non-Retrofitted

There were two model specimens.

Column size: 190.5 mm x 190.5mm

Main Bars: 8-φ 10 mm deformed bar

Shear Reinforcement: φ 8 mm @150mm with 135 degree hook

Base Beam size: 250 mm x 200 mm

Main Bars: 8-φ 12 mm top bar and 8-φ 12 mm bottom bar

Shear Reinforcement: φ 8 mm @100mm with 135 degree hook

Flat Plate Column Connections: No shear reinforcement

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Figure 3.5: Placements of top and bottom bars of Flat Plate Floor Slab

Top Bar Bottom Bar

T8@

150m

m c

/c

T8@127mm c/c [email protected] c/c

T8@

75m

m c

/c

T8@

150

mm

c/c

T8

@75

mm

c/c

84

0m

m

84

0m

m

840

mn

m

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Table 3.2: Group for Eight Frame Specimens.

Flat Plate thickness Concrete strengths

20.69 Mpa (3ksi) 27.59 Mpa (4ksi)

Group A

Non-

Retrofitted

Specimen with Flat plate

thickness 140 mm (5.5inch) S-5.5-C-3 S-5.5-C-4

Group B

Retrofitted

Specimen with Flat plate

thickness 75 mm (3inch) S-3-C-3 S-3-C-4

Specimen with Flat plate

thickness 100 mm (4inch) S-4-C-3 S-4-C-4

Specimen with Flat plate

thickness 125 mm (5 inch) S-5-C-3 S-5-C-4

Flat Plate size: length x Width = 2520mm x 840mm, Thicknesses: 140 mm

Bars Details: Bar Details was given in the Figure 3.5.

Group B: Retrofitted

There were six model specimens.

Column size: 190.5 mm x 190.5 mm

Main Bars: 8-φ 10 mm deformed bar

Shear Reinforcement: φ 8 mm @150mm with 135 degree hook

Base Beam size: 250 mm x 200 mm

Main Bars: 8-φ 12 mm top bar and 8-φ 12 mm bottom bar

Shear Reinforcement: φ 8 mm @100mm with 135 degree hook

Flat Plate size: length x Width = 2520mm x 840mm, Thicknesses: 75mm 100mm and 125mm

Bars Details: Bar Details was given in the Figure 3.5.

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Flat Plate Column Connections: U-stirrups as φ 8 mm bars were used as shear reinforcements.

Details of shear reinforcements used in flat plate as retrofitting materials are in the following

below in table 3.3.

Table 3.3: Detailing of Shear Reinforcements used in Flat Plate Column Connections

Retrofitting Work.

Flat Plate

Thickness

Concrete

Strengths

Specime

n Name

No. of

U-

stirrups

Spacing

between

column face to

1st U-stirrup

Spacing

between 1st

U-stirrup to

2nd U-stirrup

Spacing

between 2nd

U-stirrup to

3rd

75mm

(3inch)

20.70MPa

(3ksi)

S-3-C-3 32 30mm 30mm 30mm

100mm

(4inch)

20.70MPa

(3ksi)

S -4-C-3 16 40mm 40mm --

125mm

(5inch)

20.70MPa

(3ksi)

S-5-C-3 16 50mm 50mm --

75mm

(3inch)

27.59MPa

(4ksi)

S-3-C-4 32 45mm 25mm 25mm

75mm

(4inch)

27.59MPa

(4ksi)

S-4-C-4 16 45mm 25mm --

75mm

(5inch)

27.59MPa

(4ksi)

S -5-C-4 16 60mm 40mm --

All spacing was measured in the bottom surface of the flat plate.

3.2.2 Material properties

3.2.2.1 Cement

Cement is a binder, a substance that sets and hardens and can bind other materials together. The

most important uses of cement are as a component in the production of mortar in masonry, and

of concrete, a combination of cement and an aggregate to form a strong building material.

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The experimental work of this research conducted using Ordinary Portland cement (CEM I).

3.2.2.2 Fine Aggregate

Sand is a naturally occurring granular material composed of finely divided rock and mineral

particles. It is defined by size, being finer than gravel and coarser than silt. Sand can also refer to

a textural class of soil or soil type; i.e. a soil containing more than 85% sand-sized particles (by

mass).Physical and chemical properties of the sand influence the strength and durability of

concrete. Coarse Sylhet sand has been used for all specimens. Important qualities of sand those

influence the quality of fresh and hardened concrete are specific gravity, absorption capacity,

moisture content, grading and chemical properties. If the dry sand absorbs large amount of water

then w/c ratio of the fresh concrete will be changed and if the sand contains free water then the

free water participates in the hydration process affecting the design strength of concrete.

Gradation of fine aggregates has direct impact on workability of fresh concrete and strength of

hardened concrete. Higher percentage of fines will add to workability of fresh concrete. Figure

3.6 shows the gradation curve and Table 3.4 presents property test results:

Table 3.4: Physical properties of the fine aggregate (Sylhet Sand) according to ASTM

C128-88

Basic properties of Sylhet Sand Value

Oven Dry Bulk Specific Gravity 2.53

SSD Bulk Specific Gravity 2.59

Apparent Specific Gravity 2.69

Oven Dry Rodded Unit Weight 1584 kg/m3

FM value 2.88

Moisture content (%) 5.80%

Absorption capacity (%) 2.33%

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Figure 3.6: Grain Size Distribution curve of fine aggregates

3.2.2.3 Coarse Aggregate

Construction aggregate, or simply "aggregate", is a broad category of coarse particulate material

used in construction, including sand, gravel, crushed stone, slag, recycled concrete and

geosynthetic aggregates. Aggregates are the most mined materials in the world. Strength and

durability of concrete depend on the type, quality and size of the aggregates. The summary of the

physical properties of the coarse aggregate are shown in Table 3.5 and the gradation curve are

shown in figure 3.7.

Table 3.5 Physical properties of the coarse aggregate (Stone Chips) according to ASTM

C128-88

Basic properties of Stone Chips Value

Oven Dry Bulk Specific Gravity 2.61

SSD Bulk Specific Gravity 2.63

Apparent Specific Gravity 2.67

0.0

20.0

40.0

60.0

80.0

100.0

120.0

0.1 1 10 100

Per

cen

t F

inn

er b

y W

eig

ht

Grain Size(mm)

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Oven Dry Rodded Unit Weight 1429 kg/m3

FM value 5.00

Moisture content (%) 0.40%

Absorption capacity (%) 0.79%

Figure 3.7: Grain Size Distribution curve of coarse aggregates

3.2.2.4 Reinforcements

Reinforcing bars are used to take high tension, compression and shear forces induced in the

concrete member. Transfer of forces between concrete and the reinforcement depends on the

bond strength between them. At present, all commercial reinforcing bars are deformed bars and

have better bond performance with concrete than the plain reinforcing bars. Φ12 mm, Φ10 mm

and Φ8 mm bars were used for specimen constructions. Φ12 mm bars were used as longitudinal

reinforcement for base beam and Φ8 mm bars were used as stirrup and bars for columns and flat

plate slab.Φ8 mm bars are also used as U-stirrup shear reinforcements. Specimens were tested

for yield and ultimate capacity. The summary and details of the test result are given in Table 3.6.

-20.0

0.0

20.0

40.0

60.0

80.0

100.0

120.0

0.1 1 10 100

Per

cen

t F

inn

er b

y W

eig

ht

Grain Size(mm)

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Table 3.6: Strength of Reinforcing Bars

Diameter

(mm)

Elongation

(%)

Cross Section of Bar

( mm2)

Yield Strength

(MPa)

Ultimate Strength

(MPa)

12 13 113.34 545 667

10 11 78.54 543 675

8 9.50 49.10 544 680

3.2.2.5 Concrete

For preparing concrete, Ordinary Portland Cement was used along with Sylhet sand as fine

aggregate and 12.5mm downgrade stone chips as coarse aggregates.

The concrete was mixed in a mixer machine which was used for casting the entire structural

element (Base Beam, Column and Flat Plates) of the frame specimen and the casting took place

at the concrete lab in BUET. Before using concrete, slump test was carried out to keep the slump

value in between 3 to 4 inch.

3.2.2.6 Micro concrete

Micro concrete used as rebuilding material to recover clear cover of bottom side of the flat plate.

Fresh Cement used in micro-concrete mixer. The mix ratio was 1:1.1:1.6 and water cement

Figure 3.8.: Coarse Aggregate Figure 3.9: Fine Aggregate

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Figure 3.10: Concrete Mixing Figure 3.11: Slump Test

ratio was 0.34 to 0.36. No admixture was used in preparing micro concrete mixture. Fine

aggregate and coarse aggregate properties used in micro concrete mixture are given below in

Table 3.7.

Table 3.7: Properties of Micro-concrete

Properties Name Coarse Aggregate Fine Aggregate

1) Specific Gravity 2.48 2.60

2) Absorption Capacity 2.17% 1.11%

3) Fineness Modulus 1.84 2.83

Determination of Target Strength

Based on calculation several mixture proportions of concrete are selected and their 14 days and 28 days strength are determined to obtain the strengths which are shown in Table 3.8 and Table 3.9.

For flat plates two types of concrete strengths was used in this research. 20.69 MPa (3000psi) and 27.59 MPa (4000psi) were used for research. Casting concrete strengths test results for requiring targeted strength are in the following Table 3.9.

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Table 3.8: Cylinder Strength for Targeted Strength 4000 psi for Base Beam and

Column

Name of the

Specimen

Mix Ratio (Weight Base)

w/c Ratio

14 days Strengths Average

(psi)

28 days Strengths Average (psi)

(kN/m2) (psi) (kN/m2) (psi)

S-3-C-3

1:1.95:2.01 0.34 23665 3431

3600

29768 4316

4148 1:1.95:2.01 0.34 24537 3558 28149 4082

1:1.95:2.01 0.34 26280 3811 27900 4045

S-4-C-3

1:1.95:2.01 0.34 22544 3269 3401

29270 4244

4353 1:1.95:2.01 0.34 23042 3341 28772 4172

1:1.95:2.01 0.34 24786 3594 32011 4642

S-5-C-3

1:1.95:2.01 0.34 25035 3630

3666

30391 4407

4612 1:1.95:2.01 0.34 24163 3504 31139 4515

1:1.95:2.01 0.34 26654 3865 33879 4912

S-5.5-C-3

1:1.95:2.01 0.34 23489 3406

3558

33256 4822

4732 1:1.95:2.01 0.34 24119 3497 32633 4732

1:1.95:2.01 0.34 26008 3771 32011 4641

S-3-C-4

1:1.85:2.01 0.34 23489 3406

3625

34751 5039

4295 1:1.85:2.01 0.34 26008 3771 26779 3883

1:1.85:2.01 0.34 25504 3698 27327 3962

S-4-C-4

1:1.85:2.01 0.34 26260 3808

3712

33313 4830

4684 1:1.85:2.01 0.34 26008 3771 32053 4648

1:1.85:2.01 0.34 24748 3588 31550 4575

S-5-C-4 1:1.85:2.01 0.34 26008 3771 3495 32053 4648 4429

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1:1.85:2.01 0.34 23992 3491 33061 4794

1:1.85:2.01 0.34 22229 3223 26511 3844

S-5.5-C-4

1:1.85:2.01 0.34 24118 3497

3649

31298 4538

4304 1:1.85:2.01 0.34 25378 3680 27267 3954

1:1.85:2.01 0.34 26008 3771 32557 4720

Table 3.9: Cylinder Strength for Targeted Strength 3000 psi for Flat Plates.

Name of the Specimen

Mix Ratio (Weight Base)

w/c Ratio

28 days Strengths Average (psi) (kN/m2) (psi)

S-3-C-3

1:2.05:2.00 0.28 28779 4173

4173 1:2.05:2.00 0.28 26260 3808

1:2.05:2.00 0.28 31298 4539

S-4-C-3

1:2.05:2.00 0.28 27267 3955

3966 1:2.05:2.00 0.28 27267 3954

1:2.05:2.00 0.28 27519 3990

S-5-C-3

1:2.05:2.00 0.28 27015 3917

3954 1:2.05:2.00 0.28 27267 3954

1:2.05:2.00 0.28 27519 3990

S-5.5-C-3

1:2.05:2.00 0.28 26008 3771

3942 1:2.05:2.00 0.28 28275 4100

1:2.05:2.00 0.28 27267 3954

Table 3.10: Cylinder Strength for Targeted Strength 27.59 MPa (4000 psi) for Flat

Plates.

