Question

A metal rod, 20 mm diameter, is tested in tension (force applied axially). The total extension over a length of 80 mm is 3.04 x 102 mm for a pull of 25 kN. Calculate the normal stress, normal strain and modulus of elasticity (Young's modulus), assuming the rod is linear elastic over the load range.

Answer 1

Answer:stress=79.56MPa

strain=$3.8\times 10^{-4}$

Young Modulus=209.36 GPa

Explanation:

Given data

d=20 mm

Length$\left ( L\right )$=80mm

$\Delta {L}$=$3.04\times 10^{-2}$mm

Load=$25\times 10^{3}$N

$\left ( i\right )$

Stress=$\frac{Load\ applied}{cross-section}$

Stress=$\frac{25\times 10^{3}}{314.2}$

Stress=79.56MPa

$\left ( ii\right )$

Strain=$\frac{Change\ in\ length}{Length}$

Strain=$\frac{3.04\times 10^{-3}}{80}$

Strain=$3.8\times 10^{-4}$

$\left ( iii\right )$

young modulus$\left ( E\right )$=$\frac{Stress}{Strain}$

E=$\frac{79.56\times 10^{6}}{3.8\times 10^{-4}}$

E=209.36GPa