Concentric Punching Shear Strength of Reinforced 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
Concentric Punching Shear Strength of Reinforced Concrete Flat Plates
Apr 05, 2023
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Concentric Punching Shear Strength of Reinforced Concrete Flat PlatesReinforced Concrete Flat Plates
Fariborz Moeinaddini
Submitted in total fulfilment of the requirement of the degree of
Master of Engineering
Industrial Science
ii
iii
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. In
this 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
iv
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.
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 and
Stephan 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.
vi
vii
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 no unbalanced moment’, Proceedings of Concrete 2011, Concrete Institute of Australia, Perth, Australia.
• Moeinaddini, F, Abdouka, K & Gad, EF 2010, ‘Punching shear capacity of concrete slabs: a comparative study of various standards and recent analytical methods’, Post-
graduate Research, Swinburne University of Technology, Melbourne, Australia.
viii
ix
Declaration
This is to certify:
• This thesis contains no material which has been accepted for the award to the
candidate of any other degree or diploma, except where due reference is made in the
text.
• To the best of the candidate’s knowledge contains no material previously published or
written by another person except where due reference is made in the text of the
examinable outcome.
Fariborz Moeinaddini
June 2012
1.3 Thesis Organisation ...................................................................................................... 5
2 LITERATURE REVIEW ..................................................................................................... 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
2.4 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 ...................................... 37
2.7.1 Australian Standard AS 3600-2009 .................................................................... 37
xii
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
2.8 Summary ...................................................................................................................... 46
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
3.5 Summary ...................................................................................................................... 75
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
xiii
4.5 Summary ..................................................................................................................... 99
REINFORCEMENT ................................................................................................................. 101
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
5.5 Summary ................................................................................................................... 114
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…………… ...... ……………………………………………...………………….... 123
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 (Menétrey 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
xvi
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 2.24 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
xvii
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 Vtest/Vuo versus effective depth of slab, tensile reinforcement ratio and compressive
strength of concrete for T-P-M-0.5 ............................................................................................. 64
Figure 3.14 Vtest/Vuo versus effective depth of slab, tensile reinforcement ratio and compressive
strength of concrete for S-P-B-0.33 ............................................................................................ 65
Figure 3.15 Vtest/Vuo 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 Vtest/Vuo 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 Vtest/Vuo versus effective depth of slab, tensile reinforcement ratio and compressive
strength of concrete for NZS3101:2006 ...................................................................................... 71
xviii
Figure 3.19 Vtest/Vuo versus effective depth of slab, tensile reinforcement ratio and compressive
strength of concrete for CSA A23.3-04 ....................................................................................... 72
Figure 3.20 Vtest/Vuo versus effective depth of slab, tensile reinforcement ratio and compressive
strength of concrete for Eurocode2 and Model Code 90 ............................................................. 73
Figure 3.21 Vtest/Vuo 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, Lúcio & 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 Vtest/Vup versus σcp for three different methods of calculating Vup ............................ 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 Vtest/Vup versus σcp for AS3600-2009 ........................................................................ 96
Figure 4.13 Vtest/Vup versus σcp for AS3600-2009 when Vp is included ....................................... 96
xix
Figure 4.14 Vtest/Vup versus σcp for ACI 318-05 .......................................................................... 97
Figure 4.15 Vtest/Vup versus σcp for ACI 318-05 ignoring the limit on f’c .................................... 97
Figure 4.16 Vtest/Vup versus σcp for CSA A23.3-04 ..................................................................... 97
Figure 4.17 Vtest/Vup versus σcp for CSA A23.3-04 ignoring the limit on f’c ............................... 98
Figure 4.18 Vtest/Vup versus σcp for Eurocode2 ............................................................................ 98
Figure 4.19 Vtest/Vup versus σcp 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
xx
xxi
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 Vtest/Vuo 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 Vtest/Vuo 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 Vtest/Vuo 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 Vtest/Vuo 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, Lúcio & 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 Vtest/Vup for three different methods of calculating Vup ......... 89
Table 4.7 Average, SD and CV of Vtest/Vup for AS 3600-2009, ACI 318-04, CSA A23.3-04,
Eurocode2, and DIN 1045-1:2001 .............................................................................................. 95
Table 5.1 Vtest/Vuin for test specimens in which failure occurred inside the shear reinforced zone
.................................................................................................................................................. 109
Table 5.2 Vtest/Vuout for test specimens in which failure occurred outside the shear reinforced
zone ........................................................................................................................................... 111
xxii
Table 5.3 Average, SD and CV of Vtest/Vus 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
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 20th 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 plate
directly 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
2
Considering the flow of forces in the structure, significant biaxial bending moment and shear
force should transfer through the slab-column…
Fariborz Moeinaddini
Submitted in total fulfilment of the requirement of the degree of
Master of Engineering
Industrial Science
ii
iii
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. In
this 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
iv
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.
