I agree with Benjamin Franz that the ball-and-spring model of a solid is helpful and that when a solid exerts a contact force the bonds between the atoms are distorted in that region. If you take a beam, clamp down its ends and then apply a force to it off-center you can see how the bonds on the short side are distorted more than the bonds on the long side and therefore more force is exerted on the clamp that is closer to the applied force:
Noah
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