Shear Modulus and Rigidity
Shear modulus G = τ/γ measures resistance to shear deformation. It relates shear stress τ to shear strain γ. For isotropic materials, G = E/(2(1+ν)) links to Young's modulus E and Poisson's ratio ν. Essential for torsion and shear analysis.
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G = τ/γ in elastic region; τ = Gγ is Hooke's law for shear. G = E/(2(1+ν)); for steel ν≈0.3, G≈0.385E. Torsion: θ = TL/(GJ); G from measured twist. Shear wave velocity v_s = √(G/ρ) in solids.
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Why: Shear modulus governs torsional stiffness of shafts, shear deformation of beams, and elastic response to shear loading. It is one of two independent elastic constants for isotropic materials.
How: Provide shear stress and strain, or torque T, length L, twist angle θ, and polar moment J. Alternatively, derive from E and ν. The calculator includes a 40+ material database.
Run the calculator when you are ready.
🔩 Steel Shear Test
Calculate modulus from shear: 50 MPa stress, 0.00065 strain
⚙️ Shaft Torsion
Find shear modulus from torsion: 500 N·m, 1m length, 0.05 rad twist
🔧 Aluminum Material
Get shear modulus from material database
📊 From E and ν
Calculate G from Young's modulus and Poisson's ratio
🧪 Polymer Analysis
Compare shear modulus of flexible polymers
Enter Values
Calculation Mode
Shear Stress-Strain Data
For educational and informational purposes only. Verify with a qualified professional.
🔬 Physics Facts
G is also called modulus of rigidity or second Lamé parameter.
— ASTM
For incompressible materials (ν=0.5), G = E/3.
— NIST
Steel G ≈ 79 GPa; aluminum ≈ 26 GPa.
— Engineering Toolbox
Torsional stiffness k = GJ/L for uniform shaft.
— MIT OCW
What is Shear Modulus?
Shear modulus (G), also known as the modulus of rigidity or the second Lamé parameter, is a material property that measures the material's resistance to shear deformation. It quantifies the relationship between shear stress (τ) and shear strain (γ) in the elastic region, similar to how Young's modulus relates normal stress to normal strain.
Shear Deformation
Measures resistance to shape change without volume change. Higher G means stiffer material under shear loading.
Torsion Applications
Essential for analyzing shafts, springs, and rotating components. Determines angular deflection under torque.
Elastic Constants
Related to Young's modulus and Poisson's ratio. One of the fundamental elastic constants for isotropic materials.
How to Calculate Shear Modulus
Calculation Methods
- 1From Stress-Strain: Measure shear stress and strain, divide stress by strain
- 2From Torsion: Use torque, length, angle of twist, and polar moment of inertia
- 3From E and ν: Calculate G = E / (2(1+ν)) if Young's modulus and Poisson's ratio are known
- 4From Material Database: Select material from comprehensive database of 40+ materials
Measurement Tips
- • Use torsion tests for accurate shear modulus measurement
- • Ensure measurements are in the elastic (linear) region
- • Account for temperature effects on material properties
- • Consider anisotropy - G may vary with direction in composites
When to Use Shear Modulus Calculations
Torsion Design
Design shafts, axles, and rotating components. Calculate angular deflection and torsional stiffness for power transmission systems.
Connection Analysis
Analyze bolted joints, riveted connections, and welded assemblies. Determine shear strength and deformation in structural connections.
Spring Design
Design helical springs, torsion bars, and elastic elements. Calculate spring rate and energy storage capacity.
Shear Modulus Formulas
Basic Shear Modulus
Where G = shear modulus (Pa), τ = shear stress (Pa), γ = shear strain (dimensionless)
From Elastic Constants
Where E = Young's modulus, ν = Poisson's ratio. Valid for isotropic materials.
From Torsion Test
Where T = torque, L = length, θ = angle of twist (rad), J = polar moment of inertia
Torsional Stiffness
Resistance to angular deformation. Higher stiffness means less twist under torque.
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