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Concentric Punching Shear Strength ofReinforced Concrete Flat Plates
Fariborz Moeinaddini
Submitted in total fulfilment of the requirement of the degree of
Master of Engineering
June 2012
Centre for Sustainable Infrastructure, Faculty of Engineering and
Industrial Science
Swinburne University of Technology, Melbourne, Australia
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Abstract
Flat slabs are very popular and economical floor systems in the construction industry. These
floor systems, supported directly on columns, are known to be susceptible to punching shear in
the vicinity of the slab-column connection. The punching shear provisions of AS 3600-2009,
the current Australian Concrete Structures Standard, for the case of concentric loading are based
on empirical formulae developed in the early 1960s and have not improved significantly since
then. These provisions do not consider some of the important parameters affecting the capacity
of a slab such as flexural reinforcement ratio and slab thickness size effect. AS 3600-2009 only
recognises shearheads as an effective shear reinforcement to increase the concentric punching
shear strength of slabs, and it does not cover more practical types of reinforcement such as shear
studs and stirrups unlike most of European and North American codes of practice.
In this thesis, the available methods for calculating concentric punching shear strength of slabs
are reviewed. The analytical basis of previous work by other researchers was used to propose a
formula to calculate the punching shear strength of flat plates with good accuracy for a wide
range of slab thicknesses, tensile reinforcement ratios, and concrete compressive strengths. Inthis method, it is assumed that punching shear failure occurs due to the crushing of the critical
concrete strut adjacent to the column. A large number of experimental results of slab test
specimen, reported in the literature were gathered to evaluate the accuracy of the proposed
formula, as well as the punching shear formulae in some of the internationally recognised
standards such as AS 3600-2009, ACI 318-05, CSA A23.3-04, DIN 1045-1:2001, Eurocode2,
and NZS 3101:2006.
The proposed formula was also extended to cover the case of prestressed flat plates with the use
of the decompression method. Recent experimental results of prestressed slab test specimens,
published in journal papers, were collected to assess the accuracy of the proposed formula and
provisions of aforementioned standards in the prediction of the ultimate strength of prestressed
flat plates.
Furthermore, detailing considerations for the design of shear reinforcements such as shear studs
and stirrups, which are not recognised by AS 3600-2009, were discussed. Different failure
modes of flat plates with shear reinforcement were presented. A method to calculate the
strength of the slab assuming a critical crack developing inside the shear reinforced region was
proposed. This method considers the contribution of shear reinforcement intersecting with the
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critical crack and the uncracked concrete zone adjacent to the column. In addition, a control
perimeter outside the shear reinforced zone was suggested to be used with the one-way shear
formula of AS 3600-2009 to calculate the punching shear strength of flat plates outside their
shear reinforced zone. The proposed method and provisions of ACI 318-05, CSA A23.3-04,and Eurocode2 were evaluated against some of the reported experimental results on the flat
plates with shear reinforcement.
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Acknowledgement
This research was conducted at the Centre of Sustainable Infrastructure, Swinburne
University of Technology. The SUPRA scholarship provided by Swinburne University
of Technology is gratefully acknowledged.
I would like to sincerely thank my principal coordinating supervisor Dr. Kamiran
Abdouka for his invaluable guidance and constant support throughout this research. I
am also greatly indebted to my coordinating supervisor Prof. Emad Gad for his wise
suggestions and continuous help during my postgraduate studies.
I wish to express my deep gratitude to Emma Wenczel, Alireza Mohyeddin-Kermani
whom I lived with during my studies in Australia, for their encouragement,
understanding and support.
I owe special thanks to my valued friends and colleagues Anne Belski, Ianina Belski,
Bara Baraneedaran, Saleh Hassanzade, Hessam Mohseni, Siva Sivagnanasundram andStephan Zieger for their assistance and companionship during this research.
Finally, my foremost thanks and greatest gratitude goes to my beloved family Fahime,
Firoozeh, Farnaz and Faramarz for their moral support and unconditional help.
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Preface
So far, a part of this research has been presented in the following conference papers:
Moeinaddini, F & Abdouka, K 2011, Punching shear capacity of concrete slabs with nounbalanced moment, Proceedings of Concrete 2011 , Concrete Institute of Australia,Perth, Australia.
Moeinaddini, F, Abdouka, K & Gad, EF 2010, Punching shear capacity of concreteslabs: a comparative study of various standards and recent analytical methods, Post-
graduate Research, Swinburne University of Technology, Melbourne, Australia.
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Declaration
This is to certify:
This thesis contains no material which has been accepted for the award to thecandidate of any other degree or diploma, except where due reference is made in thetext.
To the best of the candidates knowledge contains no material previously published orwritten by another person except where due reference is made in the text of theexaminable outcome.
Fariborz Moeinaddini
June 2012
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Table of Content
1 INTRODUCTION ................................................................................................................ 1
1.1 Background ................................................................................................................... 1
1.2 Aim and Objectives ....................................................................................................... 5
1.3 Thesis Organisation ...................................................................................................... 5
2 LITERATURE REVIEW ..................................................................................................... 7
2.1 Introduction ................................................................................................................... 7
2.2 Reported Observations from Concentric Punching Shear Failure of Test Specimens .. 7
2.3 Mechanical Models for Punching Shear Balanced Condition ................................... 9
2.3.1 Kinnuen and Nylander Approach ......................................................................... 9
2.3.2 Truss Model by Alexander and Simmonds ......................................................... 15
2.3.3 Bond Model by Alexander and Simmonds ......................................................... 17
2.3.4 Models Based on the Failure of Concrete in Tension ......................................... 19
2.3.5 Plasticity Approach ............................................................................................. 24
2.3.6 Flexural Approach............................................................................................... 25
2.3.7 Critical Shear Crack Theory ............................................................................... 26
2.4 Punching Shear of Prestressed Flat Plates .................................................................. 27
2.4.1 Principal Tensile Stress Approach ...................................................................... 28
2.4.2 Equivalent Reinforcement Ratio Approach ........................................................ 28
2.4.3 Decompression Approach ................................................................................... 29
2.5 Methods to Increase Punching Shear Strength of Concrete Slabs .............................. 30
2.6 Shear Reinforcement for Flat Plates ........................................................................... 31
2.6.1 Shear Reinforcement for Construction of New Slabs ......................................... 31
2.6.2 Shear Reinforcement for Retrofit of Slabs .......................................................... 35
2.7 Control Perimeter Approach and Building Code Provisions ...................................... 372.7.1 Australian Standard AS 3600-2009 .................................................................... 37
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2.7.2 American Code ACI 318-05 ................................................................................ 39
2.7.3 New Zealand Standard NZS 3101:2006 .............................................................. 41
2.7.4 Canadian Standard CSA A23.3-04 ...................................................................... 41
2.7.5 Eurocode2 (2004) ................................................................................................ 43
2.7.6 British Standard BS 8110-97 ............................................................................... 44
2.7.7 German Standard DIN 1045-1:2001 .................................................................... 45
2.8 Summary ...................................................................................................................... 46
3 CONCENTRIC PUNCHING SHEAR OF FLAT PLATES ............................................... 47
3.1 Introduction ................................................................................................................. 47
3.2 Strut-and-Tie Model for Punching Shear Phenomenon ............................................... 48
3.3 Proposed Formula for the Ultimate Punching Shear Strength of Flat Plates ............... 50
3.3.1 Depth of Neutral Axis ......................................................................................... .52
3.3.2 Inclination of the Critical Strut and Critical crack .............................................. .55
3.3.3 Compressive Strength of the Concrete Strut ...................................................... .58
3.3.4 Slab Size Factor ................................................................................................... 59
3.3.5 Determination of the Parameters ......................................................................... 60
3.3.6 Example ............................................................................................................... 67
3.4 Comparison of Experimental Results with Design Standards ..................................... 68
3.5 Summary ...................................................................................................................... 75
4 CONCENTRIC PUNCHING SHEAR OF PRESTRESSED FLAT PLATES ................... 77
4.1 Introduction ................................................................................................................. 77
