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METODE CROSS

3000 kg

C 2EI

1000kg/m'

EI

5 m

2500kg

A

3.0 3.

6m

KEKAKUAN

: = 4 (EI)5

= 0.8

= 0.8 =

2.13

= 1.3 =

2.13

: = 4 ( 2 EI )6

= 1.3

= 1.3 =

2

= 0.8 =

2

1.MOMEN PRIMER TANPA GOYANGAN

= + 2500 1.25 3.25 2 +

5

K CA KCD

dCA

dCD

KDC K DB

d DC

d DB

MAC

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= ! 11 1000 5 2 !

1"2

= ! 1 1200 6 2 !

12

= + 1 1200 6 2 +

12

= = 0 kgm

MCA

MCD

MDC

MDB

MBD

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2. DISTRIBUSI MOMEN TANPA GOYANGAN

#$#$k A C

%&g AC CA CD DC

AD 0.00 0.35 0.625 0.625

253 !3"1 !438 5850

213".3 428.5 130.8 3565.4

!2"42.3 !5884.6

551. 1103.4 1838." "1".5

!28.3 !54.

53." 10.8 1".6 8".8

!28.1 !56.1

5.3 10.5 1.5 8.8

!2. !5.5

0.51 1.03 1.1 0.86

!0.2 !0.54

0.05 0.10 0.1 0.08

!0.03 !0.05

0.005 0.010 0.016 0.008

!0.003 !0.005

0.0005 0.0010 0.002 0.0008

!0.0002 !0.0005

*m&, 10003 152"."4 !1530 3"12."0

3.MOMEN PRIMER DENGAN GOYANGAN

= + 6 EI -

5 2

= ! 6 2 EI -

6 2

= + 6 EI -

5 2

4. DISTRIBUSI MOMEN DENGAN GOYANGAN

#$#$k A C

%&g AC CA CD DC

AD 0.00 0.38 0.625 0.625

0.240 0.240 !0.333 !0.333

0.018 0.035 0.058 0.02"

0.020 0.040

!0.004 !0.008 !0.013 !0.006

0.002 0.004

0.000 !0.001 !0.001 !0.001

0.000 0.0004

MDC

MAC

MCA

MCD

MDC

MBD

MDB

M

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*m&, 0.253 0.26 !0.26 !0.26

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BAGAN MOMEN TANPA GOYANGAN BAGAN MOM

!1530 3"13 !0.26

C D C

1530 !3"13 0.26

10003 !1"56 0.253

A B A

= 0.00

10003.25 + 152"."4 + !1"56 + !3"12."0

5 5

0.253 + 0.26 + 0.253 + 0.26

5 5

0.104 + 0.104 m = 230

0.208 m = 1133

m = 1133

0.208

m = 5446

5. MOMEN AKHIR

= 10003.2 + 0.253 5445.56 = 11383

= 152"." + 0.26 5445.56 = 2"83

= !152"." + !0.26 5445.56 = !2"81

= 3"12." + !0.26 5445.56 = 2461

= !3"12." + 0.26 5445.56 = !2461

= !1"56.5 + 0.253 5445.56 = !5

MAC

MCA

MCD

MDC

MDB

MBD

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1200 kg/m'

D

2 m

EI

1.25 m

1.25 m

B

0

: 4 ( 2 EI )6

: 1.3

0.35

= 1

0.625

: 4 (EI)5

: 0.8

0.625

= 1

0.35

5 1000 52 = 253 kgm

1"2

d

d

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2500 3.25 1.252 = !3"1 kgm

5

3000 3.0 3.02 = !438 kgm

6 2

3000 3.0 3.02 = 5850 kgm

6 2

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B

DB BD

0.35 0.00

0 0

!3530.8 !165.4

!344.8 !12.4

!33. !16.8

!3.3 !1.6

!0.32 !0.16

!0.03 !0.02

!0.003 !0.002

!0.0003 !0.00015

!3"12."0 !1"56.45

= 0.240

= !0.333

= 0.240

B

DB BD

0.38 0.00

0.240 0.240

0.024 0.012

0.002 0.001

0.000 0.000

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0.26 0.253

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N DENGAN GOYANGAN

!0.26

D

0.26

0.253

B

= 0.00

m = 0.00

!114

kgm

kgm

kgm

kgm

kgm

kgm

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EE BD DIA

2981

40

518

2983

1400 50 5" 22 40

1000 kg/m'

