Stress, strain and elastic modulus
The distinction between load intensity, deformation and stiffness in a small-strain elastic material model.
ENGINEERING PRINCIPLE
Within a linear elastic range, normal stress is proportional to normal strain and the proportionality is Young’s modulus.
σ = F/A; ε = ΔL/L₀; E = σ/εVariables and units
- σ = normal stress (MPa)
- ε = normal strain (mm/mm)
- E = Young’s modulus (GPa)
Worked example
A 20 kN axial load on 500 mm² gives 40 MPa. If a 100 mm gauge length elongates by 0.02 mm, ε = 0.0002 and E = 200 GPa.
Calculation method
- Use the original loaded area for nominal engineering stress.
- Use the original gauge length for engineering strain.
- Only divide stress by strain in the verified linear elastic range.
Practical applications
- Tie rods and specimens
- Material comparison
- Elastic deflection estimates
Review boundary and reference
- Stress concentrations, plasticity and temperature change invalidate a simple uniform model.
- Use certified material properties for critical work.
Formula and displayed units independently checked for the stated conditions. This is not a code-compliance design method.
Source: Standard mechanics-of-materials treatment of uniaxial elastic response; NIST SP 811 for units.