Two-parameter kinematic theory for punching shear in reinforced concrete slabs Von der Fakultät für Bauingenieurwesen der Rheinisch-Westfälischen Technischen Hochschule Aachen zur Erlangung des akademischen Grades eines Doktors der Ingenieurwissenschaften genehmigte Dissertation vorgelegt von Dominik Alexander Kueres Berichter: Univ.-Prof. Dr.-Ing. Josef Hegger Prof. Dr. Boyan Mihaylov Dr. Robert Vollum Tag der mündlichen Prüfung: 27.04.2018 Diese Dissertation ist auf den Internetseiten der Hochschulbibliothek online verfügbar.
Two-parameter kinematic theory for punching shear in reinforced concrete slabs
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Microsoft Word - 2018-08-02_Dissertation-Kueres_v157.docxVon der Fakultät für Bauingenieurwesen der Rheinisch-Westfälischen Technischen Hochschule Aachen zur Erlangung des akademischen Grades eines Doktors der
Ingenieurwissenschaften genehmigte Dissertation
vorgelegt von Dominik Alexander Kueres
Berichter: Univ.-Prof. Dr.-Ing. Josef Hegger Prof. Dr. Boyan Mihaylov Dr. Robert Vollum Tag der mündlichen Prüfung: 27.04.2018 Diese Dissertation ist auf den Internetseiten der Hochschulbibliothek online verfügbar.
Kurzfassung
In der vorliegenden Arbeit wird daher das Durchstanztragverhalten von Flachdecken und Fundamenten detailliert untersucht. Verformungsmessungen aus Versuchen und theore- tische Untersuchungen werden dafür genutzt, die Bruchkinematik beim Durchstanzen von Stahlbetonplatten genauer zu analysieren. Die Ergebnisse belegen, dass die Gesamtverfor- mung von gedrungenen Platten deutlich unterschätzt wird, sofern die Plattenrotation als einziger Freiheitsgrad (FG) berücksichtigt wird. Eine generellere Beschreibung des Ver- formungsverhaltens von schlanken und gedrungenen Platten ist möglich, wenn ein zweiter, translatorischer FG berücksichtigt wird. Auf Grundlage dieser Beobachtungen wird in dieser Arbeit ein kinematisches Durchstanzmodell für Stahlbetonplatten ohne Durchstanzbewehrung entwickelt. Dem Modell liegt die Annahme zugrunde, dass Querkräfte entlang des Versagensrisses durch vier Traganteile (Druckring, Rissreibung, Nachrisszugfestigkeit, Dübelwirkung) übertragen werden können. Dabei wird die Größe der Traganteile anhand der Plattenverformung unter Berücksichtigung beider FG abge- schätzt und die Durchstanztragfähigkeit als die Summe der berücksichtigten Traganteile berechnet. Die Auswertung des vorgeschlagenen Durchstanzmodells anhand von syste- matischen Versuchsserien und Datenbanken zeigt eine gute Übereinstimmung zwischen berechneten und gemessenen Durchstanzlasten. Insbesondere die Unterschiede zwischen Flachdecken und Fundamenten können durch das Modell anschaulich erklärt werden.
Im Rahmen der Arbeit werden weitere Untersuchungen durchgeführt, um die generelle Anwendbarkeit des Modells auf andere Fälle genauer zu analysieren. In diesem Zusam- menhang wird das Modell für vorgespannte Platten, Plattensysteme und durchstanzbe- wehrte Platten erweitert. Die Untersuchungen belegen, dass es möglich ist, das Modell um die günstigen Einflüsse aus Vorspannung, Systemwirkung und Durchstanzbewehrung zu erweitern. Darüber hinaus zeigen weiterführende Auswertungen eine gute Übereinstim- mung zwischen Vorhersagen und Versuchsergebnissen.
Abstract
As a consequence of the dangerous nature of punching failures, the punching shear behavior of reinforced concrete slabs has been in the focus of research for more than 100 years. Due to the complex interaction between bending moments and shear forces in the vicinity of slab-column connections, most of the earlier punching shear resistance models were derived in a “semi-empirical” manner by regressional analysis of the available test data. Subsequently, more general models with different theoretical backgrounds have been developed. For example, models based on kinematic failure mechanisms have been found to be in good accordance with punching tests on slender slabs. The existing kinematic models generally determine the punching strength based on suitable failure criteria relating punching failure to a certain slab rotation. Hence, slab deformations are assumed to occur as a result of flexural deformations only. Yet, measurements taken from recent punching tests with varying slenderness reveal differences between fracture kinematics of slender slabs (e.g. flat slabs) and compact slabs (e.g. column bases). In this context, the deformation behavior of compact slabs is rather dominated by translational deformations. Consequently, a general application of the existing models to both slender and compact slabs might yield inconsistent results.
In the present thesis, the punching shear behavior of reinforced concrete flat slabs and column bases is investigated in detail. Based on measurements and theoretical investiga- tions, the fracture kinematics of slabs failing in punching are analyzed. The investigations verify that the total deformation of compact slabs at punching failure is significantly underestimated by considering the slab rotation as single degree of freedom (DOF). A more general description of the deformation behavior of both slender and compact slabs is possible by introducing a second DOF considering translational deformations. Based on the aforementioned observations, a two-parameter kinematic theory for punching shear in reinforced concrete slabs without shear reinforcement is developed. In the theory, it is assumed that shear forces are transmitted along the failure crack by four shear contribu- tions, namely the contributions of compression ring, aggregate interlock, residual tensile stresses, and dowel action. The magnitude of shear contributions is estimated based on the deformed slab accounting for both DOFs. Subsequently, the punching strength is calculated by summation of the contributions. The evaluation of the proposed theory by means of systematic test series and databanks yields good agreement between predictions and experimental results. Especially, the differences between flat slabs and column bases can be explained in a consistent manner by the theory.
