We have two iron (assume real-life stiffness) manhole covers resting on friction-less, perfectly smooth shims on flat ground. One is circular and the other square.
If a force F is applied vertically downwards at the center of each manhole cover, is the pressure on the manhole shim distributed uniformly in each case? i.e. is the downward force at any given cover-contact-point on the shim the same for both manholes.