Syllabus

Module-I (Introduction to Concept of Stress and Strain) – 09 hours
Concept of the stress tensor, types of stresses, sources, and normal and shear stress and stress concentration,
Concept of strain tensor: Types, Engineering and True strains, Strain and deformation
Stress-strain diagram and its features. Stress-strain diagram for different (ductile and brittle) metals and non-metallic (wood, concrete) materials. Generalized Hooke’s Law, Poisson’s ratio, Relation between Elastic constant
Stress and strain in composite rods. Stress and strain in bolt and nut assembly. Stress due to the self-weight of members. Stress in nuts and bolts. Thermal stresses.

Module-II (Compound Stress and Strain and Shear Force and Bending Moment) – 09 hours
Stress in an inclined body, Uni/Bi-axial stresses. Principal stress. Principal planes, Morh’s circle for the stresses. Two-dimensional state of strain. Principal strain and principal axes of strain, Strain rosettes, Determination of principal strain from strain measurement, Calculation of principal stresses/strains from principal strains/stresses.
Concept of shear force. Shear Force and Bending Moment Diagrams. Differential relationship between load intensity, shear force and bending moment diagram. Moment diagram in simply supported and cantilever beams subject to concentrated load, distributed load, and varying load.

Module -IV (Stress in Shafts Subjected to Torsion)- 03 hours
Torsion in Solid and hollow circular shafts. Torque and Power transmitted by solid and hollow shafts. Strength of shafts.

Module-V (Bending Stress and Slope and Deflection)- 08 hours
Theory of simple bending of initially straight beams. Euler-Bernoulli’s Beam Equation. Moment of inertia for different cross sections. Distribution of normal and shear stresses. Beam of two materials, Composite beams, Combined bending and torsion.

Differential expression of the elastic curve, Slope and deflection of simply supported beams and cantilevers by the double integration method, Macaulay’s method and the moment area method.

Module VI (Theory of Columns, Thin-Cylinders, Theories of Failures and Energy Methods)-07 hours
Columns and Struts, Conditions of stability, Euler Crippling load, Limitations of Euler’s buckling load. Buckling of beams under different end conditions.
Thin Cylinders and Spheres, Stresses in Thin Cylinders, Strain and Joint Efficiency.
Different Theories of Failures, Application in various design problems.
Energy methods, Castigliano’s theorem, Betti’s reciprocal theorem, and Applications of the energy method to evaluate bending, buckling and torsional load.

1. Mechanical behaviour of deformable bodies under variable loading conditions and evaluation of stress-strain under unidirectional loading. Compound stress behaviour and resultant stress.

Inculcate students in relation to structural types, loading, and influences on the responses of bending torsion, and corresponding distortion.

Failure criteria of different materials and structural forms in design and analysis.

Understanding combined loading influences on structural components, including temperature.

1. Analysis of elastic solids utilizing the principles of equilibrium, superposition, and compatibility conditions under variable loadings (axial, transverse and torsional). Relationship between different elastic properties and their applications.
2. Evaluate the bending deflection, stress, and slope, including the relation between shear force and bending moment of the beam. Analytical and graphical evaluation of resultant stresses of the structural components utilizing Mohr’s circle and evaluation of principal plane.
3. To understand the beam structural stability and critical load calculations (columns and struts) under compressive loading and variable end conditions.
4. Thin cylinder stresses and concepts of theories failures for mechanical design.
5. Application of energy methods to compute responses of beam type of structure under various loadings.

S. S. Rattan, Strength of Materials, Tata Mc Graw Hill , 3rd Edition 2017

R. C. Hibbeler, Mechanics of Materials, Prentice Hall , 10TH EDITION 1st March 2022

Egor. P. Popov, Engineering Mechanics of Solids, Pearson Edu. India

James M. Gere, Barry J. Goodno, Mechanics of Materials, Cengage Learning