Shear Modulus Calculator
Calculate shear modulus (modulus of rigidity) for materials under shear stress
Calculate Shear Modulus
Force applied tangent to the surface
Area over which force is applied
Height or length perpendicular to shear plane
Horizontal displacement due to shear
Shear Modulus Results
Formula used: G = F × L / (A × Δx)
Calculation: G = 0.0 N × 0.000 m / (0.000000 m² × 0.000000 m)
Also known as: Modulus of Rigidity
Example Calculation
Steel Beam Under Shear
Applied Force (F): 50,000 N
Cross-sectional Area (A): 0.01 m² (100 cm²)
Height (L): 0.2 m (20 cm)
Displacement (Δx): 0.001 m (1 mm)
Calculation Steps
G = F × L / (A × Δx)
G = 50,000 N × 0.2 m / (0.01 m² × 0.001 m)
G = 10,000 / 0.00001
G = 1,000,000,000 Pa = 1 GPa
Common Material Values
Key Points
Higher values indicate greater resistance to shear deformation
Related to Young's modulus and Poisson's ratio
Important for torsional and shear stress analysis
Temperature and composition affect values
Understanding Shear Modulus
What is Shear Modulus?
The shear modulus (G), also known as the modulus of rigidity, is a material property that describes the material's response to shear stress. It represents the ratio of shear stress to shear strain in the linear elastic region of a material.
Why is it Important?
- •Critical for structural engineering and material selection
- •Used in torsional stress and shaft design calculations
- •Helps predict material behavior under shear loads
- •Essential for composite material analysis
Mathematical Relationships
G = F × L / (A × Δx)
G = τ / γ
- G: Shear modulus (Pa)
- F: Applied shear force (N)
- A: Cross-sectional area (m²)
- L: Original length/height (m)
- Δx: Displacement due to shear (m)
- τ: Shear stress (Pa)
- γ: Shear strain (dimensionless)
Relationship to other moduli:
G = E / [2(1 + ν)]
Where E is Young's modulus and ν is Poisson's ratio