Mechanics of Materials
Course objectives:
To understand the stresses and strains developed in bars, compounds bars, beams, shafts, cylinders and spheres and design basic components of machines.
- Introduction (2 hours)
- Classification of mechanics of materials
- External and internal forces, rigid body and deformable solid
- Assumptions in mechanics of solids
- Types of loading
- Simple stresses and strains (2 hours)
- Concept and types of stress and strain
- Elasticity and Hooke’s law, Poisson’s ratio
- Elastic constants (Young’s modulus, shear modulus and bulk modulus) and their relationship
- Stress strain diagram for ductile and brittle materials
- Ultimate stress, allowable stress and factor of safety
- Generalised Hooke’s law
- Axial loading (4 hours)
- Tension, compression and shear
- Axial deformation on a bar of constant section and varying section under uniform load, uniformly varying load, self-weight
- Thermal stress and strain
- Statically determinate and indeterminate problems
- Torsion
(6 hours)
- Theory of pure torsion and its assumptions
- Torsion moment diagram and torsional stress and twist angle variation
- Torsion of hollow and circular shaft
- Comparison between hollow and solid shaft by strength and weight
- Shafts in series and parallel
- Statically indeterminate shaft
- Torsion of noncircular solid members and thin-walled tubular members
- Composite shafts
- Bending stresses in beams (6 hours)
- Theory of pure bending and its assumptions
- Bending stresses in symmetrical sections and unsymmetrical sections
- Beams with composite sections
- Unsymmetrical bending and shear center (6 hours)
- Stress in unsymmetrical bending
- Deflection of beams in unsymmetrical bending
- Eccentric tension and compression
- Shear centre
- Determination of shear centre for C, I & L sections and box beams
- Shear stresses in beams (4 hours)
- Shear stress at a section
- Shear stress in a beam
- Relationship between shear force and shear stress in a beam
- Distribution of shear stress in common beam sections
- Principal stresses and strains (4 hours)
- Normal and tangential components of stress
- Principal planes and principal stresses
- Analytical and graphical method (Mohr’s circle) for determining stresses on principal planes and oblique section
- Mohr’s strain circle
- Strains on an oblique plane
- Curved beams (4 hours)
- Assumptions in stress distribution in curved beams
- Stresses in a curved beam, circular ring and chain link
- Stresses due to rotation
(2 hours)
- Stresses in rotating disc
- Stresses in rotating thin cylinder
- Deflection of beams (8 hours)
- Deformation of a beam under transverse loading
- General differential equation of the elastic curve
- Slope and deflection of loaded members
- Double integration method
- Moment area method
- Columns and struts (2 hours)
- Definition: column and strut, slenderness ratio, buckling factor, buckling load
- Strength of column
- Classification of columns
- End conditions and effective length of a column
- Euler’s theory of long columns: assumptions, derivations and limitations
- Design of column under central and eccentric loading
- Thin cylinders, shells and thick cylinders (4 hours)
- Stresses and strains in thin cylindrical and spherical shell due to internal pressure
- Circumferential, radial and longitudinal stresses and strains in thin cylinder
- Circumferential, radial and longitudinal stresses and strains in thick cylinder
- Shrink fit and compound cylinder
- Energy methods (4 hours)
- Strain energy, strain energy density
- Strain energy in tension, compression, shear, bending and torsion
- Strain energy due to: static loads, dynamic loads, fluctuating loads, gradually applied loads, suddenly applied loads, impact loads
- Stress concentration (2 hours)
- Stress concentration in tension and compression
- Stress concentration in bending, shear and torsion
Practical:
- To determine beam reactions for
- Simply supported beams and
- Cantilever beams
- To study torsional behavior and determine shear modulus of ductile and brittle materials for
- Circular cross section
- Non-circular cross section
- To study buckling effect in different end conditions of column
- To determine stresses and strains in
- Thin wall cylinder
- Thick wall cylinder
References:
- P, Beer and E. R. Johnson, Mechanics of materials, Tata McGraw Hill publishing company limited, 2005.
- P, Popov, Engineering Mechanics of solids, Prentice hall Inc.
- P. Boresi and O. P. Sidebottom, Advanced Mechanics of materials, Wiley
- K. Rajput, Strength of materials, S. Chand & Co. Ltd.
- Kripal singh, Mechanics of Materials, Standard Publishers Distributors, 1998
- 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:
Chapter |
Marks |
1, 13, 14 & 15 |
16 |
2, 3 & 4 |
16 |
5 & 6 |
16 |
7, 8 & 9 |
16 |
10, 11 & 12 |
16 |
Total |
80 |
*Note: There may be minor deviation in mark distribution
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