Shear Modulus Calculator
shear modulus calculator modulus of rigidity from shear stress and shear strain. Accurate engineering formulas and unit conversions for engineers, students & technicians.
Calculate Shear Modulus Calculator
Enter your engineering parameters below to compute verified physical and mathematical metrics.
Calculation Results
Calculated using verified physical methodology: Modulus of Rigidity: G = \\tau / \gamma = \E / 2(1 + \nu)
Unit Equivalents: 1\text{ GPa} = 1,000\text{ MPa} = 10^9\text{ Pa} = 145.038\text{ ksi}
Quick Summary
The Shear Modulus Calculator evaluates the Modulus of Rigidity ( = \tau / \gamma$) for solid structural materials subjected to torsional or transverse shear loads.
Formula Explanation
Modulus of Rigidity: G = \\tau / \gamma = \E / 2(1 + \nu)
Unit Equivalents: 1\text{ GPa} = 1,000\text{ MPa} = 10^9\text{ Pa} = 145.038\text{ ksi}
How It Works
The Shear Modulus Calculator evaluates the Modulus of Rigidity (G) by dividing applied shear stress ($\tau$) by the resulting angular shear strain ($\gamma$). This measures a material's structural resistance to shape distortion under transverse or torsional forces.
Step-by-Step Worked Example
Practical Problem: Calculate the Shear Modulus of a structural steel drive shaft subjected to a shear stress of 80 MPa producing an angular shear strain of 0.001 radians.
- Step 1: Identify Input Parameters: Applied Shear Stress $\tau = 80\text{ MPa}$, Shear Strain $\gamma = 0.001\text{ rad}$.
- Step 2: Convert Shear Stress to Base SI Units: $\tau = 80\text{ MPa} = 80 \times 10^6\text{ N/m}^2$.
- Step 3: Apply the Shear Modulus Formula: = \\tau / \gamma$.
- Step 4: Execute Numeric Calculation: = \frac{80 \times 10^6\text{ N/m}^2}{0.001} = 80,000,000,000\text{ Pa} = 80,000\text{ MPa}$.
- Step 5: Convert and Interpret Metric Outputs: Convert to GPa: = 80\text{ GPa}$. Convert angular shift to degrees: .001 \times \180 / \pi = 0.0573^\circ$. Convert to Imperial: .60\text{ Mpsi}$.
Real-World Calculation Examples
Scenario 1: Steel Automotive Drive Shaft
Parameters: $\tau = 79\text{ MPa}$, $\gamma = 0.001\text{ rad}$
Result: = 79.00\text{ GPa}$ (11.46 Mpsi). Standard steel torsional rigidity.
Scenario 2: Aluminum Transmission Coupling
Parameters: $\tau = 52\text{ MPa}$, $\gamma = 0.002\text{ rad}$
Result: = 26.00\text{ GPa}$ (3.77 Mpsi). Aircraft aluminum shear rigidity.
Scenario 3: Copper Electrical Bus Bar
Parameters: $\tau = 45\text{ MPa}$, $\gamma = 0.001\text{ rad}$
Result: = 45.00\text{ GPa}$ (6.53 Mpsi). Heavy current copper conductor rigidity.
Scenario 4: Structural Timber Beam
Parameters: $\tau = 5\text{ MPa}$, $\gamma = 0.005\text{ rad}$
Result: = 1.00\text{ GPa}$ (0.15 Mpsi). Parallel-to-grain wood shear stiffness.
Key Benefits of Using This Calculator
Torsional Shaft Verification
Quickly calculate shear stiffness for solid and hollow drive shafts subjected to torque loads.
Angular Deformation Output
Automatically converts radians to degrees for immediate physical interpretation of shear distortion.
High Precision Floating Point
Ensures 64-bit floating-point numeric calculation precision for mission-critical mechanical designs.
Instant Copy & Print
Export calculated metrics directly to your report or clipboard with 1-click action buttons.
Frequently Asked Questions (FAQ)
What is Shear Modulus?
Shear Modulus (G), also called Modulus of Rigidity, measures a material's resistance to angular shear deformation when subjected to shear forces.
What is the formula for Shear Modulus?
G = tau / gamma, where tau is shear stress (N/m²) and gamma is angular shear strain (radians).
How does Shear Modulus relate to Young's Modulus?
For isotropic materials: G = E / [2 * (1 + nu)], where E is Young's Modulus and nu is Poisson's ratio.
What is the Shear Modulus of structural steel?
Structural steel has a shear modulus of approximately 78 to 80 GPa (11.3 to 11.6 Mpsi).
Why is Shear Modulus smaller than Young's Modulus?
Materials deform more easily in angular shear than in axial stretch. For metals, G is roughly 38% to 40% of E.
What units are used for Shear Modulus?
The SI unit is Pascal (Pa) or Gigapascal (GPa). US Customary units use PSI or Mpsi.
What is shear strain?
Shear strain (gamma) is the change in angle (in radians) between two originally perpendicular lines in a deformed body.
How do fluids behave under shear stress?
Static fluids cannot support shear stress (G = 0 for fluids at rest); fluids flow continuously when shear is applied.
How is shear modulus measured in laboratories?
Using a torsion test machine, which twists cylindrical specimen rods and measures torque vs angle of twist.
Does temperature change shear rigidity?
Yes, thermal elevation decreases atomic bond stiffness, reducing G at elevated operating temperatures.