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Name of the Specimen

Mix Ratio (Weight Base)

w/c Ratio

28 days Strengths Average (psi) (kN/m2) (psi)

S-3-C-4

1:1.85:1.98 0.34 31014.00 4497

4503 1:1.85:1.98 0.34 30889.43 4479

1:1.85:1.98 0.34 31263.13 4533

S-4-C-4

1:1.85:1.98 0.34 30142.04 4371

4437 1:1.85:1.98 0.34 30764.87 4461

1:1.85:1.98 0.34 30889.45 4479

S-5-C-4

1:1.85:1.98 0.34 28778.59 4173

4465 1:1.85:1.98 0.34 30038.09 4356

1:1.85:1.98 0.34 33564.72 4867

S-5.5-C-4

1:1.85:1.98 0.34 28526.69 4136

4150 1:1.85:1.98 0.34 29786.20 4319

1:1.85:1.98 0.34 27519.09 3990

The compressive strength for each concrete casting was determined on 4x8 inch standard

concrete cylinders. The specimens were in the moulds for 24 hours; thereafter they were taken

from their moulds and stored at 100% relative humidity until testing. The compressive strength

was tested after 28 days for the entire specimen. Workability measurement was carried out on the

fresh concrete as fresh concrete as slump value, was approximately 3.5 inch as shown in Figure

3.12 to 3.13. It is observed that for 20.69MPa (3000psi) the average cylinder strengths is almost

4000psi but for the 27.59MPa (4000psi) the average cylinder strengths is almost 4500psi.

A measurement on hardened concrete was conducted as compressive strength according to

standard ASTM C39 / C39M.

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Figure 3.12: Concrete Cylinders are Stored

in Water.

Figure 3.13. Compressive Strength Testing

of Cylinders

Table 3.11: Specifications using in designing punching shear reinforcements of flat

plate

Specification Name Specification

Full scale flat plate panel 11ftX20ft

Service Dead Load for 3000psi concrete strength specimens

315psf

Service Dead Load for 4000psi concrete strength specimens

325 psf

Service Dead Load for all specimens 42psf

Square column size 7.46in.X7.46in.

Clear Cover in half Scale 0.35 in.

Allowable 𝜑𝑉𝑐 4𝜑 𝑓𝑐′(𝑝𝑠𝑖)𝑏0𝑑

𝜑 0.75

Before designing shear reinforcements of flat plate the theoretical punching capacity was

calculated using design specifications.

Using Table 3.10 Specifications the theoretical punching shear capacity of existing flat plate was

calculated. Although it was targeted that specimen concrete strength for 3000psi will remain

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3000psi but it was little bit higher. So for 3000psi concrete strength specimens designing for

punching shear reinforcements the concrete strengths of flat plate used 3500psi instead of

3000psi.

Table 3.12: Theoretical punching shear capacity

Specimen name Ultimate load (kip) Allowable load (kip)

S-3-C-3 27.04 9.01

S-4-C-3 27.54 16.11

S-5-C-3 28.56 24.63

S-5.5-C-3 28.80 29.42

S-3-C-4 27.04 9.63

S-4-C-4 27.81 17.22

S-5-C-4 28.56 26.33

S-5.5-C-4 28.80 31.45

3.3 Formation of Specimens

Frame specimens were formed in three different steps following the practical construction

practice. The base beam and two columns were casted horizontally but the flat plates and the

column top were casted vertically in three different time. At first the base beam and two columns

were constructed simultaneously. Subsequently the flat plate was erected, after flat plate was

prepared and lastly column top was constructed. The step by step pictorial descriptions of

specimen formation are given as follows:

3.3.1 Base Beam and columns Construction

At first base beams and two columns were constructed horizontally of length 2400mm and a

cross section of 200 mm x 250 mm. Form work was constructed to support the freshly placed

concrete and the reinforcement, as shown in the Figure 3.14. Basic concerns were the accuracy

of the design, pertaining to length and shape, as well as the finish of the beam. A number of

small mortar blocks were used on the inner base and on two sides of the formwork to maintain

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20 mm clear cover and vibrator were used for proper compaction. Element used in the

construction of the formwork was 1 inch wood. The formwork was removed after 4 days of

casting and covered with wet jute hessian to maintain the moisture level as shown in figure 3.15

to 3.18. The beams were cured with water four times in every day up to 28 days.

Figure 3.14: Formwork Ready for Base Beam and columns

Figure 3.15: Concrete pouring into Formwork Figure 3.16: Using Mechanical Vibrator

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3.3.2 Flat Plate floor slab and Column top Construction

After 32 days of construction of base beam flat plate floor slab were constructed to the proper

alignment of column position. Four different types of plate thicknesses were used such as 75

mm, 100 mm, 125mm and 140 mm to assess the effect of shear reinforcement on flat plate

column connections. Formwork was constructed to support the freshly placed concrete and the

reinforcement, as shown in the figure 3.19 to figure 3.21. A number of small mortar blocks were

used on all side to maintain 20 mm clear cover and vibrator was used for proper compaction.

Figure 3.19: Preparation of Flat Plate

Formwork

Figure 3.20: Formwork Ready for Flat Plate

Casting

Figure 3.17: Base Beams after column After

Casting.

Figure 3.18: Base Beams and Columns

Wrapped with Hessian for Curing.

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53

Figure 3.21: Reinforcments arrangement Figure 3.22: Flat Plate after Casting

Figure 3.23: Casted Column top and curing of

Flat Plate

Figure 3.24: Curing of Flat Plate and

Column top

The formwork was removed after 3 days of casting, sees Figure 3.15 to figure 3.16 and covered

with wet jute hessian to maintain the moisture level. The Flat plates were cured with water four

times in every day up to 28 days.

3.3.3 Retrofitting Work

Vertical U-stirrups used as shear reinforcement which was main component of retrofitting work.

It was made by φ 8 mm bars as shown in fig 3.25. Three different steps have done for retrofitting

work. They are

1. Hole Drilling and Cleaning

2. Application of Epoxy

3. Inserting Shear Reinforcements and Rebuilding clear cover using Micro-concrete

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Figure 3.25: U-stirrups as Shear Reinforcements.

3.3.3.1 Drilling and Cleaning

Inserting shear reinforcements into concrete, drilling is important step in retrofitting work. The

rebar diameter of shear reinforcements was 8mm, so drilling hole diameter was up to 8mm like

10mm and moderate hole lengths was 75mm to 175mm depending on the effective depth of flat

plates. If d is the effective depth of the flat plate then drilling length 𝑙 ≈ 2𝑑. Drilling angle was

maintained precisely at 45° to the surface to the required embedment depth using hammer-drill

with an appropriately sized carbide drill bit set in rotation hammer mode. Existing rebar location

was detected by Ferro scanner and marked by marker pencil. Drilling was done from soffit of the

flat plates around the column as shown in figure 3.28 to 3.29. It is important that the drilled holes

proceed up to at least just below the tensile reinforcement of the slab. Hammer drilling was

selected as proper way of drilling borehole and drilling was started about 10mm upward. Using

hand grinding machine and hammer with chisel clear cover was removed as shown in figure 3.31

to 3.32.

Load performance of chemical anchors is strongly influenced by the cleaning method such as

inadequate borehole cleaning causes poor load values. The borehole must be free of dust, debris,

water when applicable, ice, oil, grease and other contaminants. Compressed air blow from the

back of the borehole was performed at least two times. Round brash was inserted in borehole to

accomplish proper cleaning operation as shown in figure 3.35. Finally high pressure water flow

through boreholes executed proper cleaning operation as shown in figure 3.36.

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55

Figure 3.26: Ferro Scanner Figure 3.27: Ink marked loaction of drilling and location of existing flat plate rebars

Figure 3.28: Drilling Machine Figure 3.29: Drilling from soffit of the Plate using Drilling Machine

Figure 3.30: Hand Grinding Machine Figure 3.31: Removing clear cover using Hand Grinding Machine

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Figure 3.32: Hammer and Chisel Figure 3.33: Removing clear cover using Hammer and Chisel

Figure 3.34: Round Brush Figure 3.35: Cleaning borehole using Round Brush

Figure 3.36: Bore Holes washing by water spreading

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3.3.3.2 Application of Epoxy Adhesive

After drilling and cleaning bore holes, application of Epoxy was started. Epoxy provided high

bonding strength between steel and concrete so that used punching shear reinforcements could

not come out from concrete easily. An anchoring grout named Fosroc Lokfix S Base (Polyester

Resin Grouts) was used as epoxy adhesive glue as shown in figure 3.37 to 3.40. Lokfix is a two-

component polyester resin anchoring grout, meeting the requirements of retrofitting design:

Anchoring of reinforced steel bars. The details of Lokfix attached with Appendix B.

The grout mixture was inserted into borehole by expert who had done by hand and using a steel

rod to push epoxy glue to embedded depth as shown in figure 3.40 to 3.42.

Figure 3.37: Epoxy Adhesive Chemicals Figure 3.38: Epoxy ingredients

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58

Figure 3.39: Epoxy Mixure Figure 3.40: Application of Epoxy

Figure 3.41: Pushing Epoxy by Steel Bar Figure 3.42: After Application of Epoxy

3.3.3.3 Installing Punching Shear Reinforcements and Rebuilding clear cover using

Micro-concrete

Before installing punching shear reinforcements, the total length of U-stirups checked by total

length of prepared holes depth and its spacing according to the design dimensions. Within 10

minutes of Epoxy application, punching shear reinforcements was installed into poured

boreholes by hammering as shown in figure 3.43 to 3.48.

After installing punching shear reinforcements, Micro-concrete was used to rebuild clear cover

(20mm).

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Figure 3.43: Inserting Shear Reinforcement into the Flat Plate

Figure 3.44: Inserting Shear Reinforcement by Hammering

Figure 3.45: After Inserting Shear

Reinforcement

Figure 3.46: After Inserting Shear

Reinforcement around the column

Figure 3.47: Micro Concrete Mixure Figure 3.48: Rebuilding Clear cover

3.4 Experimental Set Up, Testing Procedure, Data Acquisition

The frames were tested under horizontal incremental cyclic loading along with constant axial

load. Lateral loading was applied using a loading control pattern. The specimens were tested

under cyclic loading conditions displacing them laterally, along the axis of the Flat Plates.

Loading and unloading was applied in 1 ton increments in the positive (rightward) and negative

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60

(leftward) direction for every cycle. Whereas 3 ton, 5ton, 6.5ton, 8 ton , 10 ton, 12 ton and 12.5

ton loading increments were maintained for 1st, 2nd , 3rd , 4th ,5th 6th and 7th cycle. A constant

loading rate per cycle was maintained until the specimens experienced significant loss of

capacity. The loading history applied to the specimens is shown in Table 3.13.

Table 3.13: Loading History.

Cycle Name

Rightward Leftward

Loading

Condition (ton)

Unloading

Condition (ton)

Loading

Condition (ton)

Unloading

Condition (ton)

Cycle-I 0 to 3 3 to 0 0 to -3 -3 to 0

Cycle-II 0 to 5 5 to 0 0 to -5 -5 to 0

Cycle-III 0 to 6.5 6.5 to 0 0 to -6.5 -6.5 to 0

Cycle-IV 0 to 8 8 to 0 0 to -8 -8 to 0

Cycle-V 0 to 10 10 to 0 0 to -10 -10 to 0

Cycle-VI 0 to 12 12 to 0 0 to -12 -12 to 0

Cycle-VI 0 to 12.5 12.5 to 0 0 to -12.5 -12.5 to 0

All the frames were all through white washed to find out the crack and their absolute location

before testing. The test set-up began with picking up the frame by the crane with trolley and then

placed under the testing machine. The horizontal static repeated load was applied manually by

hydraulic jack at an increasing rate of displacement. During testing of specimen, the load was

recorded and horizontal displacement was also measured by two deflection gages to identify the

deflection behavior which was engaged with column and flat plate as shown in figure 4.1 to 4.2.

