An L$8$x$4$x$1/2$ A$992$ section is connected to the flange of a W$12$x$65$ A $992$ section through $\frac{3}{8}$ in weld as shown in the figure. Assume E$70$ electrode.

$($i$)[$Consider analysis of the weld using the center of rotation method.

Divide the weld into four $4in.$ long segments. It is claimed that the center of rotation is at $\{-3,5\mathrm{.}5\}$ in$.$ from the lower left corner of the $L$ shape and $P=185$ kip. Is the claim valid? Justify your answer.

$($ii$)$ Assuming the claim in $($i$)$ is valid what is the maximum load $P$

that the weld can support?