Chapter 4 - Force System Resultants

Chapter 4 - Force System Resultants

Moment of a Force 1 Objectives 1. Introduce the concept of the moment of a force and show how to calculate it in 2 dimensions. 2. Define the moment of a couple.

3. Present methods for determining the resultants force systems. 2 Force F tends to rotate the beam clockwise about A with moment MA = FdA Force F tends to rotate the beam counterclockwise

about B with moment MB = FdB Hence support at A prevents the rotation 3 Magnitude For magnitude of MO,

MO = Fd where d = moment arm or perpendicular distance from the axis at point O to its line of action of the force Units for moment is N.m 4 Direction

FMD 5 Example1 For each case, find the moment of the force about the point O

6 A MO = 7 B

MO = 8 C m N

m m MO = 9 D m

m m N MO = 10

E MO = 11 Example2 Determine the

moment of the 800 N force about points A, B, C, and D 12 Resultant Moment cw

M Fd A 13 Principles of Moments Also known as Varignons Theorem Moment of a force about a point is equal to the sum of the moments of the

forces components about the point 14 Example 3 Determine the resultant moment

of the four forces. 15 Example4 Determine the moment of the force about A. 16 17

Example5 Determine the moment of the force about 0. 18 19 Moment of a Couple

A couple is two parallel forces having the same magnitude and opposite directions separated by a distance d. 20

Moment of a Couple Resultant Force is zero. Effect of couple is a moment 21

Moment of a Couple A Couple consists of two parallel forces, equal magnitude, opposite directions, and separated a distant d apart. A Couple Moment about any point O equals the sum of the moments of both forces. 22

Example6 150N 600N 100N 250N A 4.80m long beam is subjected to the forces shown. Reduce the given system of forces to

a) an equivalent force couple system at A b) single force or resultant 23 Important Points 1. The moment of a force indicates the tendency of the body to cause rotation about a point.

2. Magnitude M=Fd d is distance from point O to line of action of F 3. Principle of Moments 24 QUIZ 1. What is the moment of the 10 N force about point A (MA)?

F = 12 N A) 3 Nm B) 36 Nm C) 12 Nm D) (12/3) Nm E) 7 Nm d=3m A 25

QUIZ 2. Using the CW direction as positive, the net moment of the two forces about point P is A) 10 N m B) 20 N m C) - 20 N m D) 40 N m E) - 40 N m 10 N

3m P 2m 5N

26 QUIZ 3. If F1 = 1 N, x1 = 1 m, F2 = 2 N and x2 = 2 m, what is the location of FR, i.e., the distance x. A) 1 m B) 1.33 m C) 1.5 m D) 1.67 m E) 2 m

F1 x2 F2 x FR

x1 27

Recently Viewed Presentations

  • The Opportunity is Today! Our work is solemn,

    The Opportunity is Today! Our work is solemn,

    The role playing segment cemented it in her heart. Mark & Diane Britton Illinois/Wisconsin 4,472,803 Children under 18 Tim & Sherry Thomas Bruce & Marti Brumfield Roy & Betty Koopman Ken & Denise Krup Don & Nancy Estep J.P. &...
  • Tragedy and innovation: - ESF

    Tragedy and innovation: - ESF

    * Greening of economic agencies Evolution of environmental strategies in China (12) * Greening of economic agencies Evolution of environmental strategies in China (13) (Source: Shi, H. and L. Zhang, 2006) * Economic actors step in Search for more affordable...
  • Minds-On  Have you chosen the short story you

    Minds-On Have you chosen the short story you

    The film Shrek pairs characters with contrasting personalities, which gives the message that people can get along no matter how different they may be. [Perhaps not the greatest, but it is enough to get the point across, and the example...
  • Anatomical Reasoning - Indian Institute of Technology Bombay

    Anatomical Reasoning - Indian Institute of Technology Bombay

    Causal Reasoning. Reasoning about cause - effect relationships is called causal reasoning. The representation of causal knowledge in logic may be represented by means of collection of logical implications of the form : cause. effect. Causal Reasoning.
  • Apes Exam Review - Queenbegumscience

    Apes Exam Review - Queenbegumscience

    The AP Environmental Science Exam is 3 hours long and has two parts — multiple choice questions and free response questions. ... APES EXAM POWERPOINT YOUTUBE REVIEW . PART 1 OF 6. PART 2 OF 6. PART 3 OF 6....
  • Welcome to (insert course name) (customize with instructor/course/section

    Welcome to (insert course name) (customize with instructor/course/section

    Redeem an access code which may have been included in a textbook bundle you purchased from the bookstore. You can also utilize the payment grace period and choose to pay later. The grace period will be clearly identified on the...
  • Performance Appraisal Review for Staff 2014 Facilitated by

    Performance Appraisal Review for Staff 2014 Facilitated by

    Demonstrates exceptional understanding of work and the job. Identifies unique, innovative and workable solutions to problems. ... Fine-Tune the Size and Balance of the Student Body. Goal 3: Create the Optimal Campus Environment. SMART Goal Examples. Ex:
  • Exploring Majors at WKU Advising & Career Development

    Exploring Majors at WKU Advising & Career Development

    The Exploratory Program. Mission: The Exploratory Program is an initiative of the Advising & Career Development Center (ACDC) created to lead Exploratory students on a path to self discovery.