This course is to serve as an introduction to
mechanics of deformable solid bodies. The primary course objective
is to equip the students with the tools necessary to solve mechanics
problems, which involves (a) static analysis of a component to find
the internal actions (forces and moments), (b) determine stresses,
strains and deformation due to internal actions, and (c) compare
them with known acceptable values. This requires the familiarity
with the vocabulary of the subject, skill of drawing free body
diagrams and the understanding of the material behavior under loads.
It is expected to improve your engineering design skills.

Modules

Topics

1

Free body diagram with examples
on modeling of typical supports and joints, Conditions for
equilibrium in 3D and 2D, Friction: limiting and
non-limiting cases

2

Force-displacement relationship
and geometric compatibility (for small deformations) with
illustrations through simple problems on axially loaded
members and thin walled pressure vessels

3

Concept of stress at a point,
Plane stress case: transformations of stresses at a point,
Principal stresses and Mohr TMs circle

4

Displacement field, Concept of strain at a
point, Plane strain case: transformation of strain at a
point, Principal strains and Mohr TMs circle, Strain rosette

5

Discussion of experimental
results on 1D material behavior, Concepts of elasticity,
plasticity, strain hardening, failure (fracture/yielding),
Idealization of 1D stress-strain curve, Generalized Hooke
TMs law (with and without thermal strains) for isotropic
materials, Complete equations of elasticity

6

Force analysis (axial force,
shear force, bending moment and twisting moment diagrams) of
slender members

7

Torsion of circular shafts and
thin-walled tubes (plastic analysis and rectangular shafts
not to be discussed

8

Moment curvature relationship for
pure bending of beams with symmetric cross-section, bending
stress, shear stress (shear center and plastic analysis not
to be discussed)

9

Cases of combined stresses,
Concept of strain energy, Yield criteria

10

Deflection due to bending,
Integration of the momentcurvature relationship for simple
boundary conditions, Method of superposition

11

Strain energy and complementary
strain energy for simple structural elements (those under
axial load, shear force, bending moment, and torsion),
Castiglianoâ€TMs theorems for deflection analysis and
indeterminate problems

12

Concept of elastic instability,
Introduction to column buckling, Eulerâ€TMs formula
(post-buckling behavior not to be discussed)

B.E/B.Tech,M.E/M.Teach,

1. Crandall, S. H., Dahl, N. C. and Lardner, T. J. (2012). 2. An Introduction of the Mechanics of Solids, 3rd ed., Tata McGraw Hill. Shames, I. H. (2004). 3. Engineering Mechanics: Statics and Dynamics, 4th ed., Prentice Hall of India. Meriam, J. L. and Kraige, L. G. (2004). 4. Engineering Mechanics Statics, 5h ed., John Wiley and Sons. 5. Popov, E. P. (1998). Engineering Mechanics of Solids, Pearson.

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