Elastic Constants Calculator
Shear modulus follows from E = 2G(1 + ν): steel with E = 200 GPa and ν = 0.3 has G = 76.9231 GPa.
76.9230769230769 GPa
Full answer, then cut to fewer decimals (not rounded):
- 76.9230769230769 GPa
- 76.923076923076 GPa
- 76.92307692307 GPa
- 76.9230769230 GPa
- 76.923076923 GPa
- 76.92307692 GPa
- 76.9230769 GPa
- 76.923076 GPa
- 76.92307 GPa
- 76.9230 GPa
- 76.923 GPa
- 76.92 GPa
- 76.9 GPa
- Young’s modulus E
- 200 GPa
- Shear modulus G
- 76.9231 GPa
- Bulk modulus K
- 166.667 GPa
- Poisson’s ratio ν
- 0.3
- Lamé constant λ
- 115.385 GPa
Step-by-step solution
- E = 2G(1 + ν) = 3K(1 − 2ν)
- E = 9KG/(3K + G)
- E = 200 GPa, G = 76.9231 GPa, K = 166.667 GPa, ν = 0.3
Elastic Constants Formula
E = 2G(1 + ν) = 3K(1 − 2ν)
E Young’s modulus, G shear modulus, K bulk modulus, ν Poisson’s ratio
Worked Example
Steel with E = 200 GPa and ν = 0.3:
- E = 2G(1 + ν) = 3K(1 − 2ν)
- E = 9KG/(3K + G)
- E = 200 GPa, G = 76.9231 GPa, K = 166.667 GPa, ν = 0.3
Shear modulus G: 76.9231 GPa · Bulk modulus K: 166.667 GPa · Poisson’s ratio ν: 0.3 · Lamé constant λ: 115.385 GPa
More Mechanics of Materials Calculators
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Strain Energy Calculator
U = σ² A L / 2E
σ = P/A gradual, 2P/A sudden, (P/A)[1 + √(1 + 2AEh/PL)] impact
Example: A 2 m steel bar of 1000 mm² loaded gradually by 100 kN: Strain energy stored U = 50 J.
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Beam Deflection Calculator
δ = PL³/3EI, wL⁴/8EI, PL³/48EI, 5wL⁴/384EI
P point load, w load per length, L span, E Young’s modulus, I second moment of area
Example: A 2 m steel cantilever (E = 200 GPa, I = 8 × 10⁶ mm⁴) with 10 kN at the free end: Maximum deflection δ (free end) = 16.6667 mm.
-
Bending Stress Calculator
σ = M y / I = M / Z
M bending moment, y distance from the neutral axis, I second moment of area, Z = I/y
Example: A 100 × 200 mm rectangular beam carrying a 20 kN·m bending moment: Maximum bending stress σ = 30 MPa.
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Mohr’s Circle Calculator
σ₁,₂ = (σx + σy)/2 ± √[((σx − σy)/2)² + τxy²]
centre C = (σx + σy)/2, radius R = τmax
Example: σx = 80 MPa, σy = −40 MPa and τxy = 45 MPa: Major principal stress σ₁ = 95 MPa.
Frequently asked questions
What are the limits on Poisson’s ratio?
For isotropic materials −1 < ν < 0.5. At ν = 0.5 the material is incompressible and K becomes infinite.
What is E = 9KG/(3K + G) used for?
Finding E from bulk and shear moduli without knowing ν; it follows from eliminating ν between the two standard relations.
Sources
Last reviewed: . Factors are stored exactly and computed with 50-digit decimal arithmetic. See how we verify conversion factors.
Cite this page
APA
Scientific Converters. (2026, October 15). Elastic Constants Calculator. Retrieved October 25, 2026, from https://scientificconverters.com/calculators/elastic-constants-calculator/
IEEE
Scientific Converters, "Elastic Constants Calculator," scientificconverters.com. Accessed: Oct. 25, 2026. [Online]. Available: https://scientificconverters.com/calculators/elastic-constants-calculator/