Question

A bar of uniform cross-section is hanging vertically as shown in figue. Specific weight of bar is $\gamma$ and $x$ is measured from free end. Then the graph of stress induced $\sigma$ versus $x$ due to self weight is

Answer 1

Given that
Specific weight of bar$=\gamma$
$\because$ Self weight distributed over volume
$\therefore$ Load at section $\left(1\right)-\left(1\right),P_{1-1}=0$
Load at section $x-x,P_{x-x}=\gamma Ax$
(A $\to$ area of cross-section)
and load at section $\left(2\right)-\left(2\right),P_{2-2}=\gamma Al$
($l\to$ length of bar)
$\because P_{x-x}=\gamma Ax$
Hence, stress $\left({\sigma }_{x-x}\right)$ due to self weight,
${\sigma }_{x-x}=\frac{P_{x-x}}{A}=\frac{\gamma Ax}{A}=\gamma x$
$\therefore {\sigma }_{x-x}\propto x$

Why this question? Tips: Stress induced in the bar of uniform cross-section due self weight depends upon $\gamma$ and length measured from free or lower end.