Types of Supports and Their Reactions
In engineering statics, when you isolate a beam or structure you replace each support with the reaction forces it can provide. Knowing exactly how many reactions each support type gives is the key to drawing correct FBDs — and to knowing whether a structure is solvable.
Roller Support — 1 Reaction
A roller (or rocker, or smooth surface) allows rotation and sliding along the surface. It resists only one thing: movement perpendicular to the surface.
- Reactions: 1 — a single force perpendicular (normal) to the rolling surface.
- Drawn as: a circle or triangle-on-wheels under the beam; replace with one arrow perpendicular to the support surface.
Pin (Hinge) Support — 2 Reactions
A pin allows rotation but prevents translation in any direction.
- Reactions: 2 — usually drawn as horizontal and vertical components, Rx and Ry.
- Drawn as: a triangle with a pinned joint; replace with two component arrows. The resultant can point in any direction, which is why two unknowns are needed.
Fixed (Cantilever) Support — 3 Reactions
A fixed support — a beam embedded in a wall — prevents translation and rotation.
- Reactions: 3 — horizontal Rx, vertical Ry, and a reaction moment M.
- Drawn as: hatched wall at the beam end; replace with two force components plus a curved moment arrow. Forgetting the moment is the most common fixed-support error.
Cable / Link — 1 Reaction
A cable, rope, or two-force link member provides one reaction along its own axis. Cables can only pull (tension); rigid links can push or pull.
Smooth Contact — 1 Reaction
A frictionless surface touching the body gives one normal force, perpendicular to the contact surface at the contact point — same as a roller.
Summary Table
| Support | Prevents | Reactions | Unknowns |
|---|---|---|---|
| Roller | Perpendicular translation | N | 1 |
| Pin / hinge | All translation | Rx, Ry | 2 |
| Fixed | Translation + rotation | Rx, Ry, M | 3 |
| Cable / link | Motion along its axis | T (axial) | 1 |
| Smooth contact | Penetration | N | 1 |
Counting Unknowns: Is the Structure Solvable?
A planar (2D) rigid body gives you exactly three equilibrium equations: ΣFx = 0, ΣFy = 0, ΣM = 0.
- 3 unknown reactions → statically determinate: solvable with statics alone. (Classic case: one pin + one roller = 2 + 1 = 3 ✓)
- More than 3 → statically indeterminate: you need deformation methods (mechanics of materials).
- Fewer than 3 → the body is unstable — it's a mechanism, not a structure.
Worked Example: Simply Supported Beam
A beam with a pin at A and a roller at B carries a point load P.
- Isolate the beam; draw it as a horizontal line.
- Replace the pin at A with Ax and Ay; replace the roller at B with By.
- Add the load P downward.
- Three unknowns (Ax, Ay, By), three equations — determinate. ΣFx = 0 gives Ax = 0; take moments about A to find By; ΣFy = 0 gives Ay.
FAQ
What's the difference between a pin support and an internal hinge?
A pin support connects a member to the ground (2 reactions). An internal hinge connects two members to each other and transmits forces but no moment — it also gives you an extra equation (ΣM = 0 at the hinge for either side).
Why does a roller only have one reaction?
Because it can freely roll along the surface and rotate — the only motion it stops is perpendicular to the surface, so that's the only direction it can push.