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 is the ratio of extension produced in a solid/wire to the original length.