Question

What is the minimum height $\left(\text{in}\text{m}\right)$ of a brick column of uniform cross section for which column breaks due to its own weight. $[P_{\text{atmospheric}}=100\text{kPa},\rho =1.8\times {10}^3{\text{kg/m}}^3$, Breaking stress $\sigma =3.7\text{MPa}]$

Answer 1

For brick column to be safe, maximum stress in it ( due to self weight) should be less than breaking stress.
For limiting case, we can consider maximum height be $H$ of the column, for which stress reaches breaking stress (limiting value).

$P_0+\rho gH={\sigma }_B$
${10}^5+1.8\times {10}^3\times 10H=3.7\times {10}^6$
$1.8\times {10}^{4}H=(3.7-0.1){10}^6$
$1.8\times {10}^{4}H=3.6\times {10}^6$
$H=200\text{m}$