Elastic Strain Energy Calculator
Choose one method, enter values, and submit. Results appear above this form directly below the header.
Example Data Table
These sample cases show typical elastic strain energy calculations across different linear elastic situations.
| Case | Inputs | Result |
|---|---|---|
| Spring | k = 1200 N/m, x = 0.04 m | U = 0.96 J |
| Force and Deflection | F = 500 N, δ = 0.012 m | U = 3.00 J |
| Axial Bar | F = 18000 N, L = 2 m, A = 800 mm², E = 200 GPa | U = 2.025 J |
| Stress, Strain, Volume | σ = 150 MPa, ε = 0.00075, V = 0.002 m³ | U = 112.5 J |
| Torsional Shaft | T = 900 N·m, L = 1.5 m, G = 79 GPa, J = 2.5×10⁶ mm⁴ | U ≈ 3.076 J |
Formula Used
1) Spring Constant and Extension
U = ½kx², where k is spring constant and x is extension.
2) Force and Deflection
U = ½Fδ, where F is the applied force and δ is deflection.
3) Axial Bar
U = F²L / 2AE. This also equals ½Fδ, with δ = FL / AE.
4) Stress, Strain, and Volume
U = ½σεV. Energy density is u = ½σε.
5) Torsional Shaft
U = T²L / 2JG = ½Tθ, where θ = TL / JG.
Important Assumption
These formulas assume linear elastic behavior, small deformation, and material response below the elastic limit.
How to Use This Calculator
Step 1: Select the calculation method that matches your physics problem.
Step 2: Enter the required inputs and choose the correct units.
Step 3: Click Calculate Energy to process the inputs.
Step 4: Review the result summary, detailed table, and Plotly graph above the form.
Step 5: Export the result or example table as CSV or PDF for reports, notes, or documentation.
FAQs
1) What is elastic strain energy?
Elastic strain energy is the recoverable energy stored in a material or component while it deforms elastically under load.
2) When should I use the spring formula?
Use the spring equation when deformation follows Hooke’s law and the system can be modeled with a known spring constant.
3) Why do length and area matter for an axial bar?
A longer bar stores more energy for the same load, while a larger area reduces stress and deflection, changing stored energy.
4) Can I use this calculator beyond the elastic limit?
No. Once yielding or permanent deformation begins, linear elastic strain energy equations stop representing the physical response accurately.
5) What does the graph show?
The graph shows how elastic strain energy changes as deformation, load, strain, or twist increases within the selected model.
6) What is the difference between total energy and energy density?
Total energy is the full stored energy in the body. Energy density is the stored energy per unit volume.
7) Is the torsion model valid for any shaft?
It is suitable for linear elastic torsion problems when the shaft geometry and loading fit standard torsion assumptions.
8) Which units are safest to use?
Use consistent engineering units. This calculator converts selected units internally to SI before computing the final results.