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09_20_2004_handout_resultants

# 09_20_2004_handout_resultants - Handout for TAM 210/211 BL1...

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Handout for TAM 210/211 BL1 posted 19 September, 2004 Things to keep in mind for finding special equipollent systems and resultants for a system of forces and couples I. Finding the “force couple resultant” (at point P) of a system of forces and couples a. Resultant Force i. The resultant force is found by simply adding all the forces, regardless of point P = = F N n n r 1 F F v v , where F N refers to the number of applied forces ii. For finding the resultant force, I recommend the following steps: 1. Express all forces in terms of their components in an appropriate coordinate system. For this class, this will usually be the Cartesian coordinate system, e.g. k j i F z y x n n n n F F F + + = v 2. Add all forces by summing the components ( ) ( ) ( ) k j i k j i F F ... ... ... 2 1 2 1 2 1 1 1 + + + + + + + + = + + = = = = z z y y x x F z y x F F F F F F F F F F N n n n n N n n r v v b. Resultant Moment at point P i. This is the sum of the moments with respect to point P of all forces and couples = = + = + = = C m F n C F n N m P N n P N N n P P r 1 1 1 , M M M M v v v v , where F N refers to the number of applied forces, and C N refers to the number of applied couples ii. For finding the moments with respect to point P due to force n, n P M v 1. Express all forces in terms of their components in an appropriate coordinate system. For this class, this will usually be the Cartesian coordinate system, e.g. k j i F z y x n n n n F F F + + = v 2.

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