The plate on the gantry to stiffen it is an excellent plan. I think you need to consider more how you are joining the box section, and gantry sides to bearings. Currently you have drawn the box section attached on just one face which is a bit weak.

I have done a drawing for you to illustrate how I think it can be made stronger:

Click image for larger version.  Name: Mycncuk stiffened gantry 1.jpg  Views: 553  Size: 75.0 KB  ID: 4431
Click image for larger version.  Name: Mycncuk stiffened gantry 2.jpg  Views: 553  Size: 59.4 KB  ID: 4432

That way the sheet reinforces the joints in addition to the general structure. I would be inclined to weld it for good measure. If not put plates (say 20mm thick) in the ends of the box section and bolt into them.