Shear Strain Calculator
Calculate shear strain from displacement, stress-modulus, or torsional loading
Calculate Shear Strain
Horizontal displacement due to shear
Height or length perpendicular to shear plane
Shear Strain Results
Formula used: γ = x/h
Calculation: γ = 0.000000 m / 0.000 m
Unit: Shear strain is dimensionless (rad)
Example Calculation
Steel Beam Under Shear
Method: Stress and Modulus
Shear Stress (τ): 50 MPa
Shear Modulus (G): 80 GPa (typical for steel)
Calculation Steps
γ = τ / G
γ = 50 × 10⁶ Pa / 80 × 10⁹ Pa
γ = 50/80,000 = 0.000625 rad
γ = 625 μɛ or 0.0358°
Calculation Methods
Displacement Method
γ = x/h
Direct measurement of deformation
Stress-Modulus Method
γ = τ/G
Uses Hooke's law for shear
Torsion Method
γ = ρφ/L
For circular shafts under torque
Typical Strain Ranges
Key Points
Shear strain is dimensionless (measured in radians)
For small angles: γ ≈ tan(γ) ≈ x/h
Maximum strain occurs at shaft surface in torsion
Related to shear stress through shear modulus
Understanding Shear Strain
What is Shear Strain?
Shear strain (γ) is a measure of deformation representing the angular distortion of a material element when subjected to shear stress. It quantifies how much the shape of an object changes under shearing forces, expressed as the change in angle between initially perpendicular lines.
Why is it Important?
- •Essential for structural analysis and design
- •Used in torsional analysis of shafts and beams
- •Critical for material characterization and testing
- •Helps predict failure modes in materials
Mathematical Relationships
γ = x/h (displacement method)
γ = τ/G (stress-modulus method)
γ = ρφ/L (torsion method)
- γ: Shear strain (rad, dimensionless)
- x: Lateral displacement (m)
- h: Original height/length (m)
- τ: Shear stress (Pa)
- G: Shear modulus (Pa)
- ρ: Radius from neutral axis (m)
- φ: Angle of twist (rad)
- L: Length of member (m)
Note: For small angles, tan(γ) ≈ γ, so the displacement method gives approximately the same result as the angle measurement.