To investigate the generality of the proposed two-parameter kinematic theory, further investigations are carried out to extend the theory to other cases, such as prestressed slabs, continuous slabs, and shear-reinforced slabs. The investigations verify that it is possible to account for the beneficial effects of prestressing, slab continuity, and shear reinforce- ment on punching strength by means of the proposed kinematic theory. Moreover, good accordance between predictions and results of punching tests investigating the aforemen- tioned influences is found.
Preface and acknowledgements
This dissertation was written during my time as a research associate at the Institute of Structural Concrete at RWTH Aachen University. Several research projects funded by the German Research Foundation (Deutsche Forschungsgemeinschaft: DFG), the German Committee for Reinforced Concrete (Deutscher Ausschuss für Stahlbeton: DAfStb), and the Initiative PRB (Initiative Praxisgerechte Regelwerke im Bauwesen e.V.: PRB) motivated me to work on the problem of punching shear in reinforced concrete slabs. I am sincerely grateful for the support received. Moreover, I am appreciative of the opportunity to work as an assistant to the convener Univ.-Prof. Dr.-Ing. Josef Hegger of the European task group CEN/TC 250/SC 2/WG 1/TG 4, which prepared the basis for the shear, punching shear, and torsion design provisions of the second generation of Eurocode 2. The interesting presentations and discussions among the experts in the task group particularly helped me to extend my knowledge in the field.
I especially want to thank the supervisor of my doctoral thesis, Univ.-Prof. Dr.-Ing. Josef Hegger, head of the Institute of Structural Concrete at RWTH Aachen University, for the opportunity to be part of his research group. I am sincerely grateful for his encouragement, advice and inspiration throughout the last years, which significantly contributed to the success of my work. I also want to thank the members of my thesis jury, namely Prof. Dr. Boyan Mihaylov (University of Liège, Belgium) and Dr. Robert Vollum (Imperial College London, UK), for their engagement and their thourough review of my thesis. The role of Univ.-Prof. Dr.-Ing. habil. Marcus Oeser (RWTH Aachen University) as the president of the jury is also gratefully acknowledged.
The success of this thesis is also a product of the creative exchange and mutual motivation among my friends and colleagues at the Institute of Structural Concrete at RWTH Aachen University. I am truly grateful for the friendships gained during my time at the institute. In addition, I want to acknowledge the support and the friendly cooperation of the laboratory staff during the experimental investigations presented in this thesis. I also want to thank all my student assistants as well as bachelor and master students for their assistance.
Finally, I want to express my deepest gratitude to my family, in particular to my parents for raising me and providing me with an education. Their unconditional support and encouragement enabled my academic career and allowed me to achieve this important milestone. Last, but most importantely, I want to thank my wife Sophia for always having my back and supporting me. Without her patience and motivation throughout the last years, the success of my work would not have been possible. I feel indescribably happy to have her in my life.
Aachen, August 2018 Dominik Kueres
I
1.2 Objectives and contents of this thesis .............................................................. 2
2 State of the art on punching shear resistance models ......................................... 5
2.1 General ............................................................................................................. 5
2.2 Failure modes of reinforced concrete slabs under concentrated loads ............ 5
2.3 Shear transfer actions in reinforced concrete slabs under concentrated loads . 6
2.4 Overview of punching shear resistance models for reinforced concrete slabs 7
2.4.1 General .................................................................................................. 7
2.4.3 Models based on fracture mechanics .................................................. 14
2.4.4 Models based on the theory of plasticity ............................................ 17
2.4.5 Models based on kinematic failure mechanisms ................................ 19
2.5 Summary and conclusions ............................................................................. 26
3 Development of a novel punching shear reinforcement for column bases ...... 27
3.1 General ........................................................................................................... 27
3.2.1 General ................................................................................................ 27
3.2.2 Geometry of the novel punching shear reinforcement element .......... 28
3.3 Experimental investigations ........................................................................... 29
3.3.4 Test setup and measurements .............................................................. 33
3.3.5 Test procedure ..................................................................................... 35
3.4 Experimental results ....................................................................................... 36
3.4.5 Failure characteristics .......................................................................... 43
3.5.1 General ................................................................................................ 47
3.6 Summary and conclusions .............................................................................. 49
4 Fracture kinematics of reinforced concrete slabs failing in punching ............. 51
4.1 General ........................................................................................................... 51
4.2.1 General ................................................................................................ 52
4.2.3 Evaluation of location of center of rotation ........................................ 56
4.2.4 Discussion of results ............................................................................ 60
4.3 Two-parameter kinematic model for reinforced concrete slabs failing in punching ......................................................................................................... 61
4.3.1 General ................................................................................................ 61
4.3.4 Discussion of results ............................................................................ 66
4.4 Summary and conclusions .............................................................................. 67
5 Two-parameter kinematic theory for punching shear in reinforced concrete slabs without shear reinforcement ....................................................... 69
5.1 General ........................................................................................................... 69
5.2.1 General ................................................................................................ 70
5.2.4 Contribution of residual tensile stresses .............................................. 79
5.2.5 Contribution of dowel action............................................................... 81
5.3.3 Determination of punching shear resistance ....................................... 84
