Problem $1$:

The cantilever beam shown in the figures below is subjected to a concentrated load of $P$ in the $z$ direction. The cross$-$sectional dimensions of the rectangular tube shape are $b=6in.,d=10in.,$ and $t=0\mathrm{.}375in.$

$($a$)$ Compute the value of $Q$ that is associated with point H $,$ which is located to the right of the vertical centroidal axis at $z_H=1\mathrm{.}50in.$

$($b$)$ If the allowable shear stress for the rectangular tube shape is $16$ ksi, determine the maximum concentrated load $P$ than can be applied as shown to the cantilever beam.