In a 2D coplanar force system, support reactions are the forces and moments that supports exert on a structure to maintain equilibrium. Each support type restricts certain degrees of freedom and introduces a corresponding number of unknown reaction components.
Roller support
1 unknown
Prevents translation perpendicular to the rolling surface only. Free to slide along the surface and free to rotate.
1 rxn1 force (⊥ to surface)
Pin / hinge support
2 unknowns
Prevents translation in all directions but permits free rotation about the pin. Introduces both horizontal and vertical reaction forces.
2 rxnsH force + V force
Fixed / cantilever
3 unknowns
Prevents all translation and rotation. Fully constrains the structure. Introduces horizontal force, vertical force, and a reaction moment.
3 rxnsH + V forces + moment
Link / two-force member
1 unknown
Transmits force only along its own axis. Cannot carry perpendicular load or moment. Allows rotation at both ends.
1 rxnaxial force along the link
Quick-reference summary
Support
Unknowns
Reactions
Rotation?
Roller
1
⊥ force
Yes
Link / cable
1
Axial force
Yes
Pin / hinge
2
H + V forces
Yes
Fixed / cantilever
3
H + V + moment
No
Determinacy rule: A 2D system has 3 equilibrium equations (ΣFx=0, ΣFy=0, ΣM=0). When total unknowns = 3, the structure is statically determinate. Fewer → unstable. More → statically indeterminate.