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 and
Stephan 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.
vi
vii
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 no unbalanced moment’, Proceedings of Concrete 2011, Concrete Institute of Australia, Perth, Australia.
• Moeinaddini, F, Abdouka, K & Gad, EF 2010, ‘Punching shear capacity of concrete slabs: a comparative study of various standards and recent analytical methods’, Post-
graduate Research, Swinburne University of Technology, Melbourne, Australia.
viii
ix
Declaration
This is to certify:
• This thesis contains no material which has been accepted for the award to the
candidate of any other degree or diploma, except where due reference is made in the
text.
• To the best of the candidate’s knowledge contains no material previously published or
written by another person except where due reference is made in the text of the
examinable outcome.
Fariborz Moeinaddini
June 2012
1.3 Thesis Organisation ...................................................................................................... 5
2 LITERATURE REVIEW ..................................................................................................... 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
2.4 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 ...................................... 37
2.7.1 Australian Standard AS 3600-2009 .................................................................... 37
xii
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
2.8 Summary ...................................................................................................................... 46
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
3.5 Summary ...................................................................................................................... 75
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
xiii
4.5 Summary ..................................................................................................................... 99
REINFORCEMENT ................................................................................................................. 101
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
5.5 Summary ................................................................................................................... 114
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…………… ...... ……………………………………………...………………….... 123
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 (Menétrey 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
xvi
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 2.24 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
xvii
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 Vtest/Vuo versus effective depth of slab, tensile reinforcement ratio and compressive
strength of concrete for T-P-M-0.5 ............................................................................................. 64
Figure 3.14 Vtest/Vuo versus effective depth of slab, tensile reinforcement ratio and compressive
strength of concrete for S-P-B-0.33 ............................................................................................ 65
Figure 3.15 Vtest/Vuo 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 Vtest/Vuo 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 Vtest/Vuo versus effective depth of slab, tensile reinforcement ratio and compressive
strength of concrete for NZS3101:2006 ...................................................................................... 71
xviii
Figure 3.19 Vtest/Vuo versus effective depth of slab, tensile reinforcement ratio and compressive
strength of concrete for CSA A23.3-04 ....................................................................................... 72
Figure 3.20 Vtest/Vuo versus effective depth of slab, tensile reinforcement ratio and compressive
strength of concrete for Eurocode2 and Model Code 90 ............................................................. 73
Figure 3.21 Vtest/Vuo 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, Lúcio & 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 Vtest/Vup versus σcp for three different methods of calculating Vup ............................ 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 Vtest/Vup versus σcp for AS3600-2009 ........................................................................ 96
Figure 4.13 Vtest/Vup versus σcp for AS3600-2009 when Vp is included ....................................... 96
xix
Figure 4.14 Vtest/Vup versus σcp for ACI 318-05 .......................................................................... 97
Figure 4.15 Vtest/Vup versus σcp for ACI 318-05 ignoring the limit on f’c .................................... 97
Figure 4.16 Vtest/Vup versus σcp for CSA A23.3-04 ..................................................................... 97
Figure 4.17 Vtest/Vup versus σcp for CSA A23.3-04 ignoring the limit on f’c ............................... 98
Figure 4.18 Vtest/Vup versus σcp for Eurocode2 ............................................................................ 98
Figure 4.19 Vtest/Vup versus σcp 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
xx
xxi
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 Vtest/Vuo 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 Vtest/Vuo 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 Vtest/Vuo 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 Vtest/Vuo 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, Lúcio & 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 Vtest/Vup for three different methods of calculating Vup ......... 89
Table 4.7 Average, SD and CV of Vtest/Vup for AS 3600-2009, ACI 318-04, CSA A23.3-04,
Eurocode2, and DIN 1045-1:2001 .............................................................................................. 95
Table 5.1 Vtest/Vuin for test specimens in which failure occurred inside the shear reinforced zone
.................................................................................................................................................. 109
Table 5.2 Vtest/Vuout for test specimens in which failure occurred outside the shear reinforced
zone ........................................................................................................................................... 111
xxii
Table 5.3 Average, SD and CV of Vtest/Vus 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
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 20th 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 plate
directly 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
2
Considering the flow of forces in the structure, significant biaxial bending moment and shear
force should transfer through the slab-column…
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