Isotropic Shear Modulus
Find shear modulus from Young’s modulus and Poisson’s ratio.
Try this formula
Calculate shear modulus or choose another supported quantity.
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Try this formula
Calculate shear modulus or choose another supported quantity.
Use decimals or scientific notation, such as 1.2e3. Calculations update as you type.
Shear modulus
Enter the known values to see the result.
Use small strains and a homogeneous, linearly elastic material. Loads are static or slowly applied; remain below the proportional limit. The material is isotropic; this relation is not generally valid for composites or other anisotropic solids. Use E > 0 and −1 < ν < 0.5.
Difficulty
Intermediate
Read time
5 min
Prerequisites
Basic algebra, mechanics, and consistent SI units
Source
Donney Fan — MECH 360 — Mechanics of MaterialsReference equation: Axial Load — Shear Stress-Strain Diagrams. FormuLab wrote new explanations, assumptions, applications, and numerical examples.
Definition
Isotropy connects the stiffness in tension with the stiffness in shear. Two independent elastic constants determine the remaining linear elastic constants.
Variables & Units
| Symbol | Meaning | Units |
|---|---|---|
| Shear modulus | ||
| Young’s modulus | ||
| Poisson ratio |
Real-World Applications
Elastic property conversion
Obtain shear stiffness from a tensile-test modulus.
Torsion models
Supply the modulus needed for shaft-twist calculations.
Worked Example
Problem
For E = 200 GPa and ν = 0.3, find G.
Given
Solution
Final Answer
Contents
Info
Tools
Source & review
Reference equation: Axial Load — Shear Stress-Strain Diagrams. FormuLab wrote new explanations, assumptions, applications, and numerical examples.
Assumptions
- • Use small strains and a homogeneous, linearly elastic material.
- • Loads are static or slowly applied; remain below the proportional limit.
- • The material is isotropic; this relation is not generally valid for composites or other anisotropic solids.
- • Use E > 0 and −1 < ν < 0.5.
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