CONTENTS Chapter1 IntroductionI 1.1The Engineering Design Process1 1.1.1Economics of designcalculations2 1.2Design Optimization2 1.2.1Predicting the behavior of thecomponent4 1.2.2Approximate solutions5 1.3Relative Magnitude of Different Effects6 1.4Formulating and Solving Problems8 1.4.1Use of procedures9 1.4.2Inverse problems10 1.4.3Physical uniqueness and existencearguments11 1.5Review of Elementary Mechanics ofMaterials12 1.5.1Definition of stress components12 1.5.2Transformation of stresscomponents13 1.5.3Displacement and strain131.5.4Hookes law15 1.5.5Bending of beams17 1.5.6Torsion of circular bars18 1.6Summary18 Further Reading19 Problems19 Chapter2 Material Behavior and Failure25 2.1Transformation of Stresses27 2.1.1Review of two-dimensional results27 2.1.2Principal stresses in threedimensions30 2.2Failure Theories for Isotropic Materials36 2.2.1The failure surface37 2.2.2The shape of the failure envelope39 2.2.3Ductile failure (yielding)39 2.2.4 Brittle failure 50 2.3Cyclic Loading and Fatigue62 2.3.1Experimental data64 2.3.2Statistics and the size effect67 2.3.3Factors influencing the designstress72 2.3.4Effect of a superposed meanstress77 2.3.5Summary of the design process80 2.4Summary85 Further Reading86 Problems87 Chapter3 Energy Methods97 3.1Work Done on Loading and Unloading98 3.2Strain Energy100 3.3Load-Displacement Relations101 3.3.1Beams with continuously varying bending moments104 3.3.2Axial loading and torsion105 3.3.3More general expressions for strain energy107 3.3.4Strain energy associated with shear forces in beams107 3.4Potential Energy107 3.5The Principle of Stationary Potential Energy110 3.5.1Potential energy due to an external force113 3.5.2Problems with several degrees of freedom113 3.5.3Nonlinear problems116 3.6The Rayleigh-Ritz Method118 3.6.1Improving the accuracy121 3.6.2Improving the back of the envelope approximation123 3.7Castiglianos First Theorem129 3.8Linear Elastic Systems133 3.8.1Strain energy133 3.8.2Bounds on the coefficients136 3.8.3Use of the reciprocal theorem137 3.9The Stiffness Matrix138 3.9.1Structures consisting of beams140 3.9.2Assembly of the stiffness matrix143 3.10 Castiglianos Second Theorem143 3.10.1 Use of the theorem145 3.10.2 Dummy loads147 3.10.3 Unit load method150 3.10.4 Formal procedure for using Castiglianos second theorem151 3.10.5 Indeterminate problems151 3.10.6 Three-dimensional problems155 3.11 Summary157 Further Reading158 Problems158 Chapter4 Unsymmetrical Bending177 4.1Stress Distribution in Bending177 4.1.1Bending about one axis177 4.1.2Generalized bending180 4.1.3Force resultants181 4.1.4Uncoupled problems182 4.1.5Coupled problems184 4.2Displacements of the Beam187 4.3Second Moments of Area190 4.3.1Finding the centroid191 4.3.2The parallel axis theorem192 4.3.3Thin-walled sections196 4.4Further Properties of Second Moments198 4.4.1Coordinate transformation198 4.4.2Mohrs circle of second moments200 4.4.3Solution of unsymmetrical bending problems in principal coordinates203 4.4.4Design estimates for the behavior of unsymmetrical sections206 4.4.5Errors due to misalignment209 4.5Summary211 Further Reading211 Problems211 Chapter5 Nonlinear and Elastic-Plastic Bending225 5.1Kinematics of Bending225 5.2Elastic-Plastic Constitutive Behavior227 5.2.1Unloading and reloading228 5.2.2Yield during reversed loading229 5.2.3Elastic-perfectly plastic material230 5.3Stress Fields in Nonlinear and Inelastic Bending231 5.3.1Force and moment resultants232 5.4Pure Bending about an Axis of Symmetry233 5.4.1Symmetric problems forelastic-perfectly plastic materials234 5.4.2Fully plastic moment and shapefactor239 5.5Bending of a Symmetric Section about anOrthogonal Axis240 5.5.1The fully plastic case240 5.5.2Nonzero axial force243 5.5.3The partially plastic solution245 5.6Unsymmetrical Plastic Bending248 5.7Unloading， Springback and ResidualStress252 5.7.1Springback and residualcurvature254 5.7.2Reloading and shakedown257 5.8Limit Analysis in the Design of Beams258 5.8.1Plastic hinges259 5.8.2Indeterminate Problems259 5.9Summary262 Further Reading263 Problems263 Chapter6 Shear and Torsion of Thin-WalledBeams275 6.1Derivation of the Shear Stress Formula276 6.1.1Choice of cut and direction of the shearstress280 6.1.2Location and magnitude of themaximum shear stress285 6.1.3Welds， rivets， and bolts287 6.1.4Curved sections289 6.2Shear Center291 6.2.1Finding the