Seismic design aids for nonlinear pushover analysis of reinforced concrete and steel bridges

Nonlinear static monotonic (pushover) analysis has become a common practice in performance-based bridge seismic design. The popularity of pushover analysis is due to its ability to identify the failure modes and the design limit states of bridge piers and to provide the progressive collapse sequence of damaged bridges when subjected to major earthquakes. Seismic Design Aids for Nonlinear Pushover Analysis of Reinforced Concrete and Steel Bridges fills the need for a complete reference on pushover analysis for practicing engineers.

This technical reference covers the pushover analysis of reinforced concrete and steel bridges with confined and unconfined concrete column members of either circular or rectangular cross sections as well as steel members of standard shapes. It provides step-by-step procedures for pushover analysis with various nonlinear member stiffness formulations, including:

Finite segment-finite string (FSFS) Finite segment-moment curvature (FSMC) Axial load-moment interaction (PM) Constant moment ratio (CMR) Plastic hinge length (PHL)

Ranging from the simplest to the most sophisticated, the methods are suitable for engineers with varying levels of experience in nonlinear structural analysis.

The authors also provide a downloadable computer program, INSTRUCT (INelastic STRUCTural Analysis of Reinforced-Concrete and Steel Structures), that allows readers to perform their own pushover analyses. Numerous real-world examples demonstrate the accuracy of analytical prediction by comparing numerical results with full- or large-scale test results. A useful reference for researchers and engineers working in structural engineering, this book also offers an organized collection of nonlinear pushover analysis applications for students.

