Strain measurements on machine components or structural elements with rosettes are necessary in real life problems to understand actual stress states on them. Strain measurement is conveniently and accurately done with strain gages. Strain gages are consisted of thin electrical wire and are glued parallel to the direction where measurements are desired. As the material elongates (or shorten), the electrical resistance of strain gage changes. By measuring the current passing through the gage, strain can be determined accurately for the loading condition.

By measuring 3 normal strain for a point on a surface of machine component (ε1, ε2, ε3), two normal and one shear strain can be calculated for the point on xy plane (εx, εy, and γxy). The arrangement of three strain gages is shown in the figure and this configuration is called strain rosette.

This calculator was developed to use measurement results of strain rosette (ε1, ε2, ε3) to calculate strain results of εx, εy, and γxy. Calculation of rosette types with different angle setups  (e.g. 45° and 60°) can be done by simply changing angles in calculator. The formulas used for the calculations are given in the List of Equations section.

Strain Measurement With Strain Rosette
Parameter Symbol Value Unit
Measured strain-1 ε1 μm/m (μin/in)
Measured strain-2 ε2
Measured strain-3 ε3
Line-1 angle wrt x-axis θ1 deg
Line-2 angle wrt x-axis θ2
Line-3 angle wrt x-axis θ3


Note: Use dot "." as decimal separator.

Parameter Symbol Value Unit
Normal strain in x-direction εx --- μm/m (μin/in)
Normal strain in y-direction εy ---
Shear strain in xy-direction γxy ---


Normal Strain: The ratio of length change to original length of the material. ε=σ/E

Strain Gage: An electrical measurement device to measure strain.

Strain Rosette: Strain gauge arrangement to measure three normal strains (ε1, ε2, ε3).

Shear Strain: The angular distortion on element caused by shear stress. γ=τ/G. 

List of Equations:

Parameter Symbol Formula
Measured strain-1
ε1 εx(cosθ1)2y(sinθ1)2xysinθ1cosθ1
Measured strain-2 ε2 εx(cosθ2)2y(sinθ2)2xysinθ2cosθ2
Measured strain-3
ε3 εx(cosθ3)2y(sinθ3)2xysinθ3cosθ3


Link Usage
Principal Stress Calculation with Strain Results An example about the calculation of normal and shear strain and principal stresses on a machine component with the usage of strain results which have been measured with 45° Rosette.