Question

A steel post 15 cm in diameter and 3 m long is placed vertically and is required

to support a load of 10,000 kg.

(a) What is the stress in the post?

(b) What is the strain in the post?

Answer 1

Given:

$l_0=3\:\rm m$

$d=0.15\:\rm m$

$m=10000\:\rm kg$

$E=230*10^9\:\rm Pa$

(a) What is the stress in the post?

$$\sigma=\frac{F}{A}=\frac{mg}{\pi d^2/4}\\= \frac{10000*9.8}{3.14*0.15^2/4}=5.55*10^6\:\rm Pa$$

(b) What is the strain in the post?

$$\varepsilon=\frac{\sigma}{E}=\frac{5.55*10^6}{230*10^9}=2.4*10^{-5}$$