I would consider maybe more support on the back sides
of the shelves. Maybe a small cleat placed a foot or
so apart the length of the shelf. You could use a small
profile on the cleat and it will not be noticed.

I also think 46" is really pushing the limits on a
case width.

blueman wrote:

I'm building a bookcase with adjustable shelves with a 46" span that
will likely carry some heavy books.

To cover the load, I am making the shelves 1.5" thick (double 3/4"
plywood).