Use Force Method to compute all the support reactions for the following beam $($Figure $1)$ and draw the bending moment diagram. Support at A settles down by $18mm$ and support at B settles down by $6mm($these support settlements are in addition to the load acting on the beam$).$ Note that, differential temperature is also acting on the member $BC($NOT in $AB)$ as shown in the figure. A and $B$ are roller supports and $C$ is a pin support. Take E $=200$GPa, $I=120{10}^{6}m{m}^4$ and coefficient of thermal expansion, $=\frac{{10}^{-5}}{}$C$.$ Use principal of virtual work to determine deflections. You can use integration table OR formulate general equation while solving for deflections.

Figure $1$