ENGI 1313 Mechanics I

1. ENGI 1313 Mechanics I Lecture 21: Force and Couple Moment Systems

2. Lecture 21 Objective • to determine the effect of moving a force, • to find an equivalent single force-couple system for a system of forces and couples.

3. Motivation for Equivalent Systems • Force and Couple System • Number of loads acting on body • Simplify Loading • Reduce to equivalent system • Examine Effects on Body • External equivalence only • Internal effects (load-displacement) are influence but not considered in this course

4. Motivation for Equivalent Systems (cont.) ?

5. Equivalent Force • Initial Single Force • Principle of transmissibility • Sliding vector • External effect equivalence only

6. Equivalent Force and Couple • Initial Single Force • Couple moment is a free vector • Equivalent system force not on the line of action of initial system force • External effect equivalence only

7. Illustration of Equivalent Force and Couple for a Single Force System Equivalent Force (Sliding Vector) Equivalent Force (Sliding Vector) and Couple Moment (Free Vector)

8. Equivalent Force and Couple • Initial Multiple Force System • Equivalent system force not on the line of action of initial system force • Couple moment is a free vector • External effect equivalence only

9. Illustration of Equivalent Force and Couple for Multiple Force System Equivalent Force (Sliding Vector) and Couple Moment (Free Vector)

10. Equivalent Single Resultant Force • Initial Multiple Force and Couple System • FR and MRo must be perpendicular

11. Equivalent Single Resultant Force (cont.) • Technique Valid for: • Concurrent force systems • Only forces • No couple

12. Equivalent Single Resultant Force (cont.) • Technique Valid for: • Coplanar force systems • Moment axis perpendicular to plane

13. Equivalent Single Resultant Force (cont.) • Technique Valid for: • Parallel force systems • Couple moment acts only on two axes • Couple moment perpendicular to force vector

14. Comprehension Quiz 21-01 • A general system of forces and couple moments acting on a rigid body can be reduced to a ___ . • A) Single force • B) Single moment • C) Single force and two moments • D) Single force and a single moment • Answer: D

15. S R Q P Comprehension Quiz 21-02 • The forces on the pole can be reduced to a single force and a single moment at point ____ . • A) P • B) Q • C) R • D) S • E) Any of these points. • Answer: E

16. Comprehension Quiz 21-03 • Consider two couples acting on a body. The simplest possible equivalent system at any arbitrary point on the body will have • A) one force and one couple moment • B) one force • C) one couple moment • D) two couple moments • Answer: C

17. Comprehension Quiz 21-04 • Three couples act on a body. The equivalent system will be ________ at different points on the body. • A) different when located • B) the same even when located • C) zero when located • D) none of the above • Answer: B

18. Example 21-01 • For the force and couple system, find (a) the equivalent resultant force and couple moment acting at Point A and (b) the equivalent single force location along the beam AB.

19. Example 21-01 (cont.) • a) Equivalent resultant force and couple moment acting at Point A FR MA 

20. Example 21-01 (cont.) • b) Equivalent single force location along the beam AB. FR  2.10 ft

21. Example 21-02 • Example Problem 4.18. The slab is subjected to four parallel forces. Determine the magnitude and direction of a resultant force equivalent to the given force system and locate its point of application on the slab.

22. Example 21-02 (cont.) • Solution • FR = 1400 N  • x = 3.00m • y = 2.50 m

23. References • Hibbeler (2007) • http://wps.prenhall.com/esm_hibbeler_engmech_1