Mechanics of Materials

Course objectives:
To understand the stresses and strains developed in bars, compounds bars, beams, shafts, cylinders and spheres and design basic components of machines.

  1. Introduction (2 hours)
    1. Classification of mechanics of materials
    2. External and internal forces, rigid body and deformable solid
    3. Assumptions in mechanics of solids
    4. Types of loading

  2. Simple stresses and strains (2 hours)
    1. Concept and types of stress and strain
    2. Elasticity and Hooke’s law, Poisson’s ratio
    3. Elastic constants (Young’s modulus, shear modulus and bulk modulus) and their relationship
    4. Stress strain diagram for ductile and brittle materials
    5. Ultimate stress, allowable stress and factor of safety
    6. Generalised Hooke’s law

  3. Axial loading (4 hours)
    1. Tension, compression and shear
    2. Axial deformation on a bar of constant section and varying section under uniform load, uniformly varying load, self-weight
    3. Thermal stress and strain
    4. Statically determinate and indeterminate problems

  4. Torsion (6 hours)
    1. Theory of pure torsion and its assumptions
    2. Torsion moment diagram and torsional stress and twist angle variation
    3. Torsion of hollow and circular shaft
      1. Comparison between hollow and solid shaft by strength and weight
      2. Shafts in series and parallel
    4. Statically indeterminate shaft
    5. Torsion of noncircular solid members and thin-walled tubular members
    6. Composite shafts

  5. Bending stresses in beams (6 hours)
    1. Theory of pure bending and its assumptions
    2. Bending stresses in symmetrical sections and unsymmetrical sections
    3. Beams with composite sections

  6. Unsymmetrical bending and shear center (6 hours)
    1. Stress in unsymmetrical bending
    2. Deflection of beams in unsymmetrical bending
    3. Eccentric tension and compression
    4. Shear centre
    5. Determination of shear centre for C, I & L sections and box beams

  7. Shear stresses in beams (4 hours)
    1. Shear stress at a section
    2. Shear stress in a beam
    3. Relationship between shear force and shear stress in a beam
    4. Distribution of shear stress in common beam sections

  8. Principal stresses and strains (4 hours)
    1. Normal and tangential components of stress
    2. Principal planes and principal stresses
    3. Analytical and graphical method (Mohr’s circle) for determining stresses on principal planes and oblique section
    4. Mohr’s strain circle
    5. Strains on an oblique plane

  9. Curved beams (4 hours)
    1. Assumptions in stress distribution in curved beams
    2. Stresses in a curved beam, circular ring and chain link

  10. Stresses due to rotation (2 hours)
    1. Stresses in rotating disc
    2. Stresses in rotating thin cylinder

  11. Deflection of beams (8 hours)
    1. Deformation of a beam under transverse loading
    2. General differential equation of the elastic curve
    3. Slope and deflection of loaded members
    4. Double integration method
    5. Moment area method

  12. Columns and struts (2 hours)
    1. Definition: column and strut, slenderness ratio, buckling factor, buckling load
    2. Strength of column
    3. Classification of columns
    4. End conditions and effective length of a column
    5. Euler’s theory of long columns: assumptions, derivations and limitations
    6. Design of column under central and eccentric loading

  13. Thin cylinders, shells and thick cylinders (4 hours)
    1. Stresses and strains in thin cylindrical and spherical shell due to internal pressure
    2. Circumferential, radial and longitudinal stresses and strains in thin cylinder
    3. Circumferential, radial and longitudinal stresses and strains in thick cylinder
    4. Shrink fit and compound cylinder

  14. Energy methods (4 hours)
    1. Strain energy, strain energy density
    2. Strain energy in tension, compression, shear, bending and torsion
    3. Strain energy due to: static loads, dynamic loads, fluctuating loads, gradually applied loads, suddenly applied loads, impact loads

  15. Stress concentration (2 hours)
    1. Stress concentration in tension and compression
    2. Stress concentration in bending, shear and torsion


  1. To determine beam reactions for
    1. Simply supported beams and
    2. Cantilever beams
  2. To study torsional behavior and determine shear modulus of ductile and brittle materials for
    1. Circular cross section
    2. Non-circular cross section
  3. To study buckling effect in different end conditions of column
  4. To determine stresses and strains in
    1. Thin wall cylinder
    2. Thick wall cylinder


  1. P, Beer and E. R. Johnson, Mechanics of materials, Tata McGraw Hill publishing company limited, 2005.
  2. P, Popov, Engineering Mechanics of solids, Prentice hall Inc.
  3. P. Boresi and O. P. Sidebottom, Advanced Mechanics of materials, Wiley
  4. K. Rajput, Strength of materials, S. Chand & Co. Ltd.
  5. Kripal singh, Mechanics of Materials, Standard Publishers Distributors, 1998
  6. Ramammurtham, R. Narayanan, Strength of materials, Dhanapat Rai Publishing Company, 2014.

Evaluation scheme:
The questions will cover all the chapters of the syllabus. The evaluation scheme will be as indicated in the table below:



1, 13, 14 & 15


2, 3 & 4


5 & 6


7, 8 & 9


10, 11 & 12




*Note: There may be minor deviation in mark distribution

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