5.4 Inclination of critical shear crack ................................................................... 87
5.5 Evaluation of kinematic theory ...................................................................... 89
5.5.1 General ................................................................................................ 89
5.5.3 Evaluation of databanks ...................................................................... 93
5.6 Summary and conclusions ............................................................................. 97
6 Application of the two-parameter kinematic theory to prestressed concrete slabs......................................................................................................... 99
6.1 General ........................................................................................................... 99
6.2 Consideration of effects of prestressing on punching strength ...................... 99
6.2.1 General ................................................................................................ 99
6.2.4 Effect of vertical component of prestress forces ............................... 108
6.3 Evaluation of kinematic theory .................................................................... 112
6.3.1 General .............................................................................................. 112
6.3.3 Evaluation of databanks .................................................................... 114
6.4 Summary and conclusions ........................................................................... 116
7 Application of the two-parameter kinematic theory to continuous concrete slabs....................................................................................................... 119
7.1 General ......................................................................................................... 119
7.2 Consideration of effects of slab continuity on punching strength ............... 119
7.2.1 General .............................................................................................. 119
7.2.3 Consideration of effects of slab continuity ....................................... 124
7.3 Evaluation of kinematic theory .................................................................... 127
7.3.1 General .............................................................................................. 127
7.3.3 Parametric studies ............................................................................. 131
8 Application of the two-parameter kinematic theory to shear-reinforced concrete slabs ....................................................................................................... 135
8.1 General ......................................................................................................... 135
8.2 Consideration of effects of shear reinforcement on punching strength ....... 136
8.2.1 General .............................................................................................. 136
8.2.3 Maximum punching shear capacity................................................... 146
8.4 Evaluation of kinematic theory .................................................................... 152
8.4.1 General .............................................................................................. 152
8.4.3 Parametric studies ............................................................................. 154
8.5 Future research ............................................................................................. 157
9.1 General ......................................................................................................... 161
9.2 Summary ...................................................................................................... 161
V
Appendices
Appendix A Two-parameter kinematic theory describing the shear behavior of deep beams .................................................................. A-1
Appendix B Failure criterion for concrete under multiaxial states of stress ................................................................................................. B-1
Appendix C Theoretical model describing the mechanism of aggregate interlock in cracks ........................................................................... C-1
Appendix D Solution procedure of the two-parameter kinematic theory for punching shear without shear reinforcement ........................ D-1
Appendix E Databank on punching tests on reinforced concrete slabs without shear reinforcement .......................................................... E-1
Appendix F Databank on punching tests on prestressed concrete slabs without shear reinforcement .......................................................... F-1
Appendix G Theoretical model describing the effects of slab continuity on punching strength ..................................................................... G-1
Appendix H Theoretical model describing the activation of the shear reinforcement ................................................................................. H-1
Appendix I Solution procedure of the two-parameter kinematic theory for punching shear with shear reinforcement ............................... I-1
VII
Notation
The following list contains relevant units and symbols used within this thesis. Symbols, which are not contained in this list are explained in the corresponding chapter.
Units:
Force: N, kN, MN Moment: kNm, MNm Stress: N/mm², MN/m², MPa Strain: %, ‰ Distance: mm, cm, m Area: mm², cm², m² Angle: rad, °
Abbreviations:
2PKT Two-Parameter Kinematic Theory ACI Amercian Concrete Institute ASCE Amercian Society of Civil Engineers CEB Comité Euro-International du Béton CEN Comité Européen de Normalisation CMA compressive membrane action COV coefficient of variation CR center of rotation CSCT Critical Shear Crack Theory DAfStb Deutscher Ausschuss für Stahlbeton DFG Deutsche Forschungsgemeinschaft DIBt Deutsches Institut für Bautechnik DIN Deutsches Institut für Normung DOF degree of freedom EC Eurocode FIB Fédération Internationale du Béton FIP Fédération Internationale de la Précontrainte ICR instantaneous center of rotation LVDT linear variable differential transformer MC Model Code NLFEA nonlinear finite element analysis PRB Initiative Praxisgerechte Regelwerke im Bauwesen e.V. PTFE polytetrafluoroethylene
Latin upper-case letters:
Asw cross-sectional area of shear reinforcement Ax projection of area of contact in x-direction
VIII
Ay projection of area of contact in y-direction Dmax maximum aggregate size Ec Young’s modulus of concrete Es Young’s modulus of flexural reinforcement Esw Young’s modulus of shear reinforcement Fc force in compression zone Fs force in flexural reinforcement Fx resulting contact force in x-direction Fy resulting contact force in y-direction F,ai resulting normal force from aggregate interlock F,rt resulting normal force from residual tensile stresses
F,ai resulting tangential force from aggregate interlock Gf fracture energy
K anchorage stiffness Kred reduced anchorage stiffness M moment Pt prestress force Up deviation force V shear force Vai contribution of aggregate interlock Vc contribution of concrete Vcalc predicted punching strength Vcr contribution of compression ring Vda contribution of dowel action Vflex shear force associated with flexural capacity of a slab Vm shear force derived from moment equilibrium Vp vertical component of prestress force