4.2 Background .................................................................................................................. 77
4.2.1 Effect of In-plane Stresses on the Punching Shear Strength of Flat Plates ......... 78
4.2.2 Effect of Eccentricity of Prestressing Tendon on the Punching Shear Strength of
Flat Plates ............................................................................................................................ 81
4.2.3 Effect of the Vertical Component of Prestressing Tendons Passing over the Slab-
Column Connection on the Punching Shear Strength of Flat Plates ................................... 82
4.3 Ultimate Punching Shear Strength of Prestressed Flat Plates Using the Decompression
Method ..................................................................................................................................... 84
4.3.1 Available Decompression Methods ..................................................................... 86
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4.3.2 Proposed Decompression Method....................................................................... 88
4.3.3 Example .............................................................................................................. 91
4.4 Comparison of Design Standards ................................................................................ 94
4.4.1 Comparison with Experimental Results .............................................................. 94
4.5 Summary ..................................................................................................................... 99
5 CONCENTRIC PUNCHING SHEAR OF FLAT PLATES WITH SHEAR
REINFORCEMENT ................................................................................................................. 101
5.1 Introduction ............................................................................................................... 101
5.2 Detailing of Shear Reinforcement ............................................................................. 102
5.3 Ultimate Strength of Flat Plates with Shear Reinforcement ..................................... 104
5.3.1 Failure Inside the Shear Reinforced Region ..................................................... 105
5.3.2 Failure Outside the Shear Reinforced Region ................................................... 109
5.3.3 Summary of the suggested method ................................................................... 111
5.3.4 Example ............................................................................................................ 112
5.4 Comparison of Experimental Results with Design Standards .................................. 114
5.5 Summary ................................................................................................................... 114
6 SUMMARY AND CONCLUSIONS ............................................................................... 117
6.1 Summary and Findings of Literature Review ........................................................... 117
6.2 Concentric Punching Shear Strength of Flat Plates .................................................. 117
6.3 Concentric Punching Shear Strength of Prestressed Flat Plates ............................... 119
6.4 Concentric Punching Shear Strength of Flat Plates with Shear Reinforcement.........120
References ...... ....... 123Appendix A. .......... .....125
Appendix B ..... .......139
Appendix C ..... .......143
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List of Figures
Figure 1.1 Schematic view of different types of two-way concrete slabs (Wight & MacGregor
2009) ............................................................................................................................................. 1
Figure 1.2 Punching shear localised failure with pyramid-shaped failure surface (Egberts 2009 ;
Wight & MacGregor 2009) ........................................................................................................... 2
Figure 2.1 Tangential and radial cracks observed in typical punching shear test specimen (Sherif
1996) ............................................................................................................................................. 8
Figure 2.2 Comparison of deflection-load graph for slab test specimens failed by punching
shear to slab test specimens failed in flexure (Mentrey 1998) .................................................... 8
Figure 2.3 Mechanical model of Kinnunen and Nylander as shown in fib (2001) ....................... 9
Figure 2.4 Punching shear failure model proposed by Shehata and Regan (Shehata 1990) ....... 11
Figure 2.5 Radial compression stress failure proposed by Broms (1990) as shown in fib (2001)
.................................................................................................................................................... 12
Figure 2.6 Radial compression stress failure mechanism as shown in Marzouk, Rizk and Tiller
(2010) .......................................................................................................................................... 15
Figure 2.7 Truss model proposed by Alexander and Simmonds (1987) as shown in Megally
(1998) .......................................................................................................................................... 16
Figure 2.8 Curved compression strut (Alexander & Simmonds 1992) ....................................... 17
Figure 2.9 Plan view of slab and the components of Bond model proposed by Alexander and
Simmonds (1992) ........................................................................................................................ 18
Figure 2.10 Free body diagram of radial strip (Alexander & Simmonds 1992) ......................... 19
Figure 2.11 Punching shear model by Georgopoulos as shown in fib (2001) ............................ 20
Figure 2.12 Distribution of concrete tensile stresses in Georgopoulos as shown in fib (2001) .. 20
Figure 2.13 Schematic view of components of proposed method by Menetrey (2002) ............. 21
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Figure 2.14 Schematic view of model by Theodorakopoulos and Swamy (2002) ..................... 23
Figure 2.15 Plasticity model proposed by Braestrup et al. (1976) .............................................. 24
Figure 2.16 Failure pattern and parameters of the proposed method by Rankin and Long (1987)
..................................................................................................................................................... 26
Figure 2.17 Procedure to specify punching shear strength of slab according to Critical Shear
Crack Theory (Muttoni 2008)...................................................................................................... 27
Figure 2.18 Load-deflection curves of slabs strengthened by different methods (Megally &
Ghali 2000) .................................................................................................................................. 30
Figure 2.19 Shearhead reinforcement (Corley & Hawkins 1968) ............................................... 32
Figure 2.20 (a) Bent bar, (b) Single-leg stirrup , (c) Multiple-leg stirrup (d) Closed-stirrup or
Closed-tie (ACI 318-05 2005 ; Broms 2007) .............................................................................. 33
Figure 2.21 Headed shear studs (Bu 2008) .................................................................................. 33
Figure 2.22 (a) Plan view of a shearband (b) Shearbands placed in slab (Pilakoutas & Li 2003)
..................................................................................................................................................... 34
Figure 2.23 UFO shear reinforcement (Alander 2004) ............................................................... 34
Figure 2.24 Lattice shear reinforcement (Park et al. 2007) ......................................................... 35
Figure 2.25 Test specimen strengthened by steel plates (Ebead & Marzouk 2002) .................... 36
Figure 2.26 (a) Shear bolt, (b) concrete slab strengthened with shear bolts (Bu 2008)............... 36
Figure 2.27 Critical perimeter around the column as shown in AS 3600- 2009 ......................... 38
Figure 2.28 Shear reinforcement layout suggested by ACI 318-05 as shown in Kamara and
Rabbat (2005) .............................................................................................................................. 40
Figure 2.29 Critical perimeter as shown in Eurocode2 (2004) .................................................... 43
Figure 2.30 Shear reinforcement arrangement and critical perimeter outside the shear reinforced
region as shown in Eurocode2 (2004) ......................................................................................... 44
Figure 2.31 Critical perimeter as given in DIN 1045-1 (2001) ................................................... 45
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Figure 3.1 Schematic view of B-regions and D-regions in a simple structure............................ 47
Figure 3.2 Early strut-and-tie model for slab-column connection .............................................. 48
Figure 3.3 Refined Strut-and-tie model including concrete ties ................................................. 49
Figure 3.4 Punching shear by failure of concrete ties ................................................................. 49
Figure 3.5 Punching shear by crushing of concrete struts .......................................................... 50
Figure 3.6 View and cross section of the critical concrete strut around the column .................. 51
Figure 3.7 Distribution of strains, stresses and forces in elastic condition (Warner et al. 1998) 53
Figure 3.8 Strains and stresses distribution in the ultimate stage (Warner et al. 1998) .............. 53
Figure 3.9 Rectangular stress block in the ultimate stage (Warner et al. 1998) ......................... 54
Figure 3.10 Schematic view of the flexural neutral axis and the shear neutral axis
(Theodorakopoulos & Swamy 2002) .......................................................................................... 55
Figure 3.11 Observed critical crack angle versus thickness of slab ............................................ 57
Figure 3.12 Predicted angle of the critical crack using Equation 3-10 ....................................... 58
Figure 3.13 V test /V uo versus effective depth of slab, tensile reinforcement ratio and compressive
strength of concrete for T-P-M-0.5 ............................................................................................. 64
Figure 3.14 V test /V uo versus effective depth of slab, tensile reinforcement ratio and compressive
strength of concrete for S-P-B-0.33 ............................................................................................ 65
Figure 3.15 V test /V uo versus effective depth of slab, tensile reinforcement ratio and compressive
