quadratic strain gauge with leads (0°/45°/90°)

# RY Strain Gauge Rosettes with 3 Measuring Grids for Analyzing Biaxial Stress States with Unknown Principal Strain Directions

These strain gauges (SGs) are an appropriate choice for **analyzing the biaxial stress state with unknown principal strain directions**. Rosettes type RY have 3 measuring grids arranged at an angle of 0°/45°/90° (**types RY1, RY3, RY8, RY9, RY10**), or 0°/60°/120° (**types RY4, RY7**).

HBM offers you a wide selection of SG rosettes with **3 measuring grids**, with different geometries, dimensions, nominal (rated) resistances (120 and 350 ohms) and in temperature responses adapted for steel, aluminum or to customer specification.

The three measuring grids are arranged in a **quarter bridge circuit.**

## Rosette (3 grids)

## RY1

## RY8

Rectangular strain gauge with solder tabs (0°/45°/90°)

## RY3

Round strain gauge with solder tabs (0°/45°/90°)

## RY9

Stacked grids with leads (0°/45°/90°)

## RY4

Quadratic strain gauge with leads (0°/60°/120°)

## RY10

Rectangular strain gauge with solder pads and integrated strain relief (0°/45°/90°)

## RY7

Round strain gauge with solder tabs (0°/60°/120°)

## Notes on Calculating the First and Second Principal Stress

The 3 measuring grids of the rosettes are designated with the letters a, b and c. Accordingly the 3 strains εa, εb, and εc are measured with a 3 measuring grid rosette. The principal normal stresses σ1 and σ2 are calculated for the 0°/45°/90° rosette using the formula:

and for the 0°/60°/120° rosette:

The principal directions are determined below. First the tangent of an auxiliary angle ψ is calculated. For the 0°/45°/90° rosette using the formula:

and for the 0°/60°/120° rosette according to the formula:

Note: The tangent of an angle in the right-angled triangle is the ratio of the opposite side (numerator N) to the adjacent side (denominator D):

This ambiguity of the tangent makes it necessary to determine the signs of the numerator (N) and the denominator (D) before carrying out the final calculation of the two above mentioned quotients. It is important to determine the sign because that is the only way to know which quadrant of the circle the angle ψ will be found in. First determine the value of the intermediate angle ψ from the value of the tan:

Then determine the angle ϕ using the following approach:

Apply the angle ϕ that is found in this manner starting from the axis of the reference measuring grid a in a mathematically positive direction (counterclockwise). The axis of the measuring grid a forms one arm of the angle ϕ. The other arm represents the first principal direction. This is the direction of the principal normal stress σ1 (identical with the principal strain direction ε1). The point of the angle is located at the intersection of the measuring grid axes. The second principal direction (the direction of principal normal stress σ2) has the angle ϕ+90°.

The measuring grid consists of constantan; the material of the measuring grid carrier is polyimide.

**RY6/RY8 strain gauges also come with a connection cable!** One practical solution with many advantages: No soldering required at the measuring point, available in cable lengths from 0.5 m to 10 m, with RJ11 plug on request. A fluoropolymer-insulated wire on the strain gauge prevents the cable from sticking during installation. A practical solution for you...!