This document outlines the detailed syllabus for a Strength of Materials course taught by Prof. M. S. Sivakumar at Indian Institute of Technology Madras. The syllabus covers 9 chapters on topics including stress, strain, mechanical properties, bending, torsion, energy methods, and elastic stability. Specific topics include stress transformation, principal stresses, beam shear and bending, torsion formulae, Castigliani's theorem, and Euler buckling. The goal is to provide students a comprehensive overview of stress analysis, deformation, failure criteria, and design considerations for engineering structures and components.

1. Strength of Materials (Web Course)
Faculty Coordinator:
1. Prof. M. S. Sivakumar
Department of Applied Mechanics
Indian Institute of Technology
Madras Chennai – 600036
Email : mssiva@iitm.ac.in
Telephone:
Off
: 44 2257 4061
Detailed Syllabus:
Chapters:
1. Introduction to strength of materials
a. Free body diagram revisited – its importance
b. Classification of structures and components
c. Notion of stress – normal stress, shear stress and bearing stresses
d. Stresses on inclined plane in an axial member
e. Notion of strain – normal strain, shear strain
f.
Mechanical properties – elasticity, plasticity, creep, fatigue, buckling etc.
g. Deformation of axial members
h. Compatibility; Statically indeterminate problems
i.
Design considerations –
i. allowable stress, analysis of stress or strain, factor safety, etc.
ii. stress concentration factor, etc.
iii. kinds of failure, deflection type, fatigue type, etc.
j.
Thermal effects
k. Strain energy
l.
Dynamic loads

2. 2. Stress
a. Definition of stress
b. Stress at a point – matrix of stress / stress tensor
c. Symmetry of stress tensor
d. Equilibrium of a body – differential equations of equilibrium
e. Different states of stress – uniaxial, biaxial, plane stress, etc.
f.
Transformation of plane stress; extension to 3-D
g. Principal stresses and maximum shear stress
h. Mohr’s circle
3. Strain
a. Definition of strain – shear and normal strains
b. Strain at a point – matrix of strain / strain tensor
c. Symmetry of strain tensor
d. Different states of strain – uniaxial, plane strain, etc.
e. Transformation of plane strain; extension to 3-D.
f.
Principal strains
g. Mohr’s circle for plane strain
4. Mechanical properties
a. Generalized Hooke’s law
b. Lame’s constant, elastic modulus, bulk modulus
c. Relationship between different elastic constants
5. Bending
a. Relation between transverse loads, shear and bending moments
b. Shear and bending moment diagrams
c. Pure bending – beams with symmetric cross-sections
d. Beams with composite cross-section
e. Shear stresses in beams
f.
Deflections in beams

3. 6. Torsion
a. Torsional moment diagrams
b. Torsion formula for circular cross-sections
c. Maximum normal and shear stresses
d. Angle of twist
7. Applications to real world problems
a. Thin-walled pressure vessels
b. States of stress in some applications
c. Complex loading conditions
d. Design considerations
8. Energy methods
a. Stored energy in elastic members – axial, torsional, bending, etc.
b. Castigliano’s theorem
c. Application of Castigliano’s theorem to different classes of problems
d. Virtual work principles – the basis
e. Application of virtual work principles to classes of problems
f.
A peep into Finite element Method
9. Elastic stability
a. Notion of stability of equilibrium
b. Euler buckling
c. Members with eccentric loading
d. Initially imperfect columns
e. Beam-columns