General introduction to Mechanics of Solids

Review of the concepts of stress and strain

Notes

• General state of stress: 1.4
  
• Poisson’s ratio: 2.4
  
• Generalized Hooke’s law: 2.5, 2.7

Torsion (1 week)

Class Notes

• Torsion of shafts with circular cross-section: 3.1 (3.1A, B, C)
  
• Angle of twist: 3.2
  
• Statically indeterminate shafts: 3.3
• Basics of transmission shaft design: 3.4

Bending of beams (2 weeks)

Class Notes-I
Class Notes-II

• Introduction: Chapter 4 and Chapter 5 Introduction
• Shear and bending moment diagrams: 5.1
• Relationship between load, shear, and bending moment: 5.2
• Bending deformation: 4.1 (4.1A, B)
  
• Flexure formula: 4.2
  

Shear in beams and thin-walled members (1 week)

Class Notes

• Shear in straight beams: Chapter 6 Introduction
  
• Shear formula: 6.1 (6.1A, B, C)
  
• Shear flow in built-up members: 6.3, 6.4
  

Transformation of stress and strain (2 weeks)

For these topics, the coverage during the lectures will be significantly different from the textbook. Please follow the lectures.

Class Notes-I
Class Notes-II

• Plane stress transformation
  
• Principal stresses and maximum in-plane shear stress
  
• Mohr’s circle for plane stress
  
• Absolute maximum shear stress
  
• Plane strain transformation
  
• Mohr’s circle for plane strain (may be dropped)
  
• Absolute maximum shear strain
  
• Recap of material property relations
  
• Strain rosettes
  

Miscellaneous applications (2 weeks)

Class Notes-I
Class Notes-II

• Thin-walled pressure vessels: 7.6
  

• Stresses under combined loads: 8.3

• Thick-walled pressure vessels: This topic is not covered in the textbook. Please follow the lectures.

Deflection of beams (1 week)

Class Notes

• Introduction: Chapter 9 Introduction
• Deformation under transverse loading: 9.1 (9.1A, B)
• Statically indeterminate beams: 9.2
• Method of superposition: 9.4 (9.4A, B)
  

Buckling of columns (1 week)

Class Notes

• Introductin: Chapter 10 Introduction
• Stability of columns: 10.1
  
• Ideal column with pin supports: 10.1A
• Columns having various types of supports: 10.1B (The coverage in the lectures will be somewhat different.)
  

Energy methods (2 weeks)

This chapter should NOT be studied from the textbook. Please follow the lectures.

Class Notes

• External work and strain energy
  
• Elastic strain energy for various types of loading
  
• Principle of virtual work
• Castigliano’s theorem: deflections; statically indeterminate structures