The solid circular bar shown above is aluminum, $E=70$GPa,$a=2310-$

$\frac{6}{}C.$ The bar is fixed at one end and free at the other with a gap

between the free end and a fixed surface.

a$)$ Its temperature is increased by $20C.$ What is the stress, $,$ and the

axial strain $,$ in the bar?

b$)$ The same bar is heated by $30C.$ What is the stress, $,$ and the axial

strain $,$ in the bar?

c$)$ Did you need to know the diameter of the bar to solve Part a$)$ and b$)?$