5

2500kg

600 150 5" 22 4030

11383

518

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M

3000

= 1200kg/m'

2461

608

63600 3600

1500 1500

4" 4"

410 410

5013

518 5013

2461608 115 4"2

5

608 115 4"2 577

5013

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. MMEN MAK7IMUM

B&g AC

M = 11383 + 4030 ! 1 1000

2

= 11383 + 4030 ! 500 2

d m = 0

d

= 4030 ! 2 500

= 4030

1000

= 4.03 m

Mm& = 11383 + 4030 ! 1 1000

2

= 11383 + 4030 4.03 ! 1 1000

2

= 1"504 kgm

Ak$% B9%& 9;

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2

2

4.032

! 3000 ! 3

2 ! 3000 ! "000

2

2

1.822 2

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3000 kg

1250

35006 35/50

40/60

2500kg

1400 kg/m'

4500

1 40/50 2

4.5 m 50/60

& = 0."

A

4 1.5 m

3 3

M>m9 I9;$&

I BA?K 40/50 = 1 40 50 3 = 41666

12

I BA?K 35/50 = 1 35 50 3 = 364583

12

I K?M 40/60 = 1 40 60 3 = 2000012

I K?M 50/60 = 1 50 60 3 = "00000

12

1 15.18 2"."8 3.48

K9k*& d& Agk& D$#;$%*$

Titi 1K1A = K12 = K16 = 3 5 EI : 4 4

4.5 5

@m

@m

@m

@m

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= 3.333 : 3.2

= ".33

D1A = 3.333 = 0.3425

".33

D12 = 3.2 = 0.3288 =

".33

D16 = 3.2 = 0.3288

".33

D

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Titi 2

K21 = K2B = K23 = K25 = 4 4 EI :

6

= 2.666 :

= 11."

D21 = 2.66 = 0.224

11."

D2B = 4 = 0.331

11."

D23 = 2 = 0.1685

11."

D25 = 3.2 = 0.20

11."

Titi 3

K32 = K3C = K34 = 4 4 EI : 4 5

8 5

= 2 : 4

= ".2

D32 = 2 = 0.214

".200

D3C = 4 = 0.4348 =

".200

D34 = 3.2 = 0.348

".200

Titi 4

K43 = K45 = 4 30 EI : 4 15.183 EI

5 8

= 24 : .5"15

= 31.6

D43 = 23."" = 0.6

31.6 = 1

D45 = .5"2 = 0.24

31.6

D

D

D

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Titi 5

K54 = K52 = K56 = 4 3.5 EI : 4 4

8 5

= 1.5 : 3.2

= .3

D54 = 1.5 = 0.2403

.283

D52 = 3.2 = 0.43"4 =

.283

D56 = 2.333 = 0.3204

.283

Titi 6

K65 = K61 = 4 3.5 EI : 4 4 EI

6 5

= 2.33 3.2

= 5.5

D65 = 2.333 = 0.422 0.211

5.5 = 1

D61 = 3.2 = 0.58

5.5

D

D

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3000 kg

kg/m'

5 35/50 4

40/60

2500 kg 2500 kg 2500 kg 40/60 5 m

40/50 3

50/60 50/60 5 m

B C

4 2 m

2 2 2 2

EI : 4 4 EI

5

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: 3.2

0.112

1

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4 5 EI : 4 4 EI : 4 4 EI

5 8 5

4 : 2 : 3.2

= 1

EI : 4 4 EI

5

: 3.2

1

0.38 0.38KKKK

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EI : 4 3.5 EI

6

: 2.333

1

0.1484

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M!"#$it%"# M&'!" P(i'!( )M*+

M65 = ! 3000 1.50 4.50 2 ! 5 1250 6

6 1"2

M56 = + 11 1250 6 2 + 3000 4.50 1.50

1"2 6

M54 = ! 11 1250 8 2 ! 3000 6.00 2.00

1"2 8

M45 = + 3000 2.0 6.0 2 + 5 1250 8

8 1"2

M12 = ! 1 1400 6 2 ! 2500 3 3

12 6

M21 = + 1 1400 6 2 + 2500 3 3

12 6

M23 = ! 2500 2 6 2 ! 2500 4 4

8 8

! 2500 6 2 2

8

M32 = + 2500 2 6 2 + 2500 4 4

8 8

2500 6 2 2

8

M61 = M16 = M43 = M34 = M52 = M25

= 6 4 EI - = 0."6

5 2

M1A = ! 3 5 EI - = !0.41

4.52

M2B = MB2 =

= ! 6 5 EI - = !1.2

5 2

M3C = MC3 =

= ! 6 5 EI - = !1.2

5 2

M61 = M16 = = M43 = M34

AKIBA ANAN -1 ( BAA)

