3 Kuliah Momen Gaya Kopel.ppt

8/17/2019 3 Kuliah Momen Gaya Kopel.ppt

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KULIAH IV

MEKANIKA TEKNIK

MOMEN GAYA & KOPEL


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Tujuan Pembelajaran

Mahasiswa dapat:1 Menjelas!an pen"ertian m#men "a$a% dan m#men !#pel

& Men$elesai!an pers#alan tentan" m#men dan !#pel

&


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Apa itu m#men "a$a '

The moment of a force about a point provides a measure of the

tendency for rotation (sometimes called a torque). (


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MOMENT IN 2-D (continued)

In the 2-D case, the magnitude of the moment iso ! " d

#s sho$n, d is the perpendicular distance from point % to theline of action of the force.

In 2-D, the direction of % is either cloc&$ise or

counter-cloc&$ise depending on the tendency for rotation. )


5/28

M#ment in &*+

% ! " d

and the direction is

counter-cloc&$ise.

% ! ("' a) (" b)

CCW = (+)

CW = (-)

"a

b

d

%a b

%

F

" *

" y

#s sho$n, d is the

perpendicular distance

from point % to the line

of action of the force.

%ften it is easier to

determine % by using the

components of F as sho$n.

,


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E-ample 1Given: # + force is

applied to the $rench.

Find: The moment of the

force at %.

Plan: ) /esolve the forcealong * and y a*es.

2) Determine % using

scalar analysis.

Solution0 1 "y ! - + cos 23

1 4 "* ! - + sin 23

1 % ! 5-(+ cos 23)(2) 1 (+ sin 23)(6)78mm

! -99 8mm ! - !"" N#$ .


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Given: # + force isapplied to the frame

and : ! 23.

Find: The moment of the

force at #.

Plan:

) /esolve the force along * and y a*es.

2) Determine # using scalar analysis.

E%&MP'E 2

/


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E%&MP'E 2 (continued)

Solution:

1 "y ! -+ sin 23

1 4 "* ! -+ cos 23

1 # ! 5(+ cos 23)(2) 1 (+ sin 23)(6)7 8m

! "" N#$ (;a$aban)0


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CONCEPT *ESTION

. ) 6 8m ?) 6

8m

D) (@6) 8m A) 9 8mB #

d ! 6 m

" !

2. If a force of magnitude " can be applied in four different 2-D

configurations (C,,/, E F), select the cases resulting in the

ma*imum and minimum torque values on the nut. (a*, in).

#) (, C) >) (/, F)

?) (C, /) D) (, F)


10/28

6 m C 2 m G

6. Hsing the ??< direction as positive, the net moment of the

t$o forces about point C is

#) 8m >) 2 8m ?) - 2 8m

D) + 8m A) - + 8m

12


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Apa itu M#men K#pel '

11


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M#ment #3 a 4#uple

# couple is defined as t$o parallel forces $ith the same

magnitude but opposite in

direction separated by a

perpendicular distance d.

The moment of a couple is defined as

% ! " d (using a scalar analysis) or as

M O ! r , F (using a vector analysis).

ere r is any position vector from the line of action of

–F to the line of action of F . 1&


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Pr#blem 5#l6in"

# torque or moment of 2 8 m is required to rotate the $heel.

1(


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Pr#blem 5#l6in" 7&*+8

# >

! " d

2 ! " .+

" ! 6

! " d

2 ! " .6

" ! + 1)


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PO.'EM SO'/ING - SC&'&

Given0 T$o couples act on the beam. The resultant couple is

Jero.

Find0 The magnitudes of the forces

C and " and the distance d.

P'&N:

) Hse definition of a couple to find C and ".2) /esolve the 6 force in * and y directions.

6) Determine the net moment.

+) Aquate the net moment to Jero to find d. 1,


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Solution:

"rom the definition of a

coupleC ! G and

" ! 6 .

/esolve the 6 force into vertical and horiJontal

components. The vertical component is (6 cos 6K) and

the horiJontal component is (6 sin 6K) .

o$ solve this equation for d.

d ! ( L sin 6K) @ (6 cos 6K) ! 6!ML m

It $as given that the net moment equals Jero. Fo

1 N ! - (G)(2) 1 (6 cos 6K)(d) 1 (6 sin 6K)(!2) !

1.


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CONCEPT QUESTION

. In statics, a couple is defined as OOOOOOOOOO separated by a

perpendicular distance.

#) t$o forces in the same direction.

>) t$o forces of equal magnitude.

?) t$o forces of equal magnitude acting in the same direction.D) t$o forces of equal magnitude acting in opposite directions.

2. F 1 and F 2 form a couple. The moment

of the couple is given by OOOO .

#) r 1 , F 1 >) r 2 , F 1

?) F 2 , r 1 D) r 2 , F 21/


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6. # couple is applied to the beam as sho$n. Its moment equals OOOOO 8m.

#) G >) L

?) P D) 6

+

Gm 2m

G

10


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Apa itu Memindah 9a$a '

Feveral forces and a

couple moment are

acting on this vertical

section of an I-beam.?an you replace them

$ith Qust one force and

one couple moment at

point % that $ill have

the same e*ternaleffect= If yes, ho$ $ill

you do that=

1


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&N E*I/&'ENT S0STEM


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Eui6alent ;#rut the

internal effect of the force on the body does depend on

$here the force is applied).

&1


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Eui6alent ;#r


23/28

Eui6alent ;#r


24/28

Pr#blem 5#l6in" 7&*+8

Given: # 2-D force and couple

system as sho$n.

Find: The equivalent resultant force

and couple moment acting at

# and then the equivalent

single force location along

the beam #>.

Plan:

) Fum all the * and y components of the forces to find "/#.2) "ind and sum all the moments resulting from moving each

force to #.

6) Fhift the "/# to a distance d such that d ! /#@"/y&)


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Pr#blem 5#l6in" 7&*+81 4 N"/* ! 2G 1 6G sin 63

! +2!G

1 N"/y ! - 2 - 6G cos 63

! - G!6

1 /# ! - 6G cos63 (.2)

- 2(.L) 1 2G(.6)

! - .GL .m"/ ! ( +2!G2 1 (-G!6)2 )@2 ! LG!M

: ! tan- ( G!6@+2!G) ! +M!P 3 (S$ I)

The equivalent single force "/ can be located on the

beam #> at a distance d measured from #.

d ! /#@"/y ! - .GL@(-G!6) ! .2 m.

"/ d

&,


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CONCEPT QUESTION

. # general system of forces and couple moments acting on a

rigid body can be reduced to a OOO . #) single force.

>) single moment.

?) single force and t$o moments.

D) single force and a single moment.

2. The original force and couple system and an equivalent

force-couple system have the same OOOOO effect on a body. #) internal >) e*ternal

?) internal and e*ternal D) microscopic

&.


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Terima Kasih

&/


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CONCEPT *ESTION

6. The forces on the pole can be reduced to

a single force and a single moment at

point OOOO .

#) C >) ?) /

D) F A) #ny of these points.

+. ?onsider t$o couples acting on a body. The simplest possible

equivalent system at any arbitrary point on the body $ill have

#) one force and one couple moment.

>) one force.

?) one couple moment.

D) t$o couple moments.

B

BB

B

&0

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3 Kuliah Momen Gaya Kopel.ppt