Free · Physics models
Linear Elastic Shear Modulus
Relate tangential force, loaded area, shear displacement and specimen height to shear modulus.
- Formula & worked example
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Calculator inputs
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How to use this calculator
- Enter the known values in the units shown. Results update as you type.
- Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
- Use the worked example to check the method. Reset restores the starting fields.
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Formula and method
stress = 100.00; strain = 0.10000. This worked example uses the displayed units and declared assumptions.
G = stress/strain; stress = F/A; strain = x/l
Worked example
Enter these known values and leave the other values blank.
- Force magnitude (F)
- 100 N
- Area over which the force acts (A)
- 1 m²
- Transverse length (l)
- 10 m
- Displacement (Δx)
- 1 m
- Shear stress (𝜏 = F/A)
- 100 Pa
- Shear strain (γ ≈ Δx/L)
- 0.1
- Shear modulus (G)
- 0.000001 GPa
Assumptions and limitations
- For small, uniform elastic shear, stress is tangential force divided by loaded area and engineering shear strain is relative face displacement divided by specimen height. Modulus is stress divided by strain.
- The box diagram is an undeformed reference. Force acts tangentially across face area A, and the opposing faces separated by l move relative to each other by x. Plastic deformation, anisotropy and nonuniform shear are excluded.
Common questions
What assumptions apply?
For small, uniform elastic shear, stress is tangential force divided by loaded area and engineering shear strain is relative face displacement divided by specimen height. Modulus is stress divided by strain.
Which unknowns can I solve?
Editable controls preserve the supported captured inverse branches. Clear the desired unknown and provide enough independent known quantities; singular or underdetermined inverses may remain incomplete.
References
For small, uniform elastic shear, stress is tangential force divided by loaded area and engineering shear strain is relative face displacement divided by specimen height. Modulus is stress divided by strain. The box diagram is an undeformed reference. Force acts tangentially across face area A, and the opposing faces separated by l move relative to each other by x. Plastic deformation, anisotropy and nonuniform shear are excluded.