HE 2.5 in. P1 = 125 lb/ft? 12-in. diam. 12-in. diam. 6 ft 2.5 in. Top view P2 = 425 lb/ft2 Side view
A retaining wall 6 ft high is constructed of
horizontal wood planks 2.5 in. thick (actual dimension)
that are supported by vertical wood piles of a
12 in. diameter (actual dimension), as shown in the
figure. The lateral earth pressure is p1 125 lb/ft2
at the top of the wall and p2 =425 lb/ft2 at the bottom.
(a) Assuming that the allowable stress in the wood
is 1175 psi, calculate the maximum permissible
spacing s of the piles.
(b) Find the required diameter of the wood piles
so that piles and planks (t = 2.5 in.) 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.
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