MEL2010 Mechanics of Solids


  • Course Time Table:

Lectures: Tuesday, Wednesday, Friday (11:00-11:50)

Tutorials: (Thursday 8:00-8:50)

  • Course Content:

Stress and strain: Concept of stress at a point, Plane stress case: transformation of stresses at a point, principal stresses and Mohr's circle, Displacement field, Concept of strain at a point, Plane strain case: transformation of strain at a point, principal strains and Mohr's circle, Strain Rosette, Polar coordinates in stress and strain analysis. St. Venant’s principles and stress concentrations. Mechanical behaviour: Concepts of elasticity, plasticity, strain hardening, failure (fracture/yielding), Generalized Hooke's law (without and with thermal strains) for isotropic materials, orthotropic and anisotropic materials, Force displacement relationship and geometric compatibility for axially loaded members and thin walled pressure vessels. Static Analysis: Complete equations of elasticity; Force analysis (axial force, shear force, bending moment, and twisting moment diagrams) of slender members. Elastic Bending: Moment curvature relationship for pure bending of beams with symmetric cross section, bending stress, shear stress; Cases of combined stresses, Deflection due to bending, Integration of the moment curvature relationship for simple boundary conditions, Stress concentrations. Elastic torsion: Torsion of circular shafts and thin walled tubes, Stress concentrations. Strain Energy: Concept of strain energy, strain energy for simple structural elements, Castigliano's theorems for deflection analysis and indeterminate problems. Elastic Buckling: Concept of elastic instability, Introduction to column buckling, Euler's formula.


  • Reference Books:

  1. Crandall, S.H., Dahl, N.C., and Lardner, T. J., (1978), An Introduction to the Mechanics of Solids, McGraw Hill, Second Ed. with SI Units.

  2. Beer, F.P, Johnston, E.R. and De Wolf, J.T., (2004), Mechanics of Materials, Tata McGrawHill.

  3. Popov, E.P., (1990),Engineering Mechanics of Solids, First Ed. Prentice Hall

  4. Meriam, J.L. and Kraige, L.G., (1980), Engineering Mechanics, Vol. 1: Statics, 2nd Ed. John Wiley

  5. Timoshenko, S.P. and Goodier, J.N. ``Theory of Elasticity``, McGraw-Hill, International Edition, 1970.


  • Course Evaluation (Credits: 04):

60%: Continuous evaluation [Offline and Online Quizzes, Assignments, Tutorials, etc. ]

40%: Major examination


  • Summary of lectures:

Lecture 1: Introduction to the course and evaluation strategy, Forces on a body: body, surface and point forces, Free body diagram (FBD), Internal forces/actions.

Lecture 2&3: Concept of traction vector and stress at a point, Normal and shear stress, Sign convention for stress components, Plane stress, 2D stress tensor.

Lecture 4: Equilibrium equations, Symmetry of the shear stress, 2D stress transformation equations.

Lecture 5&6: Principal stresses, principal planes, plane of maximum shear stress, Mohr's circle representation of plane stress, sign conventions for constructing Mohr's circle, representation of principal stress and maximum shear stress on Mohr's circle.

Lecture 7: Analysis of deformation, displacement fields, Concept of strain at a point, normal strain, engineering shear strain, tensorial shear strain.

Lecture 8: Sign convention for strain components, plane strain, , strain components associated with arbitrary sets of axes, Mohr's circle representation of plane, principal strain and maximum shear strain.

Lecture 9: Measurement of strain, strain gage, strain rosettes, General rosette, 45 degree rosette, 60 degree rosette.

Lecture 10: 2D and 2D differential equation of equilibrium, Tensile testing, UTM, Load-displacement response of a material, stress-strain diagram.

Lecture 11: Stress-strain diagram: Elastic deformation, Modulus of elasticity, Yielding of the material, Plastic deformation, Toughness, Strain hardening, True-stress and true strain.

Lecture 12: Isotropic materials, Poisson's ratio, Elastic stress-strain relationship, Generalized Hooke's.