strength of concrete for S-P-A-0.5 .............................................................................................. 66
Figure 3.16 Plan and elevation view of test specimen 16/1 reported in (2005) ......................... 67
Figure 3.17 V test /V uo versus effective depth of slab, tensile reinforcement ratio and compressive
strength of concrete for AS 3600-2009 and ACI 318-05 ............................................................ 70
Figure 3.18 V test /V uo versus effective depth of slab, tensile reinforcement ratio and compressive
strength of concrete for NZS3101:2006 ...................................................................................... 71
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Figure 3.19 V test /V uo versus effective depth of slab, tensile reinforcement ratio and compressive
strength of concrete for CSA A23.3-04 ....................................................................................... 72
Figure 3.20 V test /V uo versus effective depth of slab, tensile reinforcement ratio and compressive
strength of concrete for Eurocode2 and Model Code 90 ............................................................. 73
Figure 3.21 V test /V uo versus effective depth of slab, tensile reinforcement ratio and compressive
strength of concrete for DIN 1045-1 ........................................................................................... 74
Figure 4.1 Prestressing actions adjacent to the slab-column connection ..................................... 78
Figure 4.2 Geometery of BD test series (Ramos, Lcio & Regan 2011) .................................... 79
Figure 4.3 Geometry of test specimens LP1, LP2 and LP3 as shown in Silva, Regan and Melo
(2005) .......................................................................................................................................... 80
Figure 4.4 Geometry of test specimens V5 and V6 reported in Kordina and Nolting (1984) as
shown in Silva, Regan and Melo (2005) ..................................................................................... 80
Figure 4.5 Elevation view of test setup of PC test series and the bending moment diagram which
was applied to the slab without presence of in-plane forces (Clement & Muttoni 2010) ........... 81
Figure 4.6 (a) Plan view of test specimens AR8-AR16 (b) Profile of prestressing tendons
(Ramos & Lucio 2006) ................................................................................................................ 83
Figure 4.7 Position of prestressing tendons in test specimens AR8-AR16 (Ramos & Lucio 2006)
..................................................................................................................................................... 83
Figure 4.8 Schematic view of deformation of slab after prestressing forces are applied ............ 85
Figure 4.9 (a) Prestressed slab (b) Prestressed slab at decompression stage (c) Punching shear
failure of prestressed slab ............................................................................................................ 86
Figure 4.10 V test /V up versus cp for three different methods of calculating V up ............................ 90
Figure 4.11 (a) Plan view (b) Elevation view of test setup of specimen D2 as reported in Silva,
Regan and Melo (2005) ............................................................................................................... 92
Figure 4.12 V test /V up versus cp for AS3600-2009 ........................................................................ 96
Figure 4.13 V test /V up versus cp for AS3600-2009 when V p is included ....................................... 96
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Figure 4.14 V test /V up versus cp for ACI 318-05 .......................................................................... 97
Figure 4.15 V test /V up versus cp for ACI 318-05 ignoring the limit on fc .................................... 97
Figure 4.16 V test /V up versus cp for CSA A23.3-04 ..................................................................... 97
Figure 4.17 V test /V up versus cp for CSA A23.3-04 ignoring the limit on fc ............................... 98
Figure 4.18 V test /V up versus cp for Eurocode2 ............................................................................ 98
Figure 4.19 V test /V up versus cp for DIN 1045-1 .......................................................................... 98
Figure 5.1 (a) Orthogonal type arrangement (b) Radial type arrangement (c) square type
arrangement of shear reinforcement for punching shear ........................................................... 102
Figure 5.2 Radial and tangential spacing between shear rows reinforcement in flat plates...... 103
Figure 5.3 Different types of punching shear failure in flat plates with shear reinforcement .. 104
Figure 5.4 (a) Critical tie in flat plates with shear reinforcement (b) Failure of the critical tie due
to the development of shear crack inside the shear reinforced region ...................................... 105
Figure 5.5 Vertical components of the critical tie which resist punching shear ....................... 106
Figure 5.6 Eurocode2 and Model Code 90 control perimeter outside the orthogonal shear
reinforced zone.......................................................................................................................... 110
Figure 5.7 (a) Top view of test specimen 12 (b) Arrangement of shear reinforcements in the test
specimen 12 (Birkle & Dilger 2008) ......................................................................................... 112
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List of Tables
Table 3.1 Main properties of test specimens and angle of the critical crack reported in (Pisanty
2005) ........................................................................................................................................... 57
Table 3.2 Average, SD and CV of V test /V uo for different combination of parameters using the
method in Broms (1990) to calculate the depth of the neutral axis............................................. 62
Table 3.3Average, SD and CV of V test /V uo for different combination of parameters using the
method in Theodorakopoulos and Swamy (2002) to calculate the depth of the neutral axis...... 62
Table 3.4 Average, SD and CV of V test /V uo for different combination of parameters using the
method in Shehata (1990) to calaculate the depth of the neutral axis ......................................... 63
Table 3.5 Average, SD and CV of V test /V uo for AS 3600-2009, ACI 318-05, NZ 3101:2006,
CSA A23.3-04, Eurocode2 and DIN 1045-1 .............................................................................. 69
Table 4.1 Failure load and details of BD test specimens (Ramos, Lcio & Regan 2011) .......... 79
Table 4.2 Failure load and detail of test specimens LP1, LP2 and LP3 (Silva, Regan & Melo
2005) ........................................................................................................................................... 80
Table 4.3 Failure load and details of test specimens V5 and V6 (Silva, Regan & Melo 2005) .. 81
Table 4.4 Failure load and details of test specimens reported in Clement and Muttoni (2010) .. 82
Table 4.5 Failure load and details of test specimen AR8-AR16 (Ramos & Lucio 2006) ........... 84
Table 4.6 Average, SD and CV of V test /V up for three different methods of calculating V up ......... 89
Table 4.7 Average, SD and CV of V test /V up for AS 3600-2009, ACI 318-04, CSA A23.3-04,
Eurocode2, and DIN 1045-1:2001 .............................................................................................. 95
Table 5.1 V test /V uin for test specimens in which failure occurred inside the shear reinforced zone
.................................................................................................................................................. 109
Table 5.2 V test /V uout for test specimens in which failure occurred outside the shear reinforcedzone ........................................................................................................................................... 111
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Table 5.3 Average, SD and CV of V test /V us for ACI 318-05, CSA A23.3, Eurocode2, and the
proposed method ....................................................................................................................... 114
Table A.1 Details of collected slab test specimens.................................................................... 130
Table A.2 Predicted punching shear strength of collected test specimens ................................ 134
Table B. 1 Details of collected prestressed slab test specimens ................................................ 140
Table B. 2 Predicted punching shear strength of collected test specimens using the suggested
method ....................................................................................................................................... 141
Table B. 3 Predicted punching shear strength of collected test specimens using formulae of
design standards......................................................................................................................... 142
Table C.1 Details of collected slab test specimens with shear reinforcement ........................... 144
Table C.2 Predicted punching shear strength of slab test specimens with shear reinforcement
using the suggested method ....................................................................................................... 145
Table C.3 Predicted punching shear strength of slab test specimens with shear reinforcement
using ACI 318-05 ...................................................................................................................... 146
Table C.4 Predicted punching shear strength of slab test specimens with shear reinforcement
using Eurocode2 ........................................................................................................................ 147
Table C.5 Predicted punching shear strength of slab test specimens with shear reinforcement
using CSA A23.3-04 ................................................................................................................. 148
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Chapter One
1 INTRODUCTION
1.1 Background
Two-way concrete slabs are widely used in many types of strucutres. They can be categorised
into slabs that are supported on beams, and slabs that are supported on columns without any
beam. The beamless slabs can be further subdivided into two categories: flat slabs, which are
supported on columns through a drop panel or column capital, and flat plates, which are
supported directly on the columns. Different types of two-way concrete slabs are shown in
Figure 1.1. The early beamless slabs were flat slabs, constructed in the early 20 th century. With
the devlopment of construction technology, flat plates were developed from the concept of flat
slabs and were increasingly built after World War II.
