NUMERICAL MODELLING OF SLAB-COLUMN JOINT OF RC FLAT PLATES by MOHAMMAD RAFIQUL ISLAM MASTER OF SCIENCE IN CIVIL ENGINEERING (STRUCTURAL) DEPARTMENT OF CIVIL ENGINEERING BANGLADESH UNIVERSITY OF ENGINEERING AND TECHNOLOGY, DHAKA, BANGLADESH FEBRUARY, 2014 ii The thesis titled “NUMERICAL MODELLING OF SLAB-COLUMN JOINT OF RC FLAT PLATES” submitted by Mohammad Rafiqul Islam, Roll No: 100704320F, Session: October/2007; has been accepted as satisfactory in partial fulfillment of the requirement for the degree of Master of Science in Civil Engineering (Structural) on 11th February, 2014. BOARD OF EXAMINERS Dr. Tahsin Reza Hossain Chairman Professor (Supervisor) Department of Civil Engineering BUET, Dhaka-1000. Dr. A.M.M. Taufiqul Anwar Professor and Head Member (Ex-Officio) Department of Civil Engineering BUET, Dhaka-1000. Dr. Khan Mahmud Amanat Professor Member Department of Civil Engineering BUET, Dhaka-1000. Dr. Sharmin Reza Chowdhury Associate Professor Member (External) Department of Civil Engineering Ahsanullah University of Science and Technology, Dhaka. iii DECLARATION It is hereby declared that except for the contents where specific references have been made to the work of others, the study contained in this thesis is the result of investigation carried out by the author. No part of this thesis has been submitted to any other University or other educational establishment for a Degree, Diploma or other qualification (except for publication). Signature of the Candidate (Mohammad Rafiqul Islam) iv CONTENTS DECLARATION ........................................................................................................iii CONTENTS ............................................................................................................... iv LIST OF FIGURES ..................................................................................................viii LIST OF TABLES ...................................................................................................xiii NOTATIONS ........................................................................................................... xiv ACKNOWLEDGRMENT ....................................................................................... xvi ABSTRACT ............................................................................................................ xvii Chapter 1 INTRODUCTION ................................................................................. 1 1.1 Background and Present State of the Problem .................................................. 1 1.2 Objectives with Specific Aims and Possible Outcome ..................................... 2 1.3 Methodology of Work ....................................................................................... 3 1.4 Outline of the Thesis ......................................................................................... 4 Chapter 2 LITERATURE REVIEW ...................................................................... 5 2.1 General .............................................................................................................. 5 2.2 Punching Shear Mechanism .............................................................................. 5 2.3 Experimental Investigations .............................................................................. 7 2.3.1 Effect of concrete strength .......................................................................... 7 2.3.2 Size effect ................................................................................................... 7 2.3.3 Effect of shear reinforcement ..................................................................... 8 2.3.4 Edge condition effect .................................................................................. 9 2.3.5 Slab-column connection behaviour .......................................................... 10 2.3.6 Shear strengthening techniques ................................................................ 10 2.3.7 Miscellaneous studies ............................................................................... 11 2.4 Analytical Investigation ................................................................................... 12 2.4.1 Beam-Strip Approach ............................................................................... 12 2.4.2 Truss Model Approach ............................................................................. 12 2.4.3 Fracture Mechanics .................................................................................. 13 2.4.4 Plasticity Model ........................................................................................ 13 2.4.5 Equivalent Frame Method ........................................................................ 14 v 2.4.6 Miscellaneous Studies .............................................................................. 14 2.5 Finite Element Method .................................................................................... 15 2.6 Slab-Column Connection under Seismic Actions ........................................... 18 2.7 Punching Shear Prediction Equations ............................................................. 21 2.7.1 Regan's equation ....................................................................................... 21 2.7.2 Bazant and Cao’s equation ....................................................................... 22 2.7.3 Gardner’s equation ................................................................................... 22 2.7.4 Code provision equations ......................................................................... 23 2.8 Remark ............................................................................................................ 27 Chapter 3 FINITE ELEMENT MODELING ...................................................... 28 3.1 General ............................................................................................................ 28 3.2 Finite Element Packages .................................................................................. 28 3.3 An Overview of ABAQUS .............................................................................. 29 3.4 Modeling of Reinforced Concrete Plate .......................................................... 31 3.4.1 Element types adopted .............................................................................. 32 3.4.2 Material properties .................................................................................... 34 3.4.3 Failure criteria for concrete ...................................................................... 42 3.5 Damage Plasticity Theories ............................................................................. 45 3.6 Nonlinear Solution Strategies .......................................................................... 