AKIBA ANAN -2 ( AA7)

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= ! 6 4 EI - = 0."6

5 2

M52 = M25

= ! 6 4 EI - = 0."6

5 2

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2 = !1635" kgm

2 = 641 kgm

2 = !13583 kgm

2 = 2"083 kgm

2 = !15450 kgm

2 = 15450 kgm

2

= !50000 kgm

2

= 50000 kgm

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DISTRIBUSI MOMEN PRIMER TANPA GOYANGAN

TITIK B 1 2 3

BATANG B2 1A 16 12 21 25 23 2B 32 3C 34

A.D 0.000 0.342 0.32" 0.32" 0.225 0.20 0.16" 0.33 0.21 0.435 0.348

MOMEN 0 0 0 !15450 15450 0 !50000 0 50000 0 0

52"1.10 50".45 50".45 253".3

108"."8 35"6.66 1"3.32 8631."8 53"4."" 108"."8 26".4"

!52."" !11455."8 !22"11."5 !1832".56

!565.0"

883.31

380".80

!2536.46 !2435.00 !2435.00 !121.50

2043.43 681.14 1362.2" 1634.4 1021.2 2043.43 510.86

66.6 1533.53 306.06 2453.65

!64".42

!44.68

50".06

!40.60 !3"1.30 !3"1.30 !1"5.65

58.50 1".50 3".00 46.80 2".25 58.50 14.63

6".00 138.00 26.00 220.80

112.43

!"4.522

6.503

!32.88 !31.563 !31.563 !15.8113."2 4.641 ".282 11.138 6."61 13."23 3.481

!12.633 !25.266 !50.532 !40.426

2.30"

!15.3

.805

!4.262 !4.0"2 !4.0"2 !2.046

10.13 3.3 6.54 8.105 5.066 10.131 2.533

!3.244 !6.48 !12."5 !10.380

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5.165

!2.500

1.11"

!1.540 !1.48 !1.48 !0.3"

2.1" 0.28 1.45 1.48 1.0"3 2.185 0.546

!0.621 !1.242 !2.483 !1."86

0.8"6

!0.434

0.305

!0.354 !0.340 !0.340 !0.10

0.41 0.138 0.25 0.330 0.206 0.413 0.103

!0.10" !0.21 !0.435 !0.348

0.156

!0.0"6

0.06"

!0.01 !0.068 !0.068 !0.034

0.08 0.02 0.054 0.064 0.040 0.080 0.020

!0.01" !0.038 !0.0 !0.061

0.032

!0.020

0.014

!0.014 !0.013 !0.013 !0.00

0.008 0.005 0.010 0.012 0.008 0.016 0.004

!0.004 !0.008 !0.015 !0.0120.00

!0.004

0.003

!0.003 !0.003 !0.003 !0.001

0.002 0.001 0.002 0.002 0.002 0.003 0.001

!0.001 !0.002 !0.003 !0.003

0.001

!0.001

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0.001

12"18.66 230."1 6620.2 !8"28.18 2510.24 10360.61 !4844".52 12"18.6 43411."6 !1"635.42 !236.53

, ! 0.002 !0.002 0.001

12918.66 23-7.91 662-.27 8928.18 2517-.24 1-36-.62 48449.52 12918.67 43411.96 19635.42 23776.53

BATANG B2 1A 16 12 21 25 23 2B 32 3C 34

MOMENAKHIR

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4 5 6 C

43 45 54 52 56 65 61 C3

0.60 0.240 0.240 0.43" 0.320 0.422 0.58 0.000

0 2"083 !13583 0 641 !1635" 0 0

253".3 0.00

4315.""

!"164.8 !11456.0

!15130.18 !488.38 !23"4.1"

483.06 "66.12 166.62 1288.16 644.08

2."8 5555."6 61".61

!121.50

81.3

1226.82 1533.53

!12"8.83 !411.05 !205.53

!40.24 !814.4" !148".35 !1085."" !542.""

