LD1, you do your homework and do good work, but please be sure to look into the effects of welding a patch in like that. I am not concerned with the patch or the welds (assuming they were done right, which is likely) but you are introducing a pretty significant non-uniformity/non-linearity into the beam with a joint, patch, and weld within the span. The upshot is that simple beam calculations/tables (and any factor of safety you thought you had based on them) go out the door. Factor of safety is only valid when the beam is consistent with the assumptions in the calculations. When it's not, the factor of safety is void.
Look at it this way -- the beam equations are based on the slopes and curvatures of the beam under flexural loading. There are assumptions about continuity. I think I touched on the calculus aspect of it in the other thread. When you increase the stiffness mid-span with a patch and welds, that is no longer a single continuous beam with continuous slopes and curvatures. You will end up with a stiffer flat spot at the patch and that makes it a different problem entirely.
