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.

Now compare the number of reactions with the number of equations you have. In two dimensions equilibrium gives you three equations. If the reactions and the equations match, the structure is statically determinate and equilibrium alone will solve it. Too few restraints and it is a mechanism — it will move. Too many and it is statically indeterminate: it stands up perfectly well, but you need to know how stiff the members are before you can find the reactions.