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 I
Statics (MET 2214)
Prof. S. Nasseri

3. What is a moment?!
A moment is a type of force. A moment is a turning force.
A turning force happens when a force is applied to something which has a pivot
Statics (MET 2214)
Prof. S. Nasseri

4. What is a moment?
pivot
pivot F r
Statics (MET 2214)
Prof. S. Nasseri

5. Some examples
Two kids are sitting at the same distance apart and have the same weight, hence the moments are equal.
Knowing the weight of the bucket, you need to know what force to apply to bring the bucket up.
Statics (MET 2214)
Prof. S. Nasseri

6. Moment of Force F around point O
The moment of a force about a point or an axis (MO), provides a measure of the tendency of the force to cause a body to rotate about the point or axis.
oz ┴ plane xy in which Fx lies.
Fx causes the pipe to turn about the z-axis.
Fx causes a moment about the z-axis = (Mo)z
Statics (MET 2214)
Prof. S. Nasseri

7. Moment of Force F around point O
Fy passes through O. Fy does not cause the pipe to turn because the line of action of the force passes through O.
NO moment!!
Statics (MET 2214)
Prof. S. Nasseri

8. Moment of Force F around point O
ox ┴ plane zy in which Fz lies.
Fz causes the pipe to turn about the x-axis
Fz causes a moment about the x-axis (Mo)x
Statics (MET 2214)
Prof. S. Nasseri

9. Direction of Moment
The direction of Mo would be specified by using the right hand rule.
Counter Clockwise (CCW) is out of the page, Clockwise (CW) is into the page.
Statics (MET 2214)
Prof. S. Nasseri

10. Moment (Scalar or Vector?!)
Moment is a vector and the direction is defined using right hand rule. Keep your fingers along the line of action of the force, and your thumb will be along the axis of the moment. M M r M F r F
Statics (MET 2214)
Prof. S. Nasseri

11. Magnitude of the Moment
Magnitude of the moment is simply force times the perpendicular distance.
Statics (MET 2214)
Prof. S. Nasseri

12. Example
If the force shown here is 2 lb, how much are the moments about A, B, C and D:
Moment about A:
2 x 8= 16 lb.in
Moment about B:
2 x 2= 4 lb.in
Moment about C:
2 x 12= 24 lb.in
Moment about D:
2 x 0= 0 lb.in
Statics (MET 2214)
Prof. S. Nasseri

13. Calculating the moment in 2-D using components
Select a positive direction (CCW or CW),
Calculate each moment and add them, using the proper sign for each term,
Always remember to write the unit of moment which is Nm or lb.f.
Statics (MET 2214)
Prof. S. Nasseri

14. Calculating the moment in 2-D using components
Example 1: In the following figure, calculate the moment about the point O:
We choose the CCW as positive direction for moment,
Moment of component of F along x about O is Fx times the perpendicular distance from O (or d1), which is clockwise, so it is
Moment of component of F along y about O is Fy times the perpendicular distance from O (or d2), which is counter clockwise, so it is
Moments add together as vectors, so the total moment is:
Statics (MET 2214)
Prof. S. Nasseri

15. Calculating the moment in 2-D using components
Example 2: In the following figure, if is 60 degrees and r is 30 mm and F is 6 N, what is the magnitude of the moment about O.
We choose the CCW as positive direction for moment,
Component of F along r (or ) produces no moment, since it passes from point O.
Component of F perpendicular to r (or ) produces the moment
So the total moment of F about O is:
Statics (MET 2214)
Prof. S. Nasseri

16. Calculating the moment in 2-D using components
Example 2: Remember:
The moment about O is also calculated using the magnitude of force F times perpendicular distance from O to the line of action of F which is d:
Moving a force along its line of action does not change its moment!
Statics (MET 2214)
Prof. S. Nasseri