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Shawn Kenny, Ph.D., P.Eng. Assistant Professor Faculty of Engineering and Applied Science Memorial University of Newfoundland ENGI.

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Presentation on theme: "Shawn Kenny, Ph.D., P.Eng. Assistant Professor Faculty of Engineering and Applied Science Memorial University of Newfoundland ENGI."— Presentation transcript:

1 Shawn Kenny, Ph.D., P.Eng. Assistant Professor Faculty of Engineering and Applied Science Memorial University of Newfoundland ENGI 1313 Mechanics I Lecture 13:Force System Resultants

2 ENGI 1313 Statics I – Lecture 13© 2007 S. Kenny, Ph.D., P.Eng. 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 ENGI 1313 Statics I – Lecture 13© 2007 S. Kenny, Ph.D., P.Eng. 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 ENGI 1313 Statics I – Lecture 13© 2007 S. Kenny, Ph.D., P.Eng. 4 Moment of a Force Tendency of a force (F x ) applied to a body to cause that body to rotate Force (F x ) is applied at a distance (d y ) from the body The force line of action is perpendicular to a line passing through the point of rotation (O) Moment (M o ) z about z-axis

5 ENGI 1313 Statics I – Lecture 13© 2007 S. Kenny, Ph.D., P.Eng. 5 Moment of a Force (cont.) Tendency of a force (F z ) applied to a body to cause that body to rotate Force (F z ) is applied at a distance (d y ) from the body The force line of action is perpendicular to a line passing through the point of rotation (O) Moment (M o ) x about x-axis

6 ENGI 1313 Statics I – Lecture 13© 2007 S. Kenny, Ph.D., P.Eng. 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 ENGI 1313 Statics I – Lecture 13© 2007 S. Kenny, Ph.D., P.Eng. 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 ENGI 1313 Statics I – Lecture 13© 2007 S. Kenny, Ph.D., P.Eng. 8 Moment Force Line of Action Find Line of Action or Force Components?  Often easier to get components Line of Action Force Component

9 ENGI 1313 Statics I – Lecture 13© 2007 S. Kenny, Ph.D., P.Eng. 9 Moment Force Line of Action (cont.) Find Line of Action O x y F d -

10 ENGI 1313 Statics I – Lecture 13© 2007 S. Kenny, Ph.D., P.Eng. 10 Moment Force Line of Action (cont.) Find Components O x y F FyFy FxFx -

11 ENGI 1313 Statics I – Lecture 13© 2007 S. Kenny, Ph.D., P.Eng. 11 Comprehension Quiz 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 Q S P R A

12 ENGI 1313 Statics I – Lecture 13© 2007 S. Kenny, Ph.D., P.Eng. 12 Example For each case illustrated, determine the moment of the force about point O. -

13 ENGI 1313 Statics I – Lecture 13© 2007 S. Kenny, Ph.D., P.Eng. 13 Example (cont.) For each case illustrated, determine the moment of the force about point O. -

14 ENGI 1313 Statics I – Lecture 13© 2007 S. Kenny, Ph.D., P.Eng. 14 Example (cont.) For each case illustrated, determine the moment of the force about point O. +

15 ENGI 1313 Statics I – Lecture 13© 2007 S. Kenny, Ph.D., P.Eng. 15 Example (cont.) For each case illustrated, determine the moment of the force about point O. +

16 ENGI 1313 Statics I – Lecture 13© 2007 S. Kenny, Ph.D., P.Eng. 16 Moment of Coplanar Force System System of Forces Acting on a Single Plane +

17 ENGI 1313 Statics I – Lecture 13© 2007 S. Kenny, Ph.D., P.Eng. 17 Moment of Coplanar Force System System of Forces Acting on a Single Plane +

18 ENGI 1313 Statics I – Lecture 13© 2007 S. Kenny, Ph.D., P.Eng. 18 Classification of Textbook Problems

19 ENGI 1313 Statics I – Lecture 13© 2007 S. Kenny, Ph.D., P.Eng. 19 Classification of Textbook Problems

20 ENGI 1313 Statics I – Lecture 13© 2007 S. Kenny, Ph.D., P.Eng. 20 Classification of Textbook Problems

21 ENGI 1313 Statics I – Lecture 13© 2007 S. Kenny, Ph.D., P.Eng. 21 Classification of Textbook Problems

22 ENGI 1313 Statics I – Lecture 13© 2007 S. Kenny, Ph.D., P.Eng. 22 Classification of Textbook Problems

23 ENGI 1313 Statics I – Lecture 13© 2007 S. Kenny, Ph.D., P.Eng. 23 References Hibbeler (2007) mech_1


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