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 d_{l} to d_{2}, 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, d_{2} = 0 which is same expression as derived previously.