Reply by EEngineer

If you use plywood expansion will not be a problem. If you are going to use solid wood, I would use a dovetail instead of a straight dado cut and just glue the end. This will provide support but still allow the length of the board to expand and contract with changes in humidity. This may be a problem in your design since you can’t use a blind dado for the dovetail and it will come out on the front of desk.

-- "Find out what you cannot do and then go do it!"