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Forces and Moments MET 2214

Forces and Moments MET 2214. Moments and Forces. Part 4. Moment of a Couple. A couple is defined as: Two parallel forces Same Magnitude Opposite direction Separated by a perpendicular distance d. -F. d. F.

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Forces and Moments MET 2214

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  1. Forces and Moments MET 2214 Statics (MET 2214) Prof. S. Nasseri

  2. Moments and Forces Part 4 Statics (MET 2214) Prof. S. Nasseri

  3. Moment of a Couple • A couple is defined as: • Two parallel forces • Same Magnitude • Opposite direction • Separated by a perpendicular distance d -F d F Statics (MET 2214) Prof. S. Nasseri

  4. So a couple moment is a free vector which can act at any point and depends only on r, not on rA and rB. Couple Moment A moment produced by a couple is called a Couple Moment. Statics (MET 2214) Prof. S. Nasseri

  5. Couple Moment Remember: Scalar Formulation: Magnitude: M = Fd Direction and sense using right-hand rule Vector Formulation: Magnitude: M = r x F Note: The moment of a coupledoes not depend on the point one takes the moment about. In other words, a moment of a couple is the same about all points in space. Statics (MET 2214) Prof. S. Nasseri

  6. M = F.d= (20)(0.15) = 3N.m Example 1 Each person in this figure is exerting a 20N force on the tube. If the distance between the two points is 150mm, what is the moment due to the forces applied. Statics (MET 2214) Prof. S. Nasseri

  7. Example 2 The crossbar wrench is used to remove a lug nut from the automobile wheel. The mechanic applies a moment couple to the wrench such that his hands are a constant distance apart. Is it necessary that a = b in order to produce the most effective turning of the nut? Explain. Also what is the effect of changing the shaft dimension c in this regard? The forces act in the vertical plane. Solution: Couple moment: Mc = F(a+b), The couple moment depends on the total distance between grips. a = b is not a necessary condition to produce the most effective turning of the nut. Changing the dimension c has no effect on turning the nut. Statics (MET 2214) Prof. S. Nasseri

  8. Example 3 Determine the resultant couple moment of the two couples that act on the pipe assembly. The distance from A to B is d = 400 mm. Express the result as a Cartesian vector. Statics (MET 2214) Prof. S. Nasseri

  9. Example 3 Statics (MET 2214) Prof. S. Nasseri

  10. Notice this is negative because we are taking moment about A ! Example 3 Statics (MET 2214) Prof. S. Nasseri

  11. Example 3 Come on! There must be an easier way!! Statics (MET 2214) Prof. S. Nasseri

  12. Example 3 • Lets check three different views and see what forces are causing moments about x, y and z axes: - z z 50N 35N 50N 0.4cos30 - 0.4sin30 - x 0.4cos30 50N y x 50N 35N y Z-view Gives moment about z Y-view Gives moment about y X-view Gives moment about x Statics (MET 2214) Prof. S. Nasseri

  13. Example 3 Statics (MET 2214) Prof. S. Nasseri

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