This systematic exploration of real-world stress analysis has been completely updated to reflect state-of-the-art methods and applications now used in aeronautical, civil, and mechanical engineering, and engineering mechanics. Distinguished by its exceptional visual interpretations of solutions, Advanced Mechanics of Materials and Applied Elasticity offers in-depth coverage for both students and engineers. The authors carefully balance comprehensive treatments of solid mechanics, elasticity, and computer-oriented numerical methods—preparing readers for both advanced study and professional practice in design and analysis.   This major revision contains many new, fully reworked, illustrative examples and an updated problem set—including many problems taken directly from modern practice. It offers extensive content improvements throughout, beginning with an all-new introductory chapter on the fundamentals of materials mechanics and elasticity.   Readers will find new and updated coverage of plastic behavior, three-dimensional Mohr’s circles, energy and variational methods, materials, beams, failure criteria, fracture mechanics, compound cylinders, shrink fits, buckling of stepped columns, common shell types, and many other topics. The authors present significantly expanded and updated coverage of stress concentration factors and contact stress developments. Finally, they fully introduce computer-oriented approaches in a comprehensive new chapter on the finite element method.

Table of Contents:
Preface         xii Acknowledgments         xiv About the Authors         xv List of Symbols         xvi   Chapter 1: Analysis of Stress         1 1.1   Introduction    1 1.2   Scope of Treatment   3 1.3   Analysis and Design   5 1.4   Conditions of Equilibrium   7 1.5   Definition and Components of Stress   9 1.6   Internal Force-Resultant and Stress Relations   13 1.7   Stresses on Inclined Sections   17 1.8   Variation of Stress within a Body   19 1.9   Plane-Stress Transformation   22 1.10 Principal Stresses and Maximum In-Plane Shear Stress   26 1.11 Mohr’s Circle for Two-Dimensional Stress   28 1.12 Three-Dimensional Stress Transformation   33 1.13 Principal Stresses in Three Dimensions   36 1.14 Normal and Shear Stresses on an Oblique Plane   40 1.15 Mohr’s Circles in Three Dimensions   43 1.16 Boundary Conditions in Terms of Surface Forces   47 1.17 Indicial Notation   48 References   49 Problems   49   Chapter 2: Strain and Material Properties         65 2.1   Introduction   65 2.2   Deformation   66 2.3   Strain Defined   67 2.4   Equations of Compatibility   72 2.5   State of Strain at a Point   73 2.6   Engineering Materials   80 2.7   Stress—Strain Diagrams   82 2.8   Elastic versus Plastic Behavior   86 2.9   Hooke’s Law and Poisson’s Ratio   88 2.10 Generalized Hooke’s Law   91 2.11 Hooke’s Law for Orthotropic Materials   94 2.12 Measurement of Strain: Strain Rosette   97 2.13 Strain Energy   101 2.14 Strain Energy in Common Structural Members   104 2.15 Components of Strain Energy   106 2.16 Saint-Venant’s Principle   108 References 110 Problems 111   Chapter 3:Problems in Elasticity         124 3.1   Introduction   124 3.2   Fundamental Principles of Analysis   125 Part A–Formulation and Methods of Solution   126 3.3   Plane Strain Problems   126 3.4   Plane Stress Problems   128 3.5   Comparison of Two-Dimensional Isotropic Problems   131 3.6   Airy’s Stress Function   132 3.7   Solution of Elasticity Problems   133 3.8   Thermal Stresses   138 3.9   Basic Relations in Polar Coordinates   142 Part B–Stress Concentrations 147 3.10 Stresses Due to Concentrated Loads   147 3.11 Stress Distribution Near Concentrated Load Acting on a Beam   151 3.12 Stress Concentration Factors   153 3.13 Contact Stresses 159 3.14 Spherical and Cylindrical Contacts   160 3.15 Contact