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### Strain Gage Rosette Equations and Calculator

Strain gage rosette equations and calculator applied to a specimen of a linear, isotropic material.

Generally, if the direction of principal stress is uncertain in structure stress measurement, a triaxial rosette gage is used and measured strain values are calculated in the following equation to find the direction of the principal stress.

The principal strains and stresses are given relative to the xy coordinate axes as shown below.  Preview: Strain Gage Rosette Calculator

Three-Element Rectangular Rosette

Maximum Principal Strain Minimum Principal Strain Principal Stresses:

Maximum Principal Stress Minimum Principal Stress Maximum Shearing Stress
τmax = ( E / ( 2 (1+ν2) ) [ 2 ( ( εA - εB ) + ( εB - εC ) ) ]1/2

Max. Shearing Strain
γmax = [ 2 { ( εA - εB )2 + ( εB - εC )2 } ]1/2

Direction of Principal angle from εa axis when εa > εc Angle of minimum principal strain to the εa axis when εa < εc
Treating the tan-1 as a single-valued function, the angle counterclockwise from gage A to the axis containing εp1 or σp1 is given by: Where:

E = Young's Modulus (N/m2, lbs/in2)
ν = Poissons Ratio
ε = strain (μm/m, μin/in)
σ = Stress (N/m2, lbs/in2)
θp = Angle (degrees)

Reference:

Roarks Formulas for Stress and Strain
KYOWA Electronic Instruments 