Table Of Content© 2012 by Taylor & Francis Group, LLC
Advances in Earthquake Engineering Series
Series Editor: Franklin Y. Cheng
Missouri University of Science and Technology
Seismic Design Aids for Nonlinear Pushover Analysis of Reinforced
Concrete and Steel Bridges
Jeffrey Ger and Franklin Y. Cheng
Seismic Design Aids for Nonlinear Analysis of Reinforced Concrete Structures
Srinivasan Chandrasekaran, Luciano Nunziante, Giorgio Serino, and
Federico Carannante
© 2012 by Taylor & Francis Group, LLC
Jeffrey Ger
Franklin Y. Cheng
Boca Raton London New York
CRC Press is an imprint of the
Taylor & Francis Group, an informa business
© 2012 by Taylor & Francis Group, LLC
CRC Press
Taylor & Francis Group
6000 Broken Sound Parkway NW, Suite 300
Boca Raton, FL 33487-2742
© 2012 by Taylor & Francis Group, LLC
CRC Press is an imprint of Taylor & Francis Group, an Informa business
No claim to original U.S. Government works
Version Date: 20110608
International Standard Book Number-13: 978-1-4398-3775-7 (eBook - PDF)
This book contains information obtained from authentic and highly regarded sources. Reasonable efforts
have been made to publish reliable data and information, but the author and publisher cannot assume
responsibility for the validity of all materials or the consequences of their use. The authors and publishers
have attempted to trace the copyright holders of all material reproduced in this publication and apologize to
copyright holders if permission to publish in this form has not been obtained. If any copyright material has
not been acknowledged please write and let us know so we may rectify in any future reprint.
Except as permitted under U.S. Copyright Law, no part of this book may be reprinted, reproduced, transmit-
ted, or utilized in any form by any electronic, mechanical, or other means, now known or hereafter invented,
including photocopying, microfilming, and recording, or in any information storage or retrieval system,
without written permission from the publishers.
For permission to photocopy or use material electronically from this work, please access www.copyright.
com (http://www.copyright.com/) or contact the Copyright Clearance Center, Inc. (CCC), 222 Rosewood
Drive, Danvers, MA 01923, 978-750-8400. CCC is a not-for-profit organization that provides licenses and
registration for a variety of users. For organizations that have been granted a photocopy license by the CCC,
a separate system of payment has been arranged.
Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used
only for identification and explanation without intent to infringe.
Visit the Taylor & Francis Web site at
http://www.taylorandfrancis.com
and the CRC Press Web site at
http://www.crcpress.com
© 2012 by Taylor & Francis Group, LLC
Disclaimer
In using the computer coding given in Seismic Design Aids, the reader accepts and
understands that no warranty is expressed or implied by the authors on the accuracy
or the reliability of the programs. The examples presented are only introductory
guidelines to explain the applications of proposed methodology. The reader must
independently verify the results and is responsible for the results.
v
© 2012 by Taylor & Francis Group, LLC
To our families for their immense love and support
Jeffrey Ger
Father—Chia Chian
Mother—Mei Yu
Wife—Jenny
Son—Max
Daughter—Christie
Franklin Y. Cheng
Wife—Pi Yu (Beatrice)
Son and daughter-in-law—George and Annie
Daughter and son-in-law—Deborah and Craig
Grandchildren—Alex, Camille, and Natalie
© 2012 by Taylor & Francis Group, LLC
Contents
Series Preface ...........................................................................................................xv
Preface....................................................................................................................xvii
Series Editor ............................................................................................................xxi
Authors .................................................................................................................xxiii
Chapter 1 Overview of Seismic Design of Highway Bridges in
the United States ..................................................................................1
1.1 Introduction ...............................................................................1
1.2 AASHTO Bridge Seismic Design Philosophy ..........................1
1.2.1 AASHO Elastic Design Procedures (1961–1974) .........2
1.2.2 AASHTO Force-Based Design Procedures
(1975–1992) ..................................................................3
1.2.3 AASHTO Force-Based Design Procedures
(1992–2008) ..................................................................5
1.2.3.1 Force-Reduction R-Factor ...........................13
1.2.3.2 Capacity Design Concept ...........................15
1.2.4 AASHTO Guide Specifications for LRFD
Seismic Bridge Design (2009) ....................................16
1.2.4.1 Nonlinear Pushover Analysis Procedure ....17
1.3 Direct Displacement-Based Design Procedures ......................18
Chapter 2 Pushover Analysis Applications .........................................................23
2.1 Displacement Capacity Evaluation for the Seismic
Design of New Bridges ............................................................23
2.2 Performance Level Verification for New Bridges
Designed by DDBD .................................................................23
2.3 Capacity/Demand Ratios for the Seismic Evaluation of
Existing Bridges ......................................................................28
2.4 Quantitative Bridge System Redundancy Evaluation ..............29
2.5 Moment–Curvature Curves and Axial Load–Moment
Interaction Curves ...................................................................31
2.6 Other Applications...................................................................31
Chapter 3 Nonlinear Pushover Analysis Procedure ...........................................35
3.1 Introduction .............................................................................35
3.2 SOL01—Elastic Static Analysis ..............................................37
3.3 SOL04—Nonlinear Static Pushover (Cyclic or
Monotonic) Analysis ................................................................38
