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Supports and reactions

A support holds the structure in place and provides reaction forces. How many unknowns it gives depends on which motions it prevents. The numbers in the figure show the number of unknowns in 2D.

\text{Roller: } 1

one force perpendicular to the surface

\text{Pin: } 2

two forces,

A_x

and

A_y

\text{Fixed: } 3

two forces and one moment

Symbols

$A_x,\ A_y$	reaction forces at support A	N
$M_A$	fixed-end moment	Nm

Example

Simply supported beam = pin + roller: $2 + 1 = 3$ unknowns.

Three equilibrium equations are exactly enough – the beam is statically determinate.

Always draw a free-body diagram: remove the supports and put the reaction forces in their place.

Practise statics and equilibrium for free →

← Equilibrium · Method of joints →

Part of Statics and Dynamics: Statics and equilibrium.