A retaining wall 5 ft high is constructed of horizontal wood planks 3 in. thick (actual dimension) that are supported by vertical wood piles of 12 in. diameter (actual dimension), as shown in the figure. The lateral earth pressure is p1= 100 lb/ft2 at the top of the wall and p2= 400 lb/ft2 at the bottom.
Assuming that the allowable stress in the wood is 1200 psi, calculate the maximum permissible spacing s of the piles
(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.)
