Problem $8\mathrm{.}2.$ The setup shown is used to test the capacity of pile foundations. A force $P=2MN$ is being applied to the high$-$strength concrete pile $(E=29\mathrm{.}1$GPa $)$ of diameter $0\mathrm{.}325m.$ The soil is exerting a linearly varying skin$-$friction along the length of the pile, with the magnitude at the ground surface being $p_0=260k\frac{N}{m}.$

a$.$ Find the axial force distribution in the concrete pile;

b$.$ Calculate the change in length of the pile due to linear elastic deformation.

Neglect the weight of the pile itself in your calculations.