# STRENGTH OF MATERIALS

1. ### STRESS AND STRAINS

• ###### Concept of elasticity, elastic limit and limit of proportionality
• Hook’s law
• Young’s modulus of elasticity
• Nominal stress
• Yield point, plastic stage
• Strain hardening
• Ultimate strength and breaking stress
• Percentage elongation
• Proof stress and working stress
• Factor of safety
• Lateral strain, Poisson’s ratio
• Volumetric strain
• Shear modulus
• Strain energy due to direct stresses
• Proof resilience and modulus of resilience
• Longitudinal and circumferential stress in seamless thin walled cylindrical shells (derivation of these formulas not required)

1. ### BEAMS AND BENDING STRESSES

• ###### Bending and shearing force
• Concept of end-supports- roller, hinged and fixed
• Concept of bending moment and shearing force
• BF and SF diagram for cantilever and simply supported beam with and without overhang subjected to concentrated and uniformly distributed load (UDL)
• ###### Bending Stresses
• Concept of bending stresses
• Theory of simple bending
• Use of equation M/I = σ/y = E/R
• Concept of moment of resistance
• Bending stress diagram
• Calculation of maximum bending in beams of rectangular, circular and I section
• Permissible bending stress, section modulus for rectangular, circular and symmetrical I section
• Comparison between I, rectangular and circular section with regard to the strength
• ###### Slope and Deflection
• Simple cases of slope and deflection in simply supported beam with UDL over whole of the length and a point load at the center
• Cantilever with UDL on whole length and a point load at the end (without derivation)
• Simple problems
• ###### Laminated spring (Semi elliptical type only)
• Determination of number of plates
• Maximum bending stress and deflection
• ###### Combined direct and bending stresses
• Simple cases of short columns of uniform section subject to eccentric loading with stress diagram

1. ### COLUMNS

• Concept of column, modes of failure
• Types of column
• Slenderness ratio
• Factors affecting strength of a column
• End restraints
• Effective length
• Strength of column by Euler formula without derivation
• Rankine Gordon formula (without derivation)

1. ### TORSION

• Concept of torsion, difference between torque and torsion
• Derivation and use of torsion equation T/J = τ/R = Gθ/L for circular shaft
• Shear stress diagram for solid and hollow circular shaft
• Comparison between solid and hollow shaft with regard to their strength and weight
• Power transmitted by shaft
• Concept of mean and maximum torque

1. ### HELICAL SPRINGS

• Closed coiled helical springs subjected to axial load
• Stress deformation
• Stiffness and angle of twist and strain energy