## Q. 2.17

A copper bar AB under a tensile load P = 500 kN hangs from a pin supported by two steel pillars. The copper bar has length of 10 m, cross sectional area of 8100 mm² and E = 103 GPa. Each pillar has height of 1 m, cross sectional area 7500 mm², and ES = 200 GPa. Determine the displacement of point A. Refer Figure 2.28.

## Verified Solution

The displacement of the point A is due to elongation of the bar due to pull of 500 kN plus the compression of the steel pillars.

$\text { Load transferred to each pillar }=\frac{500}{2}=250 kN$

Elongation of bar = $\frac{P L}{A E_{ C }}$

$=\frac{500 \times 10^3 \times 10000}{8100 \times 103 \times 10^3}=5.99 mm$

Compression of steel pillar $=\frac{P L}{A E_{ S }}$

$=\frac{250 \times 10^3 \times 1000}{7500 \times 200 \times 10^3}=0.16 mm$

∴  Displacement of point A = 5.99 + 0.16 = 6.15 mm