A structural steel rod has a radius of $10 \;mm$ and a length of $1.0 \;m$. A $100 \;kN$ force stretches it along its length. Calculate $(a)$ stress, $(b)$ elongation, and $(c)$ strain on the rod. Young's modulus, of structural steel $1 s 2.0 \times 10^{11} \;N m ^{-2}$

Answer We assume that the rod is held by a clamp at one end, and the force $F$ is applied at the other end, parallel to the length of the rod. Then the stress on the rod is given by

$\text { Stress } =\frac{F}{A}=\frac{F}{\pi r^{2}}$

$=\frac{100 \times 10^{3} N }{3.14 \times\left(10^{-2} m \right)^{2}}$

$=3.18 \times 10^{8} N m ^{-2}$

The elongation,

$\Delta L=\frac{(F / A) L}{Y}$

$=\frac{\left(3.18 \times 10^{8} N m ^{-2}\right)(1 m )}{2 \times 10^{11} N m ^{-2}}$

$=1.59 \times 10^{-3} m$

$=1.59 mm$

The strain is given by

$\text { Strain } =\Delta L / L$

$=\left(1.59 \times 10^{-3} m \right) /(1 m )$

$=1.59 \times 10^{-3}$

$=0.16 \%$