Mechanics: Statics System of Forces Draft for Information Only
ContentSystem of Forces Reduction
System of Forces ReductionWhen a force system consists of more than one force, the system of forces should be reduced to one force and one couple. System of forces, F1, F2, and F3 acting on a rigid body at points, A, B, and C, respectively can be transformed to the point of interest, O through force vector transformation,
According to force vector transformation, forces at different points of application can be moved to the point of interest, O. And the moments of forces about the point of interest, O can also be determined by the cross product of the moment arm of each force vector and the force vector.
After all force vectors are moved to point O and all moment vectors are replaced by couple vectors. The equivalent system acting at a point O on a rigid body can be determined by the vector sum of the all force vectors and the vector sum of all couple vectors at the point O. Therefore, a system of force can be reduced to an equivalent forcecouple system consists of a force vector R and a couple vector MO.
Mathematically, the force vector R and the couple vector MO of equivalent system consists can be expressed as: and The equivalent forcecouple system can then be further transferred to other points of interest through the forcecouple system transformation. Vector DecompositionThe resultant force vector and resultant couple vector can be determined in terms of rectangular compontents through vector decomposition. Imply the force vector and moment arm vector equal to: and And the resultant force vector and couple vector equal to: and The resultant force vector equal to:
Imply:
The resultant couple vector equal to: . where: Equivalent Systems of ForcesTherefore two systems of forces are equivalent at the point of interest, if: and Or in terms of rectangular components: and Types of Equivalent Systems of ForcesThe two elements of an equivalent forcecouple system at O are a resultant force vector R and a resultant couple vector MO at O.
©sideway ID: 110700014 Last Updated: 2/8/2011 Revision: 1 Ref: References
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