Answer to Question #289222 in Physics for jay

Question

A reinforced concrete square pole is to withstand a wind shear force of 450.0 kN.

Calculate the relevant cross-sectional side dimensions of the pole for a safety factor

of 9.00. [Ultimate Shear Strength of the reinforced concrete = 125 MPa]

Answer 1

Given:

$F=450*10^3\:\rm N$

$\sigma_{\max}=125*10^6\:\rm Pa$

$n=9$

The Shear Strength

$$\sigma=\frac{F}{A}=\frac{F}{a^2}=n\sigma_{\max}$$

The relevant cross-sectional side

$$a=\sqrt{F/(n\sigma_{\rm max})}$$

$$a=\sqrt{450*10^3/(9*125*10^6)}=0.02\:\rm m$$