Statics support types and reactions
A reference to the restraint and unknown reactions introduced by each support type.
| Support | What it restrains | Unknown reactions | Worked example |
|---|---|---|---|
| Pin support | Prevents translation in X and Y. Cannot slide or lift; free to rotate. | 2 unknown reactions: Aₓ, Aᵧ | Simply Supported Beam |
| Roller support | Prevents translation in one direction. Free to roll along the surface and rotate. | 1 unknown reaction: Aᵧ | Simply Supported Beam |
| Fixed support | Prevents all translation and rotation — full restraint (a built-in / cantilever end). | 3 unknown reactions: Aₓ, Aᵧ, M | Cantilever Beam |
| Smooth (frictionless) contact | A frictionless surface: the only reaction is the normal force. Set the support angle to tilt the surface — that is how a block on an incline is modelled. | 1 unknown reaction: N | Smooth Wall Reaction — Inclined Plank |
| Rocker bearing | A curved bearing that can rotate and shift, carrying force only along its normal — a bridge-bearing roller. Set the support angle to tilt the seat. | 1 unknown reaction: Aᵧ | Highway Bridge with Rocker Support |
Planar equilibrium
ΣFx = 0 · ΣFy = 0 · ΣM = 0
Determinacy counts
For one rigid body, compare the number of reaction unknowns r with 3.
For a truss, compare m + r with 2j. Fewer unknowns means unstable or a mechanism; equal means determinate if the arrangement is stable; more means indeterminate.
The count is necessary but not sufficient for stability.