Force
–System Resultants -- Moments
In a Nut Shell: In general any force
system, including couples acting on a body, can be replaced by a resultant force Fr and a resultant moment, MrP. An equipollent (or equivalent) force
system means that we may replace any system,
such as system 1 shown below with a resultant force Fr at P and a resultant couple Mr as shown in system 2 below. |
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If when summing moments in
system 1 point P is selected for all the forces in system 1, then the moment of these
forces plus the moment of all couples in system 1 must add up to MrP in system 2 at point P. Note: Although Fr does not depend on the choice of P MrP depends on the line of action of Fr. Σ Fi = Fr = Resultant Force in system 2 Σ Couples + Σ rPi x Fi = MrP
= Resultant Moment in system 2 where Fi are all the forces acting on system 1, rPi are the vectors from P to any point on the line of action for
forces Fi in
system 1. Note that couples are
independent of the point about which
moments are summed. |
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