The stress at any cross section can be found by dividing the load by the area of cross section and extension can be found by integrating extensions of a small length over whole of the length of the bar. We shall consider the following cases of variable cross section: Consider a circular bar that tapers uniformly from diameter d1 at the bigger end to diameter d2 at the smaller end, and subjected to axial tensile load P as shown in figure. Let us consider a small strip of length dx at a distance x from the bigger end. Diameter of the elementary strip:
dx = d1 - [{d1 - d2) x]/L
= d1 - kx : where k = (d1 - d2)/L
Cross sectional area of strip
Stress in the strip
Strain in strip
Elongation of the strip
The total elongation of this tapering bar can be worked out by integrating the above expression between limits x = 0 to x = L.
Putting the value of k = (d1 - d2)/ in the above expression, we obtain
