Question $5$

$8$ pts

The $4$ meter long rigid beam ABC shown in the figure is supported with a pin at A and a $2$ meter long rod at C with a cross$-$section area of $1c{m}^2.$ The beam carries a load $P=4000N$ at B and it is known that the rod has $E=200$GPa and $=2\frac{{10}^{-6}}{}C.$ If the deformation of the rod is due to elastic and thermal strains, what should be the change temperature that must be applied to the rod such that its elongation remains equal to zero when the load is applied?

Justify your answer to receive full points.

a$)T=100$

b$)T=-50C$

c$)T=50C$

d$)T=-100C$

e$)$ None of the above