Stress Distribution   163 3.16 General Contact   167 References   170 Problems   171   Chapter 4: Failure Criteria         181 4.1   Introduction   181 4.2   Failure   181 4.3   Failure by Yielding   182 4.4   Failure by Fracture   184 4.5   Yield and Fracture Criteria   187 4.6   Maximum Shearing Stress Theory   188 4.7   Maximum Distortion Energy Theory   189 4.8   Octahedral Shearing Stress Theory   190 4.9   Comparison of the Yielding Theories   193 4.10 Maximum Principal Stress Theory   195 4.11 Mohr’s Theory   195 4.12 Coulomb—Mohr Theory   196 4.13 Fracture Mechanics   200 4.14 Fracture Toughness   203 4.15 Failure Criteria for Metal Fatigue   206 4.16 Impact or Dynamic Loads   212 4.17 Dynamic and Thermal Effects   215 References   217 Problems   218   Chapter 5: Bending of Beams          226 5.1   Introduction   226 Part A–Exact Solutions   227 5.2   Pure Bending of Beams of Symmetrical Cross Section   227 5.3   Pure Bending of Beams of Asymmetrical Cross Section   230 5.4   Bending of a Cantilever of Narrow Section   235 5.5   Bending of a Simply Supported Narrow Beam   238 Part B–Approximate Solutions   240 5.6   Elementary Theory of Bending   240 5.7   Normal and Shear Stresses   244 5.8   Effect of Transverse Normal Stress   249 5.9   Composite Beams   250 5.10 Shear Center   256 5.11 Statically Indeterminate Systems   262 5.12 Energy Method for Deflections   264 Part C–Curved Beams   266 5.13 Elasticity Theory   266 5.14 Curved Beam Formula   269 5.15 Comparison of the Results of Various Theories   273 5.16 Combined Tangential and Normal Stresses   276 References   280 Problems   280   Chapter 6: Torsion of Prismatic Bars          292 6.1   Introduction   292 6.2   Elementary Theory of Torsion of Circular Bars   293 6.3   Stresses on Inclined Planes   298 6.4   General Solution of the Torsion Problem   300 6.5   Prandtl’s Stress Function   302 6.6   Prandtl’s Membrane Analogy   310 6.7   Torsion of Narrow Rectangular Cross Section   315 6.8   Torsion of Multiply Connected Thin-Walled Sections   317 6.9   Fluid Flow Analogy and Stress Concentration   321 6.10 Torsion of Restrained Thin-Walled Members of Open Cross Section   323 6.11 Curved Circular Bars: Helical Springs   327 References   330 Problems   330   Chapter 7: Numerical Methods         337 7.1   Introduction   337 Part A–Finite Difference Method   338 7.2   Finite Differences   338 7.3   Finite Difference Equations   341 7.4   Curved Boundaries   343 7.5   Boundary Conditions   346 Part B–Finite Element Method   350 7.6   Fundamentals   350 7.7   The Bar Element   352 7.8   Arbitrarily Oriented Bar Element  354 7.9   Axial Force Equation   357 7.10 Force-Displacement Relations for a Truss   359 7.11 Beam Element   366 7.12 Properties of Two-Dimensional Elements   372 7.13 General Formulation of the Finite Element Method   374 7.14 Triangular Finite Element   379 7.15 Case Studies in Plane Stress   386 7.16 Computational Tools   394 References   395 Problems   396   Chapter 8: Axisymmetrically Loaded Members          407 8.1   Introduction   407 8.2   Thick-Walled Cylinders   408 8.3   Maximum Tangential Stress   414 8.4   Application of Failure Theories   415 8.5   Compound Cylinders: Press or Shrink Fits   416 8.6   Rotating Disks of Constant Thickness   419 8.7   Design of Disk Flywheels   422 8.8   Rotating Disks of Variable Thickness   426 8.9   Rotating Disks of Uniform Stress   429 8.10 Thermal Stresses in Thin Disks   431 8.11 Thermal Stresses in Long Circular Cylinders   432 8.12 Finite Element Solution   436 8.13 Axisymmetric Element   437 References   441 Problems   442   Chapter 9:Beams on Elastic Foundations         448 9.1   Introduction   448 9.2   General Theory   448 9.3   Infinite Beams   449 9.4   Semi-Infinite Beams   454 9.5   Finite Beams   457 9.6   Classification of Beams   