48 3.6.1 Equilibrium iterations and convergence in Abaqus/Standard .................. 50 3.6.2 Equilibrium time increment in Abaqus/Explicit ....................................... 52 3.6.3 Advantages of the Abaqus/Explicit method ............................................. 53 3.7 Remark ............................................................................................................ 54 Chapter 4 VALIDATION OF NONLINEAR FINITE ELEMENT MODELING OF FLAT PLATE SLABS ........................................................................................ 55 4.1 General ............................................................................................................ 55 4.2 FE Modeling of Slab-Column Connection ...................................................... 55 4.2.1 Input data .................................................................................................. 56 4.2.2 Application of loads and boundary conditions ......................................... 56 4.2.3. Concrete damage value ............................................................................ 57 4.2.4 Mesh sensitivity analysis .......................................................................... 58 4.3 Description of Different Slabs Used in FE Modeling of Slab-Column Joint .. 60 4.3.1 FE modeling of RC flat plate (Elstner and Hognestad) ............................ 60 4.3.2 FE modeling of RC flat plate (Graf) ......................................................... 73 vi 4.3.3 FE modeling of RC flat plate (Kinnunen and Nylander) ......................... 80 4.3.4 FE modeling of RC flat plate (Jofreit and McNeice) ............................... 90 4.3.5 FE Modeling of RC Flat Plate (Tan and Teng) ........................................ 93 4.4 Remark .......................................................................................................... 102 Chapter 5 INFLUENCE OF MATERIAL AND GEOMETRIC PARAMETERS ON PUNCHING SHEAR STRENGTH .................................................................. 104 5.1 General .......................................................................................................... 104 5.2 Material Parameters ....................................................................................... 104 5.2.1 Concrete strength .................................................................................... 105 5.2.2 Flexural reinforcement ratio ................................................................... 109 5.2.3 Yield strength ......................................................................................... 110 5.2.4 Effect of compression reinforcement ..................................................... 111 5.3 Geometric Parameters ................................................................................... 114 5.3.1 Plate thickness (span-depth ratio) ........................................................... 114 5.3.2 Column size ............................................................................................ 117 5.3.3 Support condition ................................................................................... 120 5.4 Punching Shear Prediction Equation ............................................................. 121 5.5 ACI 318-08 Code Provision .......................................................................... 122 5.6 Comparison of Numerical Results with ACI 318-08 Code Provision .......... 122 5.7 Scope of Modification ................................................................................... 128 5.8 Tian Equation to Modify the ACI 318-08 Code Equation ............................ 129 5.9 Comparison of Numerical Results with Tian Equation ................................. 131 5.10 Proposed Modified Equation for Rectangular Column ............................... 137 5.11 Remark ........................................................................................................ 142 Chapter 6 BEHAVIOUR OF SLAB-COLUMN CONNECTIONS UNDER SEISMIC LOAD ..................................................................................................... 145 6.1 General .......................................................................................................... 145 6.2 Numerical Modeling of Interior Slab-Column Connections ......................... 146 6.2.1 Slab-column connections designed only for gravity load (Model-1) ..... 148 6.2.2 Slab-column connections designed only for gravity load considering effective width (Model-2) ................................................................................ 149 6.2.3 Slab-column connections of intermediate moment resisting frames (Model-3) ......................................................................................................... 150 6.2.4 Slab-column connections with drop panel (Model-4) ............................ 153 vii 6.2.5 FE model and limitation ......................................................................... 155 6.3 Performance Analysis under Gravity and Lateral Loads .............................. 156 6.4 Elastic Analysis of Flat-Plate Structures under Combined Gravity and Lateral Loads ................................................................................................................... 163 6.4.1 Flat-plate structure behave as a moment resisting frame under combined gravity and lateral loads ................................................................................... 163 6.4.2 Flat-plate structure with shear wall ........................................................ 167 6.4.3 Percentage of moment transfer through different strip of flat-plate slab system under gravity and lateral loads ............................................................ 172 6.5 Remark .......................................................................................................... 176 Chapter 7 CONCLUSIONS AND RECOMMENDATIONS ........................... 178 7.1 General .......................................................................................................... 178 7.2 Findings of the Work ..................................................................................... 178 7.3 Conclusions ................................................................................................... 182 7.4 Recommendations for Future Studies ........................................................... 183 REFERENCES ........................................................................................................ 185 Appendix A ............................................................................................................. 197 Appendix B .............................................................................................................. 