Question

Three wires of steel 1, 2 and 3, each having area A support a load W as shown in the figure below. What is the ratio between collapse load and the load corresponding to yielding of one of the wires?

• A. $3:1$
• B. $3:2$
• C. $3:25$
• D. $3:3$

Answer 1

The correct option is B $3:2$

The elongation in all wires will remain same.
$\therefore \Delta =\frac{P_{1}L}{AE}=\frac{P_{2}L}{2AE}=\frac{P_{3}L}{AE}$
$P_1=P_3=\frac{P_2}{2}$
Thus wire having higher axial load will yield first.
$P_2={\sigma }_{y}A$
$P_1=P_3=\frac{{\sigma }_{y}A}{2}$
$W_1=P_1+P_2+P_3=2{\sigma }_{y}A$
At collapse, the stress in all wires will be ${\sigma }_y$
So $W_2=3{\sigma }_{y}A$
$\frac{W_2}{W_1}=\frac{3}{2}$