vanuta: (1) Is angle beta in the xy plane? Or not in the xy plane?
(2) Why do you call alphay a normal stress, when it looks like you are using a shear force, F*cos(beta), to compute alphay?
(3) Why do you use cos(beta) to compute alphay?
(4) I am not yet confident that you have drawn the applied force, F, as it really occurs on the real assembly. Please draw a correct, quick, freehand sketch of the assembly, showing how and where the applied force(s), such as F, are really applied. And show the x, y, and z dimensions to the point of application of the applied force(s) (and applied moment(s), if any), so that we can really see how your joint is loaded.