Shear Modulus Calculator

INPUT SUMMARY

Current calculation basis

Entered values: Shear stress: 80 MPa · Shear strain: 0.001 mm/mm

Converted SI values: Shear stress: 80,000,000 Pa · Shear strain: 0.001 mm/mm

Engineering interpretation: Using the current inputs, calculate shear modulus from shear stress and shear strain. The current result is 80 GPa.

CALCULATION STEPS

How this result is assembled

1. Convert each entered value to the SI basis required by the governing relationship.
2. Substitute the converted values into G = τ / γ.
3. Evaluate the expression and report 80 GPa, then review the stated scope and assumptions.

ENGINEERING PRINCIPLE

Within the elastic range, shear stress is proportional to shear strain.

Calculate shear modulus from shear stress and shear strain.

FORMULA & VARIABLES

G = τ / γ

• G = shear modulus (Pa)
• τ = shear stress (Pa)
• γ = shear strain (dimensionless)

WORKED EXAMPLE

Current-input calculation trace

For the current entered values, the normalized engineering quantities are Shear stress: 80,000,000 Pa · Shear strain: 0.001 mm/mm. Substitution into G = τ / γ gives 80 GPa. This trace makes the active calculation reviewable; it does not replace a code-based design calculation.

FORMULA VERIFICATION

Units, scope and reference

Reference: NIST SP 811 for unit relationships; standard classical mechanics and strength-of-materials derivations for the stated scalar relation.

Internal basis: All inputs are converted to the calculator’s SI base before the formula is evaluated.

Valid conditions: Positive finite scalar input values in the current calculator model.

Limitations: The material is in its linear elastic range. This is a simple shear state.

ASSUMPTIONS

Use this result in context

• The material is in its linear elastic range.
• This is a simple shear state.

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