217 viii LIST OF FIGURES Figure 2.1 A square column tends to shear out a pyramid from a footing or flat plate ..................................................................................................................................... 6 Figure 3.1 Eight-node solid element ......................................................................... 33 Figure 3.2 Two-node truss element .......................................................................... 33 Figure 3.3 Typical uniaxial compressive and tensile stress-strain curves for concrete [Bangash (1989)] ....................................................................................................... 36 Figure 3.4 Concrete stress-strain curve .................................................................... 41 Figure 3.5 Idealised stress-strain curve for steel reinforcement ............................... 42 Figure 3.6 Yield and failure surfaces in plane stress ................................................ 44 Figure 3.7 Decomposition of the total strain into elastic and plastic components ... 47 Figure 3.8 Degradation of the elastic stiffness as characterized by damage variables ................................................................................................................................... 48 Figure 3.9 Iteration in an increment by using Newton-Raphson iterative technique51 Figure 4.1 Uniaxial tensile and compression damage value with corresponding strain value [adapted from Cicekli et al. (2007)] ....................................................... 57 Figure 4.2 Load-deflection response of a square slab (A-1a plate) for varying uniaxial tensile damage value .................................................................................... 58 Figure 4.3 Ultimate load capacity of a square slab (A-1a plate) for varying mesh size ............................................................................................................................. 59 Figure 4.4 A test slab section of Elstner and Hognestad (1956) .............................. 61 Figure 4.5 Typical finite element model of the plate with boundary condition ....... 64 Figure 4.6 Typical finite element model of the plate with loading pattern .............. 64 Figure 4.7 Typical finite element model of concrete mesh ...................................... 65 Figure 4.8 Typical tension and compression reinforcement for A-1a, A-7b and A-7 slabs ........................................................................................................................... 65 Figure 4.9 Typical bent bar reinforcement for B-16 slab ......................................... 65 Figure 4.10 First crack arises through slab at 18.1 kip cracking load and initial tensile damage of concrete ........................................................................................ 67 Figure 4.11 First crack starts through top surface at 18.1 kip cracking load and initial tensile damage of concrete on half slab .......................................................... 67 Figure 4.12 Radial crack pattern at the perimeter of the column and tensile damage of concrete at 41.33 kip load ..................................................................................... 68 Figure 4.13 Radial crack spread out with forming pyramid shape and tensile damage of concrete at 41.33 kip load on half slab .................................................... 68 Figure 4.14 Total tensile damage of concrete on top surface of slab and punching failure at 75.18 kip load ............................................................................................. 69 Figure 4.15 Total tensile damage of concrete on top surface of half slab and punching failure with a pyramid shape at 75.18 kip load .......................................... 69 Figure 4.16 Post-punching failure phenomenon of half slab .................................... 70 Figure 4.17 Steel yielded during post-punching failure ........................................... 70 Figure 4.18 Comparative load-deflection responses for A-1a .................................. 71 Figure 4.19 Comparative load-deflection responses for A-7b.................................. 71 Figure 4.20 Comparative load-deflection responses for A-7.................................... 72 Figure 4.21 Comparative load-deflection responses for B-14 .................................. 72 Figure 4.22 Comparative load-deflection responses for B-16 .................................. 73 ix Figure 4.23 Setup of slab section with straight reinforcement and 11.81 inch or 19.7 inch thick; (Graf 1938) ...................................................................................... 74 Figure 4.24 Setup of slab section with bent reinforcement and 11.81 inch or 19.7 inch thick; (Graf 1938) .............................................................................................. 74 Figure 4.25 Typical finite element model of concrete mesh .................................... 76 Figure 4.26 Typical tension reinforcement for G-1 and G-2 slabs ........................... 76 Figure 4.27 Typical tension and bent bar reinforcement for G-3 and G-4 slabs ...... 77 Figure 4.28 Comparative load-deflection responses for G-1.................................... 78 Figure 4.29 Comparative load-deflection responses for G-2.................................... 79 Figure 4.30 Comparative load-deflection responses for G-3.................................... 79 Figure 4.31 Comparative load-deflection responses for G-4.................................... 80 Figure 4.32 Plan view of 5.9 inch thick circular slab; (Kinnunen and Nylander 1960) .......................................................................................................................... 83 Figure 4.33 Typical finite element model of one-forth slab with boundary condition and loading pattern .................................................................................... 83 Figure 4.34 Typical finite element model of concrete mesh .................................... 84 Figure 4.35 Overview of one-forth slab (IB15a) with ring reinforcement ............... 84 Figure 4.36 Overview of one-forth slab (IC15a) with ring and radial reinforcement ............................................................................................................. 85 Figure 4.37 Overview of one-forth slab (IA15a) with orthogonal reinforcement .... 85 Figure 4.38 Tensile damage of concrete on bottom surface of one-forth slab (IA15a) and punching failure with a pyramid shape at 51.7 kip load ....................... 86 Figure 4.39 Tensile damage of concrete on bottom surface of one-forth slab (IB15a) and punching failure with a pyramid shape at 44.1 kip load ....................... 