Shear Modulus Calculator
Calculate shear modulus from shear stress and strain
Shear stress applied to the material
Shear strain (angular deformation)
How to Use This Calculator
Enter Shear Stress
Input the shear stress (τ) applied to the material. This is the force per unit area acting parallel to the surface. Use consistent units (MPa, psi, etc.).
Enter Shear Strain
Input the shear strain (γ) measured during the test. Shear strain is the angular deformation and is dimensionless. It represents the change in angle due to the applied shear stress.
Calculate Shear Modulus
Click "Calculate" to determine the shear modulus (G). The shear modulus represents the material's resistance to shear deformation and is also known as the modulus of rigidity.
Formula
Shear Modulus = Shear Stress ÷ Shear Strain
G = τ / γ
Where:
- G = Shear modulus (modulus of rigidity) - MPa or psi
- τ = Shear stress - MPa or psi
- γ = Shear strain (dimensionless)
Relationship to Other Moduli:
G = E / (2 × (1 + ν))
Where: E = Young's modulus, ν = Poisson's ratio
Example:
For a material with shear stress 60 MPa and shear strain 0.002:
G = 60 ÷ 0.002 = 30,000 MPa (or 30 GPa)
About Shear Modulus Calculator
The Shear Modulus Calculator is an essential tool for materials engineering that calculates the shear modulus (G), also known as the modulus of rigidity. Shear modulus is a measure of a material's resistance to shear deformation and is one of the fundamental elastic moduli used in material characterization and structural analysis.
When to Use This Calculator
- Material Testing: Determine shear modulus from torsion or shear test data
- Material Characterization: Identify elastic properties of materials
- Structural Analysis: Use shear modulus in torsion, shear, and combined loading calculations
- Research & Development: Study effects of processing on material elastic properties
- Quality Control: Verify materials meet shear modulus specifications
Why Use Our Calculator?
- ✅ Quick Calculation: Instant shear modulus from stress-strain data
- ✅ Material Property: Essential elastic modulus for material characterization
- ✅ Design Tool: Critical parameter for torsion and shear analysis
- ✅ Educational Resource: Understand shear modulus concepts and relationships
- ✅ Accurate Results: Precise calculations for engineering applications
Key Concepts
Shear Modulus (G): Also called the modulus of rigidity, it measures a material's resistance to shear deformation. It is defined as the ratio of shear stress to shear strain in the elastic region. Higher shear modulus means the material is stiffer in shear.
Relationship to Other Moduli: For isotropic materials, the shear modulus is related to Young's modulus (E) and Poisson's ratio (ν) by: G = E / (2 × (1 + ν)). This relationship allows calculating one modulus if the other two are known.
Typical Values
- Steel: ~77-82 GPa (11-12 × 10⁶ psi)
- Aluminum: ~26-27 GPa (3.8-3.9 × 10⁶ psi)
- Concrete: ~12-16 GPa (1.7-2.3 × 10⁶ psi)
- Rubber: ~0.0001-0.001 GPa (very low)
Frequently Asked Questions
What is shear modulus?
Shear modulus (G), also called modulus of rigidity, is a measure of a material's resistance to shear deformation. It is defined as the ratio of shear stress to shear strain in the elastic region: G = τ / γ. It is one of the fundamental elastic moduli along with Young's modulus and bulk modulus.
How is shear modulus related to Young's modulus?
For isotropic materials, the shear modulus (G) is related to Young's modulus (E) and Poisson's ratio (ν) by: G = E / (2 × (1 + ν)). This means if you know Young's modulus and Poisson's ratio, you can calculate the shear modulus, and vice versa.
What is the difference between shear modulus and Young's modulus?
Young's modulus (E) measures resistance to normal (tensile/compressive) deformation, while shear modulus (G) measures resistance to shear (angular) deformation. Both are elastic moduli but describe different types of deformation. Typically, G is about 40% of E for most metals.
Why is shear modulus important in engineering?
Shear modulus is essential for analyzing torsion (twisting) of shafts, shear deformation in structures, and combined loading conditions. It is used in calculations for machine components (shafts, gears), structural elements (beams under shear), and material selection for shear applications.
Can shear modulus be negative?
No, shear modulus is always positive for stable materials. It represents resistance to deformation, so a negative value would indicate that applying shear stress causes opposite deformation, which is not physically realistic for conventional materials. Negative shear modulus may appear in some advanced engineered materials but is extremely rare.