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

Cross-sectional area of the strut

$$A=0.25\pi (0.02^2-0.005^2)=0.00029\ m^2$$

Compressive Stress, 

$$\sigma=\frac{10\cdot10^3}{0.00029}=34.5\ Mpa$$

Compressive Strain 

$$ϵ=\frac{34.5\cdot10^6}{60\cdot10^9}=5.75\cdot10^{-4}$$

$$Δ L = ϵ L \\=5.75\cdot10^{-4}(1)=5.75\cdot10^{-4}m=0.575\ mm$$