A FINITE ELEMENT APPROACH TO REINFORCED …

1 A FINITE ELEMENT APPROACH TO REINFORCEDCONCRETE SLAB DESIGNA ThesisPresented toThe Academic FacultybyJames B. DeatonIn Partial Fulfillmentof the Requirements for the DegreeMaster of ScienceSchool of Civil and Environmental EngineeringGeorgia Institute of TechnologyAugust 2005 Copyrightc 2005 by James B. DeatonA FINITE ELEMENT APPROACH TO REINFORCEDCONCRETE SLAB DESIGNA pproved by:Dr. Kenneth M. Will, AdvisorSchool of Civil and Environmental EngineeringGeorgia Institute of TechnologyDr. Lawrence F. KahnSchool of Civil and Environmental EngineeringGeorgia Institute of TechnologyDr. Michael H. SwangerSchool of Civil and Environmental EngineeringGeorgia Institute of TechnologyDate Approved: 18 July 2005 ACKNOWLEDGEMENTSI would like to express my sincerest appreciation to my advisor, Dr. Kenneth M. Will, for hisguidance, expert instruction, and the investments he has made in me over the past two years,giving me the opportunity to be involved in such interesting research.

2 I would also like toextend sincere thanks to my co-advisor, Dr. Lawrence F. Kahn. I will fondly remember thehours upon hours of conversations with both of them discussing FINITE elements , reinforcedconcrete, and many other non-technical topics. I could not have asked for an advisor orco-advisor more approachable or willing to would like to acknowledge Dr. Michael H. Swanger for pushing me to a greater under-standing of my research topic through his comments during the preparation of this , I would like to thank Rob Abernathy for his assistance in the early stages ofthis people supported me in ways beyond what I could have asked for during thecompletion of this project. For this I would like to thank several mentors, including Parker, Brian Holland, Chris Dawkins, and David Conner. Also, I would like tothank David Ashley, Adam Walker, Eric Henderson, and Joshua Tarbutton for each findingunique ways to encourage me and help me through the good as well as difficult stages ofthis project.

3 Additionally, I would like to thank all the members of our small group at FirstBaptist Church of Duluth for praying for me and for hanging out with my wife when I wasstudying or writing this would not be where I am today if it weren t for the support and love of my parents,Jimmy and Wanda Deaton thank you for always helping me be my best. I would also liketo thank my family-in-law, the Mooney s, for their importantly, I would like to thank my wife, Gina, for her unwavering love andsupport throughout the completion of this project, from the first time I mentioned graduateschool to her to the final days of proofreading this thesis. I lovingly dedicate this to OF CONTENTSACKNOWLEDGEMENTS..iiiLIST OF TABLES..viiLIST OF FIGURES..viiiSUMMARY..xI INTRODUCTION.. Flat Plate Systems .. Literature Review .. Design Based on Linear analysis .. Extension to Arbitrary Structures.

4 Design Based on Non-Linear analysis .. Additional Applications .. Motivation .. Outline of Presentation ..15II REVIEW OF CONVENTIONAL REINFORCED concrete FLATPLATE DESIGN.. General ACI Requirements for REINFORCED concrete Flat Plate Design .. analysis Requirements .. Flexural Strength Requirements .. Shear Strength Requirements .. Serviceability Requirements .. Detailing of Reinforcement .. ACI Direct Design Technique .. ACI Equivalent Frame Technique .. Yield Line Method .. Strip Design Technique ..38 III APPLICATION OF THE FINITE ELEMENT METHOD TO REIN-FORCED concrete SLAB DESIGN.. Modeling of Slabs Using FINITE elements .. General Modeling Requirements .. Assumptions in REINFORCED concrete Flat Plate FINITE ELEMENT Analy-sis .. Modeling of Boundary Conditions for Flat Plate Systems .. Techniques for Flat Plate Design Using FEA Results.

5 Design Using Average Stress Resultants .. Design Using ELEMENT Forces ..54IV IMPLEMENTATION OF PROCEDURE.. Programming Introduction .. Overview of Algorithm .. Overview of GT STRUDL .. Tools Used .. Model Requirements .. Command .. Overview of User Options .. Command Syntax .. Explanation of Command .. Pre-Processing .. Determination of Cut Definition .. Formulation of Cut Coordinate System .. ELEMENT Selection Procedure .. User-Defined ELEMENT List .. Contribution from Both Sides of Cut .. ELEMENT Type Restrictions .. Further Error Checking .. Computation of Resultant Forces Along Cut .. The CALCULATE RESULTANT Command .. Computation of Design Forces .. Reduction of Multiple Load Cases to Design Envelope .. Interpretation of Results .. Design Procedure .. Initial Design Processing .. Check Specified Bar and Spacing .. Design with No User Constraints.

