PROBLEM $1(25$ pts$)$

A $1"$ plate is welded to a $2"$ thick vertical member using an E$6010$ electrode as shown. Both members are made of AISI $1020$ HR steel $($Ftu$=55$ ksi, Fty$=30$ ksi, E$=30$ Msi$).$ Forces of P$1=10$ kips $\backslash$& P$2=20$ kips is applied. Determine:

a$.$ The centroid of weld relative to point $\backslash ($ A $\backslash )$

b$.$ The area of the weld

c$.$ The torsional constant J of the weld