Problem $2.$ The figure below shows patient room section of a hospital. The figure corresponds to the floor plan of the first$-$floor slab. According to the load analysis the dead load is $56psf$ and the live load is $40psf.$ The structural framing has columns at every axis intersection, all solid and dashed lines represent beams, and floors are slabs. All elements are made with reinforced concrete.

a$)$ Determine the tributary width and tributary area of beam $2$A$-$B and beam B$3-4.$

b$)$ Ignoring the weight of beams, columns and other elements, find reactions, shear force and bending moment diagrams for beam $2$A$-$B due to service loads. Note that beams $2$ is continuous. You may use the software of your choice to perform the structural analysis $($MASTAN $2$D$,$ Visual Analysis, etc.$)$ or solve the problem by hand using Moment Distribution. Find $V_{\text{m}\text{a}\text{x}}$ and $M_{\text{m}\text{a}\text{x}}($there may be several maxima$).$

c$)$ Repeat the analysis of part b with ultimate loads.