Problem $3(40$ points$)$

We are given the statically indeterminate structure shown in Figure $1.$ Apart from the loadings, member $AB$ is also subjected to temperature effects. The crosssectional depth of member $AB$ is $h=12$ in$,$ and the thermal coefficient is $a_T=5*\frac{{10}^{-6}}{}F.$ We are also given that the effect of axial forces on the deformations can be NEGLECTED.

Important HINT: This structure is "similar" to the one in Problem $4$ of Homework $7.$ Try to solve taking advantage of the solution to that previous problem!

$1$

a$)$ Establish a primary structure $(5$ points$).$

b$)$ Establish the compatibility equation from which you will obtain the redundant force $(15$ points$).$

c$)$ Determine the support reactions of the structure $(5$ points$).$

d$)$ Determine the internal loading diagrams of the structure $(5$ points$).$

e$)$ Determine the support reactions IF THE STRUCTURE IS ONLY SUBJECTED TO THE TEMPERATURE EFFECTS $($and not the loads$)(10$ points$).$