Supports and reactions

Every structure has to pass its loads into something firmer: a column, a wall, a pier or the ground. The way it is held at those points is its support condition, and each type of support supplies a known set of reaction components. Choosing the right idealisation is the first decision in any analysis, because it fixes how many unknowns there are and how the structure will bend.

A roller or rocker allows rotation and movement along its surface, so it supplies one force perpendicular to that surface. A pin or hinge prevents movement in any direction but allows rotation, supplying two force components. A fixed support prevents movement and rotation, supplying two forces and a moment. A link or cable supplies one force along its own line. Real supports lie between these ideals: a beam resting on a brick wall is close to a roller, a steel column on a base plate with four anchor bolts is partly fixed, and an elastomeric bridge bearing behaves like a stiff spring.

In two dimensions, three equilibrium equations are available. A beam with three reaction components that are not all parallel or concurrent is statically determinate. With more, it is indeterminate and extra equations must come from deformations. With fewer, or with badly arranged supports, it is unstable. For a compound structure with internal hinges, each hinge adds one equation (zero moment at the hinge). Support settlement, temperature and creep add forces in indeterminate structures but not in determinate ones, which is one reason bridge engineers sometimes choose simply supported spans on weak ground.