Figure 1.1 Schematic view of different types of two-way concrete slabs (Wight & MacGregor 2009)
Flat plate construction is very common in parking, office, and apartment buildings. Exclusion
of the beams, drop panels, or column capitals in the structural system optimises the storey
height, formwork, labour, construction time, and the interior space of the building. This makes
flat plate construction a very desirable structural system in view of economy, construction, and
architectural desires. However, from structural point of view, supporting a relatively thin platedirectly on a column is significantly problematic due to the structural discontinuity.
a) Concrete slab, supported on
beams
b) Flat slab concrete slab c) Flat plate concrete slab
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Considering the flow of forces in the structure, significant biaxial bending moment and shear
force should transfer through the slab-column connection. In the absence of beams, drop
panels, or column capital, this region is considered as one of the most critical D-regions, in
which stresses are disturbed and strains are irregular, in concrete structures ( fib 2001).
If the shear stresses are minor, two-way concrete slabs show significant ductility, and
redistribution of moment before the strength of the slab is reached. Where two-way slabs are
supported on beams, shear force is distributed along the beams and shear stresses are not
considerable, so a very thin slab satisfies the flexural strength criterion of the design. Generally,
in this type of concrete slab, the deflection limitations determine the thickness of the slab.
In flat plates, however, there is a considerable amount of shear to be transferred through the
slab-column connection. Typically, slab thickness would be determined either by a shear
strength criterion or deflection limitations. With the increasing use of prestressing in floor
construction, designers are capable of eliminating the excessive deflection of two-way slabs by
defining the prestressing tendon profile, and generally the critical problem which governs the
design is the so called punching shear (Dilger & Ghali 1981).
The punching shear or two-way shear phenomenon is a localised failure. It occurs when the
column, punches through the slab, and it can be characterised by the truncated or pyramid
failure surface. Schematic view and a saw-cut test specimen, failed by punching shear, areshown in Figure 1.2.
Figure 1.2 Punching shear localised failure with pyramid-shaped failure surface (Egberts 2009 ;Wight & MacGregor 2009)
This type of failure is extremely dangerous and should be prevented, since it may lead to brittle,
with little or no warning, and progressive collapse of floors. One of the most notorious
examples of the devastating punching shear failure is: the collapse of Sampoong department
store in South Korea in 1995 where more than 500 people were killed and nearly 1000 were
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injured (Gardner, Huh & Chung 2002). Another example is the collapse of the Skyline Plaza in
Virginia in 1973 which killed more than 14 workers (Bu 2008).
Designers can increase the punching strength of beamless slabs by increasing the slab thickness,
introducing drop panels or column capitals, adding shear reinforcement adjacent to the column,
or even specifying concrete with higher strength. In some standards such as Eurocode2 (2004),
BS 8110 (1997), and DIN 1045-1 (2001) increase of flexural reinforcement also allows
designers to consider higher shear strength for the slabs.
Due to the importance of the punching shear phenomenon, an enormous volume of research has
been conducted on this topic. There have been significant attempts to propose a rational model
that can explain the flow of forces in the vicinity of the slab-column connection. However,
there is still no consensus in the literature on how to calculate the punching shear strength of
concrete slabs. Even internationally recognised concrete structure standards are significantly
different in their approach towards this problem.
Most of the international concrete structure standards have enhanced their formulae as insight
into this type of failure has improved in recent decades. Mostly, they adopt empirical or semi-
empirical formulae in their provisions for the punching shear phenomenon. Typically, they
distinguish between two conditions for punching shear. Firstly, where slab-column connections
are under no unbalanced moment and the loading of the slab produces symmetrical shear.Secondly, where slab-column connections undergo unbalanced moment and shear forces
simultaneously. An example for the first case is where the columns are equally spaced and the
lateral loads on the structure are carried by other structural systems such as shear walls or
bracings. An example for the second case is where the slab-column structural system resists the
lateral forces in addition to the gravity loads, or at exterior slab-column connections.
Generally, the most common solution for designers to increase the punching strength of the slab
is to use different types of shear reinforcement. Some of the most common types of shear
reinforcement for punching shear are closed ties, shearheads, bent-up bars, single leg ties, and
more recently shear studs or stud rails. The slab-column connection region is highly congested
with tensile and compressive reinforcement from the column and slab. This would be worse in
the presence of post-tensioning cables. Shear reinforcement such as shearheads, which are
bulky, are not favourable in this region. Moreover, from the economical perspective, shear
reinforcement such as closed ties are time consuming and labour intensive to install in position.
Recently, more efficient shear reinforcement such as shear studs and stud rails were developed
and became very popular and common due to their easy installation and practicality. The latter
types of shear reinforcement are recognised by most European and North American standards.
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inclination of tendons are neglected by AS 3600-2009. More recently, some promising
mechanical methods such as decompression methods have become available in the literature to
calculate the strength of prestressed flat plates with better accuracy as compared to the current
standards approaches.
Considering the gap between the Australian Standard and other international standards, and the
difficulties facing AS 3600-2009 users, there is an urgent need to review and improve the
provisions of the Australian Standard for punching shear.
1.2 Aim and Objectives
The main aim of this research project is to propose a method to calculate the concentric
punching shear strength of flat plates with more accuracy as compared to the provisions of AS3600-2009. This method should be based on a mechanical model, valid for a wide range of flat
plates and simple to use. The following objectives are covered in this project:
1. Review available mechanical methods and semi-empirical methods for concentric
punching shear strength of flat plates.
2. Propose a formula to calculate the punching shear strength of reinforced concrete flat
plates for the case of concentric punching.
3. Extend the proposed method for the case of prestressed slabs.
4. Review guidelines for detailing of shear reinforcements, and provide a method to
calculate the ultimate strength of flat plates strengthened with shear reinforcements such
as shear studs, stud rails and stirrups.
1.3 Thesis Organisation
Chapter One provides a brief background to the punching shear phenomenon and the problem
with the current Australian Standard, followed by objectives and the thesis layout.
Chapter Two is a review of the literature. Some of the influential and illustrative methods are
discussed. Different approaches by internationally recognised standards are presented.
In Chapter Three, the basis of a model developed previously by other researchers, was used to
propose a formula to calculate the punching shear strength of flat plates. Further, the accuracy
of some of the internationally recognised standards in predicting punching shear strength of flat
plates was evaluated against reported experimental results in the literature.
In Chapter Four , the proposed formula for non prestressed flat plates extended for the case ofprestressed flat plates, and provisions of various standards were assessed by some of the
available test results in the literature.
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In Chapter Five , guidelines are provided for detailing and strength considerations of flat plates
with shear reinforcements.
Chapter Six presents the conclusions from the current research project.
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Chapter Two
2 LITERATURE REVIEW
2.1 Introduction
In the last five decades a significant amount of research has been conducted on the topic of
punching shear in concrete floors. Many analytical and empirical methods have been proposed
based on the observations and results gathered during experimental tests. It is not possible to
cover all of the previous work on punching shear of concrete slabs herein. Therefore, in this
chapter, some of the methods which may be considered as main contributors to the current state
of knowledge on the punching shear phenomenon are presented. Other aspects of this type of
failure such as punching shear in prestressed slabs, and slabs strengthened by shear
reinforcement are reviewed briefly. Finally, the provisions of the current Australian Standard
for Concrete Structures (AS 3600 2009) and some of the internationally recognised standards
such as American code (ACI 318-05 2005), New Zealand standard (New Zealand Standard NZS
3101:Part 1 2006), European code (Eurocode 2 2004), British standard (BS 8110-97 1997), and
German standard (DIN 1045-1 2001) are presented.
2.2 Reported Observations from Concentric Punching Shear Failure of
Test Specimens
Punching shear failures, as explained in the literature, are local failures around the column or
the stub of test specimens. As reported in Kinnunen and Nylander (1960), the tangential andradial strains of slab test specimens were measured in their test series, and it was observed that
the strains in the tangential direction are higher than the strains in the radial direction which
resulted in the formation of radial cracks prior to tangential or circumferential cracks. These
two types of cracks are shown in Figure 2.1 for clarity.
