Uniaxial Loading

#202 / Materials Science Easy

Consider a 1 m long steel rod with a cross sectional area of 2,000 mm^2 is subjected to a 6,000 N force in the diagram below. What is the rod's elongation if the modulus of elasticity (E) is 200 GPa?

Expand Hint
$$$E=\frac{\sigma}{\varepsilon}=\frac{P/A}{\delta/L}$$$
where $$P$$ is loading, $$L$$ is the length of member, $$A$$ is the cross sectional area, $$\delta$$ is the deformation, $$\sigma$$ is the stress, $$\varepsilon$$ is the engineering strain, and $$E$$ is the modulus of elasticity
Hint 2
For uniaxial deformation:
$$$\delta =\frac{PL}{AE}$$$
where $$P$$ is loading, $$L$$ is the length of member, $$A$$ is the cross sectional area, and $$E$$ is the modulus of elasticity
For uniaxial deformation:
$$$Deformation=\delta =\frac{PL}{AE}$$$
where $$P$$ is loading, $$L$$ is the length of member, $$A$$ is the cross sectional area, and $$E$$ is the modulus of elasticity

Thus,
$$$\delta =\frac{(6,000N)(1m)}{(2,000\times 10^{-6}m^2)(200\times 10^9\frac{N}{m^2})}$$$
$$$=\frac{6000}{400,000,000}m=0.000015m=15\: \mu m$$$
$$$15\: \mu m$$$


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