An elastic bar of length L, uniform cross sectional area A, coefficient of thermal expansion a, and Young’s modulus E is fixed at the two ends. The temperature of the bar is increased by T, resulting in an axial stress $$\sigma$$. Keeping all other parameters unchanged, if the length of the bar is doubled, the axial stress would be

A tapered circular rod of diameter varying from 20 mm to 10 mm is connected to another uniform circular rod of diameter 10 mm as shown in the following figure. Both bars are made of same material with the modulus of elasticity, E = 2 $$ \times $$ 10⁵ MPa. When subjected to a load P = 30$$\pi $$ kN, the deflection at point A is _______________ mm.

The Poisson's ratio is defined as

The number of independent elastic constants for a linear elastic isotropic and homogeneous material is