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Figure 2.1 Tangential and radial cracks observed in typical punching shear test specimen (Sherif
1996)
As stated in (Regan 1981), generally the inclined radial cracks initiate at 1/2 to 2/3 of theultimate load which causes the punching failure. After the formation of inclined radial cracks,
the condition of the slab is entirely stable and it can undergo loading and reloading. As the load
increases some tangential cracks appear around the column. One of the tangential cracks will
eventually become the cone shaped surface of failure (Sherif 1996).
Figure 2.2 shows the applied load versus the deflection of test specimens reported in (Mentrey
1998). It illustrates the difference between the ductility of slabs that failed by punching
phenomenon and slabs that failed in flexure. From the sudden drop in the load-deflection graph,it can be depicted that punching failure is a sudden failure with little warning, whereas the
specimens that failed by flexure behaved in a ductile manner before their failure.
Figure 2.2 Comparison of deflection-load graph for slab test specimens failed by punching shear to
slab test specimens failed in flexure (Mentrey 1998)
Flexural failure
Punching failure
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2.3 Mechanical Models for Punching Shear Balanced Condition
2.3.1 Kinnuen and Nylander Approach
Based on observations of 61 circular slab specimens, Kinnuen and Nylander (1960) proposed amechanical model for the punching shear of slabs with circular -ring shaped- reinforcement.
They presented a structural system for the slab-column connection as shown in Figure 2.3. In
their model, the slab is divided into a compressed conical shell and rigid elements. The
compressed conical shell part is surrounded by the shear crack, and the rigid elements are
confined at the front by a tangential crack and at the sides by the radial cracks as seen in Figure
2.3(b). The rigid elements are supported by conical compressive struts around the column as
shown in Figure 2.3(c). Under load action and after the formation of tangential and radial
cracks, the rigid segments of the slab turn around their centre of rotation at the root of the shear
crack. The failure is assumed to occur when the compressive stress in the strut and the
tangential strains at the point located under the centre of rotation reach their critical values.
Assuming that the two failure criteria coincide, the depth of the neutral axis was calculated by
iteration (Sherif 1996). The critical values for the failure criteria were calibrated based on
results of experimental tests reported by (Elstner & Hognestand 1956) and (Kinnunen &
Nylander 1960). These values were different to the well known values of strain and stress for
concrete at the ultimate stage. A major drawback of this method is the complexity and iterative
procedure of calculating punching shear strength as compared to the other methods (Megally
1998).
Figure 2.3 Mechanical model of Kinnunen and Nylander as shown in fib (2001)
Compressed conical shell
Rigid elementShear crack
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Kinnunen (1963) further developed the previous model to include slabs with orthogonal
reinforcement. Three equations were derived from the equilibrium condition for the rigid
sector. Equation 2-1 was the result of moment equilibrium. Equation 2-2 was gained from the
equilibrium of forces in radial direction, and Equation 2-3 was derived from the equilibrium offorces in the vertical direction.
sin cos 2 0(2-1)cos 2 2 2 0 (2-2)
1 sin (2-3)
Where P is the force causing failure, c is the diameter of test specimen, h is the effective depth
of slab, T is the compressive force in the strut around the column, R1 , R 2 are the forces in
reinforcement crossing the shear crack in the tangential, and radial directions respectively, R4 is
the force resultant from the concrete compression zone as shown in Figure 2.3(b), is the
angle of the rigid segment slice as shown in Figure 2.3(b), is the angle between thecompressive strut and slab, y is the height of the compressive strut, y is the distance of R 4 to thebottom of slab, B is the diameter of the stub, z1 as shown in the Figure 2.3(c), and is equal to
(M+D)/P, in which M is the vertical resultant of the membrane force in the reinforcement, D isthe force from the dowel-effect of reinforcement crossing the crack.
This model involves an iterative procedure to predict the punching load. First a value for (y/h)
should be assumed. Having (y/h), can be calculated from geometry, and substituted inEquation 2-1, 2-2, and 2-3. Punching load is the convergent value of P from above equations.
2.3.1.1 Shehata and Regans model
Shehata and Regan (1989) proposed a mechanical model in which the slab is divided into rigid
segments, surrounded by radial cracks on the sides and tangential cracks at the front and the
back, as shown in Figure 2.4 (b). The reinforcement crossing the circumferential crack was
assumed to reach yield prior to the failure of slab. After yield, the rigid segments are detached
from the central conical part of the slab and turn around the centre of rotation (CR) , shown in
the Figure 2.4(a). Three criteria are defined for the failure:
Inclination of the compressive force reaching 20 from the plane of the slab.
Radial compressive strains at the face of column reaching 0.0035.
Tangential compressive strains at a distance equal to the depth of neutral axis from the
face of column reaching 0.0035.
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limitations for the strains and stresses using generally recognised properties of concrete.
Another significant difference of Broms method as compared to Kinnuen and Nylander (1960)
is that two types of compression zones were considered, namely the tangential compression
zone and the radial compression zone.
The limitation for high tangential compression strain is expressed in Equation 2-5.
0.0008 150/. 25/. fc in (MPa), and x pu in (mm) (2-5)Where x pu (mm) is the depth of the compression zone in the tangential direction, cpu is the
tangential strain in the outermost fibre of concrete at the edge of the column and x pu is theheight of the equivalent rectangular stress block with the stress equal to f c. The punching force
V for this criterion can be obtained by the use of classical bending theory assuming cpu as thecritical strain in the concrete. This is the punching shear load calculated using equilibrium and
Bernoullis compatibility conditions.
The other criterion for punching shear failure is the radial compression failure. Broms (1990)
assumed the formation of an imaginary strut around the column to transfer the applied load to
the column as shown in Figure 2.5. Broms assumed the inclination of the shear crack as 30,
the inclination of the concrete strut as 15 and the compressive strength of the strut as 1.1 f c to
account for the effect of the multi-axial state of stress on the strut. Equation 2-6 was proposed
by Broms to calculate the punching load for this criterion.
Figure 2.5 Radial compression stress failure proposed by Broms (1990) as shown in fib (2001)
2 / 30 150/0.5. 15 (2-6)Where D is the diameter of column, y is the depth of the neutral axis in the radial direction. For
the case of slabs supported on square columns with column side dimension a, D is equal to
4a/ p .
V
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Equation 2-7 is suggested by Broms to calculate the depth of the compression zone in the radial
direction.
1 2/ 1 (2-7)
Where n is the ratio of elastic modulus of steel to elastic modulus of concrete n=E s /E c, is theratio of tensile reinforcement, d is the effective depth of section, and
k =(0.5D+d/tan30 )/(0.5D+y/tan30 ).
The lesser of punching shear capacities obtained from the above criteria (V and V ) is the
ultimate capacity of the slab.
Recently, Broms (2009) improved the latter model by modifying the critical tangential strain
(Equation 2.5) to the following expression.
0.001 150// 25/. fc in (MPa), and x pu in (mm) (2-8)He also proposed the depth of compression zone to be calculated in the elastic condition as
shown in Equation 2-9.
1 2/ 1 (2-9) Where n is the ratio of modulus of elasticity of steel to E c10 the secant modulus elasticity ofconcrete for the strain of 0.001.
Broms (2005) suggested Equation 2-10 to calculate E c10 .
1 0.6 1 /150 fc in (MPa) (2-10)Where E c0 is the modulus of elasticity for concrete at zero strain which can be calculated by
Equation 2-11 as given in Model Code 90 (Model Code 90 1993).
21500/10/ fc in (MPa) (2-11)The punching shear strength based on the strain criterion, V , can be calculated from Equation 2-12.
/ / (2-12)Where l is the diameter of the test specimen or the distance between points of contra-flexure in
the slab, D is the diameter of the column, and m is the bending moment at the edge of slab-
column connection which can be calculated as following.
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1 /3 (2-13)In Equation 2-13, k u=(f sy / s E s)0.2
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(250/h) 0.35 for concrete strength more than 40MPa. The angle between the crack and the plane of
the slab was assumed to be equal to 30 .
