Strain Transformation and Rosette Gage Theory

It is often desired to measure the full state of strain on the surface of a part, that is to measure not only the two extensional strains, εx and εy, but also the shear strain, γxy, with respect to some given xy axis system. It should be clear from the previous discussion of the electrical resistance strain gage that a single gage is capable only of measuring the extensional strain in the direction that the gage is oriented. Assuming that the x and y axes are specified, it would be possible to mount two gages in the x and y directions, respectively to measure the associated extensional strains in these directions. However, there is no direct way to measure the shear strain, γxy. Nor is it possible to directly measure the principal strains since the principal directions are not generally known.