Mechanics of Materials: An Introduction to the Mechanics of Elastic and Plastic Deformation of Solids and Structural Materials, 4th Edition covers the behaviors of materials and structures under various loads, the ways in which they react to applied forces, the resulting deflections, and the stresses and strains that need to be considered when designing a mechanical component.
It begins with an introduction to the concepts of stress, strain, shear force, and bending moments, then progresses to an examination of bending, shear, and torsion in elements such as beams, cylinders, shells, and springs. A simple treatment of complex stress and strain leads to a study of the theories of elastic failure and an introduction to the experimental methods of stress and strain analysis.
Building on those fundamentals, the book then extends the scope of the materials covered into more complex areas such as unsymmetrical bending, loading and deflection of struts, rings, discs, cylinder plates, diaphragms, and thin walled sections. The finite element method, and more advanced topics such as contact and residual stresses, stress concentrations, fatigue, and creep and fracture are also covered. Each chapter contains a summary of the essential formulae developed in the chapter, as well as a large number of worked examples which progress in level of difficulty. Additionally, each chapter concludes with an extensive selection of problems for solving by the reader.
1. Introduction - p. 71 2. 4.1 Relationship between loading, shearing force, bending moment, slope and deflection - p. 71 3. 4.2 Direct integration method - p. 73 4. 4.3 Macaulay’s method - p. 78 5. 4.4 Macaulay’s method for use with uniformly distributed loads - p. 80 6. 4.5 Macaulay’s method for beams with u.d.l. applied over part of the beam - p. 81 7. 4.6 Macaulay’s method for couple applied at a point - p. 82 8. 4.7 Mohr’s “area-moment” method - p. 84 9. 4.8 Principle of superposition - p. 86 10. 4.9 Energy method - p. 87 11. 4.10 Maxwell’s theorem of reciprocal displacements - p. 87 12. 4.11 Continuous beams—Clapeyron’s “three-moment” equation - p. 89 13. Examples - p. 92 14. Problems - p. 103 15. Chapter 5. Built-in beams - p. 107 16. Chapter 6. Unsymmetrical bending - p. 119 17. Chapter 7. Shear stresses - p. 143 18. Chapter 8. Torsion - p. 163 19. Chapter 9. Torsion of noncircular and thin-walled sections - p. 181 20. Chapter 10. Thin cylinders and shells - p. 205 21. Chapter 11. Thick cylinders - p. 221 22. Chapter 12. Strain energy - p. 251 23. Chapter 13. Springs - p. 283 24. Chapter 14. Complex stresses - p. 309 25. Chapter 15. Complex strain - p. 343 26. Chapter 16. Introduction to advanced elasticity theory - p. 375 27. Abstract - p. 375 28. 16.1 Type of stress - p. 375 29. 16.2 Cartesian stress components: notation and sign convention - p. 375 30. 16.3 The state of stress at a point - p. 376 31. 16.4 Direct, shear, and resultant stresses on an oblique plane - p. 378 32. 16.5 Principal stresses and strains in three dimensions—Mohr’s circle representation - p. 382 33. 16.6 Graphical determination of the direction of the shear stress τnτn on an inclined plane in a three-dimensional principal stress system - p. 382 34. 16.7 Combined Mohr's diagram for three-dimensional stress and strain systems - p. 384 35. 16.8 Application of the combined circle to two-dimensional stress systems - p. 386 36. 16.9 Graphical construction for the state of stress at a point - p. 387 37. 16.10 Construction for the state of strain on a general strain plane - p. 388 38. 16.11 State of stress-tensor notation - p. 388 39. 16.12 The stress equations of equilibrium - p. 389 40. 16.13 Principal stresses in a three-dimensional Cartesian stress system - p. 394 41. 16.14 Eigenvalues and eigenvectors - p. 395 42. 16.15 Stress invariants - p. 396 43. 16.16 Reduced stresses - p. 398 44. 16.17 Strain invariants - p. 399 45. 