Basics of linear elasticity:
The concept of stress& strain, state of stress & Strain at a point, Equilibrium equations, The state of plane stress and plane strain. Compatibility equations, Constitutive Laws (Hooke’s Law), Stress-strain curves for brittle and ductile materials, Allowable stress, Material selection for structural performance.
Simple & Compound Stresses:
Extension / Shortening of a bar, bars with cross sections varying in steps, bars with continuously varying cross sections. Elongation due to self-weight. Volumetric strain, expression for volumetric strain, elastic constants, simple shear stress, shear strain, temperature stresses, Introduction to Plane stress, stresses on inclined sections, principal stresses & strains, Analytical & graphical method (Mohr’s Circle) to find principal stresses & strains.
Bending Moment and Shear Force in Beams:
Introduction, Types of beams, loads and reactions, shear forces and bending moments, rate of loading, sign conventions, relationship between shear force and bending moments. Shear force and bending moment diagrams for different beams subjected to concentrated loads, uniformly distributed load, (UDL) uniformly varying load (UVL) and couple for different types of beams.
Euler-Bernoulli beam theory:
The Euler-Bernoulli assumptions, Implications of the Euler-Bernoulli assumptions, the Euler-Bernoulli Beam theory derivation, Bending stress equation, Moment carrying capacity of a section. Shearing stresses in beams, shear stress across rectangular, circular, symmetrical I and T sections (Only Numerical).
Deflection of Beams:
Introduction, Differential equation for deflection. Equations for deflection, slope and bending moment. Double integration method for cantilever and simply supported beams for point load, UDL, UVL and Couple. Macaulay’s method.
Torsion of Circular Shafts and Elastic Stability of Columns:
Introduction. Pure torsion, assumptions, derivation of torsional equations, polar modulus, torsional rigidity / stiffness of shafts. Power transmitted by solid and hollow circular shafts.
Virtual work principles:
Introduction, Equilibrium and work fundamentals, Principle of virtual work, Principle of virtual work applied to mechanical systems, Principle of virtual work applied to truss structures, Principle of virtual work applied to beams. Principle of complementary virtual work, internal virtual work in beams and solids.
Energy methods:
Conservative forces, Principle of minimum total potential energy, Strain energy in springs, Strain energy in beams, Strain energy in solids, Applications to trusses, Development of a finite element formulation for trusses, Principle of minimum complementary, Energy theorems, Reciprocity theorems, SaintVenant’s principle.
Mechanical Properties of materials:
Fracture:
Type I, Type II and Type III.
Creep:
Description of the phenomenon with examples. Three stages of creep, creep properties, stress relaxation.
Fatigue:
Types of fatigue loading with examples, Mechanism of fatigue, fatigue properties, fatigue testing and S-N diagram.
Course Outcomes:
At the end of the course the student will be able to:
Question paper pattern:
Textbook/s
1 Strength of Materials S. S. Bhavaikatii Vikas Publications House, New Delhi 2012
2 Strength of Materials S. Ramamrutham Dhanapath Rai Publishing Company 2012
Reference Books
1 Introduction to Aircraft Structural Analysis T. H. G Megson ButterworthHeinemann 2007
2 Mechanics of Materials Beer. F. P. and Johnston. R McGraw Hill Publishers 2006
3 Elements of Strength of Materials Timoshenko and Young East-West Press 1976
4 Structural Analysis O. A. Bauchau and J. I. Craig Springer Dordrecht Heidelberg London New York