Chapter 10, Problem 15P

In the solution of elasticity problem of a normal point load applied to the surface of a half plane that was solved by Boussinesq in 1878, the stresses s_rand s_zare given by:

${\sigma }_z=-\frac{3P{z}^5}{2\pi R^5}$ and ${\sigma }_r=\frac{P}{2\pi }\left[\frac{1-2v}{R(R+z)}-\frac{3r^{2}z}{R^5}\right]$

where v is Poisson’s ratio. For P=2,000 lb and v =0.3 plot the stress components (each in a separate figure) as a function of r and z in the domain $0\le \theta \le 90°$ and $0.02\le R\le 0.1$ in. Plot the coordinates r and z in the horizontal plane and the stresses in the vertical direction.