31.1" 42.38 1018.12

!1"5.65

23.40

110.40 138.00

225.485 1.361 35.681

!51.6"2 !103.383 !18".043 !13.844 !68."22

55.83 111.566 153.005

!15.815.56"

!20.213 !25.266

54.61" 1.286 8.643

!8.40" !16.818 !30.53 !22.424 !11.212

5.6"1 11.383 15.611

!2.046

4.052

!5.1"0 !6.48

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10.330 3.26" 1.635

!1.36 !2.34 !4.""" !3.645 !1.823

0.816 1.631 2.23

!0.3"

0.84

!0.""3 !1.242

1."3 0.56 0.284

!0.23 !0.44 !0.86 !0.632 !0.316

0.222 0.445 0.610

!0.10

0.165

!0.14 !0.21

0.312 0.0"" 0.04"

!0.052 !0.105 !0.1"2 !0.140 !0.00

0.051 0.101 0.13"

!0.034

0.032

!0.031 !0.038

0.063 0.020 0.010

!0.011 !0.022 !0.041 !0.030 !0.015

0.010 0.021 0.028

!0.00

0.006

!0.006 !0.0080.013 0.004 0.002

!0.002 !0.004 !0.008 !0.006 !0.003

0.002 0.004 0.006

!0.001

0.001

!0.001 !0.002

0.003 0.001 0.000

0.000 !0.001 !0.002 !0.001 !0.001

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0.000 0.001 0.001

!23""0.56 23""0.56 !16108.65 5218.83 1088".82 !""1.16 ""1.16 !"818

0.000 0.000 0.000 !

2399-.56 2399-.56 161-8.65 5218.83 /// 9917.16 9917.16 9818

43 45 54 52 56 65 61 C3

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IIK B 1 2 3

BAAN B2 1A 16 12 21 25 23 2B 32 3C 34

A.D 0.000 0.342 0.32" 0.32" 0.225 0.20 0.16" 0.33 0.21 0.435 0.348

MMEN 0.000 !0.41 0."60 0.000 0.000 0."60 0.000 !1.200 0.000 !1.200 0."60

!0.05 !0.02 !0.02 !0.036

0.04 0.031 0.062 0.04 0.04 0.0"3 0.023

0.024 0.04 0.0"4 0.05

!0.3"

!0.1"3

!0.22

0.06 0.064 0.064 0.032

0.023 0.015 0.031 0.03 0.023 0.046 0.012

0.040 0.080 0.160 0.128

0.016

0.031

!0.016

0.000 0.000 0.000 0.000

!0.012 !0.008 !0.016 !0.01" !0.012 !0.024 !0.006

!0.001 !0.002 !0.004 !0.003

!0.006

0.005

!0.0010.003 0.003 0.003 0.001

!0.001 !0.001 !0.001 !0.001 !0.001 !0.002 0.000

0.001 0.001 0.003 0.002

!0.001

0.000

!0.001

0.000 0.000 0.000 0.000

0.000 0.000 0.000 0.000 0.000 0.000 0.000

DISTRIBUSI MOMEN AKIBAT GOYANGAN ,1

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0.000 0.000 0.001 0.001

0.000

0.000

0.000

0.000 0.000 0.000 0.000

0.056 !0.45 0.12 0.033 0.03 0.8"4 0.120 !1.08 0.155 !0."4 0."2

- ! 0.000 0.000 0.000

-.-56 -.745 -.712 -.-33 -.-73 -.894 -.12- 1.-87 -.155 -.947 -.792

BATANG B2 1A 16 12 21 25 23 2B 32 3C 34

MMENAKI

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4 5 6 C

43 45 54 52 56 65 61 C3

0.60 0.240 0.240 0.43" 0.320 0.422 0.58 0.000

0."60 0.000 0.000 0."60 0.000 0.000 0."60 !1.200

!0.036 0.000

0.03

0.038 0.04

!0.58 !0.240 !0.120

!0.105 !0.211 !0.385 !0.281 !0.141

!0.165 !0.330 !0.453

0.032

0.018

0.064 0.080

0.032 0.010 0.005

0.01 0.034 0.062 0.045 0.023

!0.012 !0.023 !0.032

0.000

!0.010

!0.002 !0.002

!0.012 !0.004 !0.002

0.003 0.006 0.010 0.00 0.004

!0.001 !0.002 !0.0020.001

!0.001

0.001 0.001

!0.003 !0.001 0.000

0.000 0.000 0.001 0.001 0.000

0.000 !0.001 !0.001

0.000

0.000

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0.000 0.000

0.000 0.000 0.000

0.000 0.000 0.000 0.000 0.000

0.000 0.000 0.000

0.000

0.320 !0.320 !0.288 0.6"3 !0.405 !0.40 0.40 !1.03

0.000 0.000 0.000 !

