Compute the maximum service load $P$ causing eccentric shear on the connection of the accompanying figure. The loading is $25\%$ dead load and $75\%$ live load. The bolts are $\frac{7}{8}-$in$.-$diam A $325$ bolts in a bearing$-$type connection $($A$325-$X$)$ with threads excluded from the shear plane. Assume the bracket plate has adequate strength.

$($a$)$ Use the elastic $($vector$)$ method.

$($b$)$ Use the strength method with rotation about the instantaneous center.

$($c$)$ Use AISC Manual Tables $7-7$ to $7-14,$ with interpolation.

Problem $4\mathrm{.}10$