16.18 Alternative procedure for determination of principal stresses (eigenvalues) - p. 399 46. 16.19 Octahedral planes and stresses - p. 400 47. 16.20 Deviatoric stresses - p. 402 48. 16.21 Deviatoric strains - p. 404 49. 16.22 Plane stress and plane strain - p. 404 50. 16.23 Stress–strain relations - p. 407 51. 16.24 Strain–displacement relationships - p. 408 52. 16.25 Strain equations of transformation - p. 409 53. 16.26 Compatibility - p. 410 54. 16.27 Stress function concept - p. 412 55. Examples - p. 429 56. Problems - p. 435 57. References - p. 445 58. Chapter 17. Theories of elastic failure - p. 447 59. Chapter 18. Buckling - p. 473 60. Chapter 19. Introduction to plasticity - p. 503 61. Abstract - p. 503 62. Summary - p. 503 63. Introduction - p. 504 64. 19.1 Plastic bending of rectangular-sectioned beams - p. 506 65. 19.2 Shape factor—symmetrical sections - p. 506 66. 19.3 Application to II-section beams - p. 508 67. 19.4 Partially plastic bending of unsymmetrical sections - p. 508 68. 19.5 Shape factor—unsymmetrical sections - p. 509 69. 19.6 Deflections of partially plastic beams - p. 509 70. 19.7 Length of yielded area in beams - p. 510 71. 19.8 Collapse loads—plastic limit design - p. 511 72. 19.9 Residual stresses after yielding: elastic-perfectly plastic material - p. 513 73. 19.10 Plastic torsion - p. 515 74. 19.11 Angles of twist of shafts strained beyond the elastic limit - p. 517 75. 19.12 Plastic torsion of hollow tubes - p. 517 76. 19.13 Plastic torsion of case-hardened shafts - p. 518 77. 19.14 Residual stresses after yield in torsion - p. 518 78. 19.15 Plastic bending and torsion of strain-hardening materials - p. 519 79. 19.16 Residual stresses–strain-hardening materials - p. 523 80. 19.17 Influence of residual stresses on bending and torsional strengths - p. 523 81. 19.18 Plastic yielding in the eccentric loading of rectangular sections - p. 523 82. 19.19 Plastic yielding and residual stresses under axial loading with stress concentrations - p. 525 83. 19.20 Plastic yielding of axially symmetric components - p. 526 84. Examples - p. 533 85. Problems - p. 545 86. References - p. 553 87. Chapter 20. Rotating rings, disks, and cylinders - p. 555 88. Chapter 21. Circular plates and diaphragms - p. 571 89. Chapter 22. Contact stress and stress concentrations - p. 597 90. Chapter 23. Effects of temperature and impact - p. 637 91. Chapter 24. Introduction to fatigue and fracture - p. 669 92. Chapter 25. Introduction to creep and vicoelasticiy - p. 709 93. Chapter 26. Introduction to the finite element method - p. 733 94. Abstract - p. 733 95. Introduction - p. 733 96. 26.1 Basis of the finite element method - p. 733 97. 26.2 Applicability of the finite element method - p. 734 98. 26.3 Formulation of the finite element method - p. 735 99. 26.4 General procedure of the finite element method - p. 735 100. 26.5 Fundamental arguments - p. 748 101. 26.6 The principle of virtual work - p. 751 102. 26.7 A rod element - p. 753 103. 26.8 A simple beam element - p. 760 104. 26.9 A simple triangular plane membrane element - p. 769 105. 26.10 Formation of assembled stiffness matrix by use of a degrees of freedom correspondence table - p. 772 106. 26.11 Application of boundary conditions and partitioning - p. 774 107. 26.12 Solution for displacements and reactions - p. 774 108. Examples - p. 774 109. Problems - p. 799 110. References - p. 803 111. Chapter 27. Experimental stress analysis - p. 805 112. Appendix - p. 835 113. Index - p. 837
Mechanics of Materials: An Introduction to the Mechanics of Elastic and Plastic Deformation of Solids and Structural Materials, 4th Edition covers the behaviors of materials and structures under various loads, the ways in which they react to applied forces, the resulting deflections, and the stresses and strains that need to be considered when designing a mechanical component.
