I want to recess shelves 11cm wide (by 45cm deep) by 1cm deep rabbets in the side of a particleboard cupboard (all panels are 20mm thick).

The narrow shelves are unsupported except by the rabbet. I plan to put threaded inserts in the ends of the shelves and bolt them to the inside of the cupboard to hold them into the rabbet-support.

What is the maximum weight that such shelves can support without breaking
away? Do we know a formula for such supports, i.e width of shelf, depth of rabbet, length of overhang?