-.32- -.32- -.288 -.693 -.4-5 -.47- -.47- 1.-73

43 45 54 52 56 65 61 C3

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IIK B2 1 2 3

BAAN B2 1A 16 12 21 25 23 2B 32 3C 34

A.D 0.000 0.342 0.32" 0.32" 0.225 0.20 0.16" 0.33 0.21 0.435 0.348

MMEN 0.000 0.000 0."60 0.000 0.000 0."60 0.000 0.000 0.000 0.000 0."60

!0.32" !0.316 !0.316 !0.158

!0.135 !0.0"0 !0.180 !0.216 !0.135 !0.20 !0.068

!0.0" !0.1"4 !0.388 !0.310

!0.306

!0.166

!0.1"

0.0"8 0.0"4 0.0"4 0.04

0.036 0.024 0.048 0.058 0.036 0.03 0.018

0.031 0.062 0.125 0.100

0.015

0.024

!0.01"

!0.002 !0.002 !0.002 !0.001

!0.00" !0.006 !0.012 !0.015 !0.00" !0.018 !0.005

!0.001 !0.002 !0.005 !0.004

!0.004

0.005

!0.0010.002 0.002 0.002 0.001

!0.001 !0.001 !0.001 !0.001 !0.001 !0.002 0.000

0.001 0.001 0.002 0.002

!0.001

0.000

0.000

0.000 0.000 0.000 0.000

0.000 0.000 0.000 0.000 0.000 0.000 0.000

DISTRIBUSI MOMEN AKIBAT GOYANGAN ,2

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0.000 0.000 0.001 0.000

0.000

0.000

0.000

0.000 0.000 0.000 0.000

!0.10" !0.230 0.523 !0.2"3 !0.256 0.64" !0.15 !0.218 !0.18 !0.265 0.452

- ! 0.000 0.000 0.000

-.1-9 -.23- -.523 -.293 -.256 -.649 -.175 -.218 -.187 -.265 -.452

BATANG B2 1A 16 12 21 25 23 2B 32 3C 34

MMENAKI

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4 5 6 C

43 45 54 52 56 65 61 C3

0.60 0.240 0.240 0.43" 0.320 0.422 0.58 0.000

0."60 0.000 0.000 0."60 0.000 0.000 0."60 0.000

!0.158 0.000

!0.108

!0.155 !0.1"4

!0.611 !0.1"3 !0.0"

!0.0"1 !0.181 !0.332 !0.242 !0.121

!0.144 !0.28 !0.3"4

0.04

0.02"

0.050 0.062

0.031 0.010 0.005

0.013 0.026 0.048 0.035 0.018

!0.014 !0.02 !0.03

!0.001

!0.00

!0.002 !0.002

!0.00" !0.003 !0.001

0.003 0.005 0.010 0.00 0.004

!0.001 !0.001 !0.0020.001

!0.001

0.001 0.001

!0.003 !0.001 0.000

0.000 0.000 0.001 0.001 0.000

0.000 !0.001 !0.001

0.000

0.000

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0.000 0.000

0.000 0.000 0.000

0.000 0.000 0.000 0.000 0.000

0.000 0.000 0.000

0.000

0.262 !0.262 !0.243 0.600 !0.35 !0.416 0.416 !0.133

0.000 0.000 0.000 !

-.262 -.262 -.243 -.6-- -.357 -.416 -.416 -.133

43 45 54 52 56 65 61 C3

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= 1250kg/m'

858" 3000 kg

6

2250 2813

50 "38

1432 1432

2000 2000

6431 31"858"

6"4

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kg/m' 3000 kg 24462

8

2250

1250

3058

1"42

24462

20"48

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3000 kg

1250

35006 35/50

40/60

2500kg

1400 kg/m'