The positions of the applied loads for all groups were illustrated in figure 3.49.

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2400mm

Figure 3.49: Schematic Diagram of Loading condition during test

Cyclic Load Cyclic Load

2520mm

1000mm

20 kip 20 kip

Uniform Load distribution

by weight block

Steel Stopper

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62

CHAPTER 4

ANALYSIS OF EXPERIMENTAL RESULTS AND

DISCUSSIONS

4.1 Introduction

This chapter summarizes the qualitative and quantitative experimental results from test

specimen-1 to specimen-8. The qualitative results include photographs of each specimen through

the course of testing and displaying the crack patterns. Load corresponding to displacements and

different crack history were recorded for producing the quantitative results.

4.2 Test Set Up and Testing Procedure

After curing, the specimen was carried away to set into the Hydraulic Testing Machine

cautiously to elude any significant damages. The crane and the trolley were used to carry with

appropriate workman. When the specimen was set up then the loading hydraulic jacks were

anchored into position. The horizontal hydraulic jacks were linked to the side face of flat Plate

and the vertical hydraulic jacks were set in their position at the top of the column. To apply dead

load on flat plate, the plate was loaded uniformly by equivalent weight. Before applying the

uniform dead load, two dial gauges were set and readings were taken as reference points to

determine the deflection throughout the loading regime. One dial gauge was set vertically with

flat plate within distance of effective depth of flat plate from column face and another was set

horizontally with column face at the top of the plate-column connection as shown in figure 4.1 to

4.2. Dial gauge readings were recorded after imposing the uniform vertical load on plate to

determine the amount of compressive shortening. To commence each test, the vertical hydraulic

jacks were first loaded to a combined force of 20 ton, 10 ton on each column top and Dial gauge

readings were recorded again. The test was loading controlled so that the horizontal hydraulic

jacks were responsible for imposing the cyclic loading to the specimen through complete cycles

of 3, 5, 6.5, 8, 10, 12 and 12.5 ton. All cycle consisted of first loading and unloading the

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specimens toward the positive (rightward) direction hereafter referred to as the negative

(leftward) direction.

The ultimate axial load carrying capacity of each column was 97.93kip (Considering as tied

column) and only 20.43% of total capacity was imposed on column so that there was no axial

failure of column.

Figure 4.1: Dial Gauge-1

Figure 4.2: Dial Gauge-2

4.3 Failure Modes of Flat Plate

Most of the specimens failed in flexure shear but only control specimens failed in punching

shear. Punching failure occurred with diagonal cracking emblem adjacent to the critical section

with large cracking depth, on the other hand flexural failure occurred with vertical crack emblem

commencing from bottom of the Flat Plate with large cracking depth.

Although first crack was observed in column joint with the base beam, but finally the flat plate

specimen failed with cracking in flat plate. Only one specimen was failed after the column joint

with base beam failed.

The final crack revealed in specimen at failure condition at greater distance than effective depth

of flat plate from column face is considered as flexure failure and the punching failure ensured

when final crack in specimen at failure condition revealed within effective depth of flat plate

from column face.

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All eight specimens exhibited different cracking patterns throughout the course of testing. Figure

4.3 is a photograph of a specimen just prior to testing.

Figure 4.3: Initial State of Test Specimen

4.4 Test Result of Specimen S-3-C-3

The black marked cracks, represented the cracking that appeared during the loading and

unloading from leftward and rightward, as shown in figure 4.4 to figure 4.10. The shear cracking

seemed to be more widespread. The test of specimen-S-3-C-3 was associated with its first crack

of the flat slab at positive third cycle loading at flat plate with 6.5 ton load and corresponded to a

horizontal displacement of 3.40mm and vertical displacement of 0.40mm. The flat plate failed at

negative fifth cycle loading at left side with 10 ton load to a corresponding horizontal

displacement of 26.70mm and vertical displacement of 5.30mm. Very first crack was generated

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at positive second cycle loading at left column with 5 ton load to a corresponding horizontal

displacement of 2.70 mm. The failure pattern of flat plate was flexure type.

Figure 4.4: Final crack pattern of specimen S-3-C-3

Figure 4.5: Left side crack of flat plate Figure 4.6: Right side crack of flat plate

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Figure 4.7: Left side bottom crack view after

5th Cycle

Figure 4.8: Right side bottom crack view after

5th Cycle

Figure 4.9: Left top crack view after 5th cycle Figure 4.10: Left side crack view after 5th cycle

4.5 Test Result of Specimen S-4-C-3

The black marked cracks, represented the cracking that appeared during the loading and

unloading from leftward and rightward, as shown in figure 4.11 to figure 4.16. The shear

cracking seemed to be more widespread. The test of specimen S-4-C-3 was associated with its

first crack of the slab at positive 2nd cycle loading at flat plate with 5 ton load and corresponded

to a horizontal displacement of 4.45mm and vertical displacement of 0.40mm and second crack

at flat plate at negative forth cyclic loading with 8 ton load at right side to a corresponding

horizontal displacement of 12.50mm and vertical displacement of 1.35mm. The flat plate failed

at negative 5th cycle loading at right side with 10 ton load to a corresponding horizontal

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displacement of 19.70mm and vertical displacement of 2.21mm. Very first crack was generated

at positive 2nd cycle loading at left column with 3 ton load to a corresponding horizontal

displacement of 2.30 mm. The failure pattern of flat plate was flexure type.

Figure 4.11: Final crack pattern of specimen S-4-C-3

Figure 4.12: Left side of flat plate after 5th cycle

Figure 4.13: Right side of flat plate after 5th cycle

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Figure 4.14: Left side flat plate bottom view after 5th cycle

Figure 4.15: Right side flat plate bottom view after 5th cycle

Figure 4.16: Left side flat plate top view after 5th cycle

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4.6 Test Result of Specimen S-5-C-3

The black marked cracks, represented the cracking that appeared during the loading and

unloading from leftward and rightward, as shown in figure 4.17 to figure 4.21. The shear

cracking seemed to be more widespread. The test of specimen S-5-C-3 was associated with its

first crack of the slab at flat plate at negative 3rd cycle loading with 6 ton load and corresponded

to a horizontal displacement of 3.00 mm and vertical displacement of 1.00 mm and second large

crack at flat plate at negative 4th cyclic loading with 8 ton load at right side to a corresponding

horizontal displacement of 5.10 mm and vertical displacement of 1.58 mm. The flat plate failed

at negative 5th cycle loading at left side with 10 ton load to a corresponding horizontal

displacement of 15.60 mm and vertical displacement of 2.37 mm. Very first crack was generated

at positive 2nd cycle loading at left column with 5 ton load to a corresponding horizontal

displacement of 2.45 mm. The failure pattern of flat plate was punching shear type.

Figure 4.17: Final crack pattern of specimen S-5-C-3

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Figure 4.18: Left side crack of flat plate Figure 4.19: Right side crack of flat plate

Figure 4.20: Top crack view in left side of

flat plate after 5th cycle

Figure 4.21: Bottom crack view in right side of

flat plate after 5th cycle

4.7 Test Result of Specimen S-5.5-C-3 (Control)

The black marked cracks, represented the cracking that appeared during the loading and

unloading from leftward and rightward, as shown in figure 4.22 to figure 4.28. The shear

cracking seemed to be more widespread. The test of specimen S-5.5-C-3(control) was associated

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71

with its first crack at flat plate at positive 3rd cycle loading with 6.5 ton load and corresponded to

a horizontal displacement of 3.02 mm and vertical displacement of 0.19 mm. The flat plate failed

at negative 5th cycle loading at left side with 10 ton load to a corresponding horizontal

displacement of 11.90 mm and vertical displacement of 0.85 mm. Very first crack was generated

at negative 1st cycle loading at left column with 3 ton load to a corresponding horizontal

displacement of 1.97 mm. The failure pattern of flat plate was punching type.

Figure 4.22: Final crack pattern of specimen S-5.5-C-3(Control)

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Figure 4.23: Left side crack of flat plate Figure 4.24: Right side crack of flat plate

Figure 4.25: Left side crack of flat plate after 5th cycle

Figure 4.26: Right side crack of flat plate after 5th cycle

Figure 4.27: Top crack view in flat plate after 5th cycle

Figure 4.28: Right side crack of flat plate after 5th cycle

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4.8 Test Result of Specimen S-3-C-4

The black marked cracks, represented the cracking that appeared during the loading and

unloading from leftward and rightward, as shown in figure 4.29 to figure 4.35. The shear

cracking seemed to be more widespread. The test of specimen S-3-C-4 was associated with its

first crack at flat plate at positive 3rd cycle loading with 6.5 ton load and corresponded to a

horizontal displacement of 5.35 mm and vertical displacement of 0.33 mm and second crack at

flat plate at negative 3rd cyclic loading with 6.5 ton load at right side to a corresponding

horizontal displacement of 6.80 mm and vertical displacement of 1.83 mm.. The flat plate was

failed at negative 6th cycle loading at left side with 10.5 ton load to a corresponding horizontal

displacement of 28.00 mm and vertical displacement of 4.75 mm. Very first crack was generated

at negative 1st cycle loading at left column with 5 ton load to a corresponding horizontal

displacement of 2.94 mm. The failure pattern of flat plate was flexure type.

Figure 4.29: Final crack pattern of specimen S-3-C-4

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Figure 4.30: Left side crack of flat plate Figure 4.31: Right side crack of flat plate

Figure 4.32: Left side crack view after 5th cycle

Figure 4.33: Right side crack view after 5th cycle

Figure 4.34: Left side top crack view after 5th cycle

Figure 4.35: Right column bottom crack view after 5th cycle

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4.9 Test Result of Specimen S-4-C-4

The black marked cracks, represented the cracking that appeared during the loading and

unloading from leftward and rightward, as shown in figure 4.36 to figure 4.42. The shear

cracking seemed to be more widespread. The test of specimen S-4-C-4 was associated with its

first crack at flat plate at positive 3rd cycle loading with 6.5 ton load and corresponded to a

horizontal displacement of 4.60 mm and vertical displacement of 0.62 mm and second crack at

flat plate at negative 3rd cyclic loading with 6.5 ton load at right side to a corresponding

horizontal displacement of 5.50 mm and vertical displacement of 1.79 mm.. The flat plate failed

at positive 6th cycle loading at right side with 11.5 ton load to a corresponding horizontal

displacement of 25.90 mm and vertical displacement of 10.60 mm. Very first crack was

generated at negative 1st cycle loading at left column with 3 ton load to a corresponding

horizontal displacement of 1.30 mm. The failure pattern of flat plate was flexure type.

Figure 4.36: Final crack pattern of specimen S-4-C-4

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Figure 4.37: Left side crack view of flat plate Figure 4.38: Right side crack view of flat plate

Figure 4.39: Left side bottom crack view of flat plate after 5th cycle

Figure 4.40: Right side bottom crack view of flat plate after 5th cycle

Figure 4.41: Left side crack of flat plate Figure 4.42: Right side crack of flat plate

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4.10 Test Result of Specimen S-5-C-4

The black marked cracks, represented the cracking that appeared during the loading and

unloading from leftward and rightward, as shown in figure 4.43 to figure 4.49. The shear

cracking seemed to be more widespread. The test of specimen S-4-C-4 was associated with its

first crack at flat plate at positive 3rd cycle loading with 6.5 ton load and corresponded to a

horizontal displacement of 4.70 mm and vertical displacement of 0.40 mm. The flat plate failed

at negative 6th cycle loading at right side with 10 ton load to a corresponding horizontal

displacement of 16.60 mm and vertical displacement of 1.35 mm. Very first crack was generated

at negative 2nd cycle loading at left column with 5 ton load to a corresponding horizontal

displacement of 2.35 mm. The failure pattern of flat plate was flexure type.

