Axial Load

Let’s say we have a uniaxial stress in the $x$-direction (the figure below is an uniaxial load).

• Under a direct axial tensile load, member will stretch and lengthen
• Under a direct axial compressive load, member will compress and shorten

This is often called pure tension or pure compression or “simple tension/compression” to indicate there are no other effects. Some assumptions:

• Bar is straight and made of homogeneous material
• Line of action of force contains centroid
• Section is not taken at: the ends, a discontinuity, or abrupt change in cross section

The normal stress is:

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

The strain is:

$$ϵ=\frac{l-l_0}{l_0}=\frac{\delta }{l_0}$$

Stress and strain can be expressed with Hooke’s law:

$$\sigma =Eϵ$$

where $E$ is the material-dependent Young’s Modulus (aka modulus of elasticity).

The displacement $\delta$ can be written as:

$$\delta =l-l_0=\frac{F{l}_0}{EA}=\frac{\sigma l_0}{E}$$

where $A$ is the cross-sectional area.