When a bar of length l and diameter d is rigidly fixed at the upper end and hanging freely, the total elongation produced in the bar due to its own weight is given by: (where w = weight per unit volume of the bar, and E = Modulus of elasticity)

If the bending moment diagram of a beam is parabolic under a uniformly distributed load, what is the shape of the corresponding shear force diagram?

Which of the following gives the maximum shear stress in terms of the principal stresses σ1 and σ2 under plane stress conditions?