A riveted joint by design can have some give. Welding a riveted crossmembers to the frame could be asking for trouble and cracks.

If you have loose or damaged rivets I would remove them and install new ones as original.

Grigg

•1951 GMC 250 in the Project Journals
•1948 Chevrolet 6400 - Detroit Diesel 4-53T - Roadranger 10 speed overdrive - 4 wheel disc brakes
•1952 Chevrolet 3800 pickup
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"First, get a clear notion of what you desire to accomplish, and then in all probability you will succeed in doing it..." -Henry Maudslay-