MethodWhat is calculated?
Three strains in known directions define the strain circle uniquely. For the 0°/45°/90° rosette a and c lie on one diameter, so their mean gives the circle centre; b fixes the angle. Because tan 2α is ambiguous, Keil's Tab. 9.1 assigns the angle uniquely within 0° ≤ α < 180° from the signs of numerator and denominator. The angle is measured counter-clockwise from reference direction a to principal direction 1 (ε₁).
Equations
m = (ε_a+ε_c)/2 (Keil Gl. 9.51)
tan 2α = (2ε_b − ε_a − ε_c)/(ε_a − ε_c) (Gl. 9.55), Quadrant nach Tab. 9.1
r = ½·√2·√[(ε_a−ε_b)² + (ε_c−ε_b)²] (Gl. 9.63)
ε₁,₂ = m ± r (Gl. 9.65), γ_max = 2r (Gl. 9.64)
ProcedureStep by step
- Check grid labelling a, b, c per Keil fig. 9.23 (b is 45° counter-clockwise from a).
- Enter strains with sign; correct transverse sensitivity beforehand if needed.
- Transfer the principal strains to the principal-stress calculator.
Typical mistake
Swapping grids b and c or measuring the angle clockwise – both give a principal direction off by 90°.
PracticeApplication and limits
Experimental stress analysis on components with unknown principal directions: castings, welded structures, pressure vessels, chassis components.
Homogeneous strain field under the rosette, plane stress at the free surface; prefer stacked rosettes under steep gradients.
SourceTechnical basis
Keil, Dehnungsmessstreifen, 2nd ed. 2017, sec. 9.8 evaluation of 0°/45°/90° rosettes, eqs. (9.48)–(9.66), Tab. 9.1, figs. 9.23, 9.25.
The source supports the equation structure and worked examples; this calculator does not replace calibration of the measuring chain.
FAQFrequently asked questions
Why does Z = 0, N > 0 give α = 0°?
Then ε_b = m and ε_a > ε_c: direction a already is principal direction 1.
What is the third principal strain?
Normal to the surface: ε₃ = −ν/(1−ν)·(ε₁+ε₂) per eq. 9.66; the principal-stress calculator reports it.
Does the evaluation apply dynamically?
Yes, if all three grids are sampled simultaneously; otherwise the time offset distorts the angle (Keil 10.3.3).
In the same cluster
All strain-gauge calculators