MECHANICAL ENGINEERING
SYLLABUS
Module 1
Deformation behaviour of elastic solids in equilibrium under the action of a system of forces,
method of sections. Stress vectors on Cartesian coordinate planes passing through a point, stress at
a point in the form of a matrix. Equality of cross shear, Cauchy's equation. Displacement, gradient of
displacement, Cartesian strain matrix, strain- displacement relations (small-strain only), Simple
problems to find strain matrix.Stress tensor and strain tensor for plane stress and plane strain
conditions. Principal planes and principal stress,meaning of stress invariants, maximum shear stress.
Mohr’s circle for 2D case.
Module 2
Stress-strain diagram, Stress–Strain curves of Ductile and Brittle Materials, Poisson’s ratio.
Constitutive equations-generalized Hooke’s law, equations for linear elastic isotropic solids in terms
of Young’s Modulus and Poisson’s ratio, Hooke’s law for Plane stress and plane strain conditions
(derivation not required).
Calculation of stress, strain and change in length in axially loaded members with single and
composite materials, Effects of thermal loading – thermal stress and thermal strain. Thermal stress
on a prismatic bar held between fixed supports.
Module 3
Torsional deformation of circular shafts, assumptions for shafts subjected to torsion within elastic
deformation range, derivation of torsion formula Torsional rigidity, Polar moment of inertia, basic
design of transmission shafts. Simple problems to estimate the stress in solid and hollow shafts.
Shear force and bending moment diagrams for cantilever and simply supported beams. Differential
equations between load, shear force and bending moment.
Normal and shear stress in beams: Derivation of flexural formula, section modulus, flexural rigidity,
numerical problems to evaluate bending stress, economic sections.
Shear stress formula for beams: (Derivation not required), shear stress distribution for a rectangular
section.
Module 4
Deflection of beams using Macauley’s method
Elastic strain energy and Complementary strain energy. Elastic strain energy for axial loading,
transverse shear, bending and torsional loads. Expressions for strain energy in terms of load,
geometry and material properties of the body for axial, shearing, bending and torsional loads.
Castigliano’s second theorem, reciprocal relation(Proof not required for Castigliano’s second
theorem, reciprocal relation).
Simple problems to find the deflections using Castigliano’s theorem.
Module 5
Fundamentals of bucking and stability, critical load, equilibrium diagram for buckling of an idealized
structure. Buckling of columns with pinned ends, Euler’s buckling theory for long columns. Critical
stress, slenderness ratio, Rankine’s formula for short columns.
Introduction to Theories of Failure, Rankine’s theory for maximum normal stress, Guest’s theory for
maximum shear stress, Saint-Venant’s theory for maximum normal strain, Hencky-von Mises theory
for maximum distortion energy, Haigh’s theory for maximum strain energy
Text Books
1. Mechanics of materials in S.I. Units, R .C. Hibbeler, Pearson Higher Education 2018
2. Advanced Mechanics of Solids, L. S. Srinath, McGraw Hill Education
MECHANICAL ENGINEERING
3. Design of Machine Elements, V. B Bhandari, McGraw Hill Education
Reference Books
1. Engineering Mechanics of Solids, Popov E., PHI 2002
2. Mechanics of Materials S. I. units, Beer, Johnston, Dewolf, McGraw Hills 2017
3. Mechanics of Materials, Pytel A. and J. Cengage Learning India Private Limited,
2ndEdition, 2015
4. Strength of Materials, Rattan, McGraw Hills 2011
MECHANICAL ENGINEERING
COURSE PLAN
No Topic No of lectures
1 Module 1: Stress and Strain Analysis 9 hours
Describe the deformation behaviour of elastic solids in equilibrium under the
action of a system of forces. Describe method of sections to illustrate stress as
1.1 2 hr
resisting force per unit area. Stress vectors on Cartesian coordinate planes
passing through a point and writing stress at a point in the form of a matrix.
Equality of cross shear (Derivation not required). Write Cauchy's equation
(Derivation not required),Find resultant stress, Normal and shear stress on a
1.2 2 hr
plane given stress tensor and direction cosines (no questions for finding
direction cosines).
