Strain Energy Calculator
Strain energy in an axially loaded bar is σ²AL/2E: 100 kN applied gradually to a 2 m steel bar of 1000 mm² stores 50 J.
50 J
- Maximum stress σ
- 100 MPa
- Extension δ = σL/E
- 1 mm
- Resilience per volume σ²/2E
- 25 kJ/m³
Step-by-step solution
- σ = P/A
- σ = 100 MPa
- U = (σ²/2E) × AL = 100² ÷ (2 × 200000) × 1000 × 2000 N·mm = 50 J
Strain Energy Formula
U = σ² A L / 2E
σ = P/A gradual, 2P/A sudden, (P/A)[1 + √(1 + 2AEh/PL)] impact
Worked Example
A 2 m steel bar of 1000 mm² loaded gradually by 100 kN:
- σ = P/A
- σ = 100 MPa
- U = (σ²/2E) × AL = 100² ÷ (2 × 200000) × 1000 × 2000 N·mm = 50 J
Extension δ = σL/E: 1 mm · Resilience per volume σ²/2E: 25 kJ/m³
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Mohr’s Circle Calculator
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Frequently asked questions
Why does a suddenly applied load double the stress?
The load does work P·δ instead of ½P·δ, and equating it to σ²AL/2E gives σ = 2P/A.
What is proof resilience?
The strain energy stored at the elastic limit, σ²/2E × volume; per unit volume it is the modulus of resilience.
Sources
Last reviewed: . Factors are stored exactly and computed with 50-digit decimal arithmetic. See how we verify conversion factors.
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APA
Scientific Converters. (2026, October 15). Strain Energy Calculator. Retrieved October 25, 2026, from https://scientificconverters.com/calculators/strain-energy-calculator/
IEEE
Scientific Converters, "Strain Energy Calculator," scientificconverters.com. Accessed: Oct. 25, 2026. [Online]. Available: https://scientificconverters.com/calculators/strain-energy-calculator/