chapter four laith batarseh home nextprevious end

Chapter Four

Laith Batarseh

Statics

1. MOMENT SCALAR

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Statics

MOMENT SCALAR

Definition

Moment is defined as the tendency of a body lies under force to rotate about a point not on the line of the action of that force (i.e. there is a distance between the force and the rotation point )

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The acting force

Moment arm

Description

Moment depends on two variables:

Moment is a vector quantity

Statics

MOMENT SCALAR

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Description

ForceArmTendency to rotate

Statics

MOMENT SCALAR

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Tendency for rotation

Statics

MOMENT SCALAR

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Magnitude

FD

Moment magnitude (M) = F.D

Statics

MOMENT SCALAR

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Direction

Statics

MOMENT SCALAR

Solving procedures

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1. Define the magnitudes of force (F) and arm (D)

2. Assume the positive direction (eg. Counter clock wise)

3. Find the magnitude of moment (M) as F.D

4. Give the moment the correct sign according to the tendency for rotation

Statics

MOMENT SCALAR

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Example [1]

Find the moment caused by the following forces about point O

100 N

0.5m

2m

(b)

O

100 N

0.5m

2m

(a)

O

Statics

MOMENT SCALAR

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Example [1]

Assume the CCW direction is the positive direction.

100 N

0.5m

2m

(b)

O

100 N

0.5m

2m

(a)

O

Branch (a) Mo = F.d = -(100N)(0.5m) Mo=-50 N.m=50N.m CWBranch (b) Mo=F.d = (100N)(2m) Mo=200 N.m CCW

+

+

Statics

Principle Of Moments

Principle of Moments

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some times called Vrigonon’s theorem (Vrigonon is French

mathematician 1654-1722).

State that the moment of a force about a point equals the summation

of the moments created by the force components

In two dimensional problems: the magnitude is found as M = F.d and

the direction is found by the right hand rule

In three dimensional problems: the moment vector is found by M =rxf

and the direction is determined by the vector notation (ie. i,j and k

directions)

Statics

Principle Of Moments

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Example [1]

Find the moment caused by the following forces about point O

Statics

Principle Of Moments

Example [1]

Mo,1 = 100 sin(30) (10) = 500 N.m

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+

Mo,2 =- 100 cos(30) (5) =- 433N.m+

M = Mo,1+Mo,2=500-433=67N CCW

Statics

Principle Of Moments

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Example [2]

1. Force analysis

100 cos(40)1.2 m

0.3 m

100 sin(40)

120 cos(60)

120 sin(60)

2. Moment calculations

∑ M = (100 cos(40))(1.5) –( 120 cos(60))(1.2) =43 N.m CCW +

Statics

MOMENT SCALAR

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Moment resultant

F1

F2F3

d1

d2 d3

M1O

M2

M3

Mo = ∑Mo = M1 + M2 – M3 = F1d1+F2d2 – F3d3 +

Statics

MOMENT SCALAR

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Example [2]

Find the moment caused by the following forces about point O

2m

3m

5m

1m30o

100 N

50 N

60 N

75 NO

Statics

MOMENT SCALAR

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Example [2]

2m

3m

5m

1m30o

100 N

50 N

60 N

75 NO

CWmNmNM

M

o

o

.45.272.45.272

1)30cos(755)30sin(750503602100

+

Statics

MOMENT SCALAR

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Exercise

Find the moment caused by the following forces about point O

100 N

300 N

5m

2m 45o

30oO 0.3m

Statics

MOMENT SCALAR

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Exercise

CWmNmNM

M

o

o

.897.897

5)45sin(3003.0)45cos(3002)30sin(100

+

100 N

300 N

5m

2mO 0.3m

300 sin (45)N

300 cos (45)N

100sin (30)N

100cos (30)N

Statics

MOMENT SCALAR

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Summary

Moment is the tendency to rotate produced by a force

Moment is vector quantity

The scalar magnitude of the moment equal to : F.d

The direction of the moment will be in a direction

perpendicular to the plane which contains the vectors of

the F and d