# 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

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