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How It Works
Stress (σ = F/A) measures force per unit area inside a material. Strain (ε = ΔL/L₀) measures relative deformation. Hooke's Law (σ = E·ε) connects them through Young's modulus (E), which describes a material's stiffness. These relationships apply within the elastic region, where deformation is reversible.
Example Problem
A steel rod (E = 200 GPa, cross-section = 0.001 m²) is pulled with 50,000 N. What is the stress and strain?
- σ = 50,000 / 0.001 = 50 MPa
- ε = 50 × 10&sup6; / (200 × 10&sup9;) = 0.00025 (0.025%)
Frequently Asked Questions
What is Young's modulus?
Young's modulus (E) measures material stiffness — the ratio of stress to strain in the elastic region. Steel has E ≈ 200 GPa; rubber has E ≈ 0.01 GPa.
What happens beyond the elastic limit?
Beyond the elastic limit, the material deforms permanently (plastic deformation). Hooke's Law no longer applies, and eventually the material fractures.
Is strain the same as deformation?
Not exactly. Strain is the relative deformation (ΔL/L₀), making it dimensionless. Deformation (ΔL) has units of length. Strain lets you compare materials regardless of specimen size.
Related Calculators
- Hooke's Law Calculator — calculate spring force and potential energy.
- Force Equation Calculator — find the applied force.
- Torque Calculator — analyze rotational stress.
- Thermal Expansion Calculator — find thermal strain in materials due to temperature change.
- Pressure Unit Converter — convert stress units between Pa, psi, and MPa.
Reference: Lindeburg, Michael R. 1992. Engineer In Training Reference Manual. Professional Publication, Inc. 8th Edition.