In one line
A support provides a reaction for every motion it stops: a roller gives one force, a hinge gives two forces, and a fixed support gives two forces and a moment.
Explained simply
Think about what each support prevents. A skateboard wheel stops you sinking into the floor but lets you roll sideways: one reaction. A door hinge stops the door moving in any direction but lets it rotate: two reactions. A post buried in concrete stops movement and rotation: two forces plus a moment.
Technically, reactions correspond to restrained degrees of freedom of the beam end in the plane.
How it works
- Simple support / smooth surface: one reaction normal to the surface.
- Roller support: one reaction perpendicular to the rolling surface (vertical on a horizontal surface, inclined on an inclined surface).
- Hinge (pin) support: prevents translation, allows rotation: reaction of unknown direction, shown as \( H \) and \( V \).
- Fixed support: prevents translation and rotation: \( H \), \( V \) and a fixing moment \( M \).
- Count unknowns: if the total is 3 and they are not all parallel or concurrent, the beam is determinate.
| Support | Unknowns |
|---|---|
| Roller | 1 (R) |
| Hinge | 2 (H, V) |
| Fixed | 3 (H, V, M) |
Key formula
Resultant hinge reaction: \( R = \sqrt{H^2 + V^2} \), angle \( \theta = \tan^{-1}(V/H) \) with the horizontal. H, V in kN.
Quick example
A beam on a hinge at A and a roller on a 30° incline at B: the roller reaction at B is perpendicular to the incline, so it has a horizontal component \( R_B\sin30^\circ \). Even with only vertical loads, the hinge at A then has a non-zero H.
Common mistakes
- Drawing a vertical reaction at a roller resting on an inclined surface.
- Leaving out the fixing moment at a fixed support.
- Assuming H = 0 at a hinge without checking for inclined loads or inclined roller reactions.
How MU asks it
A 3-mark part: 'Explain the types of supports with the reactions developed'. Use neat symbols, show reactions on each, and give the table. In numericals, the FBD with correct reactions earns the first method marks.