portal 7 frame 2d metode kekakuan

8/18/2019 Portal 7 Frame 2d Metode Kekakuan

1/81

PENYELESAIAN UAS "MEKANIKA REKAYASA V" (reguler)

Semester Gasal 2005/200 ! gl# 2$ %a&uar' 200

SEP $ 's*ret'+e a&, Gl-.al egrees - ree,-m (1)

Defined DOF

after boundary condit

PENYELESAIAN

Pr-ert'es e&ama&g

Bahan / material :

E = 2.00E+06

Batang 1 :

0.30m

0.50m

0.15m2

E = 2.00E+06t/m2

3.13E-03m4

t/m2

b1 =

h1 =

A1 =

I1 =

versi le

45o

6m

3m

Rigid !nneti!n

P2 = 5 tP1 (ton)

45o

3mA

B

C

D

fixed

fixed

fixed

q = 3t/m

"

#

gl!bal a$i%

&1

&2

A '

B

''"

R'(

&3

)

''#


2/81

6 m

0 degree%

Batang 3 :

0.30m

0.50m

0.15m2

E = 2.00E+06t/m2

3.13E-03m4

4.242641m

315degree%

Re3a Eleme& ,alam Matr'3s Ke3a3ua& 4ata&g

Batang EA / L 4.EI / L 2.EI / L 6.EI / L^2 12.EI / L^3 Sudut (deg) )$1 5.00E+04 4.1*E+03 2.0E+03 1.04E+03 3.4*E+02 0 1

2 *.0*E+04 5.,E+03 2.,5E+03 2.0E+03 ,.2E+02 45 0.*0*10*

3 *.0*E+04 5.,E+03 2.,5E+03 2.0E+03 ,.2E+02 315 0.*0*10*

ata .e.a&

1 = 1 !n

2 = 5 !n

= 3 !n/m

= 0 !n.m

Gaa ,a& M-me& U6u&g a,a Eleme&t 7$

a = 0 b = 0

a = , b = ,

a = , .m b = -, .m

Gaa ,a& M-me& U6u&g a,a Eleme&t 72

a = 0 b = 0

a = 0 b = 0

a = 0 .m b = 0 .m

Gaa ,a& M-me& U6u&g a,a Eleme&t 78

a = 0 b = 0

a = 0 b = 0

a = 0 .m b = 0 .m

Re3a Gaa U6u&g 4ata&g (Sum.u L-3al)

!. Btgng 7iri 8i9 ng 7anan 89

Beban FX(i) Beban FY(i) Beban MZ(i) Beban FX() Beban FY() Beban MZ()

1 0 , , 0 , -,

2 0 0 0 0 0 0

3 0 0 0 0 0 0

1 =

theta1 =

b3 =

h3 =

A3 =

I3 =

3 =

theta3 =


3/81

4e.a& atau M-me& a,a 't'3 %-'&t Stru3tur ,alam Ara9 Sum.u Gl-.al/Sum.u S

!. iti7 : 1 2

'i%. ;b ? %e%ai %mb gl!bal %tr7tr

. @e%e%aian %b l!7al element dengan '>? arah gl!bal

d.

a. 'i%laement titi7 %mb gl!bal %tr7tr ada tia element

Eleme&t ' 6

1 1 2 3 10 11 122 10 11 12 4 5 6

3 10 11 12 * ,

b. '>? %e%ai %mb gl!bal %tr7tr

? 0 0 0 d1 0 d2

Element &2!al a$i% 1 2 3 4 5 6


4/81

0 0 1 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0 0 1

Element 2:

R = 0 0 0 0

0 0 0 0

0 0 1 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0 0 1

Element 3:

R = 0 0 0 00 0 0 0

0 0 1 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0 0 1

:::; ALAM SUM4U L1KAL

Batang = 1

Elemen dalam matri7% 7e7a7an batang :

