## Evaluate elongation because of self weight of tapering rod, Mechanical Engineering

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Determine elongation because of self weight of tapering rod:

Sol.: Take a tapering rod hung vertically and firmly fixed at top position. The rod is of length L tapers uniformly from diameter dl  to d2, Let sides AC and BD meet at the point E when produced. Extension L in the length L of the rod ABDE because of self weight is

δL = extension of conical rod AEB because of self weight - extension because of conical segment CEB because of self weight - extension in rod length L because of weight of segment CED

where P is weight of segment CED and w is specific weight of bar material

Substituting the value of tensile load P in above expression, we get

From geometrical configuration

This gives :

If rod is conical,  that is, d2 = 0

which is same expression as derived previously.

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