Three round, copper alloy bars having the same length L but different shapes are shown in the figure. The first bar has a diameter d over its entire length, the second has a diameter d over one-fifth...

Three round, copper alloy bars having the same length L but different shapes are shown in the figure. The first bar has a diameter d over its entire length, the second has a diameter d over one-fifth of its length, and the third has a diameter d over onefifteenth of its length. Elsewhere, the second and third bars have a diameter 2d. All three bars are subjected to the same axial load P.

Use the following numerical data: P = 1400 kN, L = 5 m, d = 80 mm, E = 110 GPa, and n = 0.33.

(a) Find the change in length of each bar.

(b) Find the change in volume of each bar.