Figure 4.43: Final crack pattern of specimen S-5-C-4

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Figure 4.44: Left side crack view of flat plate

Figure 4.45: Right side crack view of flat plate

Figure 4.46: Left side crack view of flat plate

Figure 4.47: Right side crack view of flat plate

Figure 4.48: Left bottom crack view of flat plate after 5th cycle

Figure 4.49: Right top crack view of flat plate after 5th cycle

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4.11 Test Result of Specimen S-5.5-C-4 (Control)

The black marked cracks, represented the cracking that appeared during the loading and

unloading from leftward and rightward, as shown in figure 4.50 to figure 4.54. The shear

cracking seemed to be more widespread. The test of specimen S-5.5-C-4 was associated with its

first crack at flat plate at positive 2nd cycle loading with 5 ton load and corresponded to a

horizontal displacement of 2.67 mm and vertical displacement of 0.03 mm and second crack at

flat plate at negative 2nd cyclic loading with 5 ton load at right side to a corresponding horizontal

displacement of 3.33 mm and vertical displacement of 0.49 mm. The flat plate failed at positive

7th cycle loading at right side with 12.5 ton load to a corresponding horizontal displacement of

25.47 mm and vertical displacement of 3.36 mm. Very first crack was generated at negative 1st

cycle loading at left column with 3 ton load to a corresponding horizontal displacement of 1.32

mm. The failure pattern of flat plate was punching type.

Figure 4.50: Final crack pattern of specimen S-5.5-C-4

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Figure 4.51: Left side crack view of flat plate Figure 4.52: Right side crack view of flat

plate

Figure 4.53: Bottom crack view at left side of

flat plate after 7th cycle

Figure 4.54: Right side crack view after 7th

cycle

4.12 Load-Deformation Response

Load-deformation responses of all eight specimens were monitored by two dial gauges

throughout each test specimen. Two dial gauges were placed at the mid-height of the top column

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face to record the lateral displacement. Testing was terminated when the specimen was failed.

Figures 4.55 to figure 4.67 provide the load-deformation responses of each specimen. [The

responses from dial gauges are available in the Appendices A].

Figures 4.55 to 4.56 show that after applying leftward 10 ton cyclic load the specimen was failed

which was apparent by quick horizontal and vertical displacements. The residual vertical

displacements indicated failure status. In Figures 4.57 to 4.58, specimen failure condition is

evident by vertical displacements.

Figures 4.59 to 4.60 show that the crack in flat plate commenced after 3rd cycle cyclic loading

and the residual vertical displacements gradually increased with increasing lateral cyclic loading

but the specimen failed at 10 ton leftward cyclic loading.

The greater elasticity behaviour of flat plate specimen was revealed by Figure 4.61 to 4.62 with

minimum horizontal and vertical displacements but the specimen was failed after 5th cycle lateral

loading.

Figure 4.55: Load- Lateral Deformation Response of Specimen S-3-C-3

-15

-10

-5

0

5

10

15

-30.00 -20.00 -10.00 0.00 10.00 20.00 30.00

Cycl

ic L

oad

(to

n)

Horizontal Displacement (mm)

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82

Figure 4.56: Load- Vertical Deformation Response of Specimen S-3-C-3

-15

-10

-5

0

5

10

15

-6.00 -5.00 -4.00 -3.00 -2.00 -1.00 0.00 1.00 2.00 3.00 4.00

Cycl

ic L

oad

(to

n)

Vertical Displacements (mm)

-15

-10

-5

0

5

10

15

-25.00 -20.00 -15.00 -10.00 -5.00 0.00 5.00 10.00 15.00 20.00

Cycl

ic L

oad

(to

n)

Horizontal Displacement (mm)

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83

Figure 4.57: Load- Lateral Deformation Response of Specimen S-4-C-3

Figure 4.58: Load- Vertical Deformation Response of Specimen S-4-C-3

-15

-10

-5

0

5

10

15

-2.50 -2.00 -1.50 -1.00 -0.50 0.00 0.50 1.00 1.50 2.00 2.50

Cycl

ic L

oad

(to

n)

Vertical Displacements (mm)

-15

-10

-5

0

5

10

15

-20.00 -15.00 -10.00 -5.00 0.00 5.00 10.00 15.00

Cy

clic

Lo

ad

(to

n)

Horizontal Displacement (mm)

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84

Figure 4.59: Load-Deformation Response of Specimen S-5-C-3

Figure 4.60: Load- Vertical Deformation Response of Specimen S-5-C-3

-15

-10

-5

0

5

10

15

-2.50 -2.00 -1.50 -1.00 -0.50 0.00 0.50 1.00

Cycl

ic L

oad

(to

n)

Vertical Displacements (mm)

-15

-10

-5

0

5

10

15

-15.00 -10.00 -5.00 0.00 5.00 10.00 15.00

Cycl

ic L

oad

(to

n)

Horizontal Displacement (mm)

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85

Figure 4.61: Load-Lateral Deformation Response of Specimen S-5.5-C-3 (Control)

Figure 4.62: Load-Vertical Deformation Response of Specimen S-5.5-C-3 (Control)

Figure 4.63: Load-Lateral Deformation Response of Specimen S-3-C-4

-15

-10

-5

0

5

10

15

-1.2 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4

Cycl

ic L

oa

d (

ton

)

Veretical Displacements (mm)

-15

-10

-5

0

5

10

15

-20.00 -15.00 -10.00 -5.00 0.00 5.00 10.00 15.00 20.00 25.00 30.00 35.00

Cycl

ic L

oad

(to

n)

Horizontal Displacement (mm)

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86

Figure 4.64: Load-Vertical Deformation Response of Specimen S-3-C-4

Figure 4.65: Load-Lateral Deformation Response of Specimen S-4-C-4

-15

-10

-5

0

5

10

15

-4.00 -3.00 -2.00 -1.00 0.00 1.00 2.00 3.00 4.00 5.00 6.00

Cycl

ic L

oad

(to

n)

Vertical Displacements (mm)

-15

-10

-5

0

5

10

15

-20.00 -15.00 -10.00 -5.00 0.00 5.00 10.00 15.00 20.00 25.00 30.00

Cycl

ic L

oad

(to

n)

Horizontal Displacement (mm)

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87

Figure 4.66: Load-Vertical Deformation Response of Specimen S-4-C-4

Figure 4.67: Load-Lateral Deformation Response of Specimen S-5-C-4

-15

-10

-5

0

5

10

15

-6.00 -4.00 -2.00 0.00 2.00 4.00 6.00 8.00 10.00 12.00

Cycl

ic L

oad

(to

n)

Vertical Displacements (mm)

-15

-10

-5

0

5

10

15

-20.00 -15.00 -10.00 -5.00 0.00 5.00 10.00

Cycl

ic L

oad

(to

n)

Horizontal Displacement (mm)

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88

Figure 4.68: Load-Vertical Deformation Response of Specimen S-5-C-4

Figure 4.69: Load-Lateral Deformation Response of Specimen S-5.5-C-4(Control)

-15

-10

-5

0

5

10

15

-1.60 -1.40 -1.20 -1.00 -0.80 -0.60 -0.40 -0.20 0.00 0.20

Cycl

ic L

oad

(to

n)

Vertical Displacement (mm)

-15

-10

-5

0

5

10

15

-20.00 -15.00 -10.00 -5.00 0.00 5.00 10.00 15.00 20.00 25.00 30.00

Cycl

ic L

oad

(to

n)

Horizontal Displacement (mm)

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89

Figure 4.70: Load-Vertical Deformation Response of Specimen S-5.5-C-4(Control)

Figures 4.57 to 4.60 represent the load–displacement response of eight specimens at every

different cycle independently and a summary of the results in terms of very first crack in flat

plate, first crack in flat plate and specimen failure crack at every specimen are given in Table 4.1.

It was observed that during test the specimens have more load carrying capacity to reach collapse

type failure or final broken stage. Considering safety and ultimate capacity of testing machine

used in lab, the test with corresponding loading was carried as discussed above.

Figures 4.63 to 4.64 show that residual vertical displacement is increasing with lateral cyclic

loading and after rightward 10.5 ton lateral load the specimen was failed. The specimen in Figure

4.65 to 4.66 failed at rightward lateral cyclic loading which is elicited by quick horizontal and

vertical displacements.

Figures 4.69 to 4.70 reveal that sudden brittle failure was occurred at 12.5 ton lateral cyclic

loading by quick vertical displacements.

-15

-10

-5

0

5

10

15

-2.00 -1.00 0.00 1.00 2.00 3.00 4.00

Cycl

ic L

oad

(to

n)

Vertical Displacement (mm)

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90

Table 4.1: Summary Results of Eight Specimens

Phenomena Specimen

Name

Cycle Horizontal

Displacement (mm)

Vertical

Displacement (mm)

Horizontal

Force (ton)

First crack

in Flat Plate

S-3-C-3 Rightward 3rd

cycle (Loading)

3.40 0.40 6.5

S-4-C-3 Rightward 2nd

cycle (Loading)

4.45 0.40 5

S-5-C-3 Leftward 3rd cycle

(Loading)

3.00 1.00 6

S-5.5-C-3

(Control)

Rightward 3rd

cycle ( Unloading)

3.02 0.19 6.5

S-3-C-4 Rightward 3rd

cycle ( Loading)

5.35 0.33 6.5

S-4-C-4 Rightward 3rd

cycle ( Loading)

5.50 0.62 6.5

S-5-C-4 Rightward 3rd

cycle ( Loading)

4.70 0.40 6.5

S-5.5-C-4

(Control)

Rightward 2nd

cycle ( Loading)

2.67 0.03 5

Second

Crack in

Flat Plate

S-3-C-3 Leftward 4th cycle

(Loading)

15.3 1.94 10

S-4-C-3 Leftward 4th cycle

(Loading)

12.50 1.35 10

S-5-C-3 Leftward 4th cycle

(Loading)

5.10 1.58 8

S-5.5-C-3

(Control)

Leftward 3rd cycle

( Loading)

3.34 1.25 6.5

S-3-C-4 Leftward 3rd cycle

( Loading)

6.80 1.83 6.5

S-4-C-4 Leftward 3rd cycle

( Loading)

5.50 1.79 6.5

S-5-C-4 Leftward 2nd 4.25 1.05 5

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91

cycle ( Loading)

S-5.5-C-4

(Control)

Leftward 2nd

cycle ( Loading)

3.33 0.49 5

Very First

Crack

S-3-C-3 Rightward 2nd

cycle (Loading)

2.70 N/A 5

S-4-C-3 Rightward 2nd

cycle (Loading)

2.30 N/A 3

S-5-C-3 Rightward 2nd

cycle (Loading)

2.45 N/A 5

S-5.5-C-3

(Control)

Leftward 1st cycle

(Loading)

1.97 N/A 3

S-3-C-4 Leftward 1st cycle

(Loading)

2.94 N/A 5

S-4-C-4 Leftward 1st cycle

(Loading)

1.30 N/A 3

S-5-C-4 Leftward 2nd

cycle (Loading)

2.35

N/A 5

S-5.5-C-4

(Control)

Leftward 1st cycle

(Loading)

1.32 N/A 3

Flat Plate

Failure

Crack

S-3-C-3 Leftward 5th cycle

(Loading)

26.70 5.30 10

S-4-C-3 Leftward 5th cycle

(Loading)

19.70 2.21 10

S-5-C-3 Leftward 5th cycle

(Loading)

15.60 2.37 10

S-5.5-C-3

(Control)

Leftward 5th cycle

(Loading)

11.90 0.85 10

S-3-C-4 Leftward 6th cycle

( Loading)

28.00 4.75 10.5

S-4-C-4 Rightward 6th

cycle ( Loading)

25.90 10.60 11.5

S-5-C-4 Leftward 6th cycle

( Loading)

16.60 1.35 10

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92

S-5.5-C-4

(Control)

Rightward 7th

cycle ( Loading)

25.47 3.36 12.50

Figure 4.71: Summary Results of First Crack in Flat Plate

0

1

2

3

4

5

6

7

Horizontal Displacement (mm)

Vertical Displacement (mm)

Horizontal Force (ton)

S-3-C-3

S-4-C-3

S-5-C-3

S-5.5-C-3 (Control)

S-3-C-4

S-4-C-4

S-5-C-4

S-5.5-C-4 (Control)

0

2

4

6

8

10

12

14

16

18

Horizontal Displacement (mm)

Vertical Displacement (mm)

Horizontal Force (ton)

S-3-C-3

S-4-C-3

S-5-C-3

S-5.5-C-3 (Control)

S-3-C-4

S-4-C-4

S-5-C-4

S-5.5-C-4 (Control)

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Figure 4.72: Summary Results of Second Crack in Flat Plate

Figure 4.73: Summary Results of Very First Crack in Specimen

Figure 4.74: Summary Results of Specimen Failure

0

1

2

3

4

5

6

Horizontal Displacement (mm) Horizontal Force (ton)

S-3-C-3

S-4-C-3

S-5-C-3

S-5.5-C-3 (Control)

S-3-C-4

S-4-C-4

S-5-C-4

S-5.5-C-4 (Control)

0

5

10

15

20

25

30

Horizontal Displacement (mm)

Vertical Displacement (mm)

Horizontal Force (ton)

S-3-C-3

S-4-C-3

S-5-C-3

S-5.5-C-3 (Control)

S-3-C-4

S-4-C-4

S-5-C-4

S-5.5-C-4 (Control)

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From the above figure it is observed that first crack in flat plate was revealed with low horizontal

and vertical displacement at control (5” thickness flat plate) specimen than low thickness

retrofitted specimens of group B. The horizontal force for first crack in flat plate was

unpredictable but the second crack in flat plate was revealed at non-retrofitted specimen with

minimum horizontal displacement, vertical displacement and horizontal force than retrofitted

specimens of group B. The very first crack in specimen was developed at column joint with base

beam.

