Strength of Material
MEC-207
Simple Stresses & strains: Concept of stress and strain. Hooke’s law, Stress-Strain diagram, factor of safety, Elongation of tapering bars (circular and rectangular cross sections), Elongation due to self-weight, Saint Venant’s principle, Compound bars, state of simple shear, complementary shear stress, Volumetric stresses and Strains, Elastic constants and their relationship, Thermal stresses, Compound section subjected to thermal stresses, Sudden, gradual & impact load, Strain energy & Proof Resilience, Strain energy under normal and shear stress.
Shear Force and Bending Moment in Beams: Types of beams, supports and loadings, Definition of bending moment and shear force, Sign conventions, relationship between load intensity, Bending moment and shear force, Shear force and bending moment diagrams for statically determinate beams subjected to points load, Uniformly distributed loads, Uniformly varying loads, Couple and their combinations. Bending and Shear Stresses in Beams: Introduction, Pure bending theory, Assumptions, Derivation of bending equation, Modulus of rupture, Section modulus, Flexural rigidity, Beam of uniform strength, Expression for transverse shear stress in beams, Bending and shear stress distribution diagrams for circular, rectangular, ‘I’, and ‘T’ sections, Castigliano’s theorem, Shear Centre (only concept). Slope and deflection of Beams: Definition of slope, Deflection and curvature, Sign conventions, Derivation of moment curvature equation, Double integration method, Macaulay’s method and Principle of superposition method, Slope and deflection for standard loading cases and for determinate prismatic beams subjected to point loads, UDL, UVL and couple.
Columns: Introduction, Short, Medium and Long columns, Slenderness ratio, Euler’s theory; Assumptions, Derivation for Euler’s Buckling load for different end conditions, Limitations of Euler’s theory, Rankine-Gordon’s formula for columns. Torsion: Stresses and strains in pure torsion of solid circular shafts and hollow circular shafts, Power transmitted by shafts, Shaft in series and parallel, Combined bending and torsion. Compound stresses and strains: State of stress at a point, General two-dimensional stress system, Principal stresses and strains, Principal planes. Mohr’s circle of stresses, Theories of Failures.
Springs: Analysis of Close-coiled helical springs, Springs in series and parallel, Stress in leaf springs. Pressure vessels: Thin cylindrical and Spherical vessels subjected to internal pressure, Hoop stresses, Longitudinal stress and change in volume, Thick cylinders subjected to internal and external pressure, Lame’s equation, Radial and hoop stress distribution.