This example concerns a cleverly designed specimen for bi-axial fatigue testing subjected to a variety of bi-axial loads.  The specimen is investigated by Cláudio et al. in a recent paper which can be found here. The figure below is taken from the paper:

The missing dimensions are d=16mm, theta=21 degrees, r=25mm, R=57mm and C=49mm.

The specimen is subjected to axial loading in the 4 arms, both in-phase and various out-of-phase relationships.

It is interesting to investigate the principal stress directions over time in the center of the specimen during the different load types.