EA / 4.EI / 2.EI / 6.EI / D2 12.EI / D3

5.00E+04 4.1*E+03 2.0E+03 1.04E+03 3.4*E+02

)$ = !% theta = 1

) = %in theta = 0

!al a$i% 1 2 3 4 5 6

1 50000 0 0 -50000 0 0

2 0 34*.2222 1041.66* 0 -34*.2222 1041.66*

3 0 1041.66* 4166.66* 0 -1041.66* 203.3334 -50000 0 0 50000 0 0

5 0 -34*.2222 -1041.66* 0 34*.2222 -1041.66*

6 0 1041.66* 203.333 0 -1041.66* 4166.66*

:::; ALAM SUM4U L1KAL

Batang = 2

Elemen dalam matri7% 7e7a7an batang :

EA / 4.EI / 2.EI / 6.EI / D2 12.EI / D3

*.0*E+04 5.,E+03 2.,5E+03 2.0E+03 ,.2E+02

)$ = !% theta = 0.*0*10*

) = %in theta = 0.*0*10*

!% α1

%in α1

- %in α1

!% α1

!% α1

%in α1

- %in α1

!% α1

!% α1

%in α1

- %in α1

!% α1

!% α1

%in α1

- %in α1

!% α1

!% α1

%in α1

- %in α1

!% α1

;1C =


5/81


6/81

N-,al -r*es

a# ! A3'.at .e.a& ,' sea&6a&g .e&ta&g (3e,ua u6u&g ,'3e3a&g)

Eleme&t $ ran%!rm

!al a$i%

0 1

, 2

= , 3

0 4

, 5

-, 6

Eleme&t 2 ran%!rm

!al a$i%

0 1

0 2

= 0 30 4

0 5

0 6

Eleme&t 8 ran%!rm

!al a$i%

0 1

0 2

= 0 3

0 40 5

0 6

Susu& matr'3s .e.a& e3'?ale&

G!int ;b


7/81

1 2 0 2

1 3 0 3

2 4 0 4

A = 2 5 0 5

2 6 0 6

3 * 0 *

3 0 3 , 0 ,

4 10 0 d1

4 11 -5 d2

4 12 0 d3

*# ! 4e.a& 3-m.'&as' atau ga.u&ga& (Ae @ A6)

G!int ;b


8/81


9/81

0 *0*10.6 0 0 -*0*10.6

0 0 ,2.0,2 203.333 0

0 + 0 203.333 5,2.55* 0

0 -*0*10.6 0 0 *0*10.6

0 0 -,2.0,2 -203.333 0

0 0 203.333 2,46.2* 0

SELESAI A4LE Eleme&t -r*es ! ra

rame Stat'-& ututas

?rame 1 l!al a$i% !int e$t m e$t

0 1 1 1 0 'EA'

B#CD 2 1 1 6 'EA'

$0#8 3 1 2 0 'EA'

0 4 2 2 4.24264 'EA'

C#8$88 5 2 3 0 'EA'

!#820D2 6 2 3 4.24264 'EA'

?rame 2 l!al a$i% !int

!$0#B5C 1 2 A4LE Eleme&t %-'&t -r*es

$#0C$B 2 2 rame %-'&t ututas

8#$80 3 2 e$t e$t e$t

$0#B5C 4 3 1 1 'EA'

!$#0C$B 5 3 1 2 'EA'

$#2B 6 3 2 2 'EA'

2 3 'EA'

?rame 3 l!al a$i% !int 3 2 'EA'

$0#B5C 1 2 3 4 'EA'

$#0C$B 2 2

8#$80 3 2

!$0#B5C 4 4

!$#0C$B 5 4

$#2B 6 4

*.42163*

0.*64,,

.166 6.6566

A3C =


10/81

ons

Batang 2 :

0.30m

0.50m

0.15m2

E = 2.00E+06t/m2

3.13E-03m4

b2 =

h2 =

A2 =

I2 =

gkap


11/81

4.242641m

45 degree%

)0

0.*0*10*

-0.*0*10*

2 =

theta2 =

45o

6m

Rigid !nneti!n

P2 = 5 tP1 (ton)

