Elastic Modulus & Energy
Apply Hooke's law to compute elastic modulus E, shear modulus G and strain energy U=W²l/(2AE).
Inputs
Formula
E = σ/ε; G = τ/γ; U = W²l/(2AE)
Fundamentals
Elastic (Young's) modulus is stress over strain in the elastic range — a measure of stiffness against elastic deformation.
Hooke's law $\sigma=E\varepsilon$; a steeper slope $E$ means a 'stiffer' material. Steel ≈ $200\,\text{GPa}$, aluminium ≈ $69\,\text{GPa}$.
History
Young's modulus was introduced by T. Young (1807) on the basis of Hooke's law (1676).
Engineering applications
Used in stiffness design, material selection and deflection or natural-frequency calculation.
Glossary
| Young's $E$ | Slope of the stress–strain line (stiffness). |
| Hooke's law | Stress proportional to strain in elastic range. |
| Stress $\sigma$ | Internal force per area, $\sigma=F/A$. |
How to use
- Fill in Normal stress σ, Axial strain ε, Shear stress τ, Shear strain γ, Load W, Length l in the Inputs section (watch the unit on each field).
- Click Calculate; the tool evaluates the formula shown above.
- Read Elastic mod. E, Shear mod. G, Strain energy U in the results area.
Formula notesYoung's modulus E = σ/ε; shear G = E/(2(1+ν)); bulk K = E/(3(1−2ν)).
Formula · Worked Example · Knowledge
Formula
Hooke's law $E=\sigma/\varepsilon$, $G=\tau/\gamma$; strain energy $U=W^2 l/(2AE)$. E is the stress–strain slope.
Worked Example
σ=200 MPa, ε=0.001 → E=200 GPa; W=10000 N, l=500, A=200, E=200 GPa → U=0.625 J.
Key Points
- Higher E = stiffer material; steel E≈200 GPa.
- G, E, ν relate by $G=E/(2(1+\nu))$.
- Hooke's law holds only within the proportional limit.
Parameters
Inputs
| Parameter | Symbol | Unit | Default |
|---|---|---|---|
| Normal stress σ (MPa) | sigma | MPa | 200 |
| Axial strain ε | eps | 0.001 | |
| Shear stress τ (MPa) | tau | MPa | 80 |
| Shear strain γ | gamma | 0.001 | |
| Load W (N) | W | N | 10000 |
| Length l (mm) | l | mm | 500 |
| Area A (mm²) | A | mm² | 200 |
| Young's mod. E (GPa) | E | GPa | 200 |
Outputs
| Result | Symbol | Unit |
|---|---|---|
| Elastic mod. E | E | GPa |
| Shear mod. G | G | GPa |
| Strain energy U | U | J |
Applications
- Common engineering use cases
FAQ
What formula does this tool use?
This tool computes per ISO / AGMA / ASME standard formulas: E = σ/ε; G = τ/γ; U = W²l/(2AE)
How accurate are the results?
Results match input precision, based on SI units and common engineering approximations; for critical duty re-check with a safety factor.
Where is it used?
Common engineering use cases