1. 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

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 d F
Statics (MET 2214)
Prof. S. Nasseri

4. 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

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 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

6. 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

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
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

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