A wood pile, driven into the earth, supports a load P entirely by friction along its sides (see figure). The friction force f per unit length of pile is assumed to be uniformly distributed over the surface of the pile. The pile has length L, cross-sectional area A, and modulus of elasticity E.
(a) Derive a formula for the shortening δ of the pile in terms of P, L, E, and A.
(b) Draw a diagram showing how the compressive stress σc varies throughout the length of the pile.

L f