Mechanics of Materials
Mechanics of Materials
Mechanics of Materials
AM 551
Lecture: 4 Year: II
Tutorial: 1 Part: II
Practical: 1.5
Course objectives
To understand the stresses and strains developed in bars, compounds bars, beams, shafts, cylinders
and spheres and design basic components of machines.
1. Introduction (2 hours)
1.1 Classification of mechanics of materials
1.2 External and internal forces, rigid body and deformable solid
1.3 Assumptions in mechanics of solids
1.4 Types of loading
2. Simple stresses and strains (2 hours)
2.1 Concept and types of stress and strain
2.2 Elasticity and Hooke’s law,Poisson’s ratio
2.3 Elastic constants (Young’s modulus, shear modulus and bulk modulus) and their
relationship
2.4 Stress strain diagram for ductile and brittle materials
2.5 Ultimate stress, allowable stress and factor of safety
2.6 Generalised Hooke’s law
3. Axial loading (4 hours)
3.1 Tension, compression and shear
3.2 Axial deformation on a bar of constant section and varying section under uniform load,
uniformly varying load, self-weight
3.3 Thermal stress and strain
3.4 Statically determinate and indeterminate problems
4. Torsion (6 hours)
4.1 Theory of pure torsion and its assumptions
4.2 Torsion moment diagram and torsional stress and twist angle variation
4.3 Torsion of hollow and circular shaft
4.3.1 Comparison between hollow and solid shaft by strength and weight
4.3.2 Shafts in series and parallel
4.4 Statically indeterminate shaft
4.5 Torsion of noncircular solid members and thin-walled tubular members
4.6 Composite shafts
5. Bending stresses in beams (6 hours)
5.1 Theory of pure bending and its assumptions
5.2 Bending stresses in symmetrical sections and unsymmetrical sections
5.3 Beams with composite sections
6. Unsymmetrical bending and shear center (6 hours)
6.1 Stress in unsymmetrical bending
6.2 Deflection of beams in unsymmetrical bending
6.3 Eccentric tension and compression
6.4 Shear centre
6.5 Determination of shear centre for C, I & L sections and box beams
7. Shear stresses in beams (4 hours)
7.1 Shear stress at a section
7.2 Shear stress in a beam
7.3 Relationship between shear force and shear stress in a beam
7.4 Distribution of shear stress in common beam sections
8. Principal stresses and strains (4 hours)
8.1 Normal and tangential components of stress
8.2 Principal planes and principal stresses
8.3 Analytical and graphical method (Mohr’s circle)for determining stresses on principal
planes and oblique section
8.4 Mohr’s strain circle
8.5 Strains on an oblique plane
9. Curved beams (4 hours)
9.1 Assumptions in stress distribution in curved beams
9.2 Stressesin a curvedbeam, circular ring and chain link
10. Stresses due to rotation (2 hours)
10.1 Stresses in rotating disc
10.2 Stresses in rotating thin cylinder
11. Deflection of beams (8 hours)
Practical
1. To determine beam reactions for
1.1 Simply supported beams and
1.2 Cantilever beams
2. To study torsional behavior and determine shear modulus of ductile and brittle materials for
2.1 Circular cross section
2.2 Non-circular cross section
3. To study buckling effect in different end conditions of column
4. To determine stresses and strains in
4.1 Thin wall cylinder
4.2 Thickwall cylinder
References:
1. F. P, Beer and E. R. Johnson, Mechanics of materials, Tata McGraw Hill publishing company
limited, 2005.
2. E. P, Popov, Engineering Mechanics of solids, Prentice hall Inc.
3. A. P. Boresi and O. P. Sidebottom, Advanced Mechanics of materials, Wiley
4. R. K. Rajput, Strength of materials, S. Chand & Co. Ltd.
5. Kripal singh, Mechanics of Materials, Standard Publishers Distributors, 1998
6. S. Ramammurtham, R. Narayanan, Strength of materials, Dhanapat Rai Publishing
Company,2014.
Evaluation scheme
The questions will cover all the chapters of the syllabus. The evaluation scheme will be as indicated in
the table below:
Unit Chapter Topics Marks
1 1, 13, 14 & 15 all 16
2 2, 3 & 4 all 16
3 5&6 all 16
4 7, 8 & 9 all 16
5 10, 11 & 12 all 16
Total 80