Problem $7$: A beam is subjected to equal $17\mathrm{.}5$ kip$-$ft bending moments, as shown in the upper figure at right. The cross$-$sectional dimensions of the beam are shown in the lower figure at right. $($Note: for each part below, when drawing a stress element, draw it in the appropriate plane. Include coordinate axes and stress labels, indicating proper direction and magnitude. Show the location of the stress element on the diagrams at right or your own.$)$ a$.$ Determine the centroid location, the moment of inertia about the z axis, and the section modulus about the z axis. b$.$ Determine the bending stress at point H and state whether the normal stress at H is tension or compression. Draw a stress element representing this stress. c$.$ Determine the bending stress at point K and state whether the normal stress at K is tension or compression. Draw a stress element representing this stress. d$.$ Determine the maximum bending stress produced in the cross$-$section $($that is$,$ the bending stress with the maximum magnitude$)$ and state whether the stress is tension or compression. Draw a stress element representing this stress.

d$.$ Determine the maximum bending stress produced in the cross$-$section $($that is$,$ the bending

stress with the maximum magnitude$)$ and state whether the stress is tension or compression.

Draw a stress element representing this stress.

Please keep in mind that the asnwers should be the following:

$($a$)$ y$=6\mathrm{.}08$ in$,$ I $=1285$ in$4,$ S $=162$ in$3$

$($b$)967$ psi tension

$($c$)667$ psi compression

$($d$)1\mathrm{.}29$ ksi tension