It begins with an introduction to the concepts of stress, strain, shear force, and bending moments, then progresses to an examination of bending, shear, and torsion in elements such as beams, cylinders, shells, and springs. A simple treatment of complex stress and strain leads to a study of the theories of elastic failure and an introduction to the experimental methods of stress and strain analysis.
Building on those fundamentals, the book then extends the scope of the materials covered into more complex areas such as unsymmetrical bending, loading and deflection of struts, rings, discs, cylinder plates, diaphragms, and thin walled sections. The finite element method, and more advanced topics such as contact and residual stresses, stress concentrations, fatigue, and creep and fracture are also covered. Each chapter contains a summary of the essential formulae developed in the chapter, as well as a large number of worked examples which progress in level of difficulty. Additionally, each chapter concludes with an extensive selection of problems for solving by the reader.
1. Introduction - p. 71 2. 4.1 Relationship between loading, shearing force, bending moment, slope and deflection - p. 71 3. 4.2 Direct integration method - p. 73 4. 4.3 Macaulay’s method - p. 78 5. 4.4 Macaulay’s method for use with uniformly distributed loads - p. 80 6. 4.5 Macaulay’s method for beams with u.d.l. applied over part of the beam - p. 81 7. 4.6 Macaulay’s method for couple applied at a point - p. 82 8. 4.7 Mohr’s “area-moment” method - p. 84 9. 4.8 Principle of superposition - p. 86 10. 4.9 Energy method - p. 87 11. 4.10 Maxwell’s theorem of reciprocal displacements - p. 87 12. 4.11 Continuous beams—Clapeyron’s “three-moment” equation - p. 89 13. Examples - p. 92 14. Problems - p. 103 15. Chapter 5. Built-in beams - p. 107 16. Chapter 6. Unsymmetrical bending - p. 119 17. Chapter 7. Shear stresses - p. 143 18. Chapter 8. Torsion - p. 163 19. Chapter 9. Torsion of noncircular and thin-walled sections - p. 181 20. Chapter 10. Thin cylinders and shells - p. 205 21. Chapter 11. Thick cylinders - p. 221 22. Chapter 12. Strain energy - p. 251 23. Chapter 13. Springs - p. 283 24. Chapter 14. Complex stresses - p. 309 25. Chapter 15. Complex strain - p. 343 26. Chapter 16. Introduction to advanced elasticity theory - p. 375 27. Abstract - p. 375 28. 16.1 Type of stress - p. 375 29. 16.2 Cartesian stress components: notation and sign convention - p. 375 30. 16.3 The state of stress at a point - p. 376 31. 16.4 Direct, shear, and resultant stresses on an oblique plane - p. 378 32. 16.5 Principal stresses and strains in three dimensions—Mohr’s circle representation - p. 382 33. 16.6 Graphical determination of the direction of the shear stress τnτn on an inclined plane in a three-dimensional principal stress system - p. 382 34. 16.7 Combined Mohr's diagram for three-dimensional stress and strain systems - p. 384 35. 16.8 Application of the combined circle to two-dimensional stress systems - p. 386 36. 16.9 Graphical construction for the state of stress at a point - p. 387 37. 16.10 Construction for the state of strain on a general strain plane - p. 388 38. 16.11 State of stress-tensor notation - p. 388 39. 16.12 The stress equations of equilibrium - p. 389 40. 16.13 Principal stresses in a three-dimensional Cartesian stress system - p. 394 41. 16.14 Eigenvalues and eigenvectors - p. 395 42. 16.15 Stress invariants - p. 396 43. 16.16 Reduced stresses - p. 398 44. 16.17 Strain invariants - p. 399 45. 