Vrt contribution of residual tensile stresses VR punching strength VR,c punching strength without shear reinforcement; contribution of concrete VR,c+s punching strength inside the shear-reinforced zone VR,gov governing punching strength VR,max maximum punching strength VR,out punching strength outside the shear-reinforced zone VR,s contribution of shear reinforcement Vs contribution of shear reinforcement Vtest failure load from punching test Vv shear force derived from vertical equilibrium Vx sample COV
Latin lower-case letters:
ai distance i between control perimeter and edge of loaded area as amount of flexural reinforcement per unit length
IX
ax projection of line of contact in x-direction ay projection of line of contact in y-direction a shear span
b width; slab dimension
c column dimension d effective depth ddg factor accounting for influence of maximum aggregate size dg maximum aggregate size
dg0 reference size
e eccentricity
fc concrete compressive strength
fct concrete tensile strength
fR relative rib area
ft tensile strength of flexural reinforcement
ftw tensile strength of shear reinforcement
fy yield strength of flexural reinforcement fyw yield strength of shear reinforcement
h slab depth hc,ef effective concrete depth l length; slab dimension lk length over which t develops lt length over which t,avg is averaged mp average decompression moment m’p effective decompression moment mr radial moment mt tangential moment nr radial forces nt tangential forces ntang number of shear reinforcement elements in each perimeter pk ratio of volume of aggregate particles and volume of concrete q surface load r radius rc column radius rcr horizontal length of compression ring rpc radius of punching cone rq radius of moment contraflexure rs slab radius s tangential crack opening; spacing of flexural reinforcement bars
X
s0 radial distance between column edge and first perimeter of shear reinforcement; distance between tendons s1 radial distance between different perimeters of shear reinforcement; crack slip associated with translational DOF t; distance between tendons scr average spacing of flexural cracks sr radial spacing of perimeters of shear reinforcement ssw crack opening perpendicular to shear reinforcement ssw,0 crack opening associated with flexural DOF t,avg
ssw,1 crack opening associated with translational DOF t st tangential spacing of shear reinforcement elements in each perimeter u perimeter u0 perimeter of loaded area uedge lateral expansion of slab ui control perimeter in a distance i from the edge of the loaded area un net perimeter on the level of the flexural reinforcement uout control perimeter outside the shear-reinforced zone up deviation stress v shear force per unit length vc normalized failure load (punching strength without shear reinforcement) vmax normalized failure load (maximum punching strength)
w normal crack opening; vertical deflection w0 crack width associated with flexural DOF t,avg w1 crack width associated with translational DOF t wc critical crack opening at which tensile stresses no longer can be transmitted wflex flexural crack width wr,flex radial crack width
wsw crack opening parallel to shear reinforcement wsw,0 crack opening associated with flexural DOF t,avg
wsw,1 crack opening associated with translational DOF t x depth of compression zone xm sample mean z inner lever arm
Greek letters:
angle between shear reinforcement and plane of slab; inclination of shear crack c factor describing the concrete contribution in shear-reinforced slabs e ratio of Young’s modulus of flexural reinforcement and concrete max increase factor accounting for efficiency of various shear reinforcement systems p,i ratio of effective and average decompression moment s factor describing the shear reinforcement contribution in shear-reinforced slabs t inclination of tendon r radial curvature t tangential curvature
XI
c column penetration f flexural deformation h horizontal deformation s shear deformation sw anchorage slip t translational deformation (DOF of kinematic theory) total total vertical deformation strain c strain in concrete c,0 tensile cracking strain of concrete r radial strain s strain in flexural reinforcement t tangential strain t,avg average strain in flexural reinforcement (DOF of kinematic theory) direction of principle stresses 0 factor accounting for effect of superimposed flexure on punching strength normalized in-plane force c factor accounting for brittle behavior of concrete factor accounting for presence of transverse strains in concrete f factor accounting for rib geometry of deformed bars friction coefficient; factor accounting for shear forces and bending moments factor accounting for strength reduction of concrete struts in cracked concrete l flexural reinforcement ratio l,hog hogging reinforcement ratio l,sag sagging reinforcement ratio sw shear reinforcement ratio normal stress 1 principle stress 2 principle stress 3 principle stress ai normal stress resulting from aggregate interlock c stress in concrete g ground pressure n,r radial stress (compression negative) p average in-plane stress (compression negative) pu normal stress at projected contact line rt normal stress resulting from residual tensile stresses s stress in flexural reinforcement sw stress in shear reinforcement x horizontal stress z vertical stress shear stress ai shear stress resulting from aggregate interlock
XII
b bond stress b,red reduced bond stress pu tangential stress at projected contact line R punching strength R,c punching strength without shear reinforcement; contribution of concrete R,c+s punching strength inside the shear-reinforced zone R,gov governing punching strength R,max maximum punching strength R,out punching strength outside the shear-reinforced zone R,s contribution of shear reinforcement mechanical reinforcement ratio normalized depth of compression zone d factor accounting for size effects u factor accounting for column size factor accounting for column perimeter-depth ratio and shear span-depth ratio slab rotation R maximum rotation at punching failure R,c+s maximum rotation associated with a failure inside the shear-reinforced zone R,max maximum rotation associated with a maximum punching strength failure R,out maximum rotation associated with a failure outside the shear-reinforced zone
Other symbols:
Ø diameter; diameter of flexural reinforcement Øb inside bend diameter Øsw diameter of shear reinforcement
1
1 Introduction
1.1 Motivation
Reinforced concrete slabs subjected to concentrated loads, such as flat slabs, footings, or ground slabs, usually exhibit high concentrations of bending moments and shear forces at the intersection between slab and column. As a result, the capacity of slab- column connections is governed by either flexural or shear strength in most cases. In this context, the local shear failure, which may occur in the vicinity of slab-column connections, is usually referred to as “punching failure” in the literature. Punching failure is characterized as a very brittle failure mode if no shear reinforcement is pro- vided. Hence, punching occurs without prior notice and after small deformations. If no collapse reinforcement is applied, punching failure of a single slab-column connection may even trigger a progressive collapse of the whole structure.
