$(50$ pts$)$ The rigid beam shown below was intended to be supported by three columns, but

the center column was manufactured slightly longer than the other two, leaving a gap of

$0\mathrm{.}15$ in between the beam and outer columns under no load. The center column is wood,

with $E=1,200$ksi,$A=30i{n}^2,$ and the outer columns are concrete, each with $E=4,500$

ksi and $A=64i{n}^2{?}^2$

a$.$ What load w will cause the beam to just make contact with the outer columns?

b$.$ What is the vertical deflection of the beam under a distributed load of $8\frac{k}{f}t?$

What is the force in each column in this case?