$4.$ A $80$ mm wide rectangular tie bar is attached by fillet welds with $7$ mm throat thickness to a gusset plate at an angle of $\backslash (45^\{\backslash$circ$\}\backslash )$ as shown below. The ties carries a design axial load of $200$ kN $.$ Note that the weld is not returned at the back of the tie. Determine:

a$)$ the centroid of the weld group

b$)$ the second moment of area about a polar axis through the centroid

c$)$ the maximum shear stress acting on the weld group and its location