As a result of the dangerous nature of punching failures, punching shear behavior of reinforced concrete slabs has been in the focus of research…
Ingenieurwissenschaften genehmigte Dissertation
vorgelegt von Dominik Alexander Kueres
Berichter: Univ.-Prof. Dr.-Ing. Josef Hegger Prof. Dr. Boyan Mihaylov Dr. Robert Vollum Tag der mündlichen Prüfung: 27.04.2018 Diese Dissertation ist auf den Internetseiten der Hochschulbibliothek online verfügbar.
Kurzfassung
In der vorliegenden Arbeit wird daher das Durchstanztragverhalten von Flachdecken und Fundamenten detailliert untersucht. Verformungsmessungen aus Versuchen und theore- tische Untersuchungen werden dafür genutzt, die Bruchkinematik beim Durchstanzen von Stahlbetonplatten genauer zu analysieren. Die Ergebnisse belegen, dass die Gesamtverfor- mung von gedrungenen Platten deutlich unterschätzt wird, sofern die Plattenrotation als einziger Freiheitsgrad (FG) berücksichtigt wird. Eine generellere Beschreibung des Ver- formungsverhaltens von schlanken und gedrungenen Platten ist möglich, wenn ein zweiter, translatorischer FG berücksichtigt wird. Auf Grundlage dieser Beobachtungen wird in dieser Arbeit ein kinematisches Durchstanzmodell für Stahlbetonplatten ohne Durchstanzbewehrung entwickelt. Dem Modell liegt die Annahme zugrunde, dass Querkräfte entlang des Versagensrisses durch vier Traganteile (Druckring, Rissreibung, Nachrisszugfestigkeit, Dübelwirkung) übertragen werden können. Dabei wird die Größe der Traganteile anhand der Plattenverformung unter Berücksichtigung beider FG abge- schätzt und die Durchstanztragfähigkeit als die Summe der berücksichtigten Traganteile berechnet. Die Auswertung des vorgeschlagenen Durchstanzmodells anhand von syste- matischen Versuchsserien und Datenbanken zeigt eine gute Übereinstimmung zwischen berechneten und gemessenen Durchstanzlasten. Insbesondere die Unterschiede zwischen Flachdecken und Fundamenten können durch das Modell anschaulich erklärt werden.
Im Rahmen der Arbeit werden weitere Untersuchungen durchgeführt, um die generelle Anwendbarkeit des Modells auf andere Fälle genauer zu analysieren. In diesem Zusam- menhang wird das Modell für vorgespannte Platten, Plattensysteme und durchstanzbe- wehrte Platten erweitert. Die Untersuchungen belegen, dass es möglich ist, das Modell um die günstigen Einflüsse aus Vorspannung, Systemwirkung und Durchstanzbewehrung zu erweitern. Darüber hinaus zeigen weiterführende Auswertungen eine gute Übereinstim- mung zwischen Vorhersagen und Versuchsergebnissen.
Abstract
As a consequence of the dangerous nature of punching failures, the punching shear behavior of reinforced concrete slabs has been in the focus of research for more than 100 years. Due to the complex interaction between bending moments and shear forces in the vicinity of slab-column connections, most of the earlier punching shear resistance models were derived in a “semi-empirical” manner by regressional analysis of the available test data. Subsequently, more general models with different theoretical backgrounds have been developed. For example, models based on kinematic failure mechanisms have been found to be in good accordance with punching tests on slender slabs. The existing kinematic models generally determine the punching strength based on suitable failure criteria relating punching failure to a certain slab rotation. Hence, slab deformations are assumed to occur as a result of flexural deformations only. Yet, measurements taken from recent punching tests with varying slenderness reveal differences between fracture kinematics of slender slabs (e.g. flat slabs) and compact slabs (e.g. column bases). In this context, the deformation behavior of compact slabs is rather dominated by translational deformations. Consequently, a general application of the existing models to both slender and compact slabs might yield inconsistent results.
In the present thesis, the punching shear behavior of reinforced concrete flat slabs and column bases is investigated in detail. Based on measurements and theoretical investiga- tions, the fracture kinematics of slabs failing in punching are analyzed. The investigations verify that the total deformation of compact slabs at punching failure is significantly underestimated by considering the slab rotation as single degree of freedom (DOF). A more general description of the deformation behavior of both slender and compact slabs is possible by introducing a second DOF considering translational deformations. Based on the aforementioned observations, a two-parameter kinematic theory for punching shear in reinforced concrete slabs without shear reinforcement is developed. In the theory, it is assumed that shear forces are transmitted along the failure crack by four shear contribu- tions, namely the contributions of compression ring, aggregate interlock, residual tensile stresses, and dowel action. The magnitude of shear contributions is estimated based on the deformed slab accounting for both DOFs. Subsequently, the punching strength is calculated by summation of the contributions. The evaluation of the proposed theory by means of systematic test series and databanks yields good agreement between predictions and experimental results. Especially, the differences between flat slabs and column bases can be explained in a consistent manner by the theory.
