Use the following for problems $[1]$ thru $[$x$].$

A $\frac{1}{2^{\text{'}\text{'}}}$ plate is welded to a $\frac{1}{2^{\text{'}\text{'}}}$ thick vertical member using an E$6010$ electrode as shown. Both members are made of AISI $1020$ HR steel $(F_N=55$ksi,$F_{ty}=30$ksi,$E=30$Msi $).$

$[2]$ For the structural connection shown above, determine $($a$)$ the area of the weld, and $($b$)$ the centroid of weld relative to point $A.$

$[3]$ For the structural connection shown above, determine the torsional constant J of the weld.

$[4]$ If the structural connection shown above is subjected to a force $P=20$ kips as shown, determine the maximum shear stress at $($a$)$ the upper rightmost point of the weld pattern, $($b$)$ the upper leftmost point of the weld pattern, $($c$)$ the lower leftmost point of the weld pattern, and $($d$)$ the lower rightmost point of the weld pattern.

$[5]$ Continuing the analysis of Problem $[4],$ determine $($a$)$ the maximum stress in the weld pattern & its location, and $($b$)$ the minimum margin of safety of the weld pattern if $Fs{u}_{su}$ of the weld is $12$ ksi $.$

$[6]$ If the structural connection shown above is instead subjected to a force $P=20$ kips in the positive $x-$direction as shown, and Fsu of the weld is $12$ ksi $,$ determine the maximum shear stress at the maximum stress in the weld pattern & its location.

Please answer questions $4,5,$and $6$