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### Strain Gage Rosette Equations and Calculator

**Strength of Materials**

**Structural Deflections and Stress 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

τ_{max} = ( E / ( 2 (1+ν^{2}) ) [ 2 ( ( ε_{A} - ε_{B} ) + ( ε_{B} - ε_{C} ) ) ]^{1/2}

Max. Shearing Strain

γ_{max} = [ 2 { ( ε_{A} - ε_{B} )^{2} + ( ε_{B} - ε_{C} )^{2} } ]^{1/2}

Direction of Principal angle from ε_{a} axis when ε_{a} > ε_{c} Angle of minimum principal strain to the ε_{a} axis when ε_{a} < ε_{c}

Treating the tan^{-1} as a single-valued function, the angle counterclockwise from gage A to the axis containing ε_{p1} or σ_{p1} is given by:

Where:

E = Young's Modulus (N/m^{2}, lbs/in^{2})

ν = Poissons Ratio

ε = strain (μm/m, μin/in)

σ = Stress (N/m^{2}, lbs/in^{2})

θ_{p} = Angle (degrees)

Reference:

Roarks Formulas for Stress and Strain

KYOWA Electronic Instruments