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# Week5_1 - ENGR210 Fall 2011 4.8 Further simplification of a...

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ENGR210, Fall 2011 1 4.8 Further simplification of a force and couple system In the previous section, “equivalent systems” consist of a resultant force and a resultant moment about a point. In this section, we will learn that such systems can be further simplified into a single force system in 2D systems or into so- called a “wrench” in 3D systems.

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ENGR210, Fall 2011 2 “Concurrent force system” In a special case where all forces intersect at a common point O, then no moment is generated. As a result, the equivalent system can be represented by a single force F R .
ENGR210, Fall 2011 3 “Coplanar force system” For more general 2D systems where all forces do not intersect at a point O, a “shifted” resultant force makes an equivalent system. In figure (b), F R = F 1 + F 2 + F 3 + F 4 , M RO = r 1 x F 1 + r 2 x F 2 + r 3 x F 3 + r 4 x F 4 ( r 1 , r 2, r 3, r 4 are not shown) In figure (c), F R is shifted by d from O such that M RO = d F R (note that d is perpendicular distance from O to the line of action of F R )

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ENGR210, Fall 2011 4 Note: even if couple moments are applied in addition to forces,
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## This note was uploaded on 10/16/2011 for the course ENGR 210 taught by Professor Ko during the Fall '08 term at Boise State.

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Week5_1 - ENGR210 Fall 2011 4.8 Further simplification of a...

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