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Summary
Summary
Nonlinear analysis methods such as static pushover or limit analysis until collapse are globally considered reliable tools for seismic and structural assessment. But the accuracy of seismic capacity estimates--which can prevent catastrophic loss of life and astronomical damage repair costs--depends on the use of the correct basic input parameters.
Tools to Safeguard New Buildings and Assess Existing Ones
Seismic Design Aids for Nonlinear Analysis of Reinforced Concrete Structures simplifies the estimation of base structural parameters and enables accurate evaluation of proper bounds for the safety factor. Many design engineers make the relatively common mistake of using default properties of materials as input to nonlinear analyses without realizing that any minor variation in the nonlinear characteristics of constitutive materials, such as concrete and steel, could result in a solution error that leads to a disastrously incorrect assessment or interpretation. To achieve a more accurate pushover analysis and improve general performance-based design, this book:
Reassessing key inputs, this book analyzes boundaries using a detailed mathematical model based on international codes. It proposes design curves and tables derived from the authors' studies, detailing modeling numerical procedures step by step. The authors include analytical bounds of the structural safety factor for some typical frames, making this work a sound and valuable tool for assessment or desi
Author Notes
Chandrasekaran, Srinivasan; Nunziante, Luciano; Serino, Giorgio; Carannante, Federico
Table of Contents
Series Preface | p. ix |
Series Editor | p. xi |
Preface | p. xiii |
About the Authors | p. xvii |
Disclaimer | p. xix |
Notations | p. xxi |
Chapter 1 Axial Force-Bending Moment Yield Interaction | p. 1 |
1.1 Summary | p. 1 |
1.2 Introduction | p. 1 |
1.3 Mathematical Development | p. 3 |
1.4 Identification of Subdomains | p. 5 |
1.4.1 Subdomains 1 and 2: Collapose Caused by Yielding of Steel | p. 5 |
1.4.2 Subdomains 3 to 6: Collapse Caused by Crushing of Concrete | p. 12 |
1.5 Numerical Studies and Discussions | p. 13 |
1.6 Conclusions | p. 41 |
1.7 Numerical Procedure in Spreadsheet Format | p. 41 |
Chapter 2 Moment-Curvature Relationship for RC Sections | p. 43 |
2.1 Summary | p. 43 |
2.2 Introduction | p. 43 |
2.3 Mathematical Development | p. 45 |
2.4 Moment-Curvature in Elastic Range | p. 45 |
2.4.1 Tensile Axial Force | p. 46 |
2.4.2 No Axial Force | p. 48 |
2.4.3 Compressive Axial Force | p. 48 |
2.5 Elastic Limit Bending Moment and Curvature | p. 50 |
2.5.1 Case 1: Strain in Tension Steel Reaches Yield Limit and Stress in Concrete Vanishes | p. 50 |
2.5.2 Case 2: Strain in Tension Steel Reaches Yield Limit and Stress in Concrete Does Not Equal Zero | p. 50 |
2.5.3 Case 3: Strain in Compression Steel Reaches Elastic Limit Value | p. 52 |
2.5.4 Case 4: Strain in Extreme Compression Fiber in Concrete Reaches Elastic Limit Value | p. 53 |
2.6 Percentage of Steel for Balanced Section | p. 54 |
2.7 Ultimate Bending Moment-Curvature Relationship | p. 56 |
2.7.1 Neutral Axis Position Assuming Negative Values | p. 56 |
2.7.2 Neutral Axis Position Assuming Positive Values | p. 56 |
2.8 Numerical Studies and Discussions | p. 62 |
2.9 Conclusions | p. 85 |
2.10 Spreadsheet Program | p. 86 |
2.10.1 Step-by-Step Procedure to Use the Spreadsheet Program Given on the Web Site | p. 86 |
Chapter 3 Moment-Rotation Relationship for RC Beams | p. 89 |
3.1 Summary | p. 89 |
3.2 Introduction | p. 89 |
3.3 Mathematical Development | p. 90 |
3.4 Analytical Moment-Rotation Relationships | p. 92 |
3.4.1 Fixed Beam under Central Concentrated Load | p. 93 |
3.4.2 Simply Supported Beam under Central Concentrated Load | p. 98 |
3.4.3 Fixed Beam under Uniformly Distributed Load | p. 101 |
3.5 Numerical Studies and Discussions | p. 106 |
3.6 Conclusions | p. 114 |
3.7 Spreadsheet Program | p. 115 |
3.7.1 Step-by-Step Procedure to Use the Numerical Method on the Web Site | p. 115 |
Chapter 4 Bounds for Collapse Loads of Building Frames Subjected to Seismic Loads: A Comparison with Nonlinear Static Pushover | p. 117 |
4.1 Summary | p. 117 |
4.2 Introduction | p. 118 |
4.3 Collapse Multipliers | p. 118 |
4.3.1 Kinematic Multiplier, Kk | p. 120 |
4.3.2 Static Multiplier, Ks | p. 122 |
4.3.3 Step-by-Step Analysis for a Simple Frame with P-M Interaction | p. 124 |
4.4 Numerical Studies and Discussions | p. 131 |
4.5 Conclusions | p. 137 |
Chapter 5 Flow Rule Verification for P-M Interaction Domains | p. 139 |
5.1 Summary | p. 139 |
5.2 Introduction | p. 139 |
5.3 Mathematical Development | p. 140 |
5.3.1 Subdomains 1 to 2b(2): Collapse Caused by Yielding of Steel | p. 144 |
5.3.2 Subdomains 3 to 6b: Collapse Caused by Crushing of Concrete | p. 150 |
5.4 Plastic Strain Increment in Different Subdomains | p. 150 |
5.5 Verification of Flow Rule | p. 156 |
5.6 Conclusions | p. 157 |
Appendix Summary of P-M Relationships for Different Subdomains | p. 159 |
Chapter 6 Computer Coding for Collapse Multipliers | p. 165 |
6.1 Introduction | p. 165 |
6.2 Computer Coding for Collapse Multipliers | p. 165 |
6.2.1 Single Bay-Single Story Regular Frame | p. 165 |
6.2.2 Single Bay-Two Story Regular Frame | p. 171 |
6.2.3 Single Bay-Single Story Frame with Unequal Column Length | p. 172 |
6.2.4 Four Bay-Two Story Regular Frame | p. 174 |
6.2.5 Six Bay-Three Story Irregular Frame | p. 175 |
6.2.6 Six Bay-Three Story Regular Frame | p. 177 |
6.2.7 Five Bay-Ten Story Regular Frame | p. 179 |
6.2.8 General Procedure for Regular Frames with M Bays-N Stories | p. 182 |
6.2.9 Computer Coding to Compute Static Collapse Multipliers (LINGO) | p. 189 |
6.3 Procedure to Perform Pushover Analysis | p. 190 |
6.3.1 Step-by-Step Approach Using SAP2000 | p. 192 |
References | p. 215 |
Index | p. 219 |