A straight bar loaded along its axis carries normal stress and changes length.

For a prismatic bar with axial force $F$, area $A$, length $L$ and Young's modulus $E$, linear elasticity gives

$$\delta=\frac{FL}{AE}.$$

From stress to extension

The average normal stress is

$$\sigma=\frac{F}{A},$$

and the corresponding elastic strain is

$$\varepsilon=\frac{\sigma}{E}.$$

Because

$$\varepsilon=\frac{\delta}{L},$$

the axial-deformation formula follows directly.

Tension and compression

A tensile force produces positive extension; a compressive force produces shortening under the usual sign convention.

What controls deformation

A longer bar deforms more under the same force. Increasing its area or using a material with larger Young's modulus reduces the deformation.

Axial deformation is the simplest structural application of stress, strain and linear elasticity.