86 Figure 4.40 Tensile damage of concrete on bottom surface of one-forth slab (IC15a) and punching failure with a pyramid shape at 53.7 kip load ....................... 87 Figure 4.41 Comparative load-deflection responses for IA15a ................................ 88 Figure 4.42 Comparative load-deflection responses for IB15a ................................ 88 Figure 4.43 Comparative load-deflection responses for IC15a ................................ 89 Figure 4.44 Plan view of 1.73 inch thick slab; (Jofreit and McNeice 1971) ............ 90 Figure 4.45 Typical finite element model of concrete mesh .................................... 92 Figure 4.46 Typical tension reinforcement ............................................................... 92 Figure 4.47 Comparative load-deflection responses ................................................ 93 Figure 4.48 Plan view of 5.9 inch thick slab; (Tan and Teng) ................................. 94 Figure 4.49 Schematic diagram of single column specimen .................................... 94 Figure 4.50 Typical finite element model of the plate with boundary condition and loading pattern .................................................................................................... 97 Figure 4.51 Typical finite element model of concrete mesh .................................... 98 Figure 4.52 Typical top bar reinforcement for YL-L1 slabs .................................... 98 Figure 4.53 Typical bottom bar reinforcement for YL-L1 slabs .............................. 99 Figure 4.54 Typical top, bottom and column stub reinforcement for YL-L1 slabs . 99 Figure 4.55 Mises stress distributions through slab-column connection of half slab YL-L1 ............................................................................................................... 100 Figure 4.56 Tension damage on slab-column connection of half slab YL-L1 ....... 100 Figure 4.57 Compression damage on slab-column connection of half slab YL-L1 ................................................................................................................................. 101 Figure 4.58 Comparative horizontal force (P )-drift ratio curves for YL-L1 ......... 102 x Figure 5.1 Load-deflection responses with varying concrete compressive strength x for reinforcement ratio of 1.5% ............................................................................... 107 Figure 5.2 Variation of ultimate load capacity with varying compressive strength of concrete for different reinforcement ratio ........................................................... 107 Figure 5.3 Variation of ultimate load capacity with varying reinforcement ratio for different compressive strength of concrete ........................................................ 110 Figure 5.4 Variation of ultimate load capacity due to change in yield strength of reinforcement ........................................................................................................... 111 Figure 5.5 Influence of flexural reinforcement on load-deflection response for model slab A-1a ....................................................................................................... 112 Figure 5.6 Influence of flexural reinforcement on load-deflection response for model slab A-7b ...................................................................................................... 113 Figure 5.7 Influence of flexural reinforcement on load-deflection response for model slab A-7 ........................................................................................................ 113 Figure 5.8 Load-deflection response with varying plate thickness ........................ 115 Figure 5.9 Variation of unit shear stress due to change in plate thickness ............. 116 Figure 5.10 Influence of span-depth ratio on ultimate load capacity ..................... 116 Figure 5.11 Load-deflection responses for different column size .......................... 118 Figure 5.12 Variation of ultimate load capacity due to change in column size...... 118 Figure 5.13 Load-deflection responses for different column size .......................... 119 Figure 5.14 Variation of ultimate load capacity due to change in column size...... 119 Figure 5.15 Load-deflection responses for different edge condition of the plate ... 121 Figure 5.16 Variation of the ratio between FE shear to nominal shear according to ACI 318-08 code provision with varying compressive strength of concrete for different reinforcement ratio .................................................................................... 124 Figure 5.17 Variation of the ratio between FE shear to nominal shear according to ACI 318-08 code provision with varying reinforcement ratio for different compressive strength of concrete ............................................................................ 124 Figure 5.18 Variation of the ratio between FE shear to nominal shear according to ACI 318-08 code provision with varying yield strength of reinforcement for different compressive strength of concrete .............................................................. 125 Figure 5.19 Variation of the ratio between FE shear to nominal shear according to ACI 318-08 code provision with varying reinforcement index for different compressive strength of concrete ............................................................................ 125 Figure 5.20 Variation of the ratio between FE shear to nominal shear according to ACI 318-08 code provision with varying plate thickness ................................... 126 Figure 5.21 Variation of the ratio between FE shear to nominal shear according to ACI 318-08 code provision with varying column size ........................................ 127 Figure 5.22 Comparisons of FE shear strength and nominal shear strength according to ACI 318-08 code provision ................................................................ 128 Figure 5.23 Variation of the ratio between FE shear to nominal shear according to Tian equation with varying compressive strength of concrete for different reinforcement ratio .................................................................................................. 132 Figure 5.24 Variation of the ratio between FE shear to nominal shear according to Tian equation with varying reinforcement ratio for different compressive strength of concrete ................................................................................................. 132 Figure 5.25 Variation of the ratio between FE shear to nominal shear according to Tian equation with varying yield strength of reinforcement for different compressive strength of concrete ............................................................................ 133