Plasticity for Structural Engineers

by Chen, Wai-Fah; Han, Da-Jian

• ISBN13: 9781932159752
• ISBN10: 1932159754
• Edition: Reprint
• Format: Paperback
• Copyright: 2007-02-01
• Publisher: J. Ross Publishing

Summary

This comprehensive text addresses the elastic and plastic behaviour of general structural elements under combined stress. It sets out to examine the stress strain behaviours of materials under simple test conditions and proceeds to show how these behaviours can be generalized under combined stress.

Author Biography

Dr. Wai-Fah Chen was Professor and Dean of the College of Engineering at the University of Hawaii from 1999 to 2006. From 1976 to 1999, he was Head of the Department of Structural Engineering at Purdue University and George E. Goodwin Distinguished Professor of Civil Engineering; prior to that he taught at Lehigh University. The author of more than 300 peer-reviewed publications and author or co-author of 20 books, his primary areas of research are constitutive modeling of engineering materials, soil and concrete plasticity, structural connections, and structural stability. He received his Ph.D. from Brown University. He is a member of the U.S. National Academy of Engineering and an Honorary member of the American Society of Civil Engineers.

Table of Contents

Preface	p. v
Notation	p. xi
Fundamentals
Introduction	p. 3
Introduction	p. 3
Historical Remarks	p. 5
Plastic Behavior in Simple Tension and Compression	p. 7
Modeling of Uniaxial Behavior in Plasticity	p. 11
Index Notation	p. 26
Summary	p. 40
References	p. 40
Problems	p. 40
Answers to Selected Problems	p. 44
Yield and Failure Criteria	p. 46
Stress	p. 46
Yield Criteria Independent of Hydrostatic Pressure	p. 72
Failure Criterion for Pressure-Dependent Materials	p. 84
Anisotropic Failure/Yield Criteria	p. 99
Summary	p. 103
References	p. 104
Problems	p. 104
Answers to Selected Problems	p. 111
Elastic Stress-Strain Relations	p. 117
Strain	p. 117
Linear Elastic Isotropic Stress-Strain Relation-Hooke's Law	p. 138
Nonlinear Elastic Isotropic Stress-Strain Relation	p. 148
Principle of Virtual Work	p. 161
Drucker's Stability Postulate	p. 163
Normality, Convexity, and Uniqueness for an Elastic Solid	p. 165
Incremental Stress-Strain Relations	p. 171
Summary	p. 172
References	p. 173
Problems	p. 174
Answers to Selected Problems	p. 176
Plastic Stress-Strain Relations
Stress-Strain Relations for Perfectly Plastic Materials	p. 179
Introduction	p. 179
Plastic Potential and Flow Rule	p. 181
Flow Rule Associated with von Mises Yield Function	p. 183
Flow Rule Associated with Tresca Yield Function	p. 85
Flow Rule Associated with Mohr-Coulomb Yield Function	p. 189
Convexity, Normality, and Uniqueness for Elastic-Perfectly Plastic Materials	p. 192
A Simple Elastic-Plastic Problem: The Expansion of a Thick-Walled Cylinder	p. 197
Incremental Stress-Strain Relationships	p. 207
Prandti-Reuss Material Model (J2 Theory)	p. 210
Drucker-Prager Material Model	p. 216
General Isotropic Material	p. 221
References	p. 225
Problems	p. 226
Answers to Selected Problems	p. 230
Stress-Strain Relations for Work-Hardening Materials	p. 232
Introduction	p. 232
Deformation Theory of Plasticity	p. 233
Loading Surface and Hardening Rules	p. 239
Flow Rule and Drucker's Stability Postulate	p. 250
Effective Stress and Effective Strain	p. 256
Illustrative Examples	p. 261
Incremental Stress-Strain Relationships	p. 267
References	p. 281
Problems	p. 282
Answers to Selected Problems	p. 286
Metal Plasticity
Implementation in Metals	p. 293
Introduction	p. 293
Formulation of the Elastic-Plastic Matrix	p. 294
Finite-Element Formulation	p. 296
Numerical Algorithms for Solving Nonlinear Equations	p. 299
Numerical Implementation of the Elastic-Plastic Incremental Constitutive Relations	p. 308
Bounding Surface Theory	p. 317
Extension to Anisotropic Case	p. 326
References	p. 340
Concrete Plasticity
Implementation in Concretes	p. 345
Introduction	p. 345
Failure Criteria	p. 353
Plasticity Modehng: Hardening Behavior	p. 368
Plasticity Modeling: Softening Behavior	p. 383
References	p. 399
Appendix	p. 401
Limit Analysis
General Theorems of Limit Analysis and Their Applications	p. 409
Introduction	p. 409
Theorems of Limit Analysis	p. 411
Applications of the General Theorems	p. 421
Discontinuous Stress Fields	p. 427
Basic Techniques in Applications of the Upper-Bound Method	p. 447
Example Problems in Plane Stress, Plane Strain, and 3-D	p. 468
References	p. 486
Problems	p. 486
Answers to Selected Problems	p. 489
Limit Analysis of Engineering Structures	p. 492
Introduction	p. 492
Bending of Beams and Frames	p. 497
Combined Axial and Bending Forces in Frames and Arches	p. 506
Effect of Shear Force	p. 518
Limit Analysis of Plates	p. 526
Limit Analysis of Plates on Elastic Foundations	p. 533
Limit Analysis of Shells	p. 568
References	p. 589
Problems	p. 590
Answers to Selected Problems	p. 596
Index	p. 601
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