Are you proposing to build a bloody box girder bridge? The problem with using sections like 40mm x 5mm will be that they’re so much stiffer than what you’re securing them to, any flexing that would’ve been done over the original would now be concentrated on the edges where the reinforcing meets the original structure, this will likely cause localised fatigue and failure.
Now I’m a big fan of over engineering, as the following pic of the best ever toilet roll holder that I’ve ever seen will show.
But what you propose is excessive.
I would suggest fabricating a replacement section of @ 1.2 - 1.6 mm would be more than enough.