6 Design with Bar Size Constrained .. Design with Bar Spacing Constrained .. Shear Check .. Final Comments ..90V RESULTS AND NUMERICAL STUDIES.. Example 1 - Convergence of Area of Steel .. Example 2 - Comparison with Experimental Data .. Example 3 - Square Bay Flat Plate Structure .. Example 4 - Irregular Bay Rectangular Flat Plate Structure .. Example 5 - Square Flat Plate Fix-Supported on Two Sides ..136VI CONCLUSIONS.. Summary .. Future Work .. Recommendations for Research .. Program Enhancements ..145 APPENDIX A COMPRESSION REINFORCEMENT..148 APPENDIX B MODULE DESCRIPTIONS..150 REFERENCES..156viLIST OF Example 1 - Computed Response Quantities .. Example 2 - Experimental and FINITE ELEMENT Bending Moments .. Example 3 - Interior Region Design Results .. Example 3 - Exterior Region Design Results .. Example 3 - Interior Bending Moments for Pattern Loadings.

7 Example 3 - Interior Area of Steel Computed for Pattern Loadings .. Example 3 - Exterior Bending Moments for Pattern Loadings .. Example 3 - Exterior Area of Steel Computed for Pattern Loadings .. Example 3 - Ratio of Resultant Torsional Moment to Bending Moment forPattern Loadings .. Example 4 - N/S Interior Region Design Results .. Example 4 - N/S Exterior Region Design Results .. Example 4 - N/S Interior Bending Moments for Pattern Loadings .. Example 4 - N/S Interior Area of Steel Computed for Pattern Loadings .. Example 4 - N/S Exterior Bending Moments for Pattern Loadings .. Example 4 - N/S Exterior Area of Steel Computed for Pattern Loadings .. Example 4 - N/S Ratio of Resultant Torsional Moment to Bending Momentfor Pattern Loadings .. Example 4 - E/W Interior Region Design Results .. Example 4 - E/W Exterior Region Design Results .. Example 4 - E/W Interior Bending Moments for Pattern Loadings.

8 Example 4 - E/W Interior Area of Steel Computed for Pattern Loadings .. Example 4 - E/W Exterior Bending Moments for Pattern Loadings .. Example 4 - E/W Exterior Area of Steel Computed for Pattern Loadings . Example 4 - E/W Ratio of Resultant Torsional Moment to Bending Momentfor Pattern Loadings .. Effect of Torsion .. Computation of Depth to Neutral Axis ..149viiLIST OF Flat Plate System .. Flat Plate REINFORCED concrete Residential Structure Under Construction . General Flexure at Ultimate Capacity .. Moment Transfer Shear - Interior, Edge, and Corner Columns [27] .. Flat Plate Cross-Sectional Detailing Requirements .. Slab-Beam Layout and Dimensions .. Elevation Showing Plane Frame Analytical Model for the Equivalent ColumnMethod .. Equivalent Column with Attached Torsional Member .. Example Yield Line Patterns .. Example Strip Design Layout.

9 3D Solid Slab-to-Column Connection Detail .. Master-Slave Slab-to-Column Connection Detail .. ELEMENT Stress Resultants at a Node .. Strip Selection Based onMxxContour Plot .. Average Bending Moment Resultants at Each Node Along Cut .. ELEMENT Forces at a Node .. ELEMENT Force Resultant From Nodal Forces Along a Cut .. Bounded Region Between Start and End Node of Cut .. Cut Coordinate System: (A) General Case (B) Special Case .. ELEMENT Selection Cases 1-5 (Plan View) .. ELEMENT Selection Cases 6-10 (Plan View) .. ELEMENT Selection Cases 11-15 (Plan View) .. CALCULATE RESULTANT Command Results .. Positive Bending and Surface Naming Convention .. Direction of Reinforcing Bars for Non-Orthogonal Cut (Plan) .. Slab Cross-Section:d Distance .. Example 1 - Geometry .. Example 1 - FINITE ELEMENT Models .. Example 1 - Convergence of Key Response Quantities.

10 Example 2 - Simplified Model with Edge Beams Neglected and Space FrameMember Columns .. Example 2 - Detailed Model with Edge Beams and 3D Solid Interior Example 2 - Test Structure Top Reinforcement (Gamble, [28]) .. Example 2 - Test Structure Bottom Reinforcement (Gamble, [28]) .. Example 2 - Moment Components Corresponding to Strain Gage Example 2 - Moments in Interior Panel .. Example 2 - Total Moment in Interior Panel .. Example 3 - Geometry .. Example 3 - FINITE ELEMENT Model with Space Frame Member Columns (left)and FINITE ELEMENT Model of14of Structure with 3D Solid Columns (right) Example 3 - Pattern Live Loadings .. Example 4 - Dimensions and FINITE ELEMENT Model .. Example 5 - Geometry .. Example 5 - Bending Resultant Contours .. Example 5 - Principal Bending Vectors - M1 (top) and M2 (bottom) .. Depth to Neutral Axis Divided by concrete Cover ..149ixSUMMARYThe objective of this study was the development of a procedure in GT STRUDL todesign REINFORCED concrete flat plate systems based on the results of FINITE ELEMENT current state-of-practice of REINFORCED concrete flat plate design was reviewed, in-cluding the ACI direct design and equivalent frame techniques, the yield line method, andthe strip design method.