Axial Deformation

In the linear portion of the stress-strain diagram, the tress is proportional to strain and is given by
 

$\sigma = E \varepsilon$

 

since $\sigma = P / A$ and $\varepsilon = \delta / L$, then $\dfrac{P}{A} = E \dfrac{\delta}{L}$
 

$\delta = \dfrac{PL}{AE} = \dfrac{\sigma L}{E}$

To use this formula, the load must be axial, the bar must have a uniform cross-sectional area, and the stress must not exceed the proportional limit.
 

Simple Strain

Also known as unit deformation, strain is the ratio of the change in length caused by the applied force, to the original length.
 

Simple strain

 

$\varepsilon = \dfrac{\delta}{L}$

where δ is the deformation and L is the original length, thus ε is dimensionless.