$(35$ points$)$ A building has a column layout as shown in the following figure with $30ft$ bay in one direction and $25ft$ bay in the other. It must support a uniform dead load of $100psf$ and a uniform live load of $80psf.$

a$.$ Determine the maximum combined loads using recommended AISC expressions for LRFD if no live load reduction is considered.

b$.$ Determine the required moment and shear strength for beams and girders, and axial strength for columns, as noted below for design by LRFD$.($Note: live load reduction should be considered during calculations$)$

i$.$ The beam on column line $3$ between column lines A and $B$ if the deck spans from line $2-2$ to $3-3$ to $4-4.$

ii$.$ The girder on column line $C$ between column lines $3$ and $4$ if the deck spans from line BB to C$-$C to D$-$D$.$

iii. The column at the corner on lines $4$ and A and supporting one floor.

iv$.$ The column on the edge at the intersection of lines $C$ and $4$ and supporting one floor.

v$.$ The interior column at the intersection of column lines D and $3$ and supporting one floor.