45o

A

Dfixed

fixed

q = 3 t/m

#


12/81

ru3tur

3 4

, 10 11 12

0 0 0 -5 0

==F ? %e%ai %b gl!bal

, === '>? %e%ai %b gl!bal

raian %b gl!bal :

raian %b 4 = 1.)$ + 2.)

raian %b 5 = 1.) + 2.)$

raian %b * = 4.)$ + 5.)

raian %b = 4.) + 5.)$

RC = 1 0 0 0 0 0

0 1 0 0 0 0

l

"

gl!bal a$i%

&1 A

R'(


13/81

0 0 1 0 0 0

0 0 0 1 0 0

0 0 0 0 1 0

0 0 0 0 0 1

RC = 0.*0*10* 0.*0*10* 0 0 0 0

-0.*0*10* 0.*0*10* 0 0 0 0

0 0 1 0 0 0

0 0 0 0.*0*10* 0.*0*10* 0

0 0 0 -0.*0*10* 0.*0*10* 0

0 0 0 0 0 1

RC = 0.*0*10* -0.*0*10* 0 0 0 00.*0*10* 0.*0*10* 0 0 0 0

0 0 1 0 0 0

0 0 0 0.*0*10* -0.*0*10* 0

0 0 0 0.*0*10* 0.*0*10* 0

0 0 0 0 0 1

1 2 3 d1 d2


14/81


15/81

%i %b l!7al 7e gl!bal ==F

1 0 0 0 0 0 0

0 1 0 0 0 0 ,

= 0 0 1 0 0 0 $ ,

0 0 0 1 0 0 0

0 0 0 0 1 0 ,

0 0 0 0 0 1 -,


0.*0*10* -0.*0*10* 0 0 0 0 0

0.*0*10* 0.*0*10* 0 0 0 0 0

= 0 0 1 0 0 0 $ 00 0 0 0.*0*10* -0.*0*10* 0 0

0 0 0 0.*0*10* 0.*0*10* 0 0

0 0 0 0 0 1 0


-0.*0*10* 0.*0*10* 0 0 0 0 0

0 0 1 0 0 0 0

= 0 0 0 0.*0*10* 0.*0*10* 0 $ 0

0 0 0 -0.*0*10* 0.*0*10* 0 00 0 0 0 0 1 0

0 0 0 0 0 0 0

Element 3

0 0 0 1 1

0 , -, 2 2

0 , -, 3 3

0 0 0 4 40 = 0 Ae = 0 5 5

0 0 0 6 6

0 0 0 * *

0 0 0

0 0 0 , ,

0 0 0 10 d1

0 , -, 11 d2

0 -, , 12 d3

AMS 1 & . AM

L 1

AMS 2 & . AM

L 2

AMS 3 & . AM

L 3

# B


16/81

ata lang A :

0 d1 0

-, d2 -14

-, d3 ,

0 1 0

= 0 A = 2 -,

0 3 -,

0 4 0

0 5 0

0 6 0

0 * 0

-14 0

, , 0

A4LE %-'&t 'sla*eme&ts

%-'&t ututas asee U$ U2 U8 R$ R2 R8

e$t e$t e$t m m m Radian% Radian% Radian%

1 'EA' in;tati 0 0 0 0 0 0

2 'EA' in;tati 0 0 -0.00021 0 -0.0005, 0

3 'EA' in;tati 0 0 0 0 0 0

4 'EA' in;tati 0 0 0 0 0 0

'e!rma%i %tr7tr dalam arah ;B >@A di batang 1H %bb :

1 0 0 0 0 0 0

0 1 0 0 0 0 0

0 0 1 0 0 0 $ 0

0 0 0 1 0 0 0

0 0 0 0 1 0 -0.00021

0 0 0 0 0 1 0.0005,

∆M 1 & . %MS 1

∆M 1 &

"

gl!bal a$i%

&1

&2

A '

