A wheel applies a $40-$kN load on a semi$-$infinite elastic space, as shown inFig. P$2\mathrm{.}1.$ The modulus of elasticity of the material is $150$ MPa and Poisson's ratio is $0\mathrm{.}38.$ Assume the load is applied on the surface as a concentrated force.

Figure P $2.1$Profile of the semi $-$ infinite elastic space for Prob. $2.1.$ Calculate the following at a depth of $500$mm at the centerline of the wheel: a $.$Vertical stress b $.$Radial stress c $.$Tangential stress d $.$Horizontal shear stress in the radial direction e $.$Vertical strain f $.$Radial strain g $.$Tangential strain h $.$Vertical deformation i$.$ Horizantal deformation