Analysis of Strains from a 45-Degree Rosette

45 degree strain gauge rosettes are commonly used for measurement of strains. These rosette arrangements measure normal strains in three separate directions. From this data, the so-called "principal" strain state can be obtained. The principal strain state is just the orientation in which the shear strain is zero. At this orientation of zero shear strain, the two normal strains are called principal normal strains.

It can be quite tricky to obtain the principal strain state from the three gauge strains in a 45-degree rosette. Numerous textbooks provide equations for the principal normal strains, and generally these "just work". However, the angle of the principal strain state is often quite ambiguous. It's often difficult to figure out whether the angle is clockwise or anti-clockwise, which gauge it is relative to, and to which of the two principal normal strains it refers.

I have recently done some work on this problem in the context of measuring strains on the equine hoof wall. I have written a short description of the Analysis of Strains from a 45-Degree Rosette (PDF file; 47.9 KB). Please feel free to use this document (with an appropriate link to my blog), and please contact me regarding any corrections.