16.18 Alternative procedure for determination of principal stresses (eigenvalues) - p. 399 46. 16.19 Octahedral planes and stresses - p. 400 47. 16.20 Deviatoric stresses - p. 402 48. 16.21 Deviatoric strains - p. 404 49. 16.22 Plane stress and plane strain - p. 404 50. 16.23 Stress–strain relations - p. 407 51. 16.24 Strain–displacement relationships - p. 408 52. 16.25 Strain equations of transformation - p. 409 53. 16.26 Compatibility - p. 410 54. 16.27 Stress function concept - p. 412 55. Examples - p. 429 56. Problems - p. 435 57. References - p. 445 58. Chapter 17. Theories of elastic failure - p. 447 59. Chapter 18. Buckling - p. 473 60. Chapter 19. Introduction to plasticity - p. 503 61. Abstract - p. 503 62. Summary - p. 503 63. Introduction - p. 504 64. 19.1 Plastic bending of rectangular-sectioned beams - p. 506 65. 19.2 Shape factor—symmetrical sections - p. 506 66. 19.3 Application to II-section beams - p. 508 67. 19.4 Partially plastic bending of unsymmetrical sections - p. 508 68. 19.5 Shape factor—unsymmetrical sections - p. 509 69. 19.6 Deflections of partially plastic beams - p. 509 70. 19.7 Length of yielded area in beams - p. 510 71. 19.8 Collapse loads—plastic limit design - p. 511 72. 19.9 Residual stresses after yielding: elastic-perfectly plastic material - p. 513 73. 19.10 Plastic torsion - p. 515 74. 19.11 Angles of twist of shafts strained beyond the elastic limit - p. 517 75. 19.12 Plastic torsion of hollow tubes - p. 517 76. 19.13 Plastic torsion of case-hardened shafts - p. 518 77. 19.14 Residual stresses after yield in torsion - p. 518 78. 19.15 Plastic bending and torsion of strain-hardening materials - p. 519 79. 19.16 Residual stresses–strain-hardening materials - p. 523 80. 19.17 Influence of residual stresses on bending and torsional strengths - p. 523 81. 19.18 Plastic yielding in the eccentric loading of rectangular sections - p. 523 82. 19.19 Plastic yielding and residual stresses under axial loading with stress concentrations - p. 525 83. 19.20 Plastic yielding of axially symmetric components - p. 526 84. Examples - p. 533 85. Problems - p. 545 86. References - p. 553 87. Chapter 20. Rotating rings, disks, and cylinders - p. 555 88. Chapter 21. Circular plates and diaphragms - p. 571 89. Chapter 22. Contact stress and stress concentrations - p. 597 90. Chapter 23. Effects of temperature and impact - p. 637 91. Chapter 24. Introduction to fatigue and fracture - p. 669 92. Chapter 25. Introduction to creep and vicoelasticiy - p. 709 93. Chapter 26. Introduction to the finite element method - p. 733 94. Abstract - p. 733 95. Introduction - p. 733 96. 26.1 Basis of the finite element method - p. 733 97. 26.2 Applicability of the finite element method - p. 734 98. 26.3 Formulation of the finite element method - p. 735 99. 26.4 General procedure of the finite element method - p. 735 100. 26.5 Fundamental arguments - p. 748 101. 26.6 The principle of virtual work - p. 751 102. 26.7 A rod element - p. 753 103. 26.8 A simple beam element - p. 760 104. 26.9 A simple triangular plane membrane element - p. 769 105. 26.10 Formation of assembled stiffness matrix by use of a degrees of freedom correspondence table - p. 772 106. 26.11 Application of boundary conditions and partitioning - p. 774 107. 26.12 Solution for displacements and reactions - p. 774 108. Examples - p. 774 109. Problems - p. 799 110. References - p. 803 111. Chapter 27. Experimental stress analysis - p. 805 112. Appendix - p. 835 113. Index - p. 837