''"

R'(

&3

)

'#


17/81

0 0 0 0 0

-34*.2222 1041.66* 0 , 0.66*03,1

-1041.66* 203.333 $ 0 = , + 1.4462,51, =

0 0 0 0 0

34*.2222 -1041.66* -0.00021 , -0.66*03,

-1041.66* 4166.66* 0.0005, -, 2.6*3,22


0.*0*10* 0.*0*10* 0 0 0 0 0-0.*0*10* 0.*0*10* 0 0 0 0 -0.00021

0 0 1 0 0 0 $ 0.0005,

0 0 0 0.*0*10* 0.*0*10* 0 0

0 0 0 -0.*0*10* 0.*0*10* 0 0

0 0 0 0 0 1 0

0 0 -0.00014 0 -10.4,5*

-,2.0,2 203.333 -0.00014 0 1.0153*

-203.333 2,46.2* $ 0.0005, = 0 + 3.1630356 =

0 0 0 0 10.4,5*03

,2.0,2 -203.333 0 0 -1.0154

-203.333 5,2.55* 0 0 1.426,004


0.*0*10* -0.*0*10* 0 0 0 0 0

0.*0*10* 0.*0*10* 0 0 0 0 -0.00021

0 0 1 0 0 0 $ 0.0005,

0 0 0 0.*0*10* -0.*0*10* 0 0

0 0 0 0.*0*10* 0.*0*10* 0 0

0 0 0 0 0 1 0

∆M 2 & . %MS 2

∆M 2 &

∆M 3 & . %MS 3

∆M 3 &


18/81

0 0 0.00014 0 10.4,5*03

-,2.0,2 203.333 -0.00014 0 1.0153*

-203.333 2,46.2* $ 0.0005, = 0 + 3.1630356 =

0 0 0 0 -10.4,5*

,2.0,2 -203.333 0 0 -1.0154

-203.333 5,2.55* 0 0 1.426,004

es

asee P V2 V8 M2 M8 rameElem lemStat'-

e$t !n !n !n !n-m !n-m !n-m e$t m

in;tati 0 -,.66* 0 0 0 -10.4463 1-1 0

in;tati 0 .3133 0 0 0 -6.3260* 1-1 6

in;tati 10.4,5 -1.01, 0 0 0 -3.16304 2-1 0

in;tati 10.4,5 -1.01, 0 0 0 1.426, 2-1 4.24264

in;tati -10.4,5 -1.01, 0 0 0 -3.16304 3-1 0

in;tati -10.4,5 -1.01, 0 0 0 1.426, 3-1 4.24264

! rames

asee $ 2 8 M$ M2 M8 rameElem

e$t !n !n !n !n-m !n-m !n-m e$t

in;tati 0 0 ,.66* 0 -10.4463 0 1

in;tati 0 0 .3133 0 6.3260* 0 1

in;tati -.166 0 -6.6566 0 -3.16304 0 2

in;tati .166 0 6.6566 0 -1.426, 0 2

in;tati .166 0 -6.6566 0 -3.16304 0 3

in;tati -.166 0 6.6566 0 -1.426, 0 3

-*.42163*

0.*64,,

-.166 -6.6566


19/81


20/81

3m

3m

B

C

fixed

B


21/81

1 0 0 0 0 0

0 1 0 0 0 0

RC =

&2

'

''"

&3

)

