Q$3(30$ marks$)$ Consider a uniform rectangular beam subjected to $4-$point bending. Load at each support is $75lb.$ Beam dimensions is: length $=5in.$ height $=1in.$ thickness $=0\mathrm{.}213in.$ Distance between lower supports, $4in.$ Distance between upper supports, $2in.$ Determine the difference between the theoretical and experimental value of the axial stress at the point shown in the figure which is approximately $0\mathrm{.}2in$ below the surface. Also give the order for the dark fringes. Knowing that for the rectangular section $I=b{h}^{\frac{3}{12}}$ about the neutral axis.

The table below is the fringe onder at the center of a circular disk under diametral compression versus load. Were this disk is made from the same material, patch of the beam in this problem. And both tests where carried out at the same time, the disk dimeter is $2$ in$.$

$\backslash$table$[[P,N$