고체역학 (Gere) — Stresses in Beams (Basic Topics): Problem 5.6-23

5.6-23 A retaining wall 1.5 m high is constructed of horizontal wood planks 75 mm thick (actual dimension) that are supported by vertical wood piles of a 300 mm diameter (actual dimension), as shown in the figure. The lateral earth pressure is \(p_1 = 5 \text{ kPa}\) at the top of the wall and \(p_2 = 20 \text{ kPa}\) at the bottom. (a) Assuming that the allowable stress in the wood is 8 MPa, calculate the maximum permissible spacing \(s\) of the piles. (b) Find the required diameter of the wood piles so that piles and planks (\(t = 75 \text{ mm}\)) reach the allowable stress at the same time. Hint: Observe that the spacing of the piles may be governed by the load-carrying capacity of either the planks or the piles. Consider the piles to act as cantilever beams subjected to a trapezoidal distribution of load, and consider the planks to act as simple beams between the piles. To be on the safe side, assume that the pressure on the bottom plank is uniform and equal to the maximum pressure.