In analyzing failure pattern of frame specimen, Flat Plate of control specimen failed with

minimum horizontal and vertical displacement than retrofitted specimen but the horizontal force

at failure were same for all flat plate of 20.69MPa specimens.

Table 4.2: Summary of Maximum Horizontal and Vertical Displacement

corresponding to each cycle

Specimen

Name

Cycle Positive

Maximum

Horizontal

Displacement

(mm)

Positive

Maximum

Vertical

Displacement

(mm)

Corresponding

Load (ton)

Negative

Maximum

Horizontal

Displacement

(mm)

Negative

Maximum

Vertical

Displacement

(mm)

Corresponding

Load (ton)

S-3-C-3

Cycle I 1.90 -1.38 3 0.10 -0.48 -3

Cycle II 4.00 -4.00 5 0.40 -0.95 -5

Cycle III 8.94 -6.80 6.5 1.00 -1.30 -6.5

Cycle IV 14.65 -11.70 8 2.06 -2.1 -8

Cycle V 18.80 -26.70 10 2.55 -5.3 -10

S-4-C-3

Cycle I 1.50 -1.30 3 0.05 -0.25 -3

Cycle II 4.45 -4.70 5 0.00 -85 -5

Cycle III 6.25 -6.00 6.5 -0.03 -0.88 -6.5

Cycle IV 10.00 -12.50 8 4.40 -1.35 -8

Cycle V 13.70 -19.70 10 1.8 -2.21 -10

S-5-C-3

Cycle I 0.86 -0.83 3 0.06 -0.12 -3

Cycle II 2.45 -1.50 5 0.14 -0.22 -5

Cycle III 3.50 -4.60 6.50 0.44 -1.10 -6.50

Cycle IV 5.90 -5.10 8 -0.31 -1.60 -8

Cycle V 10.11 -15.60 10 -0.53 -2.24 -10

S-5.5-C- Cycle I 0.86 -2.58 3 0.02 -0.02 -3

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3

(Control

)

Cycle II 1.36 -2.58 5 0.11 -0.32 -5

Cycle III 3.02 -4.58 6.5 0.05 -0.23 -6.5

Cycle IV 4.32 -4.98 8 0.14 -0.27 -8

Cycle V 12.60 -11.90 10 0.19 -0.98 -10

S-3-C-4

Cycle I 1.24 -1.96 3 0.11 -0.63 -3

Cycle II 2.94 -4.76 5 1.00 -1.10 -5

Cycle III 5.35 -6.80 6.5 0.33 -1.83 -6.5

Cycle IV 11.50 -10.40 8 1.25 -2.40 -8

Cycle V 17.40 -14.50 10 2.17 -3.35 -10

Cycle VI 28.00 - 12(10.5) 4.75 - -

S-4-C-4

Cycle I 1.30 -1.48 3 0.77 -1.00 -3

Cycle II 2.95 -3.40 5 1.25 -1.20 -5

Cycle III 4.60 -5.50 6.5 0.62 -1.79 -6.5

Cycle IV 6.47 -8.50 8 1.55 -2.47 -8

Cycle V 14.64 -17.00 10 2.95 -3.91 -10

Cycle VI 25.90 - 12 10.65 - -

S-5-C-4

Cycle I 0.90 -0.85 3 0.03 -0.08 -3

Cycle II 1.60 -2.35 5 0 -0.15 -5

Cycle III 2.55 -5.70 6.5 -0.04 -0.40 -6.5

Cycle IV 4.10 -7.70 8 -0.13 -0.54 -8

Cycle V 6.20 -16.60 10 -0.03 -1.35 -10

S-5.5-C-

4

(Control

)

Cycle I 1.32 -1.43 3 0.06 -0.14 -3

Cycle II 2.67 -3.33 5 0.03 -0.49 -5

Cycle III 4.17 -5.38 6.5 -0.09 -0.68 -6.5

Cycle IV 6.93 -8.33 8 -0.25 -0.74 -8

Cycle V 9.97 -10.98 10 -0.25 -1.01 -10

Cycle VI 14.07 -16.43 12 -1.22 -0.20

Cycle

VII

25.47 - 14(12.5) 3.36 - -

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Figure 4.75: Maximum Load with Corresponding Cycle

According to 352.1R including inelastic deformations flat plate structures should have the

capability to withstand a design story drift ratio of at least 0.015. It is shown in Table 4.2

practical story drift compared with allowable minimum story drift. Except control specimen of

3ksi concrete strength, all others are effectively satisfied as per ACI 352.1R but S-5.5-C-4

specimens satisfied minimum story drift ratio requirement.

Table 4.3: Summary of Maximum Lateral Deflection and Maximum Story Drift

compared to Allowable Minimum Story Drift as per ACI 352.1R

Specimen Name Maximum Lateral Deflection (mm)

Experimental Maximum Story Drift

Allowable Minimum Story Drift as per

ACI 352.1R

S-3-C-3 26.70 0.0267 0.015

S-4-C-3 19.70 0.0197 0.015

S-5-C-3 15.60 0.0156 0.015

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

S-3-C-3 S-4-C-3 S-5-C-3 S-5.5-C-3 (Control)

S-3-C-4 S-4-C-4 S-5-C-4 S-5.5-C-4 (Control)

Cycle I

Cycle II

Cycle III

Cycle IV

Cycle V

Cycle VI

Cycle VII

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S-5.5-C-3 13.15 0.01315 0.015

S-3-C-4 19.70 0.0197 0.015

S-4-C-4 25.90 0.0259 0.015

S-5-C-4 16.60 0.0166 0.015

S-5.5-C-4 25.47 0.02547 0.015

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CHAPTER 5

SUMMARY, CONCLUSIONS AND RECOMMENDATIONS

5.1 Summary

This study aims to strengthen existing flat plate against punching shear for safety reason (without

seismic detailing before, deficiencies during design or construction, increase of applied loads) or

to comply with more stringent code requirements. Special anchors (U-stirrups) in combination

with an adhesive epoxy are used to install punching shear reinforcement into already hardened

concrete. To achieve desirable punching shear capacity under seismic loading condition, cyclic

loading test was conducted on a half scale models of eight different reinforced concrete frames;

categorized in two different groups (Group A and Group B) as in chapter 3. Finally the test

results of Groups A and B were compared.

Two types of parameters were considered in the study: Concrete strength and Flat Plate

thickness. Groups A and B were consisted of two and six specimens respectively. Specimens of

Group A were constructed with two types of concrete strengths and uniform thickness of plate.

Specimens of Group B were constructed with two types of concrete strengths with three different

flat plate thicknesses. Preparation of Group A specimens consists of two steps but preparation of

Group B specimens consists of three steps. At every different step different frame component

was constructed following the usual construction practices. Frames were tested under

incremental horizontal cyclic loading along with constant vertical load. Tests were conducted

under load controlled cyclic loading.

During testing two dial gauges were used to determine the horizontal and vertical deflections of

flat plates. Among them one was installed at the interior side of column top and just beneath the

flat plate to determine the horizontal deflection of flat plate and the other one was installed at

bottom surface of flat plate to determine the vertical deflection. From these tests the

displacement corresponding to each cyclic load was recorded. With this recorded data load-

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99

displacement response curves were prepared to compare the results of test specimens of different

group.

Finally some conclusions were drawn regarding the use of shear reinforcements as retrofitting

elements in reinforced concrete flat plate frame construction considering effects of plate

thicknesses and concrete strengths under cyclic loading.

5.2 Conclusions

Behavior of the flat plates under cyclic loading, both of the control specimens and the retrofitted

specimens, were investigated. Based on the results obtained from the tests, the following

conclusions can be drawn-

i. The failure lateral loads of the comparable specimens with 20.69MPa concrete strength

with different thicknesses of flat plates were nearly same but the failure crack pattern was

different. On the other hand in the case of specimens with 27.89MPa concrete strength. It

was observed that the failure load for control specimen was little higher than thinner

retrofitted specimens. Failure of control specimen was brittle type. The failure pattern of

the all the retrofitted specimens was ductile.

ii. Lateral and vertical displacements at failure of thicker specimens were less than

displacements of thinner specimens. These responses increased with increasing concrete

strength and decreasing plate thickness.

iii. The very first crack for all specimens appeared in the column joint with base beam at the

lower cycles. The number of cycle at which the very first crack appeared differed for

different concrete strengths and plate thicknesses.

iv. The first crack in slab for the specimens with higher plate thickness appeared at an earlier

cycle than that of thinner flat plate specimens. All other cracks in lower plate thicknesses

revealed near the column face at the lower cycle but in thicker flat plate specimens most

of the cracks revealed far from column face at the higher cycle.

v. The failure pattern of Group A was brittle but the failure pattern of Group B was ductile

type i.e. it showed the warning before specimen failed which was ensured by the residual

vertical displacements.

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vi. The specimens of Group A showed less ductile behavior but the ductility increases with

increased concrete strength and decreased flat plate thickness specimens of group B.

5.4 Recommendations for Further Study

This research suggests many recommendations for further investigation.

Non-retrofitted and retrofitted specimen with sane thicknesses and concrete strengths flat

plates should be tested to investigate the improvement of punching shear capacity more

precisely.

A comprehensive study should be made by involving both experimental and finite

element analysis.

More variables (steel ratio, column size etc) and more specimens should be considered to

investigate the effect on improving punching shear capacity.

A full scale model may be investigated to get effects of shear reinforcements on punching

shear capacity more precisely.

