고체역학 (Gere) — Axially Loaded Members: Problem 2.3-13

2.3-13 A wood pile, driven into the earth, supports a load \(P\) entirely by friction along its sides (see figure part a). The friction force \(f\) per unit length of the pile is assumed to be uniformly distributed over the surface of the pile. The pile has a length \(L\), cross-sectional area \(A\), and modulus of elasticity \(E\). (a) Derive a formula for the shortening \(\delta\) of the pile in terms of \(P, L, E,\) and \(A\). (b) Draw a diagram showing how the compressive stress \(\sigma_c\) varies throughout the length of the pile. (c) Repeat parts (a) and (b) if skin friction \(f\) varies linearly with depth (see figure part b).