[PDF] 5 MOMENTS COUPLES FORCES SYSTEMS & FORCE RESOLUTION

Le moment dû à un couple est défini par ???? = ± ???? ???? ???? s i n , où ???? est l'intensité de l'une des forces du couple, ???? est la longueur de la droite reliant les points à partir desquels les forces agissent et ???? est l'angle entre ? ???? et cette droite.
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Le moment dû à un couple est défini par ???? = ± ???? ???? ???? s i n , où ???? est l'intensité de l'une des forces du couple, ???? est la longueur de la droite reliant les points à partir desquels les forces agissent et ???? est l'angle entre ? ???? et cette droite.
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5. MOMENTS, COUPLES, FORCES SYSTEMS

& FORCE RESOLUTION (a) Translation (b) Translation & Rotation (c) Rotation

Concept of a Moment

When the Force is applied at the CG

When the Force is not applied at he CG

When the Force is not applied at the CG, & the body is hinged at the CG body

CG of the body

Objective: To explain the concept of a Moment

If a Force P is applied at the midpoint of the

free, rigid, uniform object, it will slide the object such that every point moves an equal distance. The object is said to

translate. If the same force is applied at some other point as in second figure, then the object will both translate and rotate.

If the point on the object is fixed against translation, (third figure) then the applied force causes the object to

rotate only.

Objective: Explanation of the Concept of Moment -

c ontinued This tendency of a force to produce rotation about some point is called the Moment of a force

Moment of a Force

Objective: Definition of Moment in Statics

Moment of a Force

F d

The tendency of a force to produce rotation of a body about some reference axis or point is called the MOMENT OF A FORCE

M=Fxd Objective: An example to illustrate the definition of Moment in Statics

F= 25#

15"

Lever arm

M= - F x d = -25 x 15= - 3

75 #-in

90 deg

d F

Moment = Force x Perpendicular Distance = Fxd

Example One

: Closing the D oor

Example Two:Tightening the NUT

Common Examples in the Application of the Concept of Moment Ob j ective: To ex p lain the conce p t of Moment in Statics with eve r y da y exam p les

Sign Convention for Moments

Clockwise negative

Anti-clockwise positive

Objective: To illustrat

e the sign conventions for Moment in Statics F d M = - F d What is the moment at A for the Noodle Beam fixed at A and loaded by Force F at B? A B

Objective: To illustrat

e that Moment is always Force x Distance, irrespective of the shape of the structure

Varignon's

Theorem

y x d F Fx Fy F

M=-F.d

M= -Fy.x Fx.y A A

According to Varignon's

T heorem, a Force can be resolved into its components and multiplied by the perpendicular distances for easy calculation of the Moment

Objective: To explain Varignon's

T heorem d F d F Fx Fy d cos d sin A A M ab out A= F x d sin cos d F d F d F x y

Substitute for Fx

and Fy

F x d =

sin sin cos cos d F d F d F 2 2 sin cos Fd Fd d F sin (cos 2 2 Fd Fd Fd

Proof of Varignon's

Theorem

F d F d M abo u t A= - F x d d sin d cos FdFd d F d F d F d F M x y sin (cos sin sin cos cos sin cos 2 2 y F x F On the Left hand side the Moment is got directly by multiplying F times d.On the Right hand side it is proved the Moment is -F.d using Varignon's theorem.

Proof Of Varignon's

Theorem

Ob j ective: To prove Vari g non's T heorem

Plane of the couple

d F F F F Co ncept of a Co uple When you grasp the opposite side of the steering wheel and turn it, you are applying a couple to the wheel A couple is defined as two forces (coplanar) having the same magnitude parallel lines of action but opposite sense . Couples have pure rotational effects on the body with no capacity to translate the body in the vertical or horizontal direction. (Because the sum of their horizontal and vertical components are zero) d, arm of the couple Ob j ective: To ex p lain the conce p t of a Cou p le in Statics AA A 5' 10' 15' B C D 10lb 10lb 10lb 10lb 10lb 10lb 2' 2' 2' 2' 2' 2' lb ft M A 40
2 10 2 10 lb ft M A 40
2 10 2 10 lb ft M A 40
2 10 2 10 lb ft M A 40
2 10 2 10 Effect of Couple applied at different points at the base of a Cantilever

Thus it is clear that the effect of

a couple at the base of the Cantilever is independent of it's (couple's) point of application.

Objective: To explain that the effect of a

Couple is independent

of it's point of application d

1. Introduce two equal and opposite forces at B (which does not alter the equilibrium of the structure)

F F F d

REPLACING A FORCE WITH A FORCE & A COUPLE

2. Replace the above two Forces with a Couple= F.d

Hence a Force can be replaced with an Equivalent Fore and a Couple at another point. Objective: To explain how a Force can be replaced by a Force and couple at another point F F F F d dd

FORCE SYSTEMS

Objective: To explain various types of Force systems which occur iquotesdbs_dbs19.pdfusesText_25