Question

A tapered circular rod of diameter varying from 60 mm tp 40 mm is connected to another circular tapered rod of diameter varying from 40 mm to 70 mm as shown in the figure below. Both bars are of the same material with $E=2\times {10}^5\text{MPa}$. When subjected to a load of 100 kN, the deflection at point A is mm.

• A. 1.52

Answer 1

The correct option is A 1.52

Total elongation, $\Delta ={\Delta }_{AB}+{\Delta }_{BC}$
$=\frac{4P{L}_{AB}}{\pi d_2{d}_{3}E}+\frac{4P{L}_{BC}}{\pi d_2{d}_{1}E}$
$=\frac{4\times 100\times {10}^3\times 2\times {10}^3}{\pi \times 70\times 40\times 2\times {10}^5}+\frac{4\times 100\times {10}^3\times 4\times {10}^3}{\pi \times 40\times 60\times 2\times {10}^5}$
$=0.455+1.06=1.515\text{mm}\approx 1.52\text{mm}$