USE THE SLOPES AND DEFLECTIONS OF BEAM METHOD!

PROBLEM $1(50$ points$)$

Consider the loaded beam below:

$EI,w,$ and a are constants. Note that there is a gap of $0\mathrm{.}2mm(0\mathrm{.}0002m)$ between the unloaded

beam and rigid simple support $($i$.$e$.,$ the support does not change length when the beam is resting

on it$)$ at point $B.$ Determine the support reactions at $A,B,$ and $C$ in terms of the constants.

Assume the beam is sufficiently loaded to cause it to touch the support at $B.$