Answer to Question #187717 in Mechanical Engineering for Gara

Question

Knowing that a 0.5 mm gap exist when the temperature is 20°C, determine (a) the temperature at which the normal stress in the aluminum bar will be equal to 100 MPa, (b) the corresponding exact length of the aluminum bar.

Answer 1

$$\delta=\frac{\sigma L}{E}\\0.0005=\frac{10^8 L}{75\cdot10^9}\\L=0.375\ m\\\alpha L(T-T_0)=\delta\\(23\cdot10^{-6})(0.375)(T-20)=0.0005\\T=78\degree C$$