Consider the butt joint shown. The plates are $A992(F_y=50$Ksi,$F_u=65$Ksi $).$ The bolts are $\frac{7}{8}-$in$.-$diam. in standard size holes.

$($a$)$ Compute the design tensile strength ${}_t{P}_n$ of the plates.

$($b$)$ If the connection is slip$-$critical with A$490-$SC bolts and Class A faying surfaces:

i$.$ Compute the design strength $P_n$ of the connection.

ii$.$ Compate the tensile service load capacity. $P_l=5P_d.$

$($c$)$ If the connection is bearing$-$type with $A490-x($i$.$e$.,$ threads excluded from the shear plane$)$:

i$.$ Compute the design strengh $P_n$ of the connection.

ii$.$ Compute the tensile spruice load capacity. $P_l=5P_d.$