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.
 Introduction (2 hours)
 Classification of mechanics of materials
 External and internal forces, rigid body and deformable solid
 Assumptions in mechanics of solids
 Types of loading
 Simple stresses and strains (2 hours)
 Concept and types of stress and strain
 Elasticity and Hooke’s law, Poisson’s ratio
 Elastic constants (Young’s modulus, shear modulus and bulk modulus) and their relationship
 Stress strain diagram for ductile and brittle materials
 Ultimate stress, allowable stress and factor of safety
 Generalised Hooke’s law
 Axial loading (4 hours)
 Tension, compression and shear
 Axial deformation on a bar of constant section and varying section under uniform load, uniformly varying load, selfweight
 Thermal stress and strain
 Statically determinate and indeterminate problems
 Torsion
(6 hours)
 Theory of pure torsion and its assumptions
 Torsion moment diagram and torsional stress and twist angle variation
 Torsion of hollow and circular shaft
 Comparison between hollow and solid shaft by strength and weight
 Shafts in series and parallel
 Statically indeterminate shaft
 Torsion of noncircular solid members and thinwalled tubular members
 Composite shafts
 Bending stresses in beams (6 hours)
 Theory of pure bending and its assumptions
 Bending stresses in symmetrical sections and unsymmetrical sections
 Beams with composite sections
 Unsymmetrical bending and shear center (6 hours)
 Stress in unsymmetrical bending
 Deflection of beams in unsymmetrical bending
 Eccentric tension and compression
 Shear centre
 Determination of shear centre for C, I & L sections and box beams
 Shear stresses in beams (4 hours)
 Shear stress at a section
 Shear stress in a beam
 Relationship between shear force and shear stress in a beam
 Distribution of shear stress in common beam sections
 Principal stresses and strains (4 hours)
 Normal and tangential components of stress
 Principal planes and principal stresses
 Analytical and graphical method (Mohr’s circle) for determining stresses on principal planes and oblique section
 Mohr’s strain circle
 Strains on an oblique plane
 Curved beams (4 hours)
 Assumptions in stress distribution in curved beams
 Stresses in a curved beam, circular ring and chain link
 Stresses due to rotation
(2 hours)
 Stresses in rotating disc
 Stresses in rotating thin cylinder
 Deflection of beams (8 hours)
 Deformation of a beam under transverse loading
 General differential equation of the elastic curve
 Slope and deflection of loaded members
 Double integration method
 Moment area method
 Columns and struts (2 hours)
 Definition: column and strut, slenderness ratio, buckling factor, buckling load
 Strength of column
 Classification of columns
 End conditions and effective length of a column
 Euler’s theory of long columns: assumptions, derivations and limitations
 Design of column under central and eccentric loading
 Thin cylinders, shells and thick cylinders (4 hours)
 Stresses and strains in thin cylindrical and spherical shell due to internal pressure
 Circumferential, radial and longitudinal stresses and strains in thin cylinder
 Circumferential, radial and longitudinal stresses and strains in thick cylinder
 Shrink fit and compound cylinder
 Energy methods (4 hours)
 Strain energy, strain energy density
 Strain energy in tension, compression, shear, bending and torsion
 Strain energy due to: static loads, dynamic loads, fluctuating loads, gradually applied loads, suddenly applied loads, impact loads
 Stress concentration (2 hours)
 Stress concentration in tension and compression
 Stress concentration in bending, shear and torsion
Practical:
 To determine beam reactions for
 Simply supported beams and
 Cantilever beams
 To study torsional behavior and determine shear modulus of ductile and brittle materials for
 Circular cross section
 Noncircular cross section
 To study buckling effect in different end conditions of column
 To determine stresses and strains in
 Thin wall cylinder
 Thick wall cylinder
References:
 P, Beer and E. R. Johnson, Mechanics of materials, Tata McGraw Hill publishing company limited, 2005.
 P, Popov, Engineering Mechanics of solids, Prentice hall Inc.
 P. Boresi and O. P. Sidebottom, Advanced Mechanics of materials, Wiley
 K. Rajput, Strength of materials, S. Chand & Co. Ltd.
 Kripal singh, Mechanics of Materials, Standard Publishers Distributors, 1998
 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:
Chapter 
Marks 
1, 13, 14 & 15 
16 
2, 3 & 4 
16 
5 & 6 
16 
7, 8 & 9 
16 
10, 11 & 12 
16 
Total 
80 
*Note: There may be minor deviation in mark distribution