To investigate the generality of the proposed two-parameter kinematic theory, further investigations are carried out to extend the theory to other cases, such as prestressed slabs, continuous slabs, and shear-reinforced slabs. The investigations verify that it is possible to account for the beneficial effects of prestressing, slab continuity, and shear reinforce- ment on punching strength by means of the proposed kinematic theory. Moreover, good accordance between predictions and results of punching tests investigating the aforemen- tioned influences is found.
Preface and acknowledgements
This dissertation was written during my time as a research associate at the Institute of Structural Concrete at RWTH Aachen University. Several research projects funded by the German Research Foundation (Deutsche Forschungsgemeinschaft: DFG), the German Committee for Reinforced Concrete (Deutscher Ausschuss für Stahlbeton: DAfStb), and the Initiative PRB (Initiative Praxisgerechte Regelwerke im Bauwesen e.V.: PRB) motivated me to work on the problem of punching shear in reinforced concrete slabs. I am sincerely grateful for the support received. Moreover, I am appreciative of the opportunity to work as an assistant to the convener Univ.-Prof. Dr.-Ing. Josef Hegger of the European task group CEN/TC 250/SC 2/WG 1/TG 4, which prepared the basis for the shear, punching shear, and torsion design provisions of the second generation of Eurocode 2. The interesting presentations and discussions among the experts in the task group particularly helped me to extend my knowledge in the field.
I especially want to thank the supervisor of my doctoral thesis, Univ.-Prof. Dr.-Ing. Josef Hegger, head of the Institute of Structural Concrete at RWTH Aachen University, for the opportunity to be part of his research group. I am sincerely grateful for his encouragement, advice and inspiration throughout the last years, which significantly contributed to the success of my work. I also want to thank the members of my thesis jury, namely Prof. Dr. Boyan Mihaylov (University of Liège, Belgium) and Dr. Robert Vollum (Imperial College London, UK), for their engagement and their thourough review of my thesis. The role of Univ.-Prof. Dr.-Ing. habil. Marcus Oeser (RWTH Aachen University) as the president of the jury is also gratefully acknowledged.
The success of this thesis is also a product of the creative exchange and mutual motivation among my friends and colleagues at the Institute of Structural Concrete at RWTH Aachen University. I am truly grateful for the friendships gained during my time at the institute. In addition, I want to acknowledge the support and the friendly cooperation of the laboratory staff during the experimental investigations presented in this thesis. I also want to thank all my student assistants as well as bachelor and master students for their assistance.
Finally, I want to express my deepest gratitude to my family, in particular to my parents for raising me and providing me with an education. Their unconditional support and encouragement enabled my academic career and allowed me to achieve this important milestone. Last, but most importantely, I want to thank my wife Sophia for always having my back and supporting me. Without her patience and motivation throughout the last years, the success of my work would not have been possible. I feel indescribably happy to have her in my life.
Aachen, August 2018 Dominik Kueres
I
1.2 Objectives and contents of this thesis .............................................................. 2
2 State of the art on punching shear resistance models ......................................... 5
2.1 General ............................................................................................................. 5
2.2 Failure modes of reinforced concrete slabs under concentrated loads ............ 5
2.3 Shear transfer actions in reinforced concrete slabs under concentrated loads . 6
2.4 Overview of punching shear resistance models for reinforced concrete slabs 7
2.4.1 General .................................................................................................. 7
2.4.3 Models based on fracture mechanics .................................................. 14
2.4.4 Models based on the theory of plasticity ............................................ 17
2.4.5 Models based on kinematic failure mechanisms ................................ 19
2.5 Summary and conclusions ............................................................................. 26
3 Development of a novel punching shear reinforcement for column bases ...... 27
3.1 General ........................................................................................................... 27
3.2.1 General ................................................................................................ 27
3.2.2 Geometry of the novel punching shear reinforcement element .......... 28
3.3 Experimental investigations ........................................................................... 29
3.3.4 Test setup and measurements .............................................................. 33
3.3.5 Test procedure ..................................................................................... 35
3.4 Experimental results ....................................................................................... 36
3.4.5 Failure characteristics .......................................................................... 43
3.5.1 General ................................................................................................ 47
3.6 Summary and conclusions .............................................................................. 49
4 Fracture kinematics of reinforced concrete slabs failing in punching ............. 51
4.1 General ........................................................................................................... 51
4.2.1 General ................................................................................................ 52
4.2.3 Evaluation of location of center of rotation ........................................ 56
4.2.4 Discussion of results ............................................................................ 60
4.3 Two-parameter kinematic model for reinforced concrete slabs failing in punching ......................................................................................................... 61
4.3.1 General ................................................................................................ 61
4.3.4 Discussion of results ............................................................................ 66
4.4 Summary and conclusions .............................................................................. 67
5 Two-parameter kinematic theory for punching shear in reinforced concrete slabs without shear reinforcement ....................................................... 69
5.1 General ........................................................................................................... 69
5.2.1 General ................................................................................................ 70
5.2.4 Contribution of residual tensile stresses .............................................. 79
5.2.5 Contribution of dowel action............................................................... 81
5.3.3 Determination of punching shear resistance ....................................... 84
