Series Preface | p. ix |
Series Editor | p. xi |
Preface | p. xiii |
About the Authors | p. xvii |
Disclaimer | p. xix |
Notations | p. xxi |
Axial Force-Bending Moment Yield Interaction | p. 1 |
Summary | p. 1 |
Introduction | p. 1 |
Mathematical Development | p. 3 |
Identification of Subdomains | p. 5 |
Subdomains 1 and 2: Collapose Caused by Yielding of Steel | p. 5 |
Subdomains 3 to 6: Collapse Caused by Crushing of Concrete | p. 12 |
Numerical Studies and Discussions | p. 13 |
Conclusions | p. 41 |
Numerical Procedure in Spreadsheet Format | p. 41 |
Moment-Curvature Relationship for RC Sections | p. 43 |
Summary | p. 43 |
Introduction | p. 43 |
Mathematical Development | p. 45 |
Moment-Curvature in Elastic Range | p. 45 |
Tensile Axial Force | p. 46 |
No Axial Force | p. 48 |
Compressive Axial Force | p. 48 |
Elastic Limit Bending Moment and Curvature | p. 50 |
Case 1: Strain in Tension Steel Reaches Yield Limit and Stress in Concrete Vanishes | p. 50 |
Case 2: Strain in Tension Steel Reaches Yield Limit and Stress in Concrete Does Not Equal Zero | p. 50 |
Case 3: Strain in Compression Steel Reaches Elastic Limit Value | p. 52 |
Case 4: Strain in Extreme Compression Fiber in Concrete Reaches Elastic Limit Value | p. 53 |
Percentage of Steel for Balanced Section | p. 54 |
Ultimate Bending Moment-Curvature Relationship | p. 56 |
Neutral Axis Position Assuming Negative Values | p. 56 |
Neutral Axis Position Assuming Positive Values | p. 56 |
Numerical Studies and Discussions | p. 62 |
Conclusions | p. 85 |
Spreadsheet Program | p. 86 |
Step-by-Step Procedure to Use the Spreadsheet Program Given on the Web Site | p. 86 |
Moment-Rotation Relationship for RC Beams | p. 89 |
Summary | p. 89 |
Introduction | p. 89 |
Mathematical Development | p. 90 |
Analytical Moment-Rotation Relationships | p. 92 |
Fixed Beam under Central Concentrated Load | p. 93 |
Simply Supported Beam under Central Concentrated Load | p. 98 |
Fixed Beam under Uniformly Distributed Load | p. 101 |
Numerical Studies and Discussions | p. 106 |
Conclusions | p. 114 |
Spreadsheet Program | p. 115 |
Step-by-Step Procedure to Use the Numerical Method on the Web Site | p. 115 |
Bounds for Collapse Loads of Building Frames Subjected to Seismic Loads: A Comparison with Nonlinear Static Pushover | p. 117 |
Summary | p. 117 |
Introduction | p. 118 |
Collapse Multipliers | p. 118 |
Kinematic Multiplier, Kk | p. 120 |
Static Multiplier, Ks | p. 122 |
Step-by-Step Analysis for a Simple Frame with P-M Interaction | p. 124 |
Numerical Studies and Discussions | p. 131 |
Conclusions | p. 137 |
Flow Rule Verification for P-M Interaction Domains | p. 139 |
Summary | p. 139 |
Introduction | p. 139 |
Mathematical Development | p. 140 |
Subdomains 1 to 2b(2): Collapse Caused by Yielding of Steel | p. 144 |
Subdomains 3 to 6b: Collapse Caused by Crushing of Concrete | p. 150 |
Plastic Strain Increment in Different Subdomains | p. 150 |
Verification of Flow Rule | p. 156 |
Conclusions | p. 157 |
Appendix Summary of P-M Relationships for Different Subdomains | p. 159 |
Computer Coding for Collapse Multipliers | p. 165 |
Introduction | p. 165 |
Computer Coding for Collapse Multipliers | p. 165 |
Single Bay-Single Story Regular Frame | p. 165 |
Single Bay-Two Story Regular Frame | p. 171 |
Single Bay-Single Story Frame with Unequal Column Length | p. 172 |
Four Bay-Two Story Regular Frame | p. 174 |
Six Bay-Three Story Irregular Frame | p. 175 |
Six Bay-Three Story Regular Frame | p. 177 |
Five Bay-Ten Story Regular Frame | p. 179 |
General Procedure for Regular Frames with M Bays-N Stories | p. 182 |
Computer Coding to Compute Static Collapse Multipliers (LINGO) | p. 189 |
Procedure to Perform Pushover Analysis | p. 190 |
Step-by-Step Approach Using SAP2000 | p. 192 |
References | p. 215 |
Index | p. 219 |
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