In the beam shown below, points A and B are simple supports capable of resisting vertical forces only. Point $B$ has the additional capability to resist horizontal forces as well. For the horizontal beam portion labeled $A,B,$& :

$($a$)$ Draw the free$-$body diagram, shear$-$force, and bending$-$moment diagrams $($show all values$).$

$($b$)$ If this beam has a square cross$-$section of side $h,$ identify the $($x$,$ y$)$ coordinate of the point that has the maximum normal stress $($note location of origin at A$).$

$($c$)$ For the most ductile grade of $1020$ steel available, find the minimum standard value of $h,$ use $N=2.$