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APPENDIX-A

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Table A.1: Load-Deflection Value for Specimen S-3-C-3

Load (ton)

Horizontal Deflection (mm)

Vertical Deflection (mm)

Load (ton)

Horizontal Deflection (mm)

Vertical Deflection (mm)

Cycle-I Cycle-III 0 0.00 0.00 1 0.90 -0.15 1 0.50 0.01 2 1.35 -0.05 2 1.05 0.05 3 2.20 0.15 3 1.90 0.10 4 3.60 0.40 2 1.70 0.06 5 7.30 0.70 1 1.30 0.03 6 8.34 0.95 0 0.80 0.00 6.5 8.94 1.00 -1 0.15 -0.08 6 8.94 0.98 -2 -0.45 -0.20 5 8.50 0.92 -3 -1.38 -0.48 4 7.60 0.75 -2 -1.10 -0.40 3 6.70 0.55 -1 -0.70 -0.23 2 5.20 0.35 0 0.05 -0.13 1 4.00 0.18 Cycle-II 0 2.75 0.00 0 0.10 -0.19 -1 1.65 -0.20 1 0.50 -0.15 -2 0.25 -0.40 2 1.11 -0.08 -3 -1.10 -0.60 3 1.80 0.05 -4 -2.25 -0.85 4 2.70 0.24 -5 -3.90 -1.00 5 4.00 0.4 -6 -5.80 -1.20 4 4.00 0.35 -6.5 -6.80 -1.30 3 3.80 0.25 -6 -6.80 -1.30 2 3.10 0.16 -5 -6.50 -1.25 1 2.40 0.06 -4 -6.00 -1.20 0 1.65 0 -3 -5.40 -1.10 -1 0.65 -0.1 -2 -4.10 -1.00 -2 -0.10 -0.18 -1 -2.50 -0.85 -3 -1.13 -0.3 0 -0.25 -0.40 -4 -2.00 -0.65 Cycle-IV -5 -4.00 -0.95 1 0.70 -0.25 -4 -3.60 -0.8 2 2.10 -0.12 -3 -3.00 -0.73 3 3.50 0.06 -2 -2.20 -0.65 4 5.30 0.4 -1 -1.30 -0.4 5 7.25 0.9 0 0.05 -0.28 6 9.45 1.5

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Load

(ton)

Horizontal

Deflection (mm)

Vertical

Deflection (mm)

Load

(ton)

Horizontal

Deflection (mm)

Vertical

Deflection (mm)

7 11.70 1.8 10 18.80 2.55 8 14.65 2.06 9 18.30 2.6 7 13.78 1.85 8 17.80 2.45 6 12.75 1.75 7 16.70 2.15 5 11.10 1.55 6 15.50 1.85 4 9.60 1.2 5 14.00 1.75 3 8.10 0.9 4 12.50 1.5 2 6.50 0.55 3 10.30 1.1 1 5.10 0.35 2 7.90 0.6 0 3.85 0.18 1 6.40 0.3 -1 2.10 -0.05 0 4.15 0 -2 0.50 -0.4 -1 1.85 -0.25 -3 -1.05 -0.7 -2 -0.10 -0.65 -4 -2.20 -0.95 -3 -2.30 -1.1 -5 -3.79 -1.2 -4 -4.70 -1.35 -6 -6.20 -1.3 -5 -6.90 -1.5 -7 -8.30 -1.45 -6 -8.50 -1.65 -8 -11.70 -2.1 -7 -10.10 -1.9 -7 -11.17 -1.95 -8 -11.55 -2.1 -6 -10.50 -1.9 -9 -15.30 -2.45 -5 -9.40 -1.85 -10 -26.70 -5.3 -4 -8.10 -1.6 -9 -26.70 -5.25 -3 -7.05 -1.45 -8 -26.70 -5.2 -2 -5.50 -1.3 -7 -24.20 -5 -1 -3.90 -1.1 -6 -21.50 -4.85 0 -0.80 -0.7 -5 -16.10 -3.5 Cycle-V -4 -14.10 -2.75 0 -0.70 -0.7 -3 -12.75 -1.87 1 0.40 -0.5 -2 -8.10 -1.65 2 2.10 -0.2 -1 -7.50 -1.4 3 4.10 0.05 0 -5.90 -1 4 6.10 0.45 5 8.05 0.9 6 9.60 1.2 7 11.10 1.46 8 12.90 1.75 9 15.10 2.05

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Table A.2: Load-Deflection Value for Specimen S-4-C-3

Load (ton)

Horizontal Deflection (mm)

Vertical Deflection (mm)

Load (ton)

Horizontal Deflection (mm)

Vertical Deflection (mm)

Cycle-I Cycle-III 0 0.00 0.00 1 -1.20 -0.34 1 0.15 0.01 2 -0.66 -0.30 2 0.70 0.02 3 0.45 -0.25 3 1.50 0.05 4 1.80 -0.22 2 1.45 0.04 5 2.90 -0.17 1 1.00 0.03 6 4.05 -0.13 0 0.50 0.00 6.5 5.40 -0.09 -1 -0.10 -0.05 6 6.25 -0.03 -2 -0.70 -0.15 5 6.19 -0.05 -3 -1.30 -0.25 4 6.10 -0.08 -2 -1.10 -0.24 3 5.50 -0.11 -1 -0.80 -0.22 2 4.80 -0.15 0 -0.18 -0.19 1 3.70 -0.18 Cycle-II 0 2.75 0.00 0 -0.15 -0.19 -1 1.10 -0.29 1 0.19 -0.15 -2 -0.10 -0.38 2 0.80 -0.13 -3 -1.10 -0.46 3 1.50 -0.1 -4 -2.10 -0.52 4 2.65 -0.08 -5 -3.15 -0.59 5 4.45 0 -6 -4.40 -0.63 4 4.50 -0.02 -6.5 -5.20 -0.68 3 4.15 -0.05 -6 -6.00 -0.88 2 3.40 -0.08 -5 -5.90 -0.87 1 2.50 -0.1 -4 -5.60 -0.85 0 1.72 -0.14 -3 -5.10 -0.80 -1 0.80 -0.24 -2 -4.50 -0.70 -2 0.05 -0.32 -1 -4.00 -0.60 -3 -0.80 -0.41 0 -2.95 -0.55 -4 -1.85 -0.63 Cycle-IV -5 -4.70 -0.85 1 -1.55 -0.5 -4 -4.50 -0.75 2 -0.50 -0.44 -3 -4.20 -0.65 3 0.75 -0.29 -2 -3.25 -0.48 4 2.00 -0.15 -1 -2.70 -0.4 5 3.20 0.1 0 -1.25 -0.34 6 4.50 0.13

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Load

(ton)

Horizontal

Deflection (mm)

Vertical

Deflection (mm)

Load

(ton)

Horizontal

Deflection (mm)

Vertical

Deflection (mm)

7 7.40 0.19 10 13.70 1.8 8 10.00 0.6 9 13.80 1.78 7 9.30 0.58 8 13.40 1.7 6 9.05 0.5 7 12.70 1.6 5 8.45 0.4 6 12.00 1.47 4 7.50 0.34 5 11.30 1.25 3 6.50 0.28 4 10.10 1.07 2 5.10 0.2 3 8.70 0.9 1 3.70 0.12 2 7.10 0.6 0 2.20 0 1 5.60 0.43 -1 0.90 -0.18 0 2.90 0.1 -2 -1.30 -0.35 -1 1.10 -0.15 -3 -2.60 -0.55 -2 -0.50 -0.53 -4 -3.90 -0.65 -3 -3.10 -0.78 -5 -5.50 -0.75 -4 -5.10 -0.96 -6 -6.80 -0.8 -5 -7.10 -1.06 -7 -8.60 -0.87 -6 -8.80 -1.22 -8 -12.50 -1.35 -7 -10.35 -1.33 -7 -12.15 -1.3 -8 -11.70 -1.42 -6 -11.60 -1.28 -9 -14.90 -1.6 -5 -10.50 -1.26 -10 -19.70 -2.21 -4 -9.50 -1.2 -9 -19.50 -2.2 -3 -8.80 -1.11 -8 -18.20 -2.14 -2 -6.72 -1.08 -7 -17.20 -2 -1 -5.40 -1.07 -6 -15.96 -1.95 0 -3.30 -1.05 -5 -15.55 -1.85 Cycle-V -4 -14.10 -2.75 0 -3.30 -1.05 -3 -13.80 -1.75 1 -1.30 -0.78 -2 -11.20 -1.74 2 0.20 -0.55 -1 -10.10 -1.65 3 1.90 -0.4 0 -9.70 -1.6 4 3.60 -0.15 5 6.20 0.1 6 7.40 0.23 7 8.20 0.3 8 9.10 0.46 9 11.70 1.15

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Table A.3: Load-Deflection Value for Specimen S-5-C-3

Load (ton)

Horizontal Deflection (mm)

Vertical Deflection (mm)

Load (ton)

Horizontal Deflection (mm)

Vertical Deflection (mm)

Cycle-I Cycle-III 0 0.00 0.00 1 0.55 -0.02 1 0.19 0.00 2 0.86 0.03 2 0.41 0.03 3 1.22 0.13 3 0.86 0.06 4 1.70 0.20 2 0.76 0.05 5 2.20 0.30 1 0.56 0.04 6 2.90 0.35 0 0.26 0.01 6.5 3.50 0.44 -1 -0.14 -0.02 6 3.48 0.42 -2 -0.39 -0.06 5 3.40 0.40 -3 -0.83 -0.12 4 3.02 0.32 -2 -0.74 -0.10 3 2.50 0.25 -1 -0.49 -0.08 2 2.00 0.18 0 -0.14 -0.02 1 1.40 0.12 Cycle-II 0 2.75 0.00 0 0.25 -0.02 -1 0.20 -0.05 1 0.47 0.00 -2 -0.20 -0.24 2 0.80 0.02 -3 -0.70 -0.34 3 1.12 0.05 -4 -1.25 -0.51 4 1.45 0.08 -5 -1.80 -0.71 5 2.45 0.14 -6 -3.00 -1.00 4 2.30 0.12 -6.5 -4.60 -1.10 3 2.05 0.09 -6 -4.60 -1.06 2 1.60 0.08 -5 -4.45 -1.00 1 1.25 0.06 -4 -3.95 -0.95 0 0.80 0.04 -3 -3.05 -0.88 -1 0.40 0.00 -2 -2.35 -0.85 -2 0.00 -0.04 -1 -1.45 -0.80 -3 -0.40 -0.08 0 -0.68 -0.77 -4 -0.80 -0.13 Cycle-IV -5 -1.50 -0.22 1 -0.30 -0.74 -4 -1.35 -0.21 2 0.20 -0.65 -3 -1.20 -0.18 3 0.85 -0.62 -2 -0.85 -0.14 4 1.60 -0.60 -1 -0.40 -0.11 5 2.40 -0.53 0 0.16 -0.07 6 3.15 -0.50

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Load

(ton)

Horizontal

Deflection (mm)

Vertical

Deflection (mm)

Load

(ton)

Horizontal

Deflection (mm)

Vertical

Deflection (mm)

7 4.00 -0.43 10 10.11 -0.53 8 5.90 -0.31 9 9.75 -0.58 7 5.75 -0.38 8 9.35 -0.60 6 5.50 -0.43 7 8.84 -0.63 5 5.00 -0.43 6 7.95 -0.72 4 4.15 -0.45 5 7.11 -0.80 3 3.50 -0.53 4 6.44 -0.85 2 2.65 -0.56 3 6.00 -0.88 1 2.00 -0.64 2 5.00 -0.96 0 1.23 -0.66 1 4.20 -1.03 -1 0.40 -0.73 0 3.25 -1.06 -2 -0.20 -0.80 -1 2.65 -1.11 -3 -0.85 -1.00 -2 2.00 -1.16 -4 -1.75 -1.13 -3 1.24 -1.17 -5 -2.50 -1.28 -4 0.15 -1.27 -6 -3.16 -1.43 -5 -0.90 -1.35 -7 -3.88 -1.55 -6 -1.90 -1.43 -8 -5.10 -1.60 -7 -3.70 -1.70 -7 -5.00 -1.58 -8 -5.10 -1.90 -6 -4.50 -1.56 -9 -7.55 -2.07 -5 -3.85 -1.52 -10 -15.60 -2.24 -4 -3.20 -1.47 -9 -15.50 -2.32 -3 -2.85 -1.38 -8 -15.00 -2.25 -2 -2.35 -1.30 -7 -14.35 -2.00 -1 -1.90 -1.25 -6 -13.80 -1.90 0 -1.00 -1.20 -5 -12.80 -1.85 Cycle-V -4 -14.10 -2.75 0 -1.00 -1.20 -3 -10.20 -1.66 1 -0.35 -1.16 -2 -9.10 -1.57 2 0.35 -1.13 -1 -7.20 -1.52 3 0.75 -1.09 0 -6.30 -1.50 4 1.35 -1.05 5 2.20 -1.00 6 3.40 -0.90 7 4.10 -0.85 8 5.50 -0.70 9 6.75 -0.65

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Table A.4: Load-Deflection Value for Specimen S-5.5-C-3 (Control)

Load (ton)

Horizontal Deflection (mm)

Vertical Deflection (mm)

Load (ton)

Horizontal Deflection (mm)

Vertical Deflection (mm)

