Calculate the shear strain (γ) and angular deformation of a material based on lateral deflection and height.
Last updated: March 2026 | By ForgeCalc Engineering
Shear strain (γ) is a measure of the angular deformation of a material subjected to shear stress. Unlike normal strain (which measures stretching or compressing), shear strain measures the change in angle between two lines that were originally perpendicular.
For small deformations, shear strain is approximately equal to the ratio of the lateral displacement (Δx) to the height (L) of the object. It is a dimensionless quantity, but is often expressed in radians.
Where:
• γ (gamma) is the shear strain (rad)
• Δx is the lateral displacement (m)
• L is the original height or length (m)
Shear strain is essentially the angle of deformation. For small angles, tan(θ) ≈ θ (in radians), which is why the ratio of displacement to height is used directly as the strain value.
Normal strain (ε) measures change in length (ΔL/L), while shear strain (γ) measures change in shape or angle (Δx/L).
Small strain theory assumes that the deformations are small enough that the original geometry of the object doesn't change significantly. This allows for linear mathematical models like Hooke's Law (τ = G × γ).
According to Hooke's Law for shear, shear stress (τ) is proportional to shear strain (γ) within the elastic limit: τ = G × γ, where G is the shear modulus.
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