Reply by a1Jim

It’s hard to see what the back is made of if it’s a 1/2” thick or more and attached properly you may be ok but considering you have a 50” span or more I would install at least a 3/4” by 4” horizontal member to the top edge of the back . The weight of the upper book case will rest mostly on you 4 legs but you do need to be concerned about the span. you need to be concerned about the base cabinets constitution more than the top, if the top is supported properly a 3/4” thick top will be more than enough. All of my concerns are based on the book shelf being filled with books rather than just lighter displayed items.

-- W James Brokenbourgh Custom furniture maker http://artisticwoodstudio.com/