5.4 Inclination of critical shear crack ................................................................... 87
5.5 Evaluation of kinematic theory ...................................................................... 89
5.5.1 General ................................................................................................ 89
5.5.3 Evaluation of databanks ...................................................................... 93
5.6 Summary and conclusions ............................................................................. 97
6 Application of the two-parameter kinematic theory to prestressed concrete slabs......................................................................................................... 99
6.1 General ........................................................................................................... 99
6.2 Consideration of effects of prestressing on punching strength ...................... 99
6.2.1 General ................................................................................................ 99
6.2.4 Effect of vertical component of prestress forces ............................... 108
6.3 Evaluation of kinematic theory .................................................................... 112
6.3.1 General .............................................................................................. 112
6.3.3 Evaluation of databanks .................................................................... 114
6.4 Summary and conclusions ........................................................................... 116
7 Application of the two-parameter kinematic theory to continuous concrete slabs....................................................................................................... 119
7.1 General ......................................................................................................... 119
7.2 Consideration of effects of slab continuity on punching strength ............... 119
7.2.1 General .............................................................................................. 119
7.2.3 Consideration of effects of slab continuity ....................................... 124
7.3 Evaluation of kinematic theory .................................................................... 127
7.3.1 General .............................................................................................. 127
7.3.3 Parametric studies ............................................................................. 131
8 Application of the two-parameter kinematic theory to shear-reinforced concrete slabs ....................................................................................................... 135
8.1 General ......................................................................................................... 135
8.2 Consideration of effects of shear reinforcement on punching strength ....... 136
8.2.1 General .............................................................................................. 136
8.2.3 Maximum punching shear capacity................................................... 146
8.4 Evaluation of kinematic theory .................................................................... 152
8.4.1 General .............................................................................................. 152
8.4.3 Parametric studies ............................................................................. 154
8.5 Future research ............................................................................................. 157
9.1 General ......................................................................................................... 161
9.2 Summary ...................................................................................................... 161
V
Appendices
Appendix A Two-parameter kinematic theory describing the shear behavior of deep beams .................................................................. A-1
Appendix B Failure criterion for concrete under multiaxial states of stress ................................................................................................. B-1
Appendix C Theoretical model describing the mechanism of aggregate interlock in cracks ........................................................................... C-1
Appendix D Solution procedure of the two-parameter kinematic theory for punching shear without shear reinforcement ........................ D-1
Appendix E Databank on punching tests on reinforced concrete slabs without shear reinforcement .......................................................... E-1
Appendix F Databank on punching tests on prestressed concrete slabs without shear reinforcement .......................................................... F-1
Appendix G Theoretical model describing the effects of slab continuity on punching strength ..................................................................... G-1
Appendix H Theoretical model describing the activation of the shear reinforcement ................................................................................. H-1
Appendix I Solution procedure of the two-parameter kinematic theory for punching shear with shear reinforcement ............................... I-1
VII
Notation
The following list contains relevant units and symbols used within this thesis. Symbols, which are not contained in this list are explained in the corresponding chapter.
Units:
Force: N, kN, MN Moment: kNm, MNm Stress: N/mm², MN/m², MPa Strain: %, ‰ Distance: mm, cm, m Area: mm², cm², m² Angle: rad, °
Abbreviations:
2PKT Two-Parameter Kinematic Theory ACI Amercian Concrete Institute ASCE Amercian Society of Civil Engineers CEB Comité Euro-International du Béton CEN Comité Européen de Normalisation CMA compressive membrane action COV coefficient of variation CR center of rotation CSCT Critical Shear Crack Theory DAfStb Deutscher Ausschuss für Stahlbeton DFG Deutsche Forschungsgemeinschaft DIBt Deutsches Institut für Bautechnik DIN Deutsches Institut für Normung DOF degree of freedom EC Eurocode FIB Fédération Internationale du Béton FIP Fédération Internationale de la Précontrainte ICR instantaneous center of rotation LVDT linear variable differential transformer MC Model Code NLFEA nonlinear finite element analysis PRB Initiative Praxisgerechte Regelwerke im Bauwesen e.V. PTFE polytetrafluoroethylene
Latin upper-case letters:
Asw cross-sectional area of shear reinforcement Ax projection of area of contact in x-direction
VIII
Ay projection of area of contact in y-direction Dmax maximum aggregate size Ec Young’s modulus of concrete Es Young’s modulus of flexural reinforcement Esw Young’s modulus of shear reinforcement Fc force in compression zone Fs force in flexural reinforcement Fx resulting contact force in x-direction Fy resulting contact force in y-direction F,ai resulting normal force from aggregate interlock F,rt resulting normal force from residual tensile stresses
F,ai resulting tangential force from aggregate interlock Gf fracture energy
K anchorage stiffness Kred reduced anchorage stiffness M moment Pt prestress force Up deviation force V shear force Vai contribution of aggregate interlock Vc contribution of concrete Vcalc predicted punching strength Vcr contribution of compression ring Vda contribution of dowel action Vflex shear force associated with flexural capacity of a slab Vm shear force derived from moment equilibrium Vp vertical component of prestress force