shear center 291 6.3Unsymmetrical Sections298 6.3.1Shear stress for an unsymmetricalsection298 6.3.2Determining the shear center 298 6.4Closed Sections300 6.4.1Determination of the shear stressdistribution300 6.5Pure Torsion of Closed Thin-WalledSections305 6.5.1Torsional stiffness306 6.5.2Design considerations in torsion309 6.6Finding the Shear Center for a Closed Section310 6.6.1Twist due to a shear force312 6.6.2Multicell sections315 6.7Torsion of Thin-Walled Open Sections316 6.7. lLoading of an open section away from its shear center319 6.8Summary322 Further Reading323 Problems323 Chapter7 Beams on Elastic Foundations339 7.1The Governing Equation340 7.1.1Solution of the governing equation341 7.2The Homogeneous Solution342 7.2.1The semi-infinite beam343 7.3Localized Nature of the Solution347 7.4Concentrated Force on an Infinite Beam349 7.4.1More general loading of the infinite beam350 7.5The Particular Solution351 7.5.1Uniform loading352 7.5.2 Discontinuous loads354 7.6Finite Beams356 7.7Short Beams358 7.8Summary361 Further Reading361 Problems362 Chaptar8 Membrane Stresses in Axisymmetric Shells369 8.1The Meridional Stress370 8.1.1Choice of cut373 8.2The Circumferential Stress375 8.2.1The radii of curvature377 8.2.2Sign conventions379 8.3Self-Weight 381 8.4Relative Magnitudes of Different Loads384 8.5Strains and Displacements386 8.5.1Discontinuities387 8.6Summary389 Further Reading390 Problems390 Chapter9 Axisymmetric Bending of Cylindrical Shells401 9.1Bending Stresses and Moments401 9.2Deformation of the Shell403 9.3Equilibrium of the Shell Element 405 9.4The Governing Equation406 9.4.1Solution strategy408 9.5Localized Loading of the Shell411 9.6Shell Transition Regions412 9.6. lThe cylinder to cone transition415 9.6.2Reinforcing rings417 9.7Thermal Stresses419 9.8The ASME Pressure Vessel Code421 9.9Summary421 Further Reading422 Problems422 Chapter10 Thick-Walled Cylinders and Disks429 10.1 Solution Method 429 10.1.1 Stress components and the equilibrium condition430 10.1.2 Strain， displacement， and compatibility431 10.1.3 The elastic constitutive law432 10.2 The Thin Circular Disk 434 10.3 Cylindrical Pressure Vessels440 10.4 Composite Cylinders， Limits and Fits443 10.4.1 Solution procedure444 10.4.2 Limits and fits447 10.5 Plastic Deformation of Disks and Cylinders448 10.5.1 First yield 449 10.5.2 The fully plastic solution450 10.5.3 Elastic-plastic problems452 10.5.4 Other failure modes455 10.5.5 Unloading and residual stresses456 10.6 Summary457 Further Reading458 Problems458 Chapter11 Curved Beams467 11.1 The Governing Equation467 11.1.1 Rectangular and circular cross sections470 11.1.2 The bending moment471 11.1.3 Composite cross sections474 11.1.4 Axial loading474 11.2 Radial Stresses480 11.3 Distortion of the Cross Section482 11.4 Range of Application of the Theory484 11.5 Summary485 Further Reading485 Problems485 Chapter12 Elastic Stability 491 12.1 Uniform Beam in Compression492 12.2 Effect of Initial Perturbations497 12.2.1 Eigenfunction expansions500 12.3 Effect of Lateral Load (Beam-Columns)501 12.4 Indeterminate Problems505 12.5 Suppressing Low-Order Modes506 12.6 Beams on Elastic Foundations510 12.6.1 Axisymmetric buckling of cylindrical shells512 12.6.2 Whirling of shafts513 12.7 Energy Methods518 12.7.1 Energy methods in beam problems519 12.7.2 The uniform beam in compression520 12.7.3 Inhomogeneous problems523 12.8 Quick Estimates for the Buckling Force524 12.9 Summary526 Further Reading526 Problems527 AppendixA The Finite Element Method537 A.1Approximation538 A.I.1 The "best" approximation538 A. 1.2 Choice of weight functions539 A. 1.3 Discrete approximations541 A.2Axial Loading545 A.2.1The structural mechanics approach545 A.2.2 Assembly of the global stiffness matrix547 A.2.3 The nodal forces548 A.2.4 The Rayleigh-Ritz approach549 A.2.5 Direct evaluation of the matrix equation554 A.3Solution of Differential Equations556 A.4Finite Element Solutions for the Bending of Beams558 A.4.1Nodal forces and moments562 A.5Two- and Three-Dimensional Problems565 A.6Computational Considerations566 A.6.1Data storage considerations568 A.7Use of the Finite Element Method in Design568 A.8 Summary569 Further Reading570 Problems570 AppendixB Properties of Areas577 AppendixC Stress Concentration Factors581 AppendixD Answers to Even-Numbered Problems585
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