If I create a beam in Simulation with the cross section of an angle "L" with the length of the beam along the X axis, pin both ends (immoveable), & apply a load in the Y direction at the center of the beam the resulting deformation is out of plane. Instead of just up & down in the Y direction it also bows out into the Z direction. I am using structural angle cross sections.

If I create shear & moment diagrams they match hand calcs--ie shear in the "direction 1" & moment in the "direction 2." When I look at a bending stress diagram it does not match hand calcs--even if I limit the stress plot to bending in direction 2 only. As I said--the moment in direction in 2 is correct--so should I not be able to take that moment & divide it by "S" of my structural angle cross section (bending stress = M/S) & get the bending stress? Doing this does not match the stress plot in direction 2.

I can do this with channels, square & rectangle tubes & dividing the given moment by "S" does match the Simulation bending stress in direction 2---Why does this not work if the cross section is an angle shape?

the hand calculations are based on the part staying the same shape. All of your other parts are symmetric so applying the load the center is still symmetric, but with an L-angle the lack of symmetry places the neutral axis away from the center of the face. The simulation solves for the fact that your L will start to roll because it is stiffer on one side than the other. If you mirror the L into a U-channel it should be correct because of symmetry places the force coincident to the neutral plane again.