Reference
AISC Steel Construction Manual - Bracket Connection Design
C-Shape weld: Ix = d^2(3b+d)/6, Sx = Ix/(d/2)
Direct shear: fv = P / L
Bending stress: fb = M / Sx = P*e / Sx
Combined: f_max = sqrt(fv^2 + fb^2)
Required w = f_max / (0.75*0.6*FEXX*0.707)