I agree with the comments regarding bending stresses. However, how much does the fuselage floor actually bend while in flight....don't know. Maybe it's a concern, maybe not.
If you do add a stiffener, bend the ends up into a 90, or whatever and rivet to the bulkhead, or at least over the bulkhead flange on both ends. I have also seen where folks have added stiffeners simply by bonding them on with JB Weld or pro Seal,
You'll never hear it oil can while you are flying around, but every time you clean it.......