Question

A structural steel rod has a radius of 10 mm and a length of 1 m. A 100 kN force stretches it along its length. The strain on the rod is
$(Y_{steel} = 200 × 10^9 \,N \,m^{-2})$

• A. 1.6 mm
• B. 2.6 mm
• C. 3.6 mm
• D. 4.6 mm

Answer 1

Answer: (A)

Here, $r = 10\, mm = 10 × 10^{-3}\, m$
$L = 1\, m$
$F = 100\, kN = 100 × 10^3\, N = 10^5\, N$
Stress on the rod is given by
Stress $=\frac{F}{A}=\frac{F}{\pi r^{2}}$
$=\frac{100\times10^{3}\,N}{3.14\times\left(10^{-2}\,m\right)^{2}}=3.18\times10^{8}\,N\,m^{-2}$
Elongation,
$\Delta L=\frac{\left(F / A\right)L}{Y}=\frac{\left(3.18\times10^{8}\,N\,m^{-2}\right)\left(1\,m\right)}{2\times10^{11}\,N\,m^{-2}}$
$=1.59\times10^{-3}\,m=1.59\,mm$
The strain on the rod is given by
Strain $= \frac{\Delta L}{L}$
$=\frac{1.59\times10^{-3}\,m}{1\,m}=1.59\times10^{-3}\,m=1.59\,mm$
$=1.6\,mm$