Strength of materials IS-MER0003

1. Introduction. Internal forces. Normal and shear stresses. Deformations. Normal and shear strains. Stress–strain diagram. Elastic and plastic behaviour. Yield stress. Ultimate stress. Working stress. Safety factor. 2. Geometry of cross-sections. Static moments. Centroid. Moments of inertia. Parallel-axis theorem. Principal axes. Principal moments of inertia. 3. Tension and compression. Axial force. Saint Venant’s principle. Hooke's law. Elastic modulus. Poisson's ratio. Thermal expansion coefficient. 4. Torsion. Twisting moment. Angle of twist. Shear modulus. 5. Bending stresses. Bending moment. Neutral axis. Flexure formula. Efficient cross sections. Bending with shear. Shear formula. 6. Bending deflections. Equation of the elastic curve. Double-integration method. Bracket function. 7. Combined loading. Skew bending. Eccentric axial loading. 8. Strength theories. Stress state at a point. Principal stresses. Mohr’s circles. Equivalent stress. 9. Energy theorems. Strain energy. Castigliano’s theorem. Principle of stationary potential energy. Betti’s theorem. 10. Force method. Redundant reaction. Degree of static indeterminacy. Statically determinate equivalent structure. 11. Stability of bars. Buckling. Critical load. Euler’s formula. Energy method. 12. Elastoplastic behaviour. Yield loading. Limit loading. Plastic neutral axis.