Question

A steel pipe 3.6m long is placed vertically under a sagging floor to support it The inside diameter of the pipe is 80mm and the outside diameter is 1000mm and young's modulus is 2×10^11pa.A sensitive strain guage indicates that the pipes length decreases by 0.1mm.What is the magnitude of the load that the pipe supports?

Answer 1

Find stress:

$$\sigma=\frac FA.$$

Find strain:

$$\epsilon=\frac{\Delta l}{l}.$$

Write the relation between srtress and strain:

$$\sigma=E\epsilon=E\frac{\Delta l}{l},\\\space\\ E\frac{\Delta l}{l}=\frac FA.\\\space\\ F=EA\frac{\Delta l}{l}=(2·10^{11})\bigg(\frac\pi 4(1^2-0.08^2)\bigg)\bigg(\frac{0.1}{3.6}\bigg)=\\\space\\=4.34·10^6\text{ N}.$$