A uniform solid circular bar of length L. cross sectional area A and self weight W is hanging vertically from the upper end. It is also subjected to a downward load of W at the free end. The elongation of the bar is
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T=(L−x) LW
;elongation= AY
Tdx = LAY
(L−x)Wdx
;Totalelongation=
LAYW
∫
0
L
(L−x)dx
= 2AYWL
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