Question

A twisted steel wire of length L,cross sectional area A and modulus of elasticity E in tension . The wire is stretched horizontally between two fixed points A and B but without any initial tension . A load P is then suspended from the mid -pointC of the wire .find the vertical deflection of the mid-point C of the wire . assume that the deflection is small compared to the length of the wire.

Answer 1

Workdone =$\frac{1}{2}$ ​× Stress × Strain × Volume 

Workdone =$\frac{1}{2}$ ​×Y×(strain)2×Volume

$Workdone = \frac{1}{2} ×Y×( \frac{x}{l} ) 2×AL$