Problem $2(10$ points$)$:

The frame ABCD is constructed of A$-36-$steel W$250$ X $67$ members. The distance between supports is $L=6m$ and the height of the frame is $h=1\mathrm{.}2m.$ The members are rigidly connected at B and C $.$ Determine the maximum intensity of load $q_0$ that can be safely supported by the member BC using an interaction formula. The allowable bending stress is $({}_b{)}_{\text{a}\text{l}\text{l}\text{o}\text{w}}=100$MPa.