Calculator · Structural Mechanics
Hooke's Law Calculator
In the uniaxial linear-elastic range, stress is proportional to strain and Young's modulus is the constant of proportionality. Choose which of the three you want and supply the other two.
Solve for
Inputs
Structural steel ≈ 200 GPa, aluminium ≈ 70 GPa.
Results
| Young's modulus E | 200 GPa |
|---|---|
| Stress σ | 150 MPa |
| Strain ε = σ/E | 7.5000e-4 |
| Strain in microstrain | 750 µε |
Technical reference
σ = E ε
ε = σ / E
E = σ / ε
- σ
- uniaxial normal stress[Pa]
- ε
- normal strain in the same direction[–]
- E
- Young's modulus, the elastic slope of the σ–ε curve[Pa]
This is the UNIAXIAL form. Under a biaxial or triaxial state the transverse stresses contribute through Poisson's ratio, and σ = Eε no longer gives the strain in the loading direction.
Valid only below the proportional limit. Past yield the σ–ε curve is no longer a straight line and E ceases to describe the material's response, though it still governs unloading.
E is a material property measured at a temperature; it drops measurably at elevated temperature.
Assumptions
- · Uniaxial stress state, linear-elastic, homogeneous and isotropic material.
- · Stress below the proportional limit of the material.
- · Strain measured in the same direction as the stress.
Open in the Lab
The stress and modulus of this state carry over, so the Lab reports the same σ and ε. Length (1 m) and area (500 mm²) are placeholders σ = Eε does not depend on.