I have a design where a beam is welded to a plate. The back of the plate is unsupported, but its reasonable to assume the ends of the plate are fixed. I am trying to determine the deflection of the beam when loaded, and the stress in the plate that its connected to. I have run a few studies. Does anyone know about an analytical solution to the problem or experimental solutions (empirical formula) that I could use to check my results. The image below may help clarify. I plan on changing the size and shape of the cross section in the future.