Displacement, gradient of displacement, Cartesian strain matrix, Write strain-
displacement relations (small-strain only), Simple problems to find strain
1.3 1 hr
matrix given displacement field (2D and 3D), write stress tensor and strain
tensor for Plane stress and plane strain conditions.
Concepts of principal planes and principal stress, characteristic equation of
1.4 stress matrix and evaluation of principal stresses and principal planes as an 2 hrs
eigen value problem, meaning of stress invariants, maximum shear stress
Mohr’s circle for 2D case: find principal stress, planes, stress on an arbitrary
1.5 2 hrs
plane, maximum shear stress graphically using Mohr’s circle
2 Module 2: Stress - Strain Relationships 9 hours
Stress-strain diagram, Stress–Strain curves of Ductile and Brittle Materials,
2.1 1 hr
Poisson’s ratio
Constitutive equations-generalized Hooke’s law, equations for linear elastic
isotropic solids in in terms of Young’s Modulus and Poisson’s ratio (3D).
2.2 Hooke’s law for Plane stress and plane strain conditions 2 hrs
(derivation not required),
Numerical problems
Calculation of stress, strain and change in length in axially loaded members
with single and composite materials, Effects of thermal loading – thermal
2.3 2 hrs
stress and thermal strain. Thermal stress on a prismatic bar held between
fixed supports.
2.4 Numerical problems for axially loaded members 4 hrs
Module 3: Torsion of circular shafts, Shear Force-Bending Moment Diagrams
3 9 hours
and Pure bending
Torsional deformation of circular shafts, assumptions for shafts subjected to
3.1 1 hr
torsion within elastic deformation range, derivation of torsion formula
Torsional rigidity, Polar moment of inertia, comparison of solid and hollow
3.2 1 hr
shaft. Simple problems to estimate the stress in solid and hollow shafts
Numerical problems for basic design of circular shafts subjected to externally
3.3 1 hr
applied torques
3.4 Shear force and bending moment diagrams for cantilever and simply 2 hrs
MECHANICAL ENGINEERING
supported beams subjected to point load, moment, UDL and linearly varying
load
3.5 Differential equations between load, shear force and bending moment. 1 hr
Normal and shear stress in beams: Derivation of flexural formula, section
modulus, flexural rigidity, numerical problems to evaluate bending stress,
3.6 economic sections 3 hrs
Shear stress formula for beams: (Derivation not required),numerical problem
to find shear stress distribution for rectangular section
4 Module 4: Deflection of beams, Strain energy 8 hours
Deflection of cantilever and simply supported beams subjected to point load,
4.1 moment and UDL using Macauley’s method (procedure and problems with 2 hrs
multiple loads)
Linear elastic loading, elastic strain energy and Complementary strain energy.
4.2 Elastic strain energy for axial loading, transverse shear, bending and torsional 2 hr
loads (short derivations in terms of loads and deflections).
Expressions for strain energy in terms of load, geometry and material
4.3 properties of the body for axial, shearing, bending and torsional loads. Simple 2 hrs
problems to solve elastic deformations
Castigliano’s second theorem to find displacements, reciprocal relation, (Proof
4.4 1 hr
not required for Castigliano’s second theorem and reciprocal relation).
4.5 Simple problems to find the deflections using Castigliano’s theorem 1 hr
5 Module 5: Buckling of Columns, Theories of Failure 8 hours
Fundamentals of bucking and stability, critical load, Euler’s formula for long
5.1 columns, assumptions and limitations, effect of end conditions(derivation 2 hr
only for pinned ends), equivalent length
Critical stress, slenderness ratio, Rankine’s formula for short columns,
5.2 3 hr
Problems
Introduction to Theories of Failure. Rankine’s theory for maximum normal
5.3 stress, Guest’s theory for maximum shear stress, Saint-Venant’s theory for 2 hr
maximum normal strain
Hencky-von Mises theory for maximum distortion energy, Haigh’s theory for
5.4 1 hr
maximum strain energy
