How to use this calculator
Choose the rosette type and enter the three readings in microstrain. Give E and Poisson’s ratio to convert strains to stresses.
Formulas
Each gaugeε(θ) = εxcos²θ + εysin²θ + γxysinθ cosθ
45° rosetteεx = εa, εy = εc, γxy = 2εb − εa − εc
Stressesσ1 = E(ε1 + νε2)/(1 − ν²)
Worked example
45° rosette reading 450, −200 and 100 με on steel (the default)
- εx = 450, εy = 100, γxy = 2(−200) − 550 = −950 με.
- ε1,2 = 275 ± √(175² + 475²) = 781 and −231 με.
- With E = 200 GPa, ν = 0.3: σ1 = 156.5 MPa, σ2 = 0.7 MPa.
Frequently asked questions
Why three gauges?
A plane strain state has three unknowns (εx, εy, γxy), so three independent readings fix it.
What is ε₃?
The out-of-plane strain at a free surface, −ν(ε₁ + ε₂)/(1 − ν). It matters for the absolute maximum shear strain.