### Strain Gauge Rosette Explained:

When conducting structural analysis, the behaviour of materials under varying loading conditions can be intricate, often challenging our ability to pinpoint critical stress directions accurately. With the use of a strain gauge rosette, we are able to calculate principal strains and stresses accurately in both magnitude and direction ensuring the integrity of your stress analysis results.

Uniaxial loading results in in a maximum principal stress in the same direction as the applied load, but a zero minimum principal Stress at 90 degrees to the load, as shown in Fig 1. The loading will also generate shear stress in the sample, with the maximum at 45° to the load direction.

The same uniaxial load also results in principal strains in two directions, due to the Poisson’s ratio effect, this is shown in Fig 2. This means that a strain gauge placed at 90° to the loading direction will measure a negative strain even though there is no load applied in that direction.\

A strain gauge only measures strain in the direction of the gauge grid. This works well for uniaxial loading, but in a complex loading situation, the principal stresses may not be aligned to the strain gauge grid. In addition, the direction of the principal stresses may vary during operational loading see Fig 3 and Fig 4. The use of linear gauges could then result in significant errors due to alignment errors.

A rosette with three grids in three known directions is required to fully calculate the principal strains and stresses (amplitude and direction) at a point. The two types of rosettes available have grids either 45° apart or 60° apart. The formulae for the stress calculations for the two most popular strain gauge rosette types are shown below in Fig 5;

An illustration of the potential for measurement error from site data is shown in the table below. A linear gauge was initially used with the direction based on a finite element model prediction. A rosette gauge was then used with the “A” grid placed in the same direction as the linear gauge. The biaxial stress state caused the principal stress direction to change by 22.7°, and the error in calculation became very significant at -25.4%.

The stresses are calculated using the material properties of the test sample and should always be listed in data report. If data is being correlated with modelling results, then the same properties should be used in the FEM model.

The direction of the maximum principal stress direction, 𝜑 , is calculated according to the rosette type using the formulae in Fig 5. The direction requires careful interpretation according to the quadrant that the numerator and denominator of the formula fall into. This interpretation is easily achieved using analysis software such as Catman or nCode, but the manual method is listed in the HBM catalogue and shown in Fig 6 below;