Answer to Question #104400 in Physics for Jake

Question

A tubular steel strut of outer diameter 20 mm and inner diameter 5 mm carries a compressive load of 10 kN. The strut is 1 m long and the modulus of elasticity of the material is 60 GPa. Calculate the induced compressive stress, compressive strain and the change in length that takes place during the loading.

Answer 1

The induced compressive stress:

$$\sigma=\frac{F}{A}=\frac{F}{0.25\pi(D^2-d^2)}$$

$$\sigma=\frac{10\cdot 10^3}{0.25\pi((20\cdot 10^{-3})^2-(5\cdot 10^{-3})^2)}=3.4\cdot 10^{7}\ Pa$$

Te compressive strain:

$$\epsilon=\frac{\sigma}{Y}$$

$$\epsilon=\frac{3.4\cdot 10^{7}}{60\cdot 10^{9}}=5.7\cdot 10^{-4}$$

The change in length that takes place during the loading:

$$\Delta l=\epsilon l=(5.7\cdot 10^{-4})(1)=5.7\cdot 10^{-4}\ m=0.57\ mm$$