Q$4$

A rectangular cross section beam with base, $b,$ and height, $h,$ needs to have the cross sectional area minimized. It has an applied bending moment $M=140kN-m$ and shear $V=24kN.$ The max allowable bending stress is $=165$MPa and the max shear stress is $T=50$MPa. You can calculate the shear and bending stresses by

$=\frac{6M}{b{h}^2}$

$T=\frac{3V}{2bh}$

As a final constraint, for aesthetic reasons the height cannot be more than twice the base.

$10$ points

$q,$ notimum value for $h$

$q,10$ points

Optimum value for $h$