A bar of varying section fixed at both ends is axially loaded as shown in figure $(1).$ The centrat section is follow circular section of $60mm$ outside dismeter and $45mm$ inside diameter; the other portions are $30mm$ square cross$-$section. Find the stress in each section and the change in diameters of the central section. $E=180G\frac{N}{m^2},v=0\mathrm{.}3.$

Figure $(1)$