Unit 1

Simple Stress and Strain: Introduction, Properties of Materials, Stress, Strain, Hook’s law, Poisson’s Ratio, Stress – Strain Diagram for structural steel and nonferrous materials, Principles of superposition, Total elongation of tapering bars of circular and rectangular cross sections. Elongation due to self – weight, Thermal stresses. Composite section, Volumetric strain, expression for volumetric strain, Elastic constants, relationship among elastic constants, Thermal stresses (including thermal stresses in compound bars). Strain Energy & Impact loading.

Torsion of circular shafts: Introduction – Pure torsion – torsion equation of circular shafts, Strength and stiffness, Torsional rigidity and polar modulus, Power transmitted by shaft of solid and hollow circular sections.

Unit 2

Bending moment and shear force in beams: Introduction, Types of beams loadings and supports, Shearing force in beam, Bending moment, Sign convention, Relationship between loading, shear force and bending moment, Shear force and bending moment equations, SFD and BMD with salient values for cantilever beams, simply supported beams and overhanging beams considering point loads, UDL, UVL and Couple. Bending and shear stresses in beams.

Deflection of beams: Introduction – Definitions of slope, deflection, elastic curve, deflection using Macaulay’s method, Moment Area method for prismatic beams and overhanging beams subjected to point loads, UDL and Couple.

Unit 3

Compound Stresses: Introduction, Stress components on inclined planes, General two-dimensional stress system, Principal planes and stresses and Mohr’s circle of stresses. Theories of failure.

Thick and Thin Cylinders and shells: Analysis of thin cylindrical shells and analysis of thick cylindrical shells using Lame’s equation.

Elastic stability of columns: Introduction – Short and long columns, Euler’s theory on columns, Effective length slenderness ration, radius of gyration, buckling load, Assumptions, derivations of Euler’s Buckling load for different end conditions, Limitations of Euler’s theory, Rankine’s formula and problems.

Course Objectives

The course is expected to

• Inculcate the theory of linear elastic response of materials
• Enable the student to understand, evaluate, and analyze strength and deformation of structures under various elastic loading conditions, like, axial, torsional, and bending
• Familiarize the student on various causes of instability in structures

Course Outcomes

• CO1: Apply the principles of equilibrium, superposition, and compatibility to estimate the stress-strain behavior of linear elastic solids under axial and torsional loading
• CO2: Construct shear force and bending moment diagrams, to estimate the deflection and stress distribution in beams of various cross sections
• CO3: Analyze stresses at inclined planes and construct Mohr’s circle to predict the principal and maximum shear planes and apply the theories of failure
• CO4: Determine longitudinal and circumferential stresses in thin and thick cylinders subjected to internal and external pressures
• CO5: Apply Euler’s and Rankine’s formulae to determine the buckling load of columns under different end conditions

CO – PO Mapping

Textbook(s)

• Ferdinand Beer & Russell Johnston – ‘Mechanics of Materials’ – Tata Mc Graw Hill – 2016, 7^th Edition.

Reference(s)

• James M. Gere, Barry J. Goodno- ‘Mechanics of Materials’ – Cengage Learning Custom Publishing – 2014, 8^th Edition.
• R. C. Hibbeler, – ‘Mechanics of Materials’ – Prentice Hall – 2017 – 10^th Edition
• Egor. P. Popov -‘Engineering Mechanics of Solids’ – Pearson Edu. India – 1998 – 2^nd Edition
• Mubeen – ‘Mechanics of Solids’ – Pearson India – 2012 – 2^nd Edition,
• W. A. Nash, Schaum’s Outline Series – ‘Strength of Materials’ – 2007 – 4^th Edition

Evaluation Pattern