Cycle-I Cycle-III 0 0.68 0 1 0.64 -0.07 1 0.90 0 2 0.86 -0.03 2 1.20 0.01 3 1.20 -0.01 3 1.54 0.02 4 1.68 0.01 2 1.50 0 5 2.20 0.02 1 1.18 -0.01 6 3.15 0.04 0 0.84 -0.01 6.5 3.70 0.05 -1 0.00 -0.01 6 3.45 0.05 -2 -0.88 -0.02 5 2.90 0.03 -3 -1.90 -0.02 4 2.45 0.02 -2 -1.50 -0.01 3 2.10 0 -1 -0.98 0 2 1.85 -0.02 0 -0.70 0 1 1.50 -0.03 Cycle-II 0 2.75 0.00 0 0.72 0 -1 0.45 -0.07 1 1.04 0 -2 -0.68 -0.09 2 1.38 0.01 -3 -1.40 -0.11 3 1.65 0.01 -4 -2.00 -0.12 4 1.80 0.05 -5 -2.50 -0.15 5 2.04 0.11 -6 -3.40 -0.19 4 1.90 0.08 -6.5 -3.90 -0.23 3 1.74 0.05 -6 -3.65 -0.22 2 1.50 0.02 -5 -3.15 -0.19 1 1.25 0 -4 -2.45 -0.15 0 0.95 -0.01 -3 -1.70 -0.14 -1 0.30 -0.09 -2 -1.20 -0.12 -2 -0.50 -0.15 -1 -0.50 -0.11 -3 -0.90 -0.22 0 0.15 -0.1 -4 -1.50 -0.28 Cycle-IV -5 -1.90 -0.32 1 0.55 -0.08 -4 -1.85 -0.3 2 1.18 -0.05 -3 -1.30 -0.27 3 1.80 -0.03 -2 -0.91 -0.22 4 2.40 0 -1 -0.48 -0.15 5 3.20 0.03 0 0.40 -0.09 6 3.65 0.05

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Load

(ton)

Horizontal

Deflection (mm)

Vertical

Deflection (mm)

Load

(ton)

Horizontal

Deflection (mm)

Vertical

Deflection (mm)

7 4.55 0.11 10 12.60 0.19 8 5.00 0.14 9 13.15 0.17 7 4.85 0.12 8 12.80 0.14 6 4.20 0.08 7 12.10 0.1 5 3.45 0.05 6 11.35 0.07 4 2.70 0.03 5 10.20 0.04 3 2.05 -0.01 4 9.35 0 2 1.55 -0.03 3 8.20 -0.02 1 0.95 -0.05 2 7.10 -0.07 0 0.50 -0.08 1 5.90 -0.1 -1 -0.40 -0.12 0 4.40 -0.12 -2 -0.85 -0.17 -1 1.10 -0.17 -3 -1.25 -0.18 -2 -1.30 -0.22 -4 -1.65 -0.19 -3 -2.50 -0.27 -5 -2.00 -0.21 -4 -4.00 -0.31 -6 -2.35 -0.23 -5 -4.80 -0.34 -7 -3.10 -0.24 -6 -5.80 -0.37 -8 -4.30 -0.27 -7 -6.50 -0.4 -7 -3.55 -0.27 -8 -7.00 -0.45 -6 -3.15 -0.26 -9 -8.30 -0.51 -5 -2.55 -0.25 -10 -11.90 -0.98 -4 -2.05 -0.23 -9 -11.25 -0.98 -3 -1.80 -0.22 -8 -10.20 -0.97 -2 -1.30 -0.2 -7 -9.40 -0.97 -1 -1.15 -0.17 -6 -8.20 -0.94 0 -0.45 -0.15 -5 -7.10 -0.92 Cycle-V -4 -14.10 -2.75 0 -0.45 -0.15 -3 -5.50 -0.87 1 1.05 -0.13 -2 -4.00 -0.84 2 1.70 -0.12 -1 -2.90 -0.82 3 2.45 -0.08 0 -2.45 -0.82 4 3.30 -0.02 5 4.08 0.02 6 4.55 0.05 7 4.90 0.06 8 5.40 0.09 9 6.95 0.13

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Table A.5: Load-Deflection Value for Specimen S-3-C-4

Load (ton)

Horizontal Deflection (mm)

Vertical Deflection (mm)

Load (ton)

Horizontal Deflection (mm)

Vertical Deflection (mm)

Cycle-I Cycle-III 0 0.00 0.00 1 -1.20 -0.34 1 0.15 0.01 2 -0.66 -0.30 2 0.70 0.02 3 0.45 -0.25 3 1.50 0.05 4 1.80 -0.22 2 1.45 0.04 5 2.90 -0.17 1 1.00 0.03 6 4.05 -0.13 0 0.50 0.00 6.5 5.40 -0.09 -1 -0.10 -0.05 6 6.25 -0.03 -2 -0.70 -0.15 5 6.19 -0.05 -3 -1.30 -0.25 4 6.10 -0.08 -2 -1.10 -0.24 3 5.50 -0.11 -1 -0.80 -0.22 2 4.80 -0.15 0 -0.18 -0.19 1 3.70 -0.18 Cycle-II 0 2.75 0.00 0 -0.15 -0.19 -1 1.10 -0.29 1 0.19 -0.15 -2 -0.10 -0.38 2 0.80 -0.13 -3 -1.10 -0.46 3 1.50 -0.1 -4 -2.10 -0.52 4 2.65 -0.08 -5 -3.15 -0.59 5 4.45 0 -6 -4.40 -0.63 4 4.50 -0.02 -6.5 -5.20 -0.68 3 4.15 -0.05 -6 -6.00 -0.88 2 3.40 -0.08 -5 -5.90 -0.87 1 2.50 -0.1 -4 -5.60 -0.85 0 1.72 -0.14 -3 -5.10 -0.80 -1 0.80 -0.24 -2 -4.50 -0.70 -2 0.05 -0.32 -1 -4.00 -0.60 -3 -0.80 -0.41 0 -2.95 -0.55 -4 -1.85 -0.63 Cycle-IV -5 -4.70 -0.85 1 -1.55 -0.5 -4 -4.50 -0.75 2 -0.50 -0.44 -3 -4.20 -0.65 3 0.75 -0.29 -2 -3.25 -0.48 4 2.00 -0.15 -1 -2.70 -0.4 5 3.20 0.1 0 -1.25 -0.34 6 4.50 0.13

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Load

(ton)

Horizontal

Deflection (mm)

Vertical

Deflection (mm)

Load

(ton)

Horizontal

Deflection (mm)

Vertical

Deflection (mm)

7 7.40 0.19 10 13.70 1.8 8 10.00 0.6 9 13.80 1.78 7 9.30 0.58 8 13.40 1.7 6 9.05 0.5 7 12.70 1.6 5 8.45 0.4 6 12.00 1.47 4 7.50 0.34 5 11.30 1.25 3 6.50 0.28 4 10.10 1.07 2 5.10 0.2 3 8.70 0.9 1 3.70 0.12 2 7.10 0.6 0 2.20 0 1 5.60 0.43 -1 0.90 -0.18 0 2.90 0.1 -2 -1.30 -0.35 -1 1.10 -0.15 -3 -2.60 -0.55 -2 -0.50 -0.53 -4 -3.90 -0.65 -3 -3.10 -0.78 -5 -5.50 -0.75 -4 -5.10 -0.96 -6 -6.80 -0.8 -5 -7.10 -1.06 -7 -8.60 -0.87 -6 -8.80 -1.22 -8 -12.50 -1.35 -7 -10.35 -1.33 -7 -12.15 -1.3 -8 -11.70 -1.42 -6 -11.60 -1.28 -9 -14.90 -1.6 -5 -10.50 -1.26 -10 -19.70 -2.21 -4 -9.50 -1.2 -9 -19.50 -2.2 -3 -8.80 -1.11 -8 -18.20 -2.14 -2 -6.72 -1.08 -7 -17.20 -2 -1 -5.40 -1.07 -6 -15.96 -1.95 0 -3.30 -1.05 -5 -15.55 -1.85 Cycle-V -4 -14.10 -2.75 0 -3.30 -1.05 -3 -13.80 -1.75 1 -1.30 -0.78 -2 -11.20 -1.74 2 0.20 -0.55 -1 -10.10 -1.65 3 1.90 -0.4 0 -9.70 -1.6 4 3.60 -0.15 5 6.20 0.1 6 7.40 0.23 7 8.20 0.3 8 9.10 0.46 9 11.70 1.15

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Table A.6: Load-Deflection Value for Specimen S-4-C-4

Load (ton)

Horizontal Deflection (mm)

Vertical Deflection (mm)

Load (ton)

Horizontal Deflection (mm)

Vertical Deflection (mm)

Cycle-I Cycle-III 0 0.00 0.00 1 -0.40 -0.37 1 0.20 0.05 2 0.30 -0.15 2 0.70 0.23 3 1.10 0.00 3 1.30 0.77 4 2.10 0.15 2 1.15 0.76 5 2.80 0.35 1 0.75 0.69 6 3.90 0.49 0 0.30 0.43 6.5 4.60 0.62 -1 -0.20 0.06 6 4.60 0.60 -2 -0.80 -0.40 5 4.20 0.54 -3 -1.48 -1.00 4 3.60 0.47 -2 -1.40 -0.85 3 3.10 0.32 -1 -0.90 -0.64 2 2.20 0.15 0 -0.40 -0.50 1 1.35 -0.10 Cycle-II 0 2.75 0.00 0 -0.40 -0.5 -1 -0.45 -0.47 1 0.05 -0.15 -2 -1.10 -0.75 2 0.50 0.15 -3 -1.80 -0.95 3 1.00 0.4 -4 -2.60 -1.25 4 1.70 0.6 -5 -3.40 -1.43 5 2.95 1.25 -6 -4.60 -1.69 4 2.80 1.22 -6.5 -5.50 -1.79 3 2.35 1.18 -6 -5.50 -1.84 2 1.80 1.12 -5 -4.95 -1.81 1 1.15 1.02 -4 -4.60 -1.76 0 0.60 0.86 -3 -3.90 -1.67 -1 -0.20 0.55 -2 -3.30 -1.56 -2 -0.80 0.15 -1 -2.50 -1.39 -3 -1.40 -0.15 0 -1.45 -1.10 -4 -2.20 -0.65 Cycle-IV -5 -3.40 -1.2 1 -0.85 -0.89 -4 -3.30 -1.15 2 0.05 -0.47 -3 -2.85 -1.11 3 1.10 0.2 -2 -2.30 -1.01 4 2.10 0.48 -1 -1.75 -0.88 5 3.01 1.02 0 -1.00 -0.58 6 3.90 1.21

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Load

(ton)

Horizontal

Deflection (mm)

Vertical

Deflection (mm)

Load

(ton)

Horizontal

Deflection (mm)

Vertical

Deflection (mm)

7 4.85 1.35 10 14.64 2.95 8 6.47 1.55 9 14.50 2.9 7 6.40 1.5 8 13.85 2.85 6 5.90 1.44 7 12.90 2.68 5 5.30 1.34 6 11.90 2.59 4 4.35 1.22 5 10.90 2.5 3 3.70 1.11 4 9.60 2.3 2 2.80 0.88 3 8.20 2.09 1 1.55 0.43 2 6.60 1.59 0 0.75 0.25 1 5.30 1.13 -1 -0.65 -0.83 0 3.80 0.75 -2 -1.30 -1.15 -1 2.10 0.5 -3 -2.15 -1.47 -2 0.50 0.1 -4 -3.10 -1.78 -3 -1.40 -0.5 -5 -3.50 -1.88 -4 -2.90 -1.36 -6 -4.10 -2.01 -5 -4.90 -1.96 -7 -6.90 -2.14 -6 -6.40 -2.23 -8 -8.50 -2.47 -7 -8.00 -2.49 -7 -8.20 -2.46 -8 -10.50 -2.9 -6 -7.70 -2.44 -9 -13.80 -3.25 -5 -7.50 -2.34 -10 -17.00 -3.91 -4 -6.20 -2.29 -9 -16.60 -3.77 -3 -5.25 -2.27 -8 -16.20 -3.7 -2 -4.85 -2.19 -7 -15.40 -3.62 -1 -3.89 -2.06 -6 -14.70 -3.47 0 -2.40 -1.82 -5 -12.60 -3.21 Cycle-V -4 -14.10 -2.75 0 -2.35 -1.75 -3 -9.20 -2.8 1 -1.50 -1.55 -2 -8.20 -2.61 2 -0.25 -1.25 -1 -6.00 -2.49 3 1.10 -0.65 0 -3.30 -2.05 4 2.30 0 Cycle-VI 5 3.35 0.44 0 -3.18 -2.02 6 4.50 0.76 1 -2.00 -1.75 7 5.50 1 2 -0.40 -1.25 8 6.40 1.42 3 2.10 -0.86 9 9.50 2 4 4.10 -0.2

