How it’s calculated
Normal stress is force per unit area, strain is the fractional change in length, and within the elastic (Hooke’s law) range their ratio is Young’s modulus. Assumes a uniform prismatic bar loaded axially through its centroid, with stress below the proportional limit.
Example (OpenStax University Physics, Example 12.8): a 2.0 m steel rod with A = 0.30 cm² holds a 550 kg platform, so F = 550 × 9.8 = 5,390 N. Stress = 5,390 ÷ 3.0 × 10⁻⁵ m² = 1.8 × 10⁸ Pa (180 MPa). With E = 2.0 × 10¹¹ Pa the rod stretches ΔL = 1.8 mm, a strain of 9.0 × 10⁻⁴.
Typical E values: steel 200 GPa, aluminum 70 GPa, copper 110 GPa, concrete 20 GPa (OpenStax Table 12.1).
Frequently asked questions
What units is stress in?
Pressure units: pascals (N/m²), usually MPa for metals. 1 MPa = 145.04 psi; 1 ksi = 6.895 MPa.
Is strain dimensionless?
Yes. It is length divided by length. It is often quoted in percent or microstrain (×10⁻⁶).
When does E = σ/ε stop applying?
Beyond the proportional (elastic) limit the stress–strain curve bends over; the material yields and some deformation becomes permanent. Compare stress with the material’s yield strength.
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Sources
- University Physics Vol. 1, 12.3 Stress, Strain, and Elastic Modulus — OpenStax
- NIST Guide to the SI (SP 811), Appendix B conversion factors — U.S. National Institute of Standards and Technology
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