Mechanics of Solids

Syllabus

1. Introduction (2 hours)
   1. Rigid body and deformable body
   2. Types of loads on structure
   3. Concept of elasticity
   4. Elastic and non-elastic behaviour of solids
   5. Elastic coefficients and their relations
2. Three-Dimensional Stress (6 hours)
   1. Stress tensor: definition, notation and sign convention
   2. State of stress at a point
   3. Stress acting on an arbitrarily oriented plane
   4. Stress transformation
   5. Principal stress, principal plane, octahedral stress
   6. Differential equations of motion of a deformable body
   7. Von Mises stress
3. Analysis of Deformation (6 hours)
   1. Strain at a point
   2. Small displacement theory and compatibility relations
   3. Strain tensor
   4. Normal and shear strain, plane strain
   5. Strain acting on arbitrarily oriented plane
   6. Strain transformation and principal strain
   7. Volumetric strain
4. Strain Energy and Applications of Energy Method (7 hours)
   1. Definition
   2. Strain energy density
   3. Isotropic and anisotropic elasticity
   4. Strain energy in tension, shear, bending and torsion
   5. Castigliano's theorem
   6. Dummy load method
5. Curved Beam (4 hours)
   1. Definition
   2. Assumptions in stress distribution
   3. Circumferential, radial, and axial stresses
   4. Deflection of curved beam
   5. Statically indeterminate closed ring
6. Unsymmetrical Bending and Shear Center (8 hours)
   1. Definition
   2. Bending stress due to unsymmetrical bending
   3. Deflections due to unsymmetrical bending
   4. Shear flow in thin wall beam cross section
   5. Shear center for channel section
   6. Composite beams
7. Thin and Thick Wall Cylinder (5 hours)
   1. Stress and strain in thin cylindrical shell
   2. Open and closed end thick cylinder
   3. Circumferential, radial and longitudinal stress
   4. Linear and volumetric strain
   5. Composite thick cylinders
8. Torsion (5 hours)
   1. Torsion in triangular, rectangular, and elliptical sections
   2. Torsion in narrow rectangular cross section
   3. Torsion of hollow thin wall section
9. Contact Stresses (2 hours)
   1. Point and line contact
   2. Expressions for principal stresses

Practicals

1. Non-linear behaviour of rubber in tension
2. Creep test and relaxation test on viscoelastic specimen
3. Torsion test of rectangular and triangular section rods; torsion test of circular, square and rectangular closed thin wall tubes
4. Deflections and stresses in curved beams
5. Stress and strain in thick wall cylinders
6. Determination of shear center for a beam with a channel cross section
7. Effects of suddenly applied dynamic loads; tension member under dynamic load; sudden transverse loading of a beam

Evaluation

Final exam questions cover all chapters. Approximate marks distribution (total 60 marks over 45 hours):

1. Introduction and Contact Stresses: 4 marks
2. Three-Dimensional Stress: 8 marks
3. Analysis of Deformation: 8 marks
4. Strain Energy and Applications of Energy Method: 8 marks
5. Curved Beam: 6 marks
6. Unsymmetrical Bending and Shear Center: 12 marks
7. Thin and Thick Wall Cylinder: 8 marks
8. Torsion: 6 marks