MethodWhat is calculated?
In the delta rosette the three measuring directions are 60° apart, so the circle centre is the arithmetic mean of all three strains. The equations follow from the strain circle with angles 120° and 240° for grids b and c. Keil again resolves the tangent ambiguity via the signs of numerator Z* = √3(ε_b−ε_c) and denominator N* = 2ε_a−ε_b−ε_c in Tab. 9.2.
Equations
m = (ε_a+ε_b+ε_c)/3 (Keil Gl. 9.70)
tan 2α = √3(ε_b−ε_c)/(2ε_a−ε_b−ε_c) (Gl. 9.81), Quadrant nach Tab. 9.2
r = √[((2ε_a−ε_b−ε_c)/3)² + (ε_b−ε_c)²/3] (Gl. 9.90)
ε₁,₂ = m ± r (Gl. 9.91)
ProcedureStep by step
- Check grid labelling per Keil fig. 9.24 (a, b, c counter-clockwise).
- Enter the strains with sign.
- Convert the result to stresses with the principal-stress calculator.
Typical mistake
Using the 0°/45°/90° formulas or numbering grids clockwise.
PracticeApplication and limits
Stress analysis with delta rosettes, which offer the least direction-dependent uncertainty for unknown principal directions thanks to their uniform angular spacing.
As for the rectangular rosette: homogeneous field, plane stress, equal gauge factors of all grids.
SourceTechnical basis
Keil, Dehnungsmessstreifen, 2nd ed. 2017, sec. 9.9 evaluation of 60°/120°/180° rosettes, eqs. (9.67)–(9.91), Tab. 9.2, figs. 9.24, 9.28.
The source supports the equation structure and worked examples; this calculator does not replace calibration of the measuring chain.
FAQFrequently asked questions
Why is it also called a 60°/120°/180° rosette?
Keil counts directions until returning to the reference axis; geometrically it is the same rosette.
Is the delta rosette more accurate?
The principal-strain error depends less on the principal direction, but evaluation is more involved.
What if all three strains are equal?
Then r = 0 (equi-biaxial state) and the angle is undefined; the calculator returns 0°.
In the same cluster
All strain-gauge calculators