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

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

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

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Statics (MET 2214) Prof. S. Nasseri 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 couple does 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.

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Statics (MET 2214) Prof. S. Nasseri 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. M = F.d= (20)(0.15) = 3N.m

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Statics (MET 2214) Prof. S. Nasseri 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. 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. Also what is the effect of changing the shaft dimension c in this regard? The forces act in the vertical plane. Changing the dimension c has no effect on turning the nut.

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Statics (MET 2214) Prof. S. Nasseri 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.

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

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

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

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

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

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