A stepped bar ABCD has the following dimension

Portion AB: Length 1200 mm and diameter 40 mm

Portion BC: Length 800 mm and diameter 20 mm

Portion CD: Length 1000 mm and diameter 30 mm

It is subjected to four point loads as shown in fig. Find the value of P for the equilibrium and then find the change in length of bar. Assume E=200 Gpa

Portion CD:

For equilibrium, along axial axis

$\sum F_x=0$

$P=16KN$

Now, the change in the length of bar for portion CD is,

$\delta l= \frac{PL}{AE}$ ($\phi=30mm=0.03m$)

$A=\frac{\pi *30^2}{4}$ $L=1000mm, E=200GPa=200*10^3 N/mm^2$

$A=706.85mm^2$ $P=16*1000N$

$\delta L_{CD}=\frac{16*1000*1000}{706.85*200*1000}$

$=0.1131mm$