Figure shows a bar subjected to an external tensile load P. If the bar had been of uniform crosssection, the tensile stress intensity at any section would be constant only if the self-weight of the member is ignored. If the weight of the member is also considered, the intensity of stress increases for sections at higher level. It is possible to maintain a uniform stress of all the sections by increasing the area from the lower end to the upper end. Let the areas of the upper and lower ends be A1 and A2 respectively. Let A be the area at a distance x and A + dA at a distance x + dx from the lower end. Let the weight per unit volume be w Making a force balance for the element ABCD.
σ (A + dA) = σA + w Adx
or, σdA = w Adx
or dA/A = W.σ dx
Assuming w and s to be uniform,
