From a real structure to a model

Idealisation is the act of replacing the real thing with something you can calculate. A steel beam bolted through a plate becomes a line with a support symbol at each end. A brick wall becomes a uniformly distributed load. A column base cast into a large concrete pad becomes a fixed support — or a pin, if you decide the connection is not really stiff enough to hold the rotation.

None of those replacements are true. They are all approximations, chosen because they are close enough and because they make the sums possible. The skill is knowing which approximations are safe.

A body free in a plane can do three things: move sideways, move up and down, and rotate. Those are its three degrees of freedom. To hold it still you have to remove all three. Supports do that removing, and each restraint provides one reaction.

A roller stops the beam moving vertically but lets it slide along and rotate freely, so it gives one reaction. A pin stops it moving in both directions but still lets it rotate, so it gives two. A fixed support stops all three, so it gives three, including a moment.

For one rigid body in a plane, equilibrium provides three independent equations. Three suitably arranged reaction components can restrain it and allow its reactions to be found from equilibrium. More unknown reactions require additional relationships, usually from deformation compatibility. Count the unknowns, then check the restraint geometry and internal stability. Member assemblies and structures with internal releases need additional free bodies; a reaction count alone cannot classify every structure.