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Structural Mechanics

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Structural Mechanics

This text covers the fundamental concepts of structural mechanics with applications to marine, civil, and mechanical structures. Topics include analysis of small deflections of beams, moderately large deflections of beams, columns, cables, and shafts; elastic and plastic buckling of columns, thin walled sections and plates; exact and approximate methods; energy methods; principle of virtual work; introduction to failure analysis of structures.

Mechanical EngineeringEngineering
Author
Tomasz Wierzbicki
Publisher
Massachusetts Institute of Technology
Source
LibreTexts
License
CC BY-NC-SA
Language
EN
Read online Download PDF (open licence)
Contents· 89 sections
  1. 01: The Concept of Strain
  2. 1.01: One-dimensional Strain
  3. 1.02: Extension to the 3-D case
  4. 1.03: Description of Strain in the Cylindrical Coordinate System
  5. 1.04: Kinematics of the Elementary Beam Theory
  6. 1.05: Euler-Bernoulli Hypothesis
  7. 1.06: Strain-Displacement Relation of Thin Plates
  8. 1.07: Advanced Topic- Derivation of the Strain-Displacement Relation for Thin Plates
  9. 1.08: Expanded Form of Strain-Displacement Relation
  10. 1.09: Moderately Large Deflections of Beams and Plates
  11. 1.10: Strain-Displacement Relations for Circulate Plates
  12. 02: The Concept of Stress, Generalized Stresses and Equilibrium
  13. 2.01: Stress Tensor
  14. 2.02: Advanced Topic - Local Equilibrium from the Principle of Virtual Work
  15. 2.03: Generalized Forces and Bending Moments in Plates
  16. 2.04: Advanced Topic - Principle of Virtual Work for Beams
  17. 2.05: Derivation of Equation of Equilibrium for Beams from the Principle of Virtual Work
  18. 2.06: Advanced Topic - Mathematical Theory of Beams
  19. 2.07: Equilibrium in the Theory of Moderately Large Deflections of Beams
  20. 2.08: Equilibrium of Rectangular Plates
  21. 2.09: Circular Plates
  22. 03: Development of Constitutive Equations of Continuum, Beams and Plates
  23. 3.01: Prologue to Development of Constitutive Equations for Continuum, Beams and Plates
  24. 3.02: Elasticity Law in 3-D Continuum
  25. 3.03: Specification to the 2-D Continuum
  26. 3.04: Hook’s Law in Generalized Quantities for Beams
  27. 3.05: Inconsistencies in the Elementary Beam Theory
  28. 3.06: Derivation of Constitutive Equations for Plates (Advanced)
  29. 3.07: Stress Formula for Plates
  30. 04: Solution Method for Beam Deflections
  31. 4.01: Governing Equations
  32. 4.02: General Properties of the Beam Governing Equation- General and Particular Solutions
  33. 4.03: Statically Determined Beams
  34. 4.04: Continuity Conditions, an Example
  35. 05: Moderately Large Deflection Theory of Beams
  36. 5.01: General Formulation
  37. 5.02: Solution for a Beam on Roller Support
  38. 5.03: Solution for a Beam with Fixed Axial Displacements
  39. 5.04: Galerkin Method of Solving Non-linear Differential Equation
  40. 5.05: Generalization to Arbitrary Non-linear Problems in Plates and Shells
  41. 06: Bending Response of Plates and Optimum Design
  42. 6.01: Beam Deflection Equation
  43. 6.02: Deflections of Circular Plates
  44. 6.03: Equivalence of Square and Circular Plates
  45. 6.04: Design Concept for Plates
  46. 6.05: Sandwich Plates
  47. 6.06: Stiffened Plates
  48. 6.07: Plates versus Grillages
  49. 6.08: The Concept of Equivalent Thickness
  50. 6.09: Shear Lag
  51. 07: Energy Methods in Elasticity
  52. 7.01: The Concept of Potential Energy
  53. 7.02: Equivalence of the Minimum Potential Energy and Principle of Virtual Work
  54. 7.03: Two Formulations for Beams
  55. 7.04: Fourier Series Expansion and the Ritz Method
  56. 7.05: Solution by Taylor expansion
  57. 7.06: Castigliano Theorem
  58. 08: Stability of Elastic Structures
  59. 8.01: Prelude to Stability of Elastic Structures
  60. 8.02: Trefftz Condition for Stability
  61. 8.03: Stability of Elastic Column Using the Energy Method
  62. 8.04: Effect of Structural Imperfections
  63. 8.05: Stability in Tension
  64. 8.06: Plastic Buckling of Columns
  65. 8.07: Mode Transition (Advanced)
  66. 09: Advanced Topic in Column Buckling
  67. 9.01: The Tallest Column
  68. 9.02: Deflection Behavior for Beam with Compressive Axial Loads and Transverse Loads
  69. 9.03: Snap-through of a Two Bar System
  70. 9.04: Dynamic Snap-Through
  71. 10: Buckling of Plates and Sections
  72. 10.01: Governing Equations and Boundary Conditions
  73. 10.02: Buckling of a Simply Supported Plate
  74. 10.03: Effect of Boundary Conditions
  75. 10.04: Buckling of Sections
  76. 10.05: Post-buckling Response of Plates (Advanced)
  77. 10.06: Ultimate Strength of Plates
  78. 10.07: Effect of Initial Imperfection
  79. 11: Fundamental Concepts in Structural Plasticity
  80. 11.01: Hardening Curve and Yield Curve
  81. Unloading Condition
  82. 11.03: Incompressibility
  83. 11.04: Yield Condition
  84. 11.05: Isotropic and Kinematic Hardening
  85. 11.06: Flow Rule
  86. 11.07: Derivation of the Yield Condition from First Principles (Advanced)
  87. 11.08: Tresca Yield Condition
  88. 11.09: Experimental Validation
  89. 11.10: Example of the Design against First Yield