Stress, Strain & Young Modulus

Stress:

The stress of a material is defined as the ratio of force to the area. It is the ratio of force that acts on a material to the area of the material.

\( \scriptsize Stress, \: \sigma \)= \( \frac{Force}{Area} \\ = \frac{F}{A} \)

Stress is frequently represented by a lowercase Greek letter sigma (σ)

Its unit is Nm^-2 or N/m²

Example 6.3.1:

A metal rod is being compressed by a machine with a force of 750 N. The cross-sectional area of the metal rod is 30 cm² . What is the compressive stress on the metal rod?

Solution:

Force = 750 N

Area = 30 cm²
convert to m² (divide by 10,000)

= \( \frac{30}{10000} = \scriptsize 0.003 \:m^2\)

\( \scriptsize Stress, \: \sigma = \normalsize \frac{force}{area} \\ = \normalsize \frac{750}{0.003} \\ = \scriptsize 250000\: Nm^{-2} \\ = \scriptsize 2.5 \: \times \: 10^{5}\: Nm^{-2}\)

Strain:

Strain energyEnergy is the ability to do work. Energy exists in several forms such as heat, kinetic or mechanical energy, light, potential energy, and electrical energy. Units of Energy: The SI unit... More is the potential energy stored within an elastic material as a result of its deformation when an external force is applied. It is the ratio of extension produced in a solid/wire to the original length.

\(\scriptsize Strain, \: \epsilon = \normalsize \frac{Extension}{Original \: Length}\\= \normalsize \frac{e}{L}\\= \normalsize \frac{metre}{metre}\)

Strain has no unit, i.e. it is a dimensionless quantity because both the change and original dimension are measured in the same units (e.g.,