Consider a tapering rod hung vertically and firmly fixed at the top position. The rod is of length L and it tapers uniformly from diameter dl to d2, Let the sides AC and BD meet at point E when produced. Extension δL in the length L of the rod ABDE due to self weight is
δL = extension of conical rod AEB due to self weight – extension due to conical segment CEB due to self weight – extension in rod length L due to weight of segment CED.
where P is the weight of segment CED and w is the specific weight of bar material
Substituting this value of tensile load P in the above expression, we get
From the geometrical configuration
If the rod is conical, i.e., d2 = 0
δL = wL2/6E
which is the same expression as derived earlier
