Has there been any study regarding deflection on edge joined boards?  When designing a shelf unit recently I was using sagulator to project the amount of sag that would occur with 1 inch thick shelves 36 inches long by 11 1/4 wide. The wood is african mahogany.  The shelf will be supported by medal paddle supports  - 2 on each end and across the back (that's what I was trying to determine).  Sagulator does not address that but does anticipate using a lip.  Based on sagulator the expected weight should be supported adequately but what if I am wrong about the weight to be supported?  So then I got thinking about the fact that I typically make shelves out of three pieces edge joined together using dominos.  Would that not make the shelf piece more rigid and less likely to sag than a shelf made of one piece of wood the same size?   Does anyone know of any fact based guidelines for this?

Thanks in advance

Not sure if this American Woodworker article is helpful to you: https://www.popularwoodworking.com/projects/aw-extra-3614-stronger-shelves/

There is nothing that can provide more rigidity to a shelving than a vertical support in the middle. One way to hide the centre support, in the case of a bookcase, is to glue a bookspine to the front edge of the support so the support looks like a book on the shelf (the support is trimmed narrower to accommodate the spine). In the credenza shown below, the dadoed centre support is hidden behind the sliding doors.