## Tuesday, March 5, 2019

### Lectures notes On Mechanics of Solids

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1. Definition of stress, stress tensor, normal and shear stresses in axially loaded members.
Stress & Strain :- Stress-strain relationship, Hooke’s law, Poisson’s ratio, shear stress, shear strain, modulus of rigidity. Relationship between material properties of isotropic materials. Stress-strain diagram for uniaxial loading of ductile and brittle materials. Introduction to mechanical properties of metals-hardness,impact.
Composite Bars In Tension & Compression:-Temperature stresses in composite rods – statically indeterminate problem.
2. Two Dimensional State of Stress and Strain: Principal stresses, principal strains and principal axes, calculation of principal stresses from principal strains.Stresses in thin cylinder and thin spherical shells under internal pressure , wire winding of thin cylinders.
3. Torsion of solid circular shafts, twisting moment, strength of solid and hollow circular shafts and strength of shafts in combined bending and twisting.
4. Shear Force And Bending Moment Diagram: For simple beams, support reactions for statically determinant beams, relationship between bending moment and shear force, shear force and bending moment diagrams.
5. Pure bending theory of initially straight beams, distribution of normal and shear stress, beams of two materials.
6. Deflection of beams by integration method and area moment method.
Module – IV
7. Closed coiled helical springs.
8. Buckling of columns : Euler’s theory of initially straight columns with various end conditions, Eccentric loading of columns. Columns with initial curvature.

Content:-
Module 1:
Lecture 1: Introduction: Definition of stress, stress tensor, normal and shear stresses in axially loaded members.
Lecture 2:
Numerical problems on stress, shear stress in axially loaded members.
Lecture 3:
Stress & Strain :- Stress-strain relationship, Hooke’s law, Poisson’s ratio, shear stress,
Lecture 4:
Numerical problems on Stress-strain relationship, Hooke’s law, Poisson’s ratio, shear stress
Lecture 5:
Shear strain, modulus of rigidity, bulk modulus. Relationship between material properties of isotropic materials.
Lecture 6:
Numerical problems on shear strain, modulus of rigidity
Lecture 7:
Stress-strain diagram for uniaxial loading of ductile and brittle materials.
Lecture 8:
Introduction to mechanical properties of metalshardness, impact
Lecture 9:
Composite Bars In Tension & Compression:- Temperature stresses in composite rods statically indeterminate problem.
Lecture 10:
Numerical problems on composite bars and temperature stress.
Module 2:
Lecture 1: Two Dimensional State of Stress and Strain: Principal stresses. Numerical examples
Lecture 2: .Numerical examples on calculation of principal stresses
Lecture 3: Mohr’s circle method and numerical examples.
Lecture 4: Principal strain calculation and numerical examples
Lecture 5: Calculation of principal stresses from principal strains
Lecture 6: Thin cylinder and thin spherical shells under internal pressure and numerical examples
Lecture 7: Wire winding of thin cylinders. Numerical examples.
Lecture 8: Torsion of solid circular shafts, twisting moment. Numerical examples
Lecture 9: Strength of solid and hollow circular shafts. Numerical examples.
Lecture 10: Strength of shafts in combined bending and twisting. Numerical examples
Module 3:
Lecture 1: Shear Force And Bending Moment Diagram: For simple beams, support reactions for statically determinant beams, relationship between bending moment and shear force.
Lecture 2:
Calculation of SF and BM of cantilever beam, simply supported beam and shear force and bending moment diagrams
Lecture 3:
Calculation of SF and BM of overhanging beams. Point of contra flexure, maximum bending moment.
Lecture 4:
Numerical examples on calculation of SF and BM of overhanging beams
Lecture 5:
Pure bending theory of initially straight beams,
Lecture 6:
Numerical examples on pure bending
Lecture 7:
Distribution of normal and shear stresses in beams of

two materials.
Lecture 8:
Numerical examples on calculation of normal and shear

stresses in beams of two materials.
Lecture 9:
Deflection of beams by integration method
Lecture 10:
Numerical examples on deflection of beams by

integration method
Lecture 11: Deflection in beams by moment area method
Lecture 12:
Numerical examples on deflection of beams by moment area method
Module 4:
Lecture 1: Closed coiled helical springs: Axial load, axial torque, strain energy in spring, numerical examples.
Lecture 2: Spring under impact loading and numerical examples.
Lecture 3: Springs in series and numerical examples
Lecture 4: Springs in parallel and numerical examples.
Lecture 5: Buckling of columns : Euler’s theory of initially straight columns with various end conditions- Column hinged at both ends, Column fixed at both ends, numerical examples
Lecture 6: Column fixed at one end and hinged at other end, Column fixed at one end and free at other end numerical examples.
Lecture 7: Eccentric loading of columns. Columns with initial curvature
Lecture 8: Numerical examples on Eccentric loading of columns.

Author Details
Prepared by
"Prof. P. R. Dash"

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