Forces and Moments MET 2214 Statics MET 2214

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

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

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

Example 1 Each person in this figure is exerting a 20 N force on the tube. If the distance between the two points is 150 mm, what is the moment due to the forces applied. M = F. d= (20)(0. 15) = 3 N. m 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. 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

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

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

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

Example 3 Come on! There must be an easier way!! 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: - z z 50 N 35 N 50 N 0. 4 sin 30 0. 4 cos 30 y 35 N X-view Gives moment about x Statics (MET 2214) Prof. S. Nasseri x 0. 4 cos 30 - 50 N Y-view Gives moment about y x 50 N Z-view y Gives moment about z

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