## Uniaxial Loading

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?

##
__
__**Hint**

**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**

**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,

$$$\delta =\frac{(6,000N)(1m)}{(2,000\times 10^{-6}m^2)(200\times 10^9\frac{N}{m^2})}$$$

$$$=\frac{6000}{400,000,000}m=0.000015m=15\: \mu m$$$

$$$15\: \mu m$$$