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**Forces and Moments MET 2214 Ok. Lets get started.**

My name is Dr Simin Nasseri, a faculty member here at MET and I am going to teach this course MET ????, Course name. Statics (MET 2214) Prof. S. Nasseri

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

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**Moment of a Couple A couple is defined as: Two parallel forces**

Same Magnitude Opposite direction Separated by a perpendicular distance d d F Statics (MET 2214) Prof. S. Nasseri

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**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 rA and rB. Statics (MET 2214) Prof. S. Nasseri

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**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. Statics (MET 2214) Prof. S. Nasseri

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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 Statics (MET 2214) Prof. S. Nasseri

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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

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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

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

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**Notice this is negative because we are taking moment about A !**

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

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**Example 3 Come on! There must be an easier way!! Statics (MET 2214)**

Prof. S. Nasseri

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Example 3 Lets check three different views and see what forces are causing moments about x, y and z axes: - z z 35N 50N 50N - 0.4cos30 - 0.4sin30 0.4cos30 x y x 50N 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

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

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