/ 0.8 170 0.85 (2-17)
Where f c2max is the compressive strength of the concrete strut, 1 is the principal tensile strain in
the cracked concrete. Tiller (1995) did not specify how to calculate 1.
Figure 2.6 Radial compression stress failure mechanism as shown in Marzouk, Rizk and Tiller
(2010)
Marzouk, Rizk and Tiller (2010) improved the latter method by using Equation 2-18 to calculate
the depth of the compression zone.
0.67. 35/. fc in (MPa) (2-18)Where n is the ratio of modulus of elasticity of steel to modulus of elasticity of concrete, e isthe ratio of reinforcement for a basic yield strength (500MPa) and can be calculated as e= (f sy /500) 0.02 where is the ratio of reinforcement and f sy is the yield strength of the tensilereinforcement. Also they suggested a range for the angle of the critical crack ( ) depending on
the thickness of the slab i.e. 25-35 for slabs less than 250mm thick, 35-45 for slabs 250mm-
500mm thick and 45-60 for slabs thicker than 500mm.
2.3.2 Truss Model by Alexander and Simmonds
Alexander and Simmonds (1987) approached the punching shear phenomenon by proposing
formation of a three dimensional truss around the column. The components of the truss are
shown in Figure 2.7. The truss is broken down into the flexural tensile reinforcement acting as
ties, and the compression concrete zones acting as struts. As shown in Figure 2.7, two types of
struts are assumed, shear struts and anchoring struts. The shear struts are assumed to have an
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d = cover of tensile reinforcing bar,
d= effective depth of slab,
c= dimension of column face,
Abar = area of single reinforcing bar,
f c' = compressive cylinder strength of concrete,
f sy= yield strength of tensile reinforcement steel.
Having , the punching strength of the slab for concentric load can be calculated from Equation2-20.
(2-20)Where is the effectiveness of the tensile reinforcement as explained earlier.
2.3.3 Bond Model by Alexander and Simmonds
Alexander and Simmonds modified and developed their Truss model to the so called Bond
model. By monitoring the strains of the test specimens reported in (Alexander 1990),
Alexander and Simmonds (1992) suggested the shear struts are arch shaped as shown in Figure2.8, and the geometry of the shear arch cannot be obtained by the amount of tensile
reinforcement. This is in contrast with the assumptions of the shear struts in the Truss model.
Figure 2.8 Curved compression strut (Alexander & Simmonds 1992)
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Instead, they proposed a Bond model in which the slab is composed of four radial strips and
four quadrant slabs as shown in Figure 2.9. The assumptions of this model are:
All the loads are transferred to the column through the radial strips, and the quadrants
components of the slab transfer the loads to the side faces of the radial strips.
The total load on each strip is 2 w and w is the ultimate internal shear that can be
resisted by the slab on each side face of the strip.
The strength of the radial strips is limited by the flexural strength of the strip M s.
M s is the sum of the flexural strengths of the slab at the ends of the strip- M neg and M pos.
According to (Alexander 1999) M s can be approximated by Equation (2.21).
0.9 (2.21)
Where a is the width of the strip -side dimension of column-, neg is the ratio of topreinforcement at the column end of the strip and pos is the ratio of bottom reinforcement atthe shear zero end of the strip.
Figure 2.9 Plan view of slab and the components of Bond model proposed by Alexander and
Simmonds (1992)
A free body diagram of the radial strip is shown in Figure 2.10. If l is the length of applied
uniform distributed load then from equilibrium, M s=wl 2 and the maximum load P s carried by a
strip is given by Equation 2-22.
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Figure 2.11 Punching shear model by Georgopoulos as shown in fib (2001)
The depth of compression zone was assumed to be 0.2 of the effective depth of the slab. The
stress distribution in the expected punching failure surface was assumed to be a polynomial of
third order as shown in Figure 2.12.
Figure 2.12 Distribution of concrete tensile stresses in Georgopoulos as shown in fib (2001)
As shown in Figure 2.11, Z b is the resultant tensile force in the cracked section. Georgopoulos
estimated Z b by integration of the stresses along the surface of failure. Consequently, he
proposed the following equation to calculate the punching strength of slabs.
cos /0.75 0.4130.17 /cot /2 0.2 0 (2-25)Where is the inclination of the failure surface, is the ratio of the diameter of the column tothe effective depth of the slab, f cube is the compressive strength of concrete of a cube test
specimen in MPa.
Georgopoulos suggested the following equation to predict the inclination of the critical crack
causing punching failure.
tan 0.56/ 0.3 (2-26)
Where is the tensile reinforcement ratio.
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2.3.4.2 Model by Mentrey
Mentrey (1996, 2002) assumed a strut-and-tie pattern which transfers the load from its point of
application to the column. He considered the failure to occur when the strength of the tie,
adjacent to the column, reaches the failure limit. The contributors to tensile strength of the tie
are shown in Figure 2.13.
Figure 2.13 Schematic view of components of proposed method by Menetrey (2002)
In this method, Menetrey included the tensile capacity of the concrete, the effect of dowel action
of the flexural reinforcement, the strength of the shear reinforcement and the vertical component
of the prestressing force. Equation 2-27 is suggested to calculate the ultimate punching shear
strength of a given slab.
(2-27)Where, F ct is the vertical component of the concrete tensile strength of the hypothetical tie
shown in Figure 2.13, F dow is the dowel-effect contribution from the flexural reinforcement
crossing the punching crack, F sw is the contribution from shear reinforcement if there is any,
and F p is the contribution of vertical component of forces of prestressing tendons crossing the
punching crack.
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F ct can be calculated by Equation 2-28,
/ (2-28)Where r s is the radius of the column, r 1=r s+d/10tan30 , r 2=r s+d/tan30 , s is the length of the
punching shear crack and is equal to ((r 2-r 1)2+(0.9d) 2), f t is the uniaxial tensile strength of theconcrete, is a factor to take into account the influence of the flexural reinforcement ratio - - and can be calculated by the following expression.
=min(0.87, -0.1 2+0.46 +0.35)
and take into account the size effect on the tensile strength of the concrete and areexpressed as followings.
=min(0.625, 0.1(h/r s)2+0.5(h/r s)+1.25)
=1.6(1+d/d a)-0.5
Where h is the thickness of slab, and d a is the maximum aggregate size in concrete.
The contribution of the dowel-effect F dow is the summation of dowel-effect of each reinforcing
bar crossing the failure surface and can be calculated by the following expression.
1/2 1 30 (2-29)Where s is the diameter of the flexural reinforcement crossing the punching shear criticalcrack, f c is the uniaxial compressive strength of the concrete, f sy is the yield stress of the
reinforcing bars, = s /f sy, and s is the stress in the tensile reinforcement at punching which can
be quantified by the following equation.
/ 30 (2-30)
Where is the area of reinforcing bars crossing the punching shear failure surface.It should be noted for calculating s that the punching strength of the slab is needed, so thecalculation of punching shear strength is an iterative procedure in this method.
If adequate anchorage is provided, F sw can be calculated by Equation 2-31.
sin (2-31)Where Asw is the area of the shear reinforcement intersecting with the punching shear crack, f sw is the yield strength of the shear reinforcement steel, and sw is the angle between the shearreinforcement and the plane of the slab.
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The contribution of prestressing F p is given as following expression.
sin (2-32)Where A p is the area of prestressing steel crossing the failure surface, p is the stress in the
tendons, and p is the inclination of the tendon with the plane of slab as shown in Figure 2.13.
2.3.4.3 Theodorakopoulos and Swamy approach
Theodorakopoulos and Swamy (2002) proposed a method for representing the punching shear
phenomenon by considering a criterion for the tensile strength of the compression zone in the
vicinity of the column. The punching shear strength was related to the tensile strength of the
compressed concrete around the column. It was assumed that there are two types of neutral
axes adjacent to the column, namely flexural and shear. The location of the flexural neutral axis
was calculated assuming the ultimate stage in flexure and the location of the shear neutral axis
was assumed to be 0.25 of the effective depth of the slab. Equation 2-33 was suggested to
calculate the mean of the depth of the neutral axes. This will be explained further in Chapter
Three.