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Load (ton) Horizontal Deflection (mm) Vertical Deflection (mm)

5 6.10 0.42 6 7.30 0.65 7 9.10 0.9 8 10.60 1.25 9 12.20 1.88 10 13.40 2.5 10.5 16.20 4.25 10 25.90 10.65 9 25.90 10.65 8 25.90 10.65 7 25.90 8.9 6 25.90 8.2 5 25.40 7.95 4 24.20 7.61 3 23.00 7 2 21.00 5.8 1 18.00 4.72 0 15.00 3.56

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Table A.7: Load-Deflection Value for Specimen S-5-C-4

Load (ton)

Horizontal Deflection (mm)

Vertical Deflection (mm)

Load (ton)

Horizontal Deflection (mm)

Vertical Deflection (mm)

Cycle-I Cycle-III 0 0.00 0.00 1 -0.10 -0.09 1 0.20 0.00 2 0.20 -0.07 2 0.48 0.01 3 0.65 -0.06 3 0.90 0.03 4 1.10 -0.06 2 0.90 0.03 5 1.50 -0.06 1 0.60 0.02 6 2.10 -0.06 0 0.30 0.00 6.5 2.55 -0.04 -1 -0.05 -0.04 6 2.55 -0.04 -2 -0.42 -0.06 5 2.35 -0.07 -3 -0.85 -0.08 4 1.95 -0.09 -2 -0.75 -0.07 3 1.60 -0.10 -1 -0.38 -0.06 2 1.15 -0.13 0 0.00 -0.06 1 0.70 -0.13 Cycle-II 0 2.75 0.00 0 0.00 -0.06 -1 -0.25 -0.21 1 0.25 -0.06 -2 -0.80 -0.22 2 0.50 -0.05 -3 -1.25 -0.22 3 0.85 -0.04 -4 -1.85 -0.25 4 1.20 -0.03 -5 -2.50 -0.29 5 1.60 0 -6 -3.70 -0.30 4 1.60 -0.02 -6.5 -5.70 -0.40 3 1.35 -0.03 -6 -5.70 -0.38 2 0.95 -0.03 -5 -4.85 -0.35 1 0.60 -0.04 -4 -4.20 -0.34 0 0.28 -0.05 -3 -3.65 -0.33 -1 -0.20 -0.07 -2 -3.00 -0.33 -2 -0.50 -0.09 -1 -2.35 -0.32 -3 -0.85 -0.11 0 -1.35 -0.32 -4 -1.35 -0.13 Cycle-IV -5 -2.35 -0.15 1 -0.90 -0.32 -4 -2.38 -0.14 2 -0.20 -0.3 -3 -2.10 -0.13 3 0.60 -0.28 -2 -1.75 -0.13 4 1.20 -0.26 -1 -1.10 -0.12 5 1.60 -0.25 0 -0.45 -0.12 6 2.60 -0.2

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Load

(ton)

Horizontal

Deflection (mm)

Vertical

Deflection (mm)

Load

(ton)

Horizontal

Deflection (mm)

Vertical

Deflection (mm)

7 2.90 -0.16 10 6.20 -0.03 8 4.10 -0.13 9 6.40 -0.06 7 4.00 -0.12 8 6.00 -0.1 6 3.60 -0.13 7 5.40 -0.12 5 3.10 -0.15 6 4.70 -0.12 4 2.55 -0.23 5 4.11 -0.2 3 2.00 -0.26 4 3.44 -0.25 2 1.50 -0.28 3 2.70 -0.28 1 1.00 -0.3 2 1.90 -0.36 0 0.25 -0.32 1 1.20 -0.4 -1 -0.65 -0.36 0 0.30 -0.45 -2 -1.30 -0.38 -1 -0.55 -0.49 -3 -2.15 -0.39 -2 -1.65 -0.51 -4 -3.00 -0.41 -3 -2.90 -0.51 -5 -3.75 -0.48 -4 -3.80 -0.57 -6 -4.75 -0.5 -5 -4.90 -0.65 -7 -5.50 -0.51 -6 -5.25 -0.73 -8 -7.70 -0.54 -7 -6.30 -1 -7 -7.30 -0.53 -8 -8.50 -1.2 -6 -7.10 -0.51 -9 -10.50 -1.28 -5 -6.40 -0.5 -10 -16.60 -1.35 -4 -5.50 -0.5 -9 -16.60 -1.32 -3 -5.00 -0.49 -8 -15.00 -1.3 -2 -3.90 -0.48 -7 -14.00 -1.2 -1 -3.00 -0.48 -6 -13.80 -1.1 0 -2.00 -0.48 -5 -12.80 -0.85 Cycle-V -4 -14.10 -2.75 0 -1.99 -0.48 -3 -10.20 -0.65 1 -1.10 -0.48 -2 -9.10 -0.57 2 -0.60 -0.46 -1 -7.20 -0.55 3 0.15 -0.43 0 -6.30 -0.55 4 0.95 -0.39 5 1.80 -0.35 6 2.40 -0.3 7 3.10 -0.2 8 3.88 -0.19 9 4.75 -0.1

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Table A.8: Load-Deflection Value for Specimen S-5.5-C-4 (Control)

Load (ton)

Horizontal Deflection (mm)

Vertical Deflection (mm)

Load (ton)

Horizontal Deflection (mm)

Vertical Deflection (mm)

Cycle-I Cycle-III 0 0.00 0.00 1 -0.43 -0.30 1 0.27 0.02 2 0.17 -0.29 2 0.67 0.05 3 1.17 -0.25 3 1.32 0.06 4 1.87 -0.23 2 1.22 0.06 5 2.57 -0.20 1 0.77 0.05 6 3.17 -0.14 0 0.42 0.01 6.5 4.17 -0.09 -1 -0.13 -0.05 6 4.17 -0.11 -2 -0.54 -0.10 5 4.02 -0.17 -3 -1.43 -0.14 4 3.52 -0.20 -2 -1.23 -0.13 3 2.87 -0.20 -1 -0.83 -0.12 2 2.27 -0.21 0 -0.18 -0.11 1 1.52 -0.24 Cycle-II 0 2.75 0.00 0 -0.18 -0.11 -1 -0.25 -0.30 1 0.27 -0.1 -2 -1.03 -0.35 2 0.67 -0.06 -3 -1.83 -0.40 3 1.12 -0.02 -4 -2.53 -0.45 4 1.67 0 -5 -3.23 -0.53 5 2.67 0.03 -6 -4.48 -0.59 4 2.63 0.02 -6.5 -5.38 -0.68 3 2.37 0 -6 -5.38 -0.67 2 1.77 -0.03 -5 -5.13 -0.66 1 1.22 -0.06 -4 -4.63 -0.65 0 0.72 -0.1 -3 -4.03 -0.63 -1 0.07 -0.15 -2 -3.41 -0.61 -2 -0.53 -0.18 -1 -2.58 -0.57 -3 -1.23 -0.2 0 -1.43 -0.49 -4 -2.18 -0.32 Cycle-IV -5 -3.33 -0.49 1 -0.88 -0.47 -4 -3.33 -0.48 2 0.17 -0.43 -3 -2.93 -0.47 3 1.27 -0.41 -2 -2.48 -0.43 4 2.17 -0.4 -1 -1.83 -0.37 5 3.47 -0.35 0 -0.88 -0.31 6 4.07 -0.32

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Load

(ton)

Horizontal

Deflection (mm)

Vertical

Deflection (mm)

Load

(ton)

Horizontal

Deflection (mm)

Vertical

Deflection (mm)

7 5.02 -0.3 10 9.97 -0.25 8 6.93 -0.25 9 9.97 -0.27 7 6.93 -0.26 8 9.37 -0.33 6 6.47 -0.29 7 8.77 -0.36 5 5.92 -0.33 6 8.12 -0.4 4 5.27 -0.35 5 7.42 -0.45 3 4.57 -0.37 4 6.57 -0.5 2 3.77 -0.41 3 5.67 -0.53 1 2.72 -0.43 2 4.57 -0.55 0 1.97 -0.44 1 3.42 -0.56 -1 0.37 -0.47 0 2.37 -0.57 -2 -0.73 -0.5 -1 0.97 -0.6 -3 -2.33 -0.55 -2 -0.38 -0.65 -4 -3.23 -0.6 -3 -2.33 -0.7 -5 -4.03 -0.63 -4 -3.43 -0.78 -6 -4.83 -0.65 -5 -4.43 -0.81 -7 -6.23 -0.67 -6 -5.33 -0.83 -8 -8.33 -0.74 -7 -5.58 -0.85 -7 -8.33 -0.72 -8 -7.83 -0.87 -6 -6.83 -0.7 -9 -8.78 -0.94 -5 -6.33 -0.68 -10 -10.98 -1.01 -4 -5.53 -0.65 -9 -11.23 -0.99 -3 -4.83 -0.63 -8 -9.73 -0.96 -2 -4.03 -0.63 -7 -9.33 -0.94 -1 -3.23 -0.62 -6 -8.53 -0.91 0 -1.83 -0.6 -5 -8.13 -0.9 Cycle-V -4 -14.10 -2.75 0 -1.78 -0.6 -3 -6.13 -0.87 1 -0.83 -0.59 -2 -4.83 -0.86 2 0.27 -0.57 -1 -3.63 -0.84 3 1.62 -0.55 0 -2.28 -0.82 4 2.82 -0.52 Cycle-VI 5 4.57 -0.5 0 -2.28 -0.82 6 5.22 -0.47 1 -1.53 -0.79 7 5.87 -0.46 2 0.02 -0.75 8 6.67 -0.4 3 2.27 -0.69

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9 7.77 -0.38 4 3.57 -0.65 Load

(ton)

Horizontal

Deflection (mm)

Vertical

Deflection (mm)

Load

(ton)

Horizontal

Deflection (mm)

Vertical

Deflection (mm)

5 4.77 -0.59 -7 -12.93 -1.1 6 6.87 -0.55 -6 -11.83 -1.07 7 7.37 -0.51 -5 -10.83 -1.05 8 7.97 -0.44 -4 -10.13 -1.03 9 9.07 -0.39 -3 -9.33 -1.01 10 10.37 -0.35 -2 -6.53 -1 11 11.57 -0.32 -1 -5.43 -0.97 12 14.07 -0.2 0 -3.33 -0.95 11 13.62 -0.21 Cycle-VII 10 13.07 -0.22 0 -3.33 -0.95 9 12.57 -0.25 1 -1.43 -0.9 8 12.07 -0.28 2 -0.43 -0.85 7 11.47 -0.3 3 1.57 -0.81 6 10.57 -0.32 4 3.87 -0.75 5 9.57 -0.37 5 5.57 -0.7 4 8.47 -0.43 6 6.57 -0.6 3 7.57 -0.47 7 7.87 -0.57 2 6.57 -0.53 8 9.67 -0.4 1 4.97 -0.56 9 10.77 -0.32 0 3.77 -0.59 10 11.87 -0.27 -1 1.37 -0.63 11 12.97 -0.15 -2 0.07 -0.65 12 14.57 0.14 -3 -1.23 -0.7 12.5 25.47 3.36 -4 -3.53 -0.75 12 25.47 3.35 -5 -5.03 -0.8 11 25.47 3.35 -6 -5.73 -0.85 10 25.47 3.35 -7 -7.03 -0.9 9 25.47 3.35 -8 -8.03 -0.95 8 23.77 3.2 -9 -9.28 -0.99 7 22.67 3.04 -10 -11.03 -1.01 6 21.77 2.7 -11 -13.08 -1.03 5 20.67 2.54 -12 -16.43 -1.22 4 19.57 2.25 -11 -15.93 -1.2 3 17.57 2.05 -10 -15.43 -1.18 2 15.07 1.73 -9 -14.58 -1.16 1 13.77 1.26 -8 -13.83 -1.13 0 12.32 1.01

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APPENDIX-B

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