Author Notes

Series Preface	p. xv
Preface	p. xvii
Series Editor	p. xxi
Authors	p. xxiii
Chapter 1 Overview of Seismic Design of Highway Bridges in the United States	p. 1
1.1 Introduction	p. 1
1.2 AASHTO Bridge Seismic Design Philosophy	p. 1
1.2.1 AASHO Elastic Design Procedures (1961-1974)	p. 2
1.2.2 AASHTO Force-Based Design Procedures (1975-1992)	p. 3
1.2.3 AASHTO Force-Based Design Procedures (1992-2008)	p. 5
1.2.3.1 Force-Reduction i?-Factor	p. 13
1.2.3.2 Capacity Design Concept	p. 15
1.2.4 AASHTO Guide Specifications for LRFD Seismic Bridge Design (2009)	p. 16
1.2.4.1 Nonlinear Pushover Analysis Procedure	p. 17
1.3 Direct Displacement-Based Design Procedures	p. 18
Chapter 2 Pushover Analysis Applications	p. 23
2.1 Displacement Capacity Evaluation for the Seismic Design of New Bridges	p. 23
2.2 Performance Level Verification for New Bridges Designed by DDBD	p. 23
2.3 Capacity/Demand Ratios for the Seismic Evaluation of Existing Bridges	p. 28
2.4 Quantitative Bridge System Redundancy Evaluation	p. 29
2.5 Moment-Curvature Curves and Axial Load-Moment Interaction Curves	p. 31
2.6 Other Applications	p. 31
Chapter 3 Nonlinear Pushover Analysis Procedure	p. 35
3.1 Introduction	p. 35
3.2 SOL01-Elastic Static Analysis	p. 37
3.3 SOL04-Nonlinear Static Pushover (Cyclic or Monotonic) Analysis	p. 38
3.3.1 Flowchart in SOL04	p. 38
3.3.2 Nonlinear Pushover Procedure	p. 39
3.4 Material Library	p. 41
3.4.1 Elastic 3D Prismatic Beam Material (3D-BEAM)	p. 41
3.4.2 Bilinear Hysteresis Model (BILINEAR)	p. 41
3.4.3 Gap/Restrainer Model (GAP)	p. 41
3.4.4 Takeda Hysteresis Model (TAKEDA)	p. 42
3.4.5 Bilinear Moment-Rotation Model (HINGE)	p. 43
3.4.6 Bilinear Hysteresis Model (IA_BILN)	p. 43
3.4.7 Finite-Segment Steel Stress-Strain Hysteresis Model (STABILITY1)	p. 43
3.4.8 Finite-Segment Reinforced Concrete Stress-Strain Hysteresis Model (R/CONCRETE1)	p. 45
3.4.9 Finite Segment-Moment Curvature Model (MOMCURVA1)	p. 52
3.4.10 Plate Material (PLATE)	p. 53
3.4.11 Point Material (POINT)	p. 53
3.4.12 Brace Material (BRACE)	p. 53
3.5 Element Library	p. 54
3.5.1 Elastic 3D Prismatic Element (3D-BEAM)	p. 54
3.5.2 Spring Element (SPRING)	p. 55
3.5.3 Inelastic 3D Beam Element (IE3DBEAM)	p. 58
3.5.4 Finite-Segment Element (STABILITY)	p. 59
3.5.5 Plate Element (PLATE)	p. 60
3.5.6 Point Element (POINT)	p. 61
3.5.7 Brace Element (BRACE)	p. 62
3.6 Material-Element Cross Reference	p. 62
Chapter 4 Nonlinear Bending Stiffness Matrix Formulations	p. 63
4.1 Bilinear Interaction Axial Load-Moment Method	p. 63
4.2 Plastic Hinge Length Method	p. 65
4.3 Constant Moment Ratio Method	p. 72
4.4 Finite Segment-Finite String Method	p. 79
4.5 Finite Segment-Moment Curvature Method	p. 81
4.6 Concrete Column Failure Modes	p. 82
4.7 Bilinear Moment-Curvature Curves	p. 91
4.8 Column Axial Load-Moment Interaction	p. 93
4.9 Column Axial Load-Plastic Curvature Capacity Curve	p. 94
Chapter 5 Analytical Formulation for Structures	p. 97
5.1 Joint Definition and Degrees of Freedom	p. 97
5.1.1 Global Coordinate System	p. 97
5.1.2 Joint Coordinate System	p. 97
5.1.3 Rigid Body Constraints	p. 98
5.1.4 Condensed Degrees of Freedom	p. 101
5.1.5 Global Degrees of Freedom	p. 101
5.2 Inelastic IE3DBEAM Element	p. 101
5.2.1 Element Coordinate System and Degrees of Freedom	p. 102
5.2.2 Element Stiffness Matrix in ECS	p. 103
5.2.3 Element Stiffness Matrix in Terms of Global Degrees of Freedom	p. 106
5.2.4 Element Geometric Stiffness Matrix in Gdof	p. 109
5.3 Finite-Segment Element	p. 111
5.3.1 Element Coordinate System and Degrees of Freedom	p. 111
5.3.2 Element Stiffness Matrix in ECS	p. 111
5.4 Brace Element	p. 113
5.4.1 Element Coordinate System and Degrees of Freedom	p. 113
5.4.2 Element Stiffness Matrix in ECS	p. 114
5.4.3 Element Stiffness Matrix in Gdof	p. 114
5.5 Plate Element	p. 115
5.5.1 Element Coordinate System and Degrees of Freedom	p. 116
5.5.2 Element Stiffness Matrix in ECS	p. 116
5.5.3 Element Stiffness Matrix in Gdof	p. 117
5.6 Unbalanced Forces	p. 118
5.6.1 Unbalanced Element Forces	p. 118
5.6.2 Global Unbalanced Joint Forces	p. 119
5.6.3 Assembly of the Global Structural and Geometric Stiffness	p. 120
Chapter 6 Input Data for INSTRUCT Program	p. 125
Notes on Input	p. 125
6.1 STRUCTURE-Define the Structural Model	p. 126
6.1.1 Joints and Degrees of Freedom	p. 127
6.1.2 Materials and Hysteresis Models	p. 130
6.1.3 Geometric Stiffness Data	p. 149
6.1.4 Element Data	p. 150
6.1.5 Mass	p. 158
6.1.6 Damping	p. 159
6.2 SOL01-Elastic Static Solution	p. 159
6.2.1 Joint Loads	p. 159
6.2.2 Element Loads	p. 160
6.3 SOL04-Incremental Static (Pushover) Solution	p. 162
6.3.1 Output Data to Plot Files	p. 162
6.3.2 Joint Loads	p. 164
6.3.3 Element Loads	p. 164
6.3.4 Load Factors	p. 164
6.4 BUG-Set Bug Options	p. 165
6.5 READ-Read Plot Files	p. 166
6.6 NOECHO-Inhibit Input Echo	p. 166
6.7 DUMP-Print Memory	p. 166
6.8 RELEASE-Release Memory	p. 166
6.9 STOP-Terminate Execution	p. 167
Chapter 7 Numerical Examples	p. 169
7.1 Structural Limit State Indicators	p. 169
7.2 Member Yield Indicators	p. 170
7.3 Numerical Examples	p. 170
7.3.1 Example 1: Moment-Curvature Analysis	p. 170
7.3.2 Example 2: Single-Column Bent	p. 182
7.3.3 Example 3: Steel Member Plastic Analysis	p. 189
7.3.4 Example 4: Two-Column Bent (Displacement Control)	p. 194
7.3.5 Example 5: Two-Column Bent (Force Control)	p. 230
7.3.6 Example 6: Column with Rectangular Section	p. 240
7.3.7 Example 7: Three-Column Bent (with 3D-BEAM, IE3DBEAM, SPRING, PLATE, and POINT elements)	p. 244
7.3.8 Example 8: Four-Column Bent	p. 247
7.3.9 Example 9: Pile Cap Bent	p. 251
7.3.10 Example 10: Cross Frame Analysis	p. 260
7.3.11 Example 11: Column with Shear Failure	p. 265
7.3.12 Example 12: Beam-Column Joint Failure	p. 275
7.3.12.1 For Test Specimen #1	p. 275
7.3.12.2 For Test Specimen #2	p. 277
7.3.13 Example 13: Cyclic Response of a Cantilever Beam	p. 287
Appendix A Stiffness Matrix Formulation for Bilinear PM Method	p. 293
Appendix B Stiffness Matrix Formulation for Finite Segment	p. 297
Appendix C Unbalanced Forces of a Finite Segment	p. 313
Appendix D Nonlinear Incremental Solution Algorithms	p. 315
Appendix E Plastic Curvature Capacities and Neutral Axis Depth in Columns	p. 319
Appendix F Elastic and Inelastic Time History Analysis	p. 325
Appendix G Elastic and Inelastic Response Spectra	p. 335
Appendix H Response Spectrum Analysis of Multiple-dof System	p. 347
Appendix I Polynomial Curve Fitting	p. 357
Appendix J Plate Element Stiffness Matrix	p. 363
References	p. 367
Index	p. 371

Available:*

On Order

Summary

Summary

Author Notes

Table of Contents