Course Details
Subject {L-T-P / C} : CE2003 : Mechanics of Solids { 3-0-0 / 3}
Subject Nature : Theory
Coordinator : Prof. Uttam Kumar Mishra
Syllabus
Concept of Stress and Strain
Definition of stress, Normal and Shearing stresses and corresponding strains in axially loaded members, Stress-Strain relationship and its diagram for uniaxial loading for ductile and brittle materials, Stress tensor, Generalised Hooke's Law, Poisson's ratio, relationship between elastic constants, Working stress, Factor of safety. Composite bars in tension and compression, temperature stresses in composite rods, statically indeterminate problems in axial tension and compression.
Thin Cylinders and Spherical Shells
Bi-axial Stresses in thin cylinders and thin spherical shells under internal pressure, wire winding of thin cylinders.
Transformation of Plane Stress and Plane Strain
Two dimensional state of stress, principal stresses and principal planes, Mohr's circle of stress, Two dimensional state of strain, principal strains and principal axes of strain, Mohr's circle of strain, measurement of strain by strain gauge and strain rosettes, determination of principal strains from strain measurements, calculation of principal stresses from principal strains.
Torsion of Circular Shafts and Helical Springs
Torsion formula, strength of solid and hollow circular shafts, design of circular members in torsion, power transmitted, and close coiled helical springs.
Analysis of beams
Members subjected to flexural loads, relationships between load, shearing force and bending moment, shear force and bending moment diagrams of cantilever and simply supported beams, elastic curve. Theory of simple and non-uniform bending of initially straight beams, bending stresses in beams, shearing stresses in beams, beams of two materials, carriage springs. Slope and deflection of beams by integration method and moment area method.
Columns
Euler's theory for initially straight columns with various end conditions, eccentric loading of columns, stresses in short struts with eccentric loading, Kern of rectangular and circular sections
Course Objectives
- Understand the fundamental concepts of stress and strain and the relationship between both through the stress-strain equations, Working stress, Factor of safety, temperature stresses, Bi-axial Stresses in thin cylinders and thin spherical shells under internal pressure, wire winding, Transformation of Plane Stress and Plane Strain
- Analysis and design of shafts and close coiled helical springs subject to torsional load
- Analysis of beams subjected to flexural loads, relationships between load, shearing force and bending moment, shear force and bending moment diagrams of cantilever and simply supported beams, elastic curve. Theory of simple and non-uniform bending of initially straight beams, bending stresses in beams, shearing stresses in beams, beams of two materials, carriage springs. Slope and deflection of beams by integration method and moment area method.
- Understand the concept of buckling, Stability of short and long columns
Course Outcomes
This subject is about the performance of deformable solids in various materials under the action of different kinds of loads, Understand the fundamental concepts of stress and strain and the relationship between both through the strain-stress equations in order to solve problems for simple tri-dimensional elastic solids, Analysis and design of shafts and close coiled helical springs subject to torsional load, Analysis of beams subjected to flexural loads, Understand the concept of buckling, Stability of short and long columns
Essential Reading
- S.P.Timoshenko and D.H.Young, Elements of Strength of Materials, Affiliated East West Press Pvt. Ltd.
- E.P.Popov, Engineering Mechanics of Solids, Prentice Hall of India Pvt. Ltd., New Delhi.
Supplementary Reading
- I.H.Shames, Introduction to Solid Mechanics, Prentice Hall of India Pvt. Ltd., New Delhi.
- G.H.Ryder, Strength of Materials, ELBS