2 / (2-33)In Equation 2-33, X f is the depth of the flexural neutral axis and X s is the depth of the shearneutral axis.
As show in Figure 2.14, the ultimate punching strength of slab - V u- consists of the contribution
of the tensile strength of the compression zone, V c , and the contribution of the dowel-effect of
flexural reinforcement.
Figure 2.14 Schematic view of model by Theodorakopoulos and Swamy (2002)
d n
V u
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For simplicity, Theodorakopoulos and Swamy incorporated a larger control perimeter as
compared to the perimeter of the compression zone around the column to account for the dowel-
effect action. A control perimeter, similar to BS 8110-97 (1997), was adopted in this method as
expressed in Equation 2-34.
4 12 (2-34)Where a is the side dimension of the column and d is the effective depth of the slab.
The ultimate punching shear strength of the slab was expressed as the following equation.
cot (2-35)Where f ct is the splitting strength of concrete, equal to 0.27(f cube )
2/3 , and q was taken as 30, d n is
calculated by Equation 2-33, and b p is calculated by Equation 2-34.
2.3.5 Plasticity Approach
Braestrup et al. (1976) proposed an upper bound model on the basis of the theory of plasticity
for punching shear phenomenon. Geometrical parameters of the model are shown in Figure
2.15. In this model, it was assumed that the vertical load V was applied to the slab by the
column with the diameter of d . The maximum diameter of punching shear failure surface is d 1.
The punching failure surface was assumed to shape as curve A-B-E, shown in Figure 2.15. Thecurve of the failure surface is expressed as r=r(x), and the angle of displacement vector is
expressed as = (x).
The work done by the punching force ( W v) should be equal to the dissipated energy ( W e) at the
punching shear crack surface. Equation 2-36 was suggested to express the dissipated energy
and Equation 2-37 was suggested to express the work done by the applied load.
Figure 2.15 Plasticity model proposed by Braestrup et al. (1976)
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0.5 2 (2-36)
(2-37)
Where is the displacement, =1-f ct /f c(k-1), =1-f ct /f c(k+1), k=(1+sin )/(1-sin ), f ct is thetensile strength of concrete, and is the friction angle of concrete as shown in Figure 2.15.
The above equations will give an upper bound punching shear strength of the slab. By
optimisation, Braestrup et al. (1976) suggested the failure surface consists of a linear conical
part (A-B) and a curved part (B-E). Thus the ultimate punching strength is the sum of P 1 which
takes into account the straight line part (A-B) as expressed in Equation 2-39 and P 2 which takes
into account the curved part as expressed in Equation 2-40.
(2-38) (2-39) 0.5 (2-40)
Where h is the thickness of the slab, h0 is the depth of inclined straight line, a=d/2+h 0 tan ,b=c tan , and c= (a 2-b 2).
One of the common criticisms of this method is that it ignores the effect of tensile reinforcement
on the punching shear strength of slabs.
2.3.6 Flexural Approach
A considerable number of slab test specimens, reported in the literature, have a failure load not
significantly different to their flexural capacity. As a result, some researchers such as Gesund
and Goli (1980), Gesund (1981), and Rankin and Long (1987) assumed the punching shear as a
secondary failure phenomenon and attempted to propose a method which relates the punchingshear strength of slabs to the flexural capacity of the slabs.
In this section, the flexural method proposed in Rankin and Long (1987), is reviewed. Rankin
and Long (1987) suggested that the flexural punching strength of a prototype test specimen can
be calculated from Equation 2-41.
/ / / (2-41)Where, k y1 is moment factor for overall yielding of tensile reinforcement, and for square slabssupported on a square column is equal to 8(s/(a-c)-0.172) where a, c, s are shown in Figure
2.16.
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k b is the ratio of the applied load to the internal bending moment at the column periphery which
is equal to (25/(ln(2.5a/c) 1.5).
r f is a factor to allow for the shape of column which is equal to 1.0 for circular columns and 1.15
for square column.
M b is the bending moment resistance, and can be calculated by f syd 2(1-0.59( f sy /f c)).
M bal is the balanced moment of resistance which was suggested to be calculated by 0.333f cd 2.
Figure 2.16 Failure pattern and parameters of the proposed method by Rankin and Long (1987)
Rankin and Long (1987) also specified a criterion for failure caused by internal diagonal
tension cracking. They suggested Equation 2-42 to calculate the latter strength of slabs.
1.66 100. fc in (MPa),V shear in (N), c and d in (mm) (2-42)The lesser of V flex and V shear is the punching shear strength of the slab.
2.3.7 Critical Shear Crack Theory
Muttoni (2008) presented a different failure criterion for punching shear based on the opening ofa critical shear crack in the vicinity of the column. According to Muttoni and Schwarts (1991),
the width of the critical shear crack ( wc) is proportional to the product of the rotation of the slab
times the effective depth of slab ( y d ). Another relevant parameter in view of critical crack
theory is the roughness of the critical shear crack which is related to the size of the aggregates in
the concrete. With the mentioned assumptions and available experimental results, Equation 2-
43 was proposed to calculate the punching strength of concrete slabs.
S a
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.y / fc in (MPa),V shear in (N),b 0 , d, d g , and d g0 in (mm) (2-43)Where b0 is the control perimeter at the distance equal to d/2 from the face of column, d g0 is the
reference aggregate size and considered to be 16mm, and d g is the maximum aggregate size inthe concrete.
Rotation of slab ( y ) is related to the applied load V as given in Equation 2-44.
y 1.5 . (2-44)Where r s is plastic radius around the column which can be taken as the distance between the
centre of column to the point of contraflexure, and V flex can be calculated from yield-line theory.
To calculate the punching strength of a given slab, an iterative procedure is required.
Alternatively, the load-rotation curve can be drawn using Equation 2-44 and the failure criterion
can be drawn using Equation 2-43. The intersection of these curves determines the failure load
of the slab ( V uo). The latter procedure is shown in Figure 2.17.
Figure 2.17 Procedure to specify punching shear strength of slab according to Critical Shear Crack
Theory (Muttoni 2008)
2.4 Punching Shear of Prestressed Flat Plates
The present section reviews some of the theoretical approaches to include the effect of
prestressing forces in the calculation of punching shear strength of flat plates. According to
Regan and Braestrup (1985), the available models for punching of prestressed slabs can be
categorised to the following approaches.
V uo
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2.4.1 Principal Tensile Stress Approach
In this approach, the effect of prestressing was taken into account by approximation of principal
tensile stresses on the control perimeter, and consideration of the vertical component of the
tendon forces crossing the control perimeter. An example of this approach is Equation 2-45,
suggested by ACI-ASCE Committee 423 (1974), and adopted in ACI 318-05 (2005) code.
/ 0.29 0.3 / fc in (MPa) (2-45)Where u is the length of control perimeter at a distance of d/2 from the face of column, cp is the
mean effective prestressing stress in the concrete, and V p is the vertical component of
prestressing tendons crossing the control perimeter.
2.4.2 Equivalent Reinforcement Ratio Approach
In this approach, the effect of prestressing is considered by adding the equivalent reinforcement
ratio to the actual reinforcement ratio of the slab. The sum of the ordinary reinforcement and
the equivalent reinforcement is used in the formula, which predicts the punching strength of the
slab. There are various proposed methods to convert the prestressing stress to the equivalent
reinforcement ratio.
As cited in Sundquist (2005), FIP recommendations (1980) specifies the equivalent
reinforcement ratio by Equation 2-46.
/ (2-46)Another method for calculating equivalent reinforcement ratio proposed by Nylander,
Kinnunen, and Ingvarsson, which is cited in Regan and Braestrup (1985), is given in Equation
2-47.
./ . (2-47)
Where p is the prestressing steel ratio, f 0.2 is the 0.2% proof stress of the tendons, and pe is theeffective prestress of the tendons.
Clearly, this approach is not suitable for methods which do not include the effect of the tensile
reinforcement on the punching shear strength of slabs.
