Question

A bar of uniform cross sectional area “A” and length “L” hangs vertically from a rigid support of the density of a material as \(\rho\) kg/m³ . Derive the expression for maximum stress induced and elongation produced in the bar due to its own weight.

Answer 1

Consider a small section of length δx, at a distance x from the free end. The deformation δ\(\Delta\)is given by

δ\(\Delta\) = \(\frac{W_s}A.\frac{\delta x}E\)

where W_s = weight of portion below the section = A.x.\(\lambda\)

\(\therefore\) Total deformation of the rod

Maximum stress induced in the strip