Vrt contribution of residual tensile stresses VR punching strength VR,c punching strength without shear reinforcement; contribution of concrete VR,c+s punching strength inside the shear-reinforced zone VR,gov governing punching strength VR,max maximum punching strength VR,out punching strength outside the shear-reinforced zone VR,s contribution of shear reinforcement Vs contribution of shear reinforcement Vtest failure load from punching test Vv shear force derived from vertical equilibrium Vx sample COV
Latin lower-case letters:
ai distance i between control perimeter and edge of loaded area as amount of flexural reinforcement per unit length
IX
ax projection of line of contact in x-direction ay projection of line of contact in y-direction a shear span
b width; slab dimension
c column dimension d effective depth ddg factor accounting for influence of maximum aggregate size dg maximum aggregate size
dg0 reference size
e eccentricity
fc concrete compressive strength
fct concrete tensile strength
fR relative rib area
ft tensile strength of flexural reinforcement
ftw tensile strength of shear reinforcement
fy yield strength of flexural reinforcement fyw yield strength of shear reinforcement
h slab depth hc,ef effective concrete depth l length; slab dimension lk length over which t develops lt length over which t,avg is averaged mp average decompression moment m’p effective decompression moment mr radial moment mt tangential moment nr radial forces nt tangential forces ntang number of shear reinforcement elements in each perimeter pk ratio of volume of aggregate particles and volume of concrete q surface load r radius rc column radius rcr horizontal length of compression ring rpc radius of punching cone rq radius of moment contraflexure rs slab radius s tangential crack opening; spacing of flexural reinforcement bars
X
s0 radial distance between column edge and first perimeter of shear reinforcement; distance between tendons s1 radial distance between different perimeters of shear reinforcement; crack slip associated with translational DOF t; distance between tendons scr average spacing of flexural cracks sr radial spacing of perimeters of shear reinforcement ssw crack opening perpendicular to shear reinforcement ssw,0 crack opening associated with flexural DOF t,avg
ssw,1 crack opening associated with translational DOF t st tangential spacing of shear reinforcement elements in each perimeter u perimeter u0 perimeter of loaded area uedge lateral expansion of slab ui control perimeter in a distance i from the edge of the loaded area un net perimeter on the level of the flexural reinforcement uout control perimeter outside the shear-reinforced zone up deviation stress v shear force per unit length vc normalized failure load (punching strength without shear reinforcement) vmax normalized failure load (maximum punching strength)
w normal crack opening; vertical deflection w0 crack width associated with flexural DOF t,avg w1 crack width associated with translational DOF t wc critical crack opening at which tensile stresses no longer can be transmitted wflex flexural crack width wr,flex radial crack width
wsw crack opening parallel to shear reinforcement wsw,0 crack opening associated with flexural DOF t,avg
wsw,1 crack opening associated with translational DOF t x depth of compression zone xm sample mean z inner lever arm
Greek letters:
angle between shear reinforcement and plane of slab; inclination of shear crack c factor describing the concrete contribution in shear-reinforced slabs e ratio of Young’s modulus of flexural reinforcement and concrete max increase factor accounting for efficiency of various shear reinforcement systems p,i ratio of effective and average decompression moment s factor describing the shear reinforcement contribution in shear-reinforced slabs t inclination of tendon r radial curvature t tangential curvature
XI
c column penetration f flexural deformation h horizontal deformation s shear deformation sw anchorage slip t translational deformation (DOF of kinematic theory) total total vertical deformation strain c strain in concrete c,0 tensile cracking strain of concrete r radial strain s strain in flexural reinforcement t tangential strain t,avg average strain in flexural reinforcement (DOF of kinematic theory) direction of principle stresses 0 factor accounting for effect of superimposed flexure on punching strength normalized in-plane force c factor accounting for brittle behavior of concrete factor accounting for presence of transverse strains in concrete f factor accounting for rib geometry of deformed bars friction coefficient; factor accounting for shear forces and bending moments factor accounting for strength reduction of concrete struts in cracked concrete l flexural reinforcement ratio l,hog hogging reinforcement ratio l,sag sagging reinforcement ratio sw shear reinforcement ratio normal stress 1 principle stress 2 principle stress 3 principle stress ai normal stress resulting from aggregate interlock c stress in concrete g ground pressure n,r radial stress (compression negative) p average in-plane stress (compression negative) pu normal stress at projected contact line rt normal stress resulting from residual tensile stresses s stress in flexural reinforcement sw stress in shear reinforcement x horizontal stress z vertical stress shear stress ai shear stress resulting from aggregate interlock
XII
b bond stress b,red reduced bond stress pu tangential stress at projected contact line R punching strength R,c punching strength without shear reinforcement; contribution of concrete R,c+s punching strength inside the shear-reinforced zone R,gov governing punching strength R,max maximum punching strength R,out punching strength outside the shear-reinforced zone R,s contribution of shear reinforcement mechanical reinforcement ratio normalized depth of compression zone d factor accounting for size effects u factor accounting for column size factor accounting for column perimeter-depth ratio and shear span-depth ratio slab rotation R maximum rotation at punching failure R,c+s maximum rotation associated with a failure inside the shear-reinforced zone R,max maximum rotation associated with a maximum punching strength failure R,out maximum rotation associated with a failure outside the shear-reinforced zone
Other symbols:
Ø diameter; diameter of flexural reinforcement Øb inside bend diameter Øsw diameter of shear reinforcement
1
1 Introduction
1.1 Motivation
Reinforced concrete slabs subjected to concentrated loads, such as flat slabs, footings, or ground slabs, usually exhibit high concentrations of bending moments and shear forces at the intersection between slab and column. As a result, the capacity of slab- column connections is governed by either flexural or shear strength in most cases. In this context, the local shear failure, which may occur in the vicinity of slab-column connections, is usually referred to as “punching failure” in the literature. Punching failure is characterized as a very brittle failure mode if no shear reinforcement is pro- vided. Hence, punching occurs without prior notice and after small deformations. If no collapse reinforcement is applied, punching failure of a single slab-column connection may even trigger a progressive collapse of the whole structure.
As a result of the dangerous nature of punching failures, punching shear behavior of reinforced concrete slabs has been in the focus of research…
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