A hanger is made of two bars of different sizes. Each bar has a square cross-section. The hanger is loaded by three-point loads in the mid vertical plane as shown in the figure. Ignore the self-weight of the hanger. What is the maximum tensile stress in N/mm² anywhere in the hanger without considering stress concentration effects?

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

In a material under a state of plane strain, a 10×10 mm square centered at a point gets deformed as shown in the figure. If the shear strain $$\gamma_{xy}$$ at this point is expressed as 0.001k (in rad), the value of k is

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.