Plasticity for Structural Engineers
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Plasticity for Structural Engineers is a practical work that provides engineers and students in structural engineering or structural mechanics with the background needed to make the transition from fundamental theory to computer implementation and engineering practice. It sets out initially to examine the stress-strain behaviors of materials under simple test conditions, goes on to show how these behaviors can be generalized under combined stresses, and finally outlines the finite element implementation of the generalized stress-strain relations for the solution of practical steel and concrete structural problems. Plasticity for Structural Engineers not only offers the reader an understanding of the fundamental principles and theory of plasticity in a form that does not require extensive mathematical experience, but also provides the reader with a compact and convenient summary of the modern development of concrete plasticity and limit analysis in structural engineering.
Preface vNotation xiFundamentalsIntroduction 3Introduction 3Historical Remarks 5Plastic Behavior in Simple Tension and Compression 7Modeling of Uniaxial Behavior in Plasticity 11Index Notation 26Summary 40References 40Problems 40Answers to Selected Problems 44Yield and Failure Criteria 46Stress 46Yield Criteria Independent of Hydrostatic Pressure 72Failure Criterion for Pressure-Dependent Materials 84Anisotropic Failure/Yield Criteria 99Summary 103References 104Problems 104Answers to Selected Problems 111Elastic Stress-Strain Relations 117Strain 117Linear Elastic Isotropic Stress-Strain Relation-Hooke's Law 138Nonlinear Elastic Isotropic Stress-Strain Relation 148Principle of Virtual Work 161Drucker's Stability Postulate 163Normality, Convexity, and Uniqueness for an Elastic Solid 165Incremental Stress-Strain Relations 171Summary 172References 173Problems 174Answers to Selected Problems 176Plastic Stress-Strain RelationsStress-Strain Relations for Perfectly Plastic Materials 179Introduction 179Plastic Potential and Flow Rule 181Flow Rule Associated with von Mises Yield Function 183Flow Rule Associated with Tresca Yield Function 85Flow Rule Associated with Mohr-Coulomb Yield Function 189Convexity, Normality, and Uniqueness for Elastic-Perfectly Plastic Materials 192A Simple Elastic-Plastic Problem: The Expansion of a Thick-Walled Cylinder 197Incremental Stress-Strain Relationships 207Prandti-Reuss Material Model (J2 Theory) 210Drucker-Prager Material Model 216General Isotropic Material 221References 225Problems 226Answers to Selected Problems 230Stress-Strain Relations for Work-Hardening Materials 232Introduction 232Deformation Theory of Plasticity 233Loading Surface and Hardening Rules 239Flow Rule and Drucker's Stability Postulate 250Effective Stress and Effective Strain 256Illustrative Examples 261Incremental Stress-Strain Relationships 267References 281Problems 282Answers to Selected Problems 286Metal PlasticityImplementation in Metals 293Introduction 293Formulation of the Elastic-Plastic Matrix 294Finite-Element Formulation 296Numerical Algorithms for Solving Nonlinear Equations 299Numerical Implementation of the Elastic-Plastic Incremental Constitutive Relations 308Bounding Surface Theory 317Extension to Anisotropic Case 326References 340Concrete PlasticityImplementation in Concretes 345Introduction 345Failure Criteria 353Plasticity Modehng: Hardening Behavior 368Plasticity Modeling: Softening Behavior 383References 399Appendix 401Limit AnalysisGeneral Theorems of Limit Analysis and Their Applications 409Introduction 409Theorems of Limit Analysis 411Applications of the General Theorems 421Discontinuous Stress Fields 427Basic Techniques in Applications of the Upper-Bound Method 447Example Problems in Plane Stress, Plane Strain, and 3-D 468References 486Problems 486Answers to Selected Problems 489Limit Analysis of Engineering Structures 492Introduction 492Bending of Beams and Frames 497Combined Axial and Bending Forces in Frames and Arches 506Effect of Shear Force 518Limit Analysis of Plates 526Limit Analysis of Plates on Elastic Foundations 533Limit Analysis of Shells 568References 589Problems 590Answers to Selected Problems 596Index 601
