(Solved): A rigid beam BG is supported by a smooth pin C and by rods (1) and (2), that are attached to the be ...

A rigid beam BG is supported by a smooth pin C and by rods (1) and (2), that are attached to the beam at points $D$ and $B$ respectively. Both rods are identical with stiffness $k$ and thermal expansion coefficient $?$. The beam is horizontal $(?=0)$ when only rod $(2)$ is attached and $P=0$. During fabrication, rod (1) was made $\stackrel{?}{?}$ shorter than needed, as illustrated in the figure below (where $\stackrel{?}{?}?L$ ). In order to build the assembly, rod (1) was placed in the oven to increase its length so that it would fit between pins D and F. Hint: Assume SMALL deformations! Since $\stackrel{?}{?}?$ $L$, you can assume that both rods have the same stiffness $\mathrm{k}$. (a) What is the temperature needed to fix rod (1) to the pin $F$. (b) After assembly, rod (1) returns to its original temperature and a vertical force $P$ is applied at $G$ as indicated. Obtain an expression for the strain in rod (1), ${?}_1$. Your answer should be a function of $\mathrm{P},?,\stackrel{?}{?},\mathrm{L}$ and $\mathrm{k}$.