JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD

Prerequisites

Strength of Materials I & II

Course Objectives:

• To Introduce fundamental elasticity model of deformation in rectangular and polar coordinate.
• To Give foundation for 2D and 3D study in solid mechanics problems.
• To Introduce to torsion and warping of prismatic structure

Course Outcomes

At the end of the course the student will able to

• The more fundamental elasticity model of deformation should replace elementary strength of material analysis.
• Able to understand theory, formulate and to present solutions to a wide class of problems in 2D and 3D
• Acquire the foundation for advanced study in areas of solid mechanics

UNIT - I

Introduction: Elasticity - notation for forces and stress - components of stresses - components of strain - Hooks law. Plane stress and plane strain analysis - differential equations of equilibrium - boundary conditions – Strain Displacement Relations - compatibility equations - stress function

UNIT - II

Two dimensional problems in rectangular coordinates - solution by polynomials - Saint-Venants principle - determination of displacements - bending of simple beams – Simple Supported and Cantilever Beam.

UNIT - III

Two dimensional problems in polar coordinates - stress distribution symmetrical about an axis - pure bending of curved bars - strain components in polar coordinates - displacements for symmetrical stress distributions Edge Dislocation - general solution of two-dimensional problem in polar coordinates - application to Plates with Circular Holes – Rotating Disk. Bending of Prismatic Bars: Stress function - bending of cantilever - circular cross section - elliptical cross section - rectangular cross section.

UNIT - IV

Analysis of stress and strain in three dimensions - principal stress - stress ellipsoid - director surface - determination of principal stresses Stress Invariants - max shear stresses Stress Tensor – Strain Tensor- Homogeneous deformation - principal axes of strain-rotation. General Theorems: Differential equations of equilibrium - conditions of compatibility - determination of displacement - equations of equilibrium in terms of displacements - principle of super position - uniqueness of solution - the reciprocal theorem Strain Energy.

UNIT - V

Torsion of Circular Shafts - Torsion of Straight Prismatic Bars – Saint Venants Method - torsion of prismatic bars - bars with elliptical cross sections - membrane analogy - torsion of a bar of narrow rectangular bars - solution of torsional problems by energy method - torsion of shafts, tubes, bars etc. Torsion of Rolled Profile Sections.

TEXT BOOKS:

• 1. Theory of Elasticity by Timoshenko, McGraw-Hill Publications.
• 2. Theory of Plasticity by J. Chakarbarthy, McGraw-Hill Publications. R18 B.TECH CIVIL ENGG. III YEAR

REFERENCES:

• 1. Theory of Elasticity by Y.C.Fung.
• 2. Theory of Elasticity by Gurucharan Singh. R18 B.TECH CIVIL ENGG. III YEAR