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# Mechanics of Materials

VTU
Subject code
18ME32
Semester
3rd Sem

## MECHANICS OF MATERIALS 18ME32

### Module-1

Stresses and Strains: Introduction, Properties of materials, Stress, Strain and Hooke’s law, Stress strain diagram for brittle and ductile materials, True stress and strain, Calculation of stresses in straight, Stepped and tapered sections, Composite sections, Stresses due to temperature change, Shear stress and strain, Lateral strain and Poisson’s ratio, Elastic constants and relations between them.

### Module-2

Analysis of Stress and Strain: Introduction to three dimensional state of stress, Stresses on inclined planes, Principal stresses and maximum shear stress, Principal angles, Shear stresses on principal planes, Maximum shear tress, Mohr circle for plane stress conditions. Cylinders: Thin cylinder: Hoop’s stress, maximum shear stress, circumferential and longitudinal strains, Thick cylinders: Lames equations.

### Module-3

Shear Force and Bending Moment: Type of beams, Loads and reactions, Relationship between loads, shear forces and bending moments, Shear force and bending moments of cantilever beams, Pin support and roller supported beams subjected to concentrated loads, uniformly distributed constant / varying loads. Stress in Beams: Bending and shear stress distribution in rectangular, I and T section beams.

### Module-4

Theories of Failure: Maximum Principal stress theory, Maximum shear stress theory. Torsion: Circular solid and hallow shafts, Torsional moment of resistance, Power transmission of straight and stepped shafts, Twist in shaft sections, Thin tubular sections, Thin walled sections.

### Module-5

Columns: Buckling and stability, Critical load, Columns with pinned ends, Columns with other support conditions, Effective length of columns, Secant formula for columns. Strain Energy: Strain energy due to axial, shear, bending, torsion and impact load. Castigliano’s theorem I and II and their applications.