4500

1 40/50 2

4.5 m 50/60

& = 0."0

A

4 1.5 m

3 3

M>m9 I9;$&

I BA?K 40/50 = 1 40 50 3 = 41666

12

I BA?K 35/50 = 1 35 50 3 = 364583

12

I K?M 40/60 = 1 40 60 3 = 2000012

I K?M 50/60 = 1 50 60 3 = "00000

12

K9k&k*& A%>*d

K16 = K25 = K34 = 20000 = 1440

500

K2B = K3C = "00000 = 1800

500

K1A = "00000 = 2000450

K21 = 41666 = 6"4.44

@m

@m

@m

@m

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600

K23 = 41666 = 520.83

800

K54 = 364583 = 455.3

800

K56 = 364583 = 60.64

600

K!0%0" R!0ti

D$&m%$ K9k&k*& 7#&d&; K = 1000

K16 = K25 = K34 = 1.440

K2B = K3C = 1.800

K1A = 2.000

K21 = 0.6"4

K23 = 0.521

K54 = 0.456

K56 = 0.608

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3000 kg

kg/m'

5 35/50 4

40/60

2500 kg 2500 kg 2500 kg 40/60 5 m

40/50 3

50/60 50/60 5 m

B C

4 2 m

2 2 2 2

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M!"#$it%"# M&'!" P(i'!( )M*+

M65 = ! 3000 1.50 4.50 2 ! 5 1250 6

6 1"2

M56 = + 11 1250 6 2 + 3000 4.50 1.50

1"2 6

M54 = ! 11 1250 8 2 ! 3000 6.00 2.00

1"2 8

M45 = + 3000 2.0 6.0 2 + 5 1250 8

8 1"2

M12 = ! 1 1400 6 2 ! 2500 3 3

12 6

M21 = + 1 1400 6 2 + 2500 3 3

12 6

M23 = ! 2500 2 6 2 ! 2500 4 4

8 8

! 2500 6 2 2

8

M32 = + 2500 2 6 2 + 2500 4 4

8 8

2500 6 2 2

8

M!"#$it%"# Ni0i )t$&+

= !15450 kgm

= 15450 + !50000 = !34550 kgm

= 50000 kgm

= 2"083 kgm

= !13583 + 641 = !5"43 kgm

= !1635" kgm

1 = 2 2 + 0.6"4 + 1.44 ! 0.5 2 =

1A = 0.5 2 = 0.138

.26"

12 = 0.6"4 = 0.0"6

.26" = 0.431

16 = 1.440 = 0.1"8

1

2

3

4

5

6

M!"#$it%"# 0" M*

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.26"

2 = 2 1.8 + 0.521 + 0.6"4 + 1.44 =

2B = 1.8 = 0.202 0.60602

8."106

23 = 0.5208 = 0.0588."106 = 0.50

21 = 0.6"44 = 0.08

8."106

25 = 1.44 = 0.16

8."106

3 = 2 1.8 + 0.521 + 1.44 = .5

3C = 1.8 = 0.23"

.521 32 = 0.5208 = 0.06" = 0.5

.521

34 = 1.44 = 0.1"1

.521

4 = 2 1.44 + 0.456 = 3."1

43 = 1.44 = 0.38

3."15 = 0.5

45 = 0.455 = 0.12

3."15

5 = 2 1.44 + 0.456 + 0.608 = 5.00

52 = 1.44 = 0.288

5.006

54 = 0.455 = 0.0"1 = 0.5

5.006

56 = 0.606 = 0.121

5.006

6 = 2 0.608 + 1.44 = 4.0"5

65 = 0.606 = 0.148

4.0"53 = 0.5

61 = 1.44 = 0.352

4.0"53

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= ! !15450 = 2125.5 kgm

.2

= ! !34550 = 38.4 kgm

8."

= ! 50000 = !664.5 kgm

.52

= ! 2"083 = !60.8 kgm

3."

