analysis of biaxial stress state with unknown principal directions
Strains on the surface of a component are measured in an experimental stress analysis using rosettes with 3 measuring grids (strain gages). Using measurement results and taking into consideration material properties (modulus of elasticity and transverse strain index), the magnitude and direction of mechanical strains are determined using Hooke’s Law.
The three rosettes available in the 0°/45°/90° and 0°/60°/120° designs are designated by the letters a, b and c. 3 strains, ea, eb, and ec are measured accordingly using a rosette with 3 measuring grids.
After the principal normal stresses s1 and s2 are measured, the principal directions are determined. To do this, an angle j is determined. This angle is arranged 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 j. The other arm represents the first principal direction. This is the direction of the principal normal strain s1 (identical with the principal strain direction e1).
The second principal direction (direction of principal normal strain s2) has an angle of j+90°.