Analysis & loading · Sections & mechanics

Strain rosette (0/45/90) calculator

Principal strains, direction and principal stresses (plane stress) from a 0°/45°/90° rosette.

Standard: Rectangular strain gauge rosette

Inputs in the worked example

The live calculator starts with these values; change any of them and every result, check and diagram updates instantly.

Diagram for the worked example

γxy = 2ε45 − ε0 − ε90 = 2*300-450--120 = 270 µε
Centre = (450+-120)/2 = 165 µε
Radius = SQRT(((450--120)/2)^2+(270/2)^2) = 315.36 µε
ε1 = 165+315.36 = 480.36 µε
ε2 = 165-315.36 = -150.36 µε
θp from 0° gauge = DEGREES(ATAN2(450--120,270))/2 = 12.673 °
σ1 = E(ε1 + νε2)/(1 − ν²) = 2.000e+5*(480.36+0.3*-150.36)*1E-6/(1-0.3^2) = 95.659 MPa
σ2 = 2.000e+5*(-150.36+0.3*480.36)*1E-6/(1-0.3^2) = -1.3736 MPa

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For preliminary design and education. Check every result against the current standard and your own engineering judgement before use.