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