ix
© 2012 by Taylor & Francis Group, LLC
x Contents
3.3.1 Flowchart in SOL04 ...................................................38
3.3.2 Nonlinear Pushover Procedure ..................................39
3.4 Material Library ......................................................................41
3.4.1 Elastic 3D Prismatic Beam Material (3D-BEAM) ......41
3.4.2 Bilinear Hysteresis Model (BILINEAR) ...................41
3.4.3 Gap/Restrainer Model (GAP) .....................................41
3.4.4 Takeda Hysteresis Model (TAKEDA) ........................42
3.4.5 Bilinear Moment-Rotation Model (HINGE) ..............43
3.4.6 Bilinear Hysteresis Model (IA_BILN).......................43
3.4.7 Finite-Segment Steel Stress–Strain Hysteresis
Model (STABILITY1) ................................................43
3.4.8 Finite-Segment Reinforced Concrete
Stress–Strain Hysteresis Model (R/CONCRETE1) ......45
3.4.9 Finite Segment–Moment Curvature Model
(MOMCURVA1) ........................................................52
3.4.10 Plate Material (PLATE) .............................................53
3.4.11 Point Material (POINT) .............................................53
3.4.12 Brace Material (BRACE) ...........................................53
3.5 Element Library .......................................................................54
3.5.1 Elastic 3D Prismatic Element (3D-BEAM) ...............54
3.5.2 Spring Element (SPRING) .........................................55
3.5.3 Inelastic 3D Beam Element (IE3DBEAM) ................58
3.5.4 Finite-Segment Element (STABILITY) .....................59
3.5.5 Plate Element (PLATE) ..............................................60
3.5.6 Point Element (POINT) ..............................................61
3.5.7 Brace Element (BRACE) ...........................................62
3.6 Material-Element Cross Reference ..........................................62
Chapter 4 Nonlinear Bending Stiffness Matrix Formulations ...........................63
4.1 Bilinear Interaction Axial Load–Moment Method .................63
4.2 Plastic Hinge Length Method ..................................................65
4.3 Constant Moment Ratio Method .............................................72
4.4 Finite Segment–Finite String Method .....................................79
4.5 Finite Segment–Moment Curvature Method...........................81
4.6 Concrete Column Failure Modes ............................................82
4.7 Bilinear Moment–Curvature Curves .......................................91
4.8 Column Axial Load–Moment Interaction ...............................93
4.9 C olumn Axial Load–Plastic Curvature Capacity Curve.........94
Chapter 5 Analytical Formulation for Structures ...............................................97
5.1 Joint Definition and Degrees of Freedom ................................97
5.1.1 Global Coordinate System..........................................97
5.1.2 Joint Coordinate System .............................................97
© 2012 by Taylor & Francis Group, LLC
Contents xi
5.1.3 Rigid Body Constraints ..............................................98
5.1.4 Condensed Degrees of Freedom ..............................101
5.1.5 Global Degrees of Freedom .....................................101
5.2 Inelastic IE3DBEAM Element ..............................................101
5.2.1 Element Coordinate System and Degrees of
Freedom ....................................................................102
5.2.2 Element Stiffness Matrix in ECS .............................103
5.2.3 Element Stiffness Matrix in Terms of Global
Degrees of Freedom .................................................106
5.2.4 Element Geometric Stiffness Matrix in Gdof ..........109
5.3 Finite-Segment Element ........................................................111
5.3.1 Element Coordinate System and Degrees of
Freedom ....................................................................111
5.3.2 Element Stiffness Matrix in ECS .............................111
5.4 Brace Element ........................................................................113
5.4.1 Element Coordinate System and Degrees of
Freedom ....................................................................113
5.4.2 Element Stiffness Matrix in ECS .............................114
5.4.3 Element Stiffness Matrix in Gdof ............................114
5.5 Plate Element .........................................................................115
5.5.1 Element Coordinate System and Degrees of
Freedom ....................................................................116
5.5.2 Element Stiffness Matrix in ECS .............................116
5.5.3 Element Stiffness Matrix in Gdof ............................117
5.6 Unbalanced Forces ................................................................118
5.6.1 Unbalanced Element Forces .....................................118
5.6.2 Global Unbalanced Joint Forces ...............................119
5.6.3 Assembly of the Global Structural and
Geometric Stiffness ..................................................120
Chapter 6 Input Data for INSTRUCT Program ................................................125
Notes on Input ..................................................................................125
6.1 STRUCTURE—Define the Structural Model ......................126
6.1.1 Joints and Degrees of Freedom ................................127
6.1.2 Materials and Hysteresis Models .............................130
6.1.3 Geometric Stiffness Data .........................................149
6.1.4 Element Data ............................................................150
6.1.5 Mass .........................................................................158
6.1.6 Damping ...................................................................159
6.2 SOL01—Elastic Static Solution ............................................159
6.2.1 Joint Loads ...............................................................159
6.2.2 Element Loads ..........................................................160
6.3 SOL04—Incremental Static (Pushover) Solution .................162
© 2012 by Taylor & Francis Group, LLC
