Calculator
Example data
| Method | Inputs | Output γ | Percent | Angle (deg) |
|---|---|---|---|---|
| Stress & Modulus | τ = 25 MPa, G = 79 GPa | 0.000316 | 0.0316% | 0.0181° |
| Stress & Modulus | γ = 0.002, G = 26 GPa | 0.002000 | 0.2000% | 0.1146° |
| Displacement | Δx = 0.8 mm, h = 20 mm | 0.040000 | 4.0000% | 2.2906° |
| Angle | θ = 1.5° | 0.026186 | 2.6186% | 1.5000° |
| Angle | γ = 0.10 | 0.100000 | 10.0000% | 5.7106° |
Formula used
- γ = τ / G (linear elastic shear, stress & modulus)
- γ = Δx / h (simple shear geometry)
- γ = tan(θ) and θ = arctan(γ)
How to use
- Select a method that matches your known values.
- Choose what you want to solve for.
- Enter the available measurements and pick units.
- Set decimal precision if you need cleaner reporting.
- Click Calculate to view results above the form.
- Use the CSV or PDF buttons to export summaries.
Understanding shear strain
Shear strain (γ) measures how much a material layer slides relative to another layer. It is defined as the ratio of lateral shift to the layer spacing, so it has no units. In lab reports, γ is often small: 0.0003 is common for stiff metals under moderate load, while elastomers can reach 0.10 or higher. It is widely used in torsion, shear panels, and adhesive joint analysis.
Why strain is dimensionless
Because γ is a ratio, changing length units does not change the value. For example, Δx = 0.8 mm and h = 20 mm gives γ = 0.04, and the same geometry in meters still gives 0.04. This calculator also shows percent strain, computed as 100×γ, to make small values easier to read.
Elastic relationship between stress and modulus
In linear elastic shear, shear stress τ and shear modulus G are linked by τ = G·γ. If τ = 25 MPa and G = 79 GPa, then γ = 25×10^6 / 79×10^9 ≈ 0.000316. This proportional rule is valid before yielding or significant nonlinearity begins.
Typical shear modulus data points
Shear modulus depends strongly on material. Structural steels are often near 75–85 GPa, many aluminum alloys near 25–28 GPa, and rigid plastics commonly fall around 0.8–2.5 GPa. Soft rubber-like materials can be in the 0.3–5 MPa range, which explains their large strains at low stresses.
Interpreting percent strain and limits
Engineers frequently flag strain levels. Values below 0.1% (γ < 0.001) are usually considered small for metals, while several percent may indicate large deformation, joint slip, or approaching failure depending on context. Always compare computed γ with allowable strain from your design code or test specification.
Geometry method using displacement and thickness
When you can measure sliding directly, use γ = Δx / h. A common fixture might shear a 10 mm adhesive layer by 0.2 mm, giving γ = 0.02 (2%). If h is very small, measurement error in Δx becomes important, so using consistent units and calibrated gauges improves accuracy.
Angle method and the small-angle rule
Simple shear can be expressed with the shear angle θ. The exact relationship is γ = tan(θ), and θ = arctan(γ). For small deformation, tan(θ) ≈ θ when θ is in radians, so γ ≈ θ(rad). Example: θ = 1.5° equals 0.02618 rad, close to γ ≈ 0.02618.
Practical reporting tips
Report the method, inputs, and unit system alongside results. Include both γ and percent strain, plus θ when it helps communication. If you are solving for τ or G, state the assumed elastic range and temperature. Exporting CSV or PDF helps preserve calculations for drawings, QA records, and troubleshooting.
FAQs
What is shear strain in simple terms?
Shear strain (γ) is how much one face slides relative to another, divided by the thickness between them. It is dimensionless, so a value like 0.02 means a 2% shear deformation.
Which formula should I use: τ/G or Δx/h?
Use γ = τ/G when you know shear stress and shear modulus in the elastic range. Use γ = Δx/h when you measure sliding displacement and layer thickness directly, such as in adhesive or gasket tests.
Is γ the same as the shear angle θ?
Not always. The exact link is γ = tan(θ). For small angles, tan(θ) ≈ θ when θ is in radians, so γ ≈ θ(rad). The calculator shows both θ and γ for clarity.
How do I convert degrees to radians for shear angle?
Radians = degrees × π/180. For example, 1.5° × π/180 ≈ 0.02618 rad. When angles are small, this radian value is also a good approximation of γ.
What are typical shear modulus values?
Many steels are around 75–85 GPa, many aluminum alloys around 25–28 GPa, rigid plastics around 0.8–2.5 GPa, and soft rubber-like materials can be roughly 0.3–5 MPa. Always verify your specific grade.
What does percent shear strain mean?
Percent shear strain is 100×γ. If γ = 0.000316, that is 0.0316%. Percent format helps compare tiny elastic strains and larger deformations in one consistent scale.
Why does my result look too large or too small?
Check units, especially MPa vs GPa, and mm vs m. Also confirm you selected the correct method and variable to solve. Large γ may be real for soft materials, but could signal an input mismatch.