Course Title: 
Mechanics of Solids
Year Taught: 
Subject Core
School of Engineering

'Mechanics of Solids' is a course offered in the third semester of B. Tech. in Mechanical Engineering program at School of Engineering, Amrita Vishwa Vidyapeetham.

Unit 1

Simple Stress and Strain
Introduction, Properties of Materials, Stress, Strain, Hook’s law, Poisson’s Ratio, Stress – Strain Diagram for structural steel and nonferrous materials, Principles of superposition, Total elongation of tapering bars of circular and rectangular cross sections. Elongation due to self – weight, Thermal stresses.

Composite section, Volumetric strain, expression for volumetric strain, Elastic constants, relationship among elastic constants, Thermal stresses (including thermal stresses in compound bars). Strain Energy & Impact loading.

Compound Stresses
Introduction, Stress components on inclined planes, General two-dimensional stress system, Principal planes and stresses and Mohr’s circle of stresses.

Unit 2

Torsion of circular shafts
Introduction – Pure torsion-torsion equation of circular shafts, Strength and stiffness, Torsional rigidity and polar modulus, Power transmitted by shaft of solid and hollow circular sections.

Bending moment and shear force in beams
Introduction, Types of beams loadings and supports, Shearing force in beam, Bending moment, Sign convention, Relationship between loading, shear force and bending moment, Shear force and bending moment equations, SFD and BMD with salient values for cantilever beams, simply supported beams and overhanging beams considering point loads, UDL, UVL and Couple. Bending and shear stresses in beams.

Unit 3

Deflection of beams
Introduction – Definitions of slope, deflection, Elastic curve-derivation of differential equation of flexure, Sign convention Slope and deflection for standard loading classes using Macaulay’s method for prismatic beams and overhanging beams subjected to point loads, UDL and Couple.

Thick and Thin Cylinders and shells
Analysis of thincylindrical shells and analysis of thick cylindrical shells using Lame’s equation.

Elastic stability of columns
Introduction – Short and long columns, Euler’s theory on columns, Effective length slenderness ration, radius of gyration, buckling load, Assumptions, derivations of Euler’s Buckling load for different end conditions, Limitations of Euler’s theory, Rankine’s formula and problems.

  • R. C. Hibbeler, - ‘Mechanics of Materials’ - Prentice Hall - 2013 - 9th Edition
  • James M. Gere -‘Mechanics of Materials’ - CENGAGE Learning Custom Publishing - 2012 - 8th Edition
  • Ferdinand Beer & Russell Johnstan - ‘Mechanics of Materials’ - TATA McGraw Hill - 2003 - S.I. Units
  • Egor.P. Popov - ‘Engineering Mechanics of Solids’ - Pearson Edu. India - 1998 - 2nd Edition
  • Mubeen - ‘Mechanics of Solids’ - Pearson India - 2012 - 2nd Edition,
  • W. A. Nash, Schaum’s Outline Series - ‘Strength of Materials’ - 2007 - 4th Edition