= ! !5"43 = 1186." kgm

5.00

= ! !1635" = 3""4. kgm

4.0"5

: ; -.9

T II = 2 1.440 + 1.440 + 1.440 = 8.64

#61 = 3 1.440

= 0.508.640

#52 = 3 1.440

= 0.5t ; 1.5

8.640

#43 = 3 1.440

= 0.58.640

=!5 3500

= !2025 kgm8.640

T I = 22.000 + 1.800 + 1.800

= 8.4352.0 0." 2

#1A=

3 2.000= 0.3"5

2 0."0

8.435

#2B=

3.0 1.800= 0.640

8.435 t ; 1.68

#3C=

3.00 1.800=

0.640

8.435

=!5 3500 + 4500

= !16"66 kgm8.43

' -1

' -2

' -3

' -4

' -5

' -6

' -II

' -I

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2 = !1635" kgm

2 = 641 kgm

2 = !13583 kgm

2 = 2"083 kgm

2 = !15450 kgm

2 = 15450 kgm

2

= !50000 kgm

2

= 50000 kgm

.2

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6 !0.148 !0.121

!0.352

= !2025 = 3""5

!0.500 335 + 3"58 = !3658 !0.148 !280 = 42

!0.500 !280 + 520 = !3620

!0.500 !656" + !1252 = 3"10 !0.352 !2025 + 3"58 = !680

= !53"3 = 335

!0.500

!0.1"8

1 !0.0"6 !0.08

!0.138

= !16"66 = 2125

!0.3"5 3"58 = !1564 !0.138 1.111 !16"66 = 25"3

!0.640 520 = !4815 !0.0"6 38 = !30

m 0II m 06

m 1II m 16

m 0I m 01

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!0.640 !1252 = 801 !0.1"8 !2025 + 3""5 = !3"0

= !22544 = 3"58

!0.3"5

& = 0."0

A

m 1I m 11

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5 !0.0"1 !0.120 4

!0.288 !0.380

= 118 =

!0.0"1 !656" = 5"8 !0.120 118 =

!0.288 !2025 + 520 = !1580

!0.121 3""5 = !485 !0.380 !2025 + !1252 =

= !280 =

!0.500 !0.500

!0.162 !0.1"1

2 !0.058 !0.06" 3

!0.202 !0.23"

= 38 =

!0.202 !16"66 = 342 !0.23" !16"66 =

!0.08 3"58 = !308 !0.06" 520 =

m 05 m 04

m 15 m 14

m 02 m 03

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!0.162 !2025 + 118 = 136

!0.058 !664 = 38" !0.1"1 !2025 + !61 =

= 520 =

!0.640 !0.640

B C

m 12 m 13

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61

!143

1245

656"

664

4060

!521

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1856

1252

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TABE< HASI< ITERASI

N>

0 2125 38 !664 !61 118 3""5 !2025 !16"66

1 3"58 520 !1252 !656" !280 335 !53"3 !22544

2 5256 "012 414 !546 262 4004 !8626 !2508

3 6014 "802 142 !4"68 815 4"2 !10"6 !26532

4 6468 102"0 2040 !438 11"8 53"" !12534 !241

5 64 10603 241 !3"2 144" 5815 !13554 !2"68

6 6"21 10803 2653 !305 1610 6088 !14211 !28316

031 10"31 2802 !3531 113 6265 !14631 !2853

8 101 11013 28"6 !3420 18 63" !148"" !286

" 145 11065 2"56 !334" 1820 6451 !1500 !286

10 13 110"8 2""4 !3303 184 64" !151" !28823

11 1"1 1111" 301" !324 1864 652 !15248 !28860

12 202 11132 3034 !3256 185 6546 !152"2 !28883

13 210 11141 3044 !3244 1882 655 !15320 !288"

14 214 11146 3050 !323 1886 6565 !15338 !28"0

15 21 11150 3054 !3232 188" 650 !15350 !28"12

16 21" 11152 305 !322" 18"1 653 !1535 !28"16

1 220 11154 3058 !322 18"2 655 !15361 !28"1"1" 221 11154 305" !3226 18"3 656 !15364 !28"20

20 222 11155 3060 !3225 18"3 65 !15366 !28"21

21 222 11155 3060 !3225 18"3 658 !1536 !28"22

22 222 11156 3061 !3224 18"4 658 !15368 !28"22

23 222 11156 3061 !3224 18"4 658 !1536" !28"22

24 222 11156 3061 !3224 18"4 658 !1536" !28"23

25 222 11156 3061 !3224 18"4 658 !1536" !28"23

26 222 11156 3061 !3224 18"4 658 !1536" !28"23

m 01 m 02 m 03 m 04 m 05 m 06 m 0II m 0I

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2 222 11156 3061 !3224 18"4 658 !1536" !28"23