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2.4.3 Decompression Approach
Regan (1985) proposed a decompression method for the punching shear phenomenon. The state
of decompression occurs when compression stress, resulting from prestressing forces, is
cancelled out by the effect of transverse loading at a specific region (Silva, Regan & Melo
2005). In a decompression method for punching shear of slabs, it was assumed the punching
strength after the decompression stage is equal to the strength of a geometrically similar
concrete slab with the same number of reinforcement and no prestressing forces. Thus it is
possible to determine the punching resistance of prestressed slabs by adding the decompression
load to the punching strength of the ordinary concrete slab with the same amount of
reinforcement. The required bending moment for decompression of a given section can be
calculated from Equation 2-48.
/6 (2-48)Where cp* is the compressive stress in the outermost compressive fibre of the section due to
prestressing after losses.
According to Regan and Braestrup (1985) the decompression load can be taken as following.
2 for circular slabs
4 / for rectangular slabs with breadth b, and main span l.In Regan and Braestrup (1985), the punching shear strength of concrete slabs with noprestressing was suggested to be calculated from the draft of British code CP 110 as following.
0.27 500/ 100 f cube in (MPa), d in (mm) (2-49)Where in Equation 2-49 is the sum of ordinary reinforcement area ( Asr ) and bondedprestressing steel area ( Asp).
/ (2-50)Where b is the breadth of the section and d is the equivalent effective depth of the steel and can
be calculated as expressed in Equation 2-51.
. / . (2-51)Where f 0.2 is the 0.2% proof stress of the prestressing steel, f sy is the yield strength of ordinary
reinforcement, d p is the effective depth of prestressing steel, and d r is the effective depth ofordinary reinforcement.
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2.5 Methods to Increase Punching Shear Strength of Concrete Slabs
In Polak, El-Salakawy and Hammill (2005), three common methods to increase the punching
shear strength of concrete slabs are categorised as followings:
Expanding the area which transfers shear stresses from slab to column. In this method
designers normally increase the thickness of the slab in the vicinity of column by
introducing drop panels or column capitals. Other possibility is to increase the
dimensions of the column which results in a larger area resisting shear stresses.
Using concrete with higher compressive strength which results in a higher punching
shear strength.
Providing different types of shear reinforcement such as shearheads, stirrups, bent-up
bars, or shear studs in the area adjacent to the column.
In a study by Megally and Ghali (2000), four different methods were used to strengthen 150mm
thick slabs. Drop panel, column capital, stirrups (closed-ties) and shear stud rails (SSR). Then
a comparison was made between the performance and amount of increase in punching shear
capacity of slabs. The slabs were loaded to the point of failure, and the load-deflection curve
for each slab was plotted as shown in Figure 2.18. Drop panel and column capital resulted in an
increase of the punching shear strength of the slab but not the ductility of the slab. As shown,
shear studs increased both the strength and ductility of the slab. Further, it was observed in this
case that stirrups only slightly increased the punching shear strength of the test specimen due to
lack of proper anchorage (Megally & Ghali 2000).
Figure 2.18 Load-deflection curves of slabs strengthened by different methods (Megally & Ghali
2000)
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Although all the aforementioned methods increased the punching shear strength of the tested
slabs, the issue of ductility, which is a desirable behaviour of structures in seismic regions, was
not improved by most of the provided strengthening techniques except for the slab strengthened
with shear studs. Other important considerations to decide the best strengthening method can beeconomy, and practicality of the method. Designers prefer the use of shear reinforcement to
increase the punching strength of concrete slabs due to its advantages over the other methods.
In the 70s and 80s a significant amount of research was conducted on the performance of slabs
with shear reinforcement and consequently design provisions were introduced into design
codes.
2.6 Shear Reinforcement for Flat Plates
As mentioned, different types of shear reinforcement were proposed by structural engineers to
increase strength and ductility of concrete slabs. The role of shear reinforcement in the slab is
mainly to arrest the opening of the critical shear crack, increase the compression zone and
aggregate interlock which result in increase of shear strength.
In design, the radial spacing and placement of shear reinforcement is very important, and
designers should detail the position of shear reinforcement in a way that they intersect with the
inclined shear cracks. In addition, desirable types of shear reinforcement should have a good
tensile capacity, adequate ductility and enough anchorage (Polak, El-Salakawy & Hammill2005). Providing that the shear reinforcements are placed and designed properly, it can increase
the punching shear and rotation capacity of the slab significantly. Preferably, punching shear
strength of slabs should be increased to the extent that the flexural failure occurs prior to the
punching shear failure. Generally, there are two categories of shear reinforcement for punching
shear, namely shear reinforcement for construction of new slabs and shear reinforcement for
retrofit of existing slabs.
2.6.1
Shear Reinforcement for Construction of New SlabsShear reinforcement for a new slab can be classified as follow (Polak, El-Salakawy & Hammill
2005).
Shearheads, made of different types of structural steel sections as shown in Figure 2.19.
Stirrups, single or double leg bar, bent bars, and closed-ties. This type of shear
reinforcement is made from the normal reinforcing bars as shown in Figure 2.20 .
Stud rails, shear studs, and shear bolts which are called headed shear reinforcements asshown in Figure 2.21.
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(a) (b)
(c) (d)
Figure 2.20 (a) Bent bar, (b) Single-leg stirrup , (c) Multiple-leg stirrup (d) Closed-stirrup or
Closed-tie (ACI 318-05 2005 ; Broms 2007)
The headed studs were presented in Dilger and Ghali (1981) for the first time. Since it is a very
convenient and practical type of shear reinforcement, extensive research has been conducted on
the performance of slabs strengthened with headed shear studs. In this type of shear
reinforcement, the problem of anchorage has been solved by providing large flat heads at the
both ends with the area of 10 times the stem cross-sectional area. This shear reinforcement is
available in the form of shear stud rails (SSR) in the market as shown in Figure 2.21. SSR areeasy to install, and adequate anchorage is achievable in relatively thin slabs. Most of the tests
on slabs strengthened with headed shear studs, show a ductile and satisfactory performance
(Polak, El-Salakawy & Hammill 2005), and consequently, this type of reinforcement has been
adopted by most of internationally recognised standards as an effective shear reinforcement for
slabs.
Figure 2.21 Headed shear studs (Bu 2008)
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In recent years, other types of shear reinforcement for punching shear have been made available
in the marketplace such as Shearbands, UFOs, and lattice.
Shearbands were tested in the University of Sheffield and reported in Pilakoutas and Li (2003).
These are high ductile thin steel strips with punched holes as shown in Figure 2.22(a). The
holes are provided to increase the anchorage of strips as experimentally proven. These strips are
easily bent and shaped to place in a way to cross the shear cracks as shown in Figure 2.22(b). A
significant improvement in the ductility and strength of slabs was observed in the test specimens
reinforced with this type of shear reinforcement (Pilakoutas & Li 2003).
(a)
(b)
Figure 2.22 (a) Plan view of a shearband (b) Shearbands placed in slab (Pilakoutas & Li 2003)
UFOs are steel plates which are shaped like a cone and placed at the slab-column connection to
intersect with the critical shear crack. There are some perforated holes to allow for the
continuation of column reinforcements. This shear reinforcement is shown in Figure 2.23.
Figure 2.23 UFO shear reinforcement (Alander 2004)
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A lattice is made of top, bottom, and web bars which are welded and prefabricated in the factory
as shown in Figure 2.24. Lattice performance as a punching shear reinforcement was first
reported in Park et al. (2007). According to the experimental observations, the strength and
ductility of the test specimens reinforced with these were increased up to 1.4, and 9.2 timesrespectively as compared to the specimen with no shear reinforcement (Park et al. 2007).
Another advantage of this system is that even after failure, due to truss action of lattice system,
it can avoid sudden failure of the slab.
Figure 2.24 Lattice shear reinforcement (Park et al. 2007)
2.6.2 Shear Reinforcement for Retrofit of Slabs
Punching shear strength of existing concrete slabs may need to be increased due to the corrosion
of rebars, change in the amount of imposed load, or errors in the structural design. There are