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

0.000
Shear Modulus (GPa)
0.00
Shear Stress (MPa)
0.000
Shear Strain (×10⁻³)

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

Steel75 GPa
Aluminum26 GPa
Copper44 GPa
Brass35 GPa
Titanium44 GPa
Lead6 GPa

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