(Solution) - A retaining wall 5 ft high is constructed of horizontal -(2025 Original AI-Free Solution)

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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.