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Equilibrium

A body at rest (or moving at constant velocity) is in equilibrium. Then the sum of all forces is zero in each direction, and the sum of all moments about any point is zero. In the plane this gives three equations.

∑Fx=0\sum F_x = 0horizontal equilibrium
∑Fy=0\sum F_y = 0vertical equilibrium
∑MO=0\sum M_O = 0moment equilibrium about any point O

Symbols

∑\sumthe sum of
OOany moment point

Example

4 m beam, load P=10P = 10 kN 1 m from A.

Moments about A: B⋅4=10⋅1⇒B=2.5B\cdot 4 = 10\cdot 1 \Rightarrow B = 2.5 kN.

Vertical: A=10−2.5=7.5A = 10 - 2.5 = 7.5 kN.

Take moments about a point where an unknown force acts – it then drops out of the equation.
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Part of Statics and Dynamics: Statics and equilibrium.