1. Lecture 13: Force System Resultants
ENGI 1313 Mechanics I
Lecture 13: Force System Resultants

2. Chapter 4 Objectives
To discuss the concept of the moment of a force and show how to calculate it in two and three dimensions.
To provide a method for finding the moment of a force about a specified axis.
To define the moment of a couple.
To present methods for determining the resultants of non-concurrent force systems.
To indicate how to reduce a simple distributed loading to a resultant force having a specified location.

3. Lecture 13 Objectives
to examine concepts of the moment of a force in scalar notation
to examine concepts in vector algebra on the cross product with respect to the moment of a force

4. Moment of a Force
Moment (Mo)z about z-axis
Tendency of a force (Fx) applied to a body to cause that body to rotate
Force (Fx) is applied at a distance (dy) from the body
The force line of action is perpendicular to a line passing through the point of rotation (O)

5. Moment of a Force (cont.)
Moment (Mo)x about x-axis
Tendency of a force (Fz) applied to a body to cause that body to rotate
Force (Fz) is applied at a distance (dy) from the body
The force line of action is perpendicular to a line passing through the point of rotation (O)

6. Moment of a Force (cont.)
The force line of action passes through the point of rotation (O)
Therefore no tendency for rotation is possible.
No moment about O

7. Moment of a Force Definition
Scalar Magnitude
Direction
Right-hand rule
Moment axis to plane of F and d
Moment axis intersects Point O
Sense
Arrowhead curl
Counter-clockwise is positive +

8. Moment Force Line of Action
Find Line of Action or Force Components?
Often easier to get components
Line of Action
Force Component

9. Moment Force Line of Action (cont.)
Find Line of Action - x O y d F

10. Moment Force Line of Action (cont.)
Find Components - x O y Fx Fy F

11. Comprehension Quiz 13-01
If a force of magnitude F can be applied in four different 2-D configurations (P,Q,R, & S), select the cases resulting in the maximum and minimum (Max, Min) torque (moment) values on the wrench about Point A.
A) (Q, P)
B) (R, S)
C) (P, R)
D) (Q, S)
Answer: D P S A R Q

12. Example 13-01
For each case illustrated, determine the moment of the force about point O. -

13. Example (cont.)
For each case illustrated, determine the moment of the force about point O. -

14. Example (cont.)
For each case illustrated, determine the moment of the force about point O. +

15. Example (cont.)
For each case illustrated, determine the moment of the force about point O. +

16. Moment of Coplanar Force System
System of Forces Acting on a Single Plane +

17. Moment of Coplanar Force System
System of Forces Acting on a Single Plane +

18. Classification of Textbook Problems

19. Classification of Textbook Problems

20. Classification of Textbook Problems

21. Classification of Textbook Problems

22. Classification of Textbook Problems

23. References Hibbeler (2007)