28 222 11156 3061 !3224 18"4 658 !1536" !28"23

2" 222 11156 3061 !3224 18"4 658 !1530 !28"23

30 222 11156 3061 !3224 18"4 658 !1530 !28"23

31 222 11156 3061 !3224 18"4 658 !1530 !28"23

32 222 11156 3061 !3224 18"4 658 !1530 !28"23

33 222 11156 3061 !3224 18"4 658 !1530 !28"23

34 222 11156 3061 !3224 18"4 658 !1530 !28"23

35 222 11156 3061 !3224 18"4 658 !1530 !28"2336 222 11156 3061 !3224 18"4 658 !1530 !28"23

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TITIK 1

M 1A = 0 + 2.00 1.50 222 + 1 0.500

0."00

M 16 = 0 + 1.44 2 222 + 658 +

M 12 = !15450 + 0.6"4 2 222 + 11156

TITIK 2

M 21 = 15450 + 0.6"4 2 11156 + 222

M 2B = 0 + 1.800 2 11156 + !28"23

M 23 = !50000 + 0.521 2 11156 + 3061

M 25 = 0 + 1.440 2 11156 + 18"4 +

TITIK 3

M 32 = 50000 + 0.521 2 3061 + 11156

M 3C = 0 + 1.800 2 3061 + !28"23

M 34 = 0 + 1.440 2 3061 + !3224 +

TITIK 4M 45 = 2"083 + 0.456 2 !3224 + 18"4

M 43 = 0 + 1.440 2 !3224 + 3061 +

TITIK 5

M 56 = 641 + 0.608 2 18"4 + 658

M 52 = 0 + 1.440 2 18"4 + 11156 +

M 54 = !14025 + 0.456 2 18"4 + !3224

TITIK 6

M 61 = 0 + 1.440 2 658 + 222 +

M 65 = !1635" + 0.608 2 658 + 18"4 +

MOMEN PER

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TAKABEYA

!28"23 = !1040 = !1046" kgm

!1536" = 8141 = 8141 kgm

= 2328 = 2328 kgm

= 0 0 kgm

= 35"60 = 35"60 kgm

= !11"00 = !11"00 kgm

= !3685 = !3685 kgm

!1530 = 1224 = 1224 kgm

= !1 0 kgm

= 58""" = 58""" kgm

=

= !41041 = !41041 kgm

=

!1536" = !1"58 = !1"58 kgm

= 0 0 kgm

= 2008 = 2008 kgm

!1536" = !2008 = !2008 kgm

= 0 0 kgm

= 13"3" = 1408 kgm

!1530 = !613 = !466 kgm

= !1368 = !13621 kgm= !442 0 kgm

!1530 = 214 = 214 kgm

0 = !214 = !214 kgm

= 0 0 kgm

!28"23 = !16 kgm

!1536" = !12308 kgm

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KN? = 0.000

= 0.000

M1A + MB2 + M2B + M3C + MC3 !

!1 !2 !1

!1040 + !16 + !11"00 + !41041 + !12308 !!4.5 !5.0 !5

232 + 5"33 + 1060 ! 8000

18"30 ! 8000 = 10"30

BAGAN MOMEN )#'+

5719 21292 13621 12412

6 5 4

5719 1-586

8279 1288-

2328 23941 36785 14797

1 2 3

285 8147

1-291 -

A B

MMEN ?AFANAN

BAAN 1!2 ( DAI IIK 1)

M = 2"14 + 524 ! 1

2

= 2"14 + 524 ! 1 1500 2

= 2"14 + 524 ! 50

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dm 524 ! 2 50

d

= 524

1500= 5.02 m9#9;

M m& = 2"14 + 524 5.02 ! 1 1500 5.02

2

= 2185 kgm

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1 + 2 = 0

3500 + 4500 = 0

OK

12412

512-

9676

17682

C

G

G

G

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2

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BAAN 2!3 (DAI IIK 2)

M3 = !2328 + 4"4" 3 ! 0

M6 = !2328 + 4"4" 6 ! 2000 3

M" = !2328 + 4"4" " ! 2000 6 !

BAAN 5!4 ( DAI IIK 5 )

( & ) Ak$% B9%& M9;&

M = 13621 + 4"4 ! 1

2

= 13621 + 4"4 ! 1 1200

2

= 13621 + 4"4 ! 600 2

dm 4"4 ! 2 600

d

= 4"4

1200

= 4.145 m9#9;

M m& = 13621 + 4"4 4.1446 ! 1 1200 4.145

2

= 23"28 kgm

( % ) Ak$% B9%& 9;

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= 1251" kgm

=

= 21366 kgm

2000 3 = 24214

2

2

2

1140 kgm

2

2