Problem $1$

A steel wire with length $L$ has a cross$-$sectional area equal to A and is stretched tightly between the midpoints of the simple beam and the free end of the cantilever beam as shown in the figure.

Figure $1$: Simply supported beam with gap

a$)$ Determine the force in the wire if the temperature in the wire is changed by $T.$

b$)$ Determine the deflection of the end of the cantilever beam, the deflection of the center of the simply supported beam, and the corresponding change in length of the cable.

Hint: The solutions posted in appendix C of the textbook can be used to solve this problem.

Take $E_{\text{w}\text{i}\text{r}\text{e}}=20$GPa,$A=160m{m}^2,$ and $L=5m.$

Take $a={12}^{***}{10}^{-6}\frac{1}{}C$ and $T=-50C.$

For both beams, take $E_{\text{b}\text{e}\text{a}\text{m}}=10$GPa,$I=10**{10}^{6}m{m}^4,$ and $a=0\mathrm{.}8m.$