Mechanics: Statics System of Forces Draft for Information Only
ContentSystem of Forces Transformation
System of Forces TransformationSometimes a system of forces acting on a rigid body is needed to be transformed into an equivalent system at the point of interest. Force CoupleA couple of force F is applied at points A, B on a rigid body.
The equivalent system is a free couple vector M acting on any location of the rigid body.
Consider the moment MBA at point B, the tendency of rotation above B is caused by the applied force F at A. The applied force F at B can be considered as the reaction supporting force. Both the magnitude and direction of the moment vector MBA is same as the couple vector M.
Force VectorSuppose a force vector acting at point A on the rigid body is to be considered at point B.
When only a single force F is applied at point A on the rigid body, the moment of the force at point A about point B is also equal to MBA .
To simulate the force couple condition, two forces, F and F with magnitude equal to the applied force F are attached at point B. After this transformation, a force couple of moment MBA is formed with an additional force F acting at point B.
Force F acting at point A is now moved to point B. The formed force couple of moment MBA can be replaced by a couple vector M. The couple vector M is a free vector and it can be located at point B for convenience.
Therefore the equivalent system of a force vector F acting at point A on a rigid body can be transformed to an arbitrary point B by moving the force vector to pont B and adding a couple vector M with moment equals to the moment MBA of the force vector F about point B. At which, the force vector F tend to provide the same linear motion and the couple vector M tend to provide the same rotational motion as the force vector F at point A. The equivalent system of combining a force vector and a couple vector is named as forcecouple system. And the couple vector is
©sideway ID: 110700010 Last Updated: 12/7/2011 Revision: 1 Ref: References
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