A steel I$-$beam is continuous over two $40ft$ spans and supports two $45$kip point loads.

a$)$ If support B was removed, calculate the downwards deflection of point B on the beam. Assume $E=29,000$ksi and $I=11,000i{n}^4.$

b$)$ If support B was removed and the $45$ kip loads are also removed, how far up would point B move if an upwards force of $1$ kip was applied at B$?$ This is just a point loaded beam with $1$ kip upwards.

c$)$ Calculate how much of the total $90$ kip applied load shown will be carried by support B and draw the shear force and bending moment diagrams for the member. You will need answers to part A and $B$ to solve this.