458 9.7   Beams Supported by Equally Spaced Elastic Elements   458 9.8   Simplified Solutions for Relatively Stiff Beams   460 9.9   Solution by Finite Differences   461 9.10 Applications  464 References   466 Problems   466   Chapter 10: Applications of Energy Methods         469 10.1   Introduction   469 10.2   Work Done in Deformation   470 10.3   Reciprocity Theorem   471 10.4   Castigliano’s Theorem   472 10.5   Unit- or Dummy-Load Method   479 10.6   Crotti—Engesser Theorem   481 10.7   Statically Indeterminate Systems   483 10.8   Principle of Virtual Work   486 10.9   Principle of Minimum Potential Energy   487 10.10 Deflections by Trigonometric Series   489 10.11 Rayleigh—Ritz Method   493 References   496 Problems   496   Chapter 11: Stability of Columns         505 11.1   Introduction   505 11.2   Critical Load   505 11.3   Buckling of Pinned-End Columns   507 11.4   Deflection Response of Columns   509 11.5   Columns with Different End Conditions   511 11.6   Critical Stress: Classification of Columns   513 11.7   Allowable Stress   517 11.8   Imperfections in Columns   519 11.9   Eccentrically Loaded Columns: Secant Formula   520 11.10 Energy Methods Applied to Buckling   522 11.11 Solution by Finite Differences   529 11.12 Finite Difference Solution for Unevenly Spaced Nodes   534 References   536 Problems   536   Chapter 12: Plastic Behavior of Materials          545 12.1   Introduction   545 12.2   Plastic Deformation   546 12.3   Idealized Stress—Strain Diagrams   546 12.4   Instability in Simple Tension   549 12.5   Plastic Axial Deformation and Residual Stress   551 12.6   Plastic Defection of Beams   553 12.7   Analysis of Perfectly Plastic Beams   556 12.8   Collapse Load of Structures: Limit Design   565 12.9   Elastic—Plastic Torsion of Circular Shafts   569 12.10 Plastic Torsion: Membrane Analogy   573 12.11 Elastic—Plastic Stresses in Rotating Disks   575 12.12 Plastic Stress—Strain Relations   578 12.13 Plastic Stress—Strain Increment Relations   583 12.14 Stresses in Perfectly Plastic Thick-Walled Cylinders   586 References   590 Problems   590   Chapter 13:Plates and Shells          598 13.1   Introduction   598 Part A–Bending of Thin Plates   598 13.2   Basic Assumptions   598 13.3   Strain—Curvature Relations   599 13.4   Stress, Curvature, and Moment Relations   601 13.5   Governing Equations of Plate Deflection   603 13.6   Boundary Conditions   605 13.7   Simply Supported Rectangular Plates   607 13.8   Axisymmetrically Loaded Circular Plates   610 13.9   Deflections of Rectangular Plates by the Strain-Energy Method   613 13.10 Finite Element Solution   615 Part B–Membrane Stresses in Thin Shells   618 13.11 Theories and Behavior of Shells   618 13.12 Simple Membrane Action   618 13.13 Symmetrically Loaded Shells of Revolution   620 13.14 Some Common Cases of Shells of Revolution   622 13.15 Thermal Stresses in Compound Cylinders   626 13.16 Cylindrical Shells of General Shape   628 References   631 Problems   631   Appendix A: Problem Formulation and Solution         637   Appendix B: Solution of the Stress Cubic Equation         640 B.1   Principal Stresses   640 B.2   Direction Cosines   641   Appendix C: Moments of Composite Areas            645 C.1   Centroid   645 C.2   Moments of Inertia   648 C.3   Parallel-Axis Theorem   649 C.4   Principal Moments of Inertia   652   Appendix D: Tables and Charts         659 D.1   Average Properties of Common Engineering Materials   660 D.2   Conversion Factors: SI Units to U.S. Customary Units   662 D.3   SI Unit Prefixes   662 D.4   Deflections and Slopes of Beams   663 D.5   Reactions Deflections of Statically Indeterminate Beams   664 D.6   Stress Concentration Factors for Bars and Shafts with Fillets, Grooves, and Holes   665   Answers to Selected Problems         669   Index         677