Question

A structural steel rod has a radius of $10\, mm$ and length of $1.0 \,m$. A $100 \,kN$ force stretches it along its length. Young’s modulus of structural steel is $2 \times 10^{11}\, Nm^{-2}$. The percentage strain is about

• A. $0.16\%$
• B. $0.32\%$
• C. $0.08\%$
• D. $0.24\%$

Answer 1

Answer: (A)

Given: $F= 100 kN=10^5N$
$Y=2\times10^{11}\,Nm^{-2}
\ell_{0}=1.0\,m$
radius $r = 10 mm = 10^{2}m$
From formula, $Y= \frac{Stress}{Strain}$
$\Rightarrow Strain =\frac{Stress}{Y}=\frac{F}{AY}$
$=\frac{10^{5}}{\pi r^{2}Y}=\frac{10^{5}}{3.14\times10^{-4} \times2\times10^{11}}$
$=\frac{1}{628}$
Therefore % strain $=\frac{1}{628}\times100=0.16\%$