Two $\backslash (\backslash$mathrm$\{$C$\}10\backslash$times $20\backslash )$ channels are welded together to make a tube section as shown below.

$(1)$ For a shear force, $\backslash ($ V$\_\{$y$\}\backslash ),$ as indicated below compute the shear flow distribution around the section. Use symmetry, maintain the coordinate system at the Center of Gravity, and at the start of each plate, and all answers shall be given in terms of $\backslash ($ V $/$ I $\backslash ).$

$(2)$ If a shear force $\backslash ($ V$\_\{$y$\}=250\backslash$mathrm$\{$kips$\}\backslash )$ is assumed constant along the length of the member and spot welds are provided every $6$ inches along the length at the seam, what is the minimum required strength of a weld $($it is assumed that $\backslash ($ V$\_\{$y$\}\backslash )$ is the maximum design shear force$).$ You will need $\backslash ($ I$\_\{$z$\}\backslash )$ for this part.

Section properties are provided in the attachment $-$ use decimal values. You can neglect fillets at the corner of the channels. All calculations shall be in kips and inches.