Mechanical Engineering $-$ Machine DesignFigure $2$ shows a rectangular steel bar welded $($the weld is shown as thick lines$)$ to a $250-$mm steel channel. For the welding configuration shown in the figure,

a$.$ Prove that the moment of inertia for the weld group in terms of the weld throat length $t$ are, $I_{Gx}=(3077{10}^6)*tm{m}^4$ and $I_{Gy}=(1418{10}^6)*tm{m}^4.$

b$.$ From previous analysis, it has been proven that the weld corner with the longest distance from the weld group centroid is critical. Based on this information, determine the required weld size $h$ if the load $F$ is $16kN,$ E$60$ welding rod $)$ is used and safety factor $SF=2\mathrm{.}5$ based on yielding is imposed.