Shear Modulus Calculator

What Is Shear Modulus?

Shear modulus (also called rigidity modulus) measures how resistant a material is to shear deformation. It relates shear stress to shear strain in the elastic range. Stiffer materials have higher shear modulus values.

Shear Modulus Formula

$$G = \frac{\tau}{\gamma}$$

$\tau$ is shear stress and $\gamma$ is shear strain (dimensionless). Example: 50 MPa shear stress with strain 0.001 gives $G = 50{,}000$ MPa = 50 GPa, typical for steel.

Relationship to Other Moduli

For isotropic materials, $G = E / (2(1 + \nu))$ where $E$ is Young's modulus and $\nu$ is Poisson's ratio. Shear modulus appears in torsion, beam shear, and rubber mount design.

Frequently Asked Questions

What are typical shear modulus values?

Steel is about 75–80 GPa, aluminum about 26 GPa, and rubber is much lower, often under 0.01 GPa.

Is shear strain dimensionless?

Yes. Shear strain is a ratio of displacement to length, so it has no units. Shear modulus then has the same units as stress.

How is this different from Young's modulus?

Young's modulus relates normal stress to normal strain. Shear modulus relates shear stress to shear strain.

Can G be calculated from a torsion test?

Yes. Measure torque, twist angle, and specimen geometry, then compute τ and γ to find G.

What if shear strain is zero?

Shear modulus is undefined when strain is zero. Enter a positive strain value from test data or theory.

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Shear Modulus Calculator

What Is Shear Modulus?

Shear Modulus Formula

Relationship to Other Moduli

Frequently Asked Questions

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