A uniform timber pile which has been driven to a depth L in clay carries an applied load F at the top. This load is resisted entirely by friction f along the pile which varies in the parabolic manner f=ky^2.

a) Determine the total shortening of the pile in terms of F, L, A, and E;

b) If F=96 kips, L=40 ft., A=100in2, and E=1.5 x 106 psi, how much does such a pile shorten?

Hint: From the equilibrium requirement, first determine the constant k.

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