The rectangular cross$-$section of a beam is subjected to a positive moment $M.$ The beam is

made of a material whose stress$-$strain law is given by $\frac{}{E}=B{}^n,$ where $E$ is a given reference

modulus, $B$ and $n$ are given constants, and $0n1.$

a$.$ Derive the equation that relates the curvature of the beam to the applied moment.

b$.$ Determine the $($total$)$ compressive force acting on the top half of the beam's cross$-$

section.