''#


22/81

0 0 1 0 0 0

0 0 0 1 0 0

0 0 0 0 1 0

0 0 0 0 0 1

0.*0*106*12 -0.*0*10* 0 0 0 0

0.*0*106*12 0.*0*10* 0 0 0 0

0 0 1 0 0 0

0 0 0 0.*0*10* -0.*0*10* 0

0 0 0 0.*0*10* 0.*0*10* 0

0 0 0 0 0 1

0.*0*106*12 0.*0*10* 0 0 0 0-0.*0*106*12 0.*0*10* 0 0 0 0

0 0 1 0 0 0

0 0 0 0.*0*10* 0.*0*10* 0

0 0 0 -0.*0*10* 0.*0*10* 0

0 0 0 0 0 1

d3

12

0 - - - - - -

1041.666* - - - - - -

203.3333 - - - - - -0 - - - - - -

-1041.66* - - - - - -

4166.666* - - - - - -

6

RC =

RC

=


23/81

6

-14*3.13, 80.339 80.329 0.01 0.33 0.32 0.01

14*3.13,1 80.329 80.339 80.019 0.32 0.33 80.019

2,46.2*3 0.01 80.019 - 80.019 0.01 -

14*3.13,1 0.33 0.32 80.019 80.339 80.329 80.019

-14*3.13, 0.32 0.33 0.01 80.329 80.339 0.015,2.5565 0.01 80.019 - 80.019 0.01 -

,

,

14*3.13,1

14*3.13,1

2,46.2*3

-14*3.13,

-14*3.13,

5,2.5565

)e7: >@

1216,3.42 0.00 0.00 80.659 - -

0.00 *2040.65 1,04.63 - 80.659 80.0190.00 1,04.63 15,51.* - 80.019 -


24/81


25/81

0 -

-14 -

, -

- ===F 0

0.00 ===F .44E-00

0.00 ===F 2.64E-00*

%b l!7al '>?

0 1 1 - 0

0 2 2 - 0

= 0 3 3 - 0

0 4 d1 - 0

-0.00020,,156 5 d2 - -0.00021

0.0005,263, 6 d3 - 0.0005,


26/81

%b l!7al '>? / %b gl!bal )e7 :

0 1 1 0 -

B#CD08B 2 2 ,.66*03 0.00

$0#2B5 3 3 10.4462, 0.00

0 4 d1 0 -

C#8$82B$ 5 d2 .3132,* 80.009

!#820D2 6 d3 -6.3260*4 0.00

%b l!7al '>?

-0.00014432* 1 $)+d2)$) 80.009 0-0.00014432* 2 $)+d2)$) 0.00 0

= 0.0005,263, 3 d3 - 0

0 4 4 - 0

0 5 5 - 0

0 6 6 - 0

%b l!7al '>? / %b gl!bal )e7 :!$0#B5DC 1 $)+d2)$) 0 810.509

$#0C$C5C 2 $)+d2)$) 0 1.0

8#$8085B 3 d3 0 3.16

$0#B5DC 4 4 0 10.50

!$#0C$C5C 5 5 0 81.09

$#2B005 6 6 0 1.43

%b l!7al '>?

0.00014432* 1 d1 80.009 0

-0.00014432* 2 d2 0.00 0

= 0.0005,263, 3 d3 - 0

0 4 * - 0

0 5 - 0

0 6 , - 0

%b l!7al '>? / %b gl!bal )e7 :


27/81

$0#B5DC 1 d1 0 10.50

$#0C$C5C 2 d2 0 1.0

8#$8085B 3 d3 0 3.16

!$0#B5DC 4 * 0 810.509

!$#0C$C5C 5 0 81.09

$#2B005 6 , 0 1.43

- ===F 0

0.0000 ===F 3.,1E-006

0.0000 ===F -5E-006

- ===F 0

0.0000 ===F -4E-006

0.0000 ===F -2E-006

0.0000 ===F 1.,*E-005

0.0000 ===F -4E-005

0.0000 ===F -4E-006

0.0000 ===F -2E-005

0.0000 ===F 4.16E-005

0.0000 ===F 4.2E-00*

0.0000 ===F -2E-005

0.0000 ===F -4E-005

0.0000 ===F -4E-006

0.0000 ===F 1.,*E-005

0.0000 ===F 4.16E-005

0.0000 ===F 4.2E-00*


28/81


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31/81

1 0 0 0 0 0 50000 0

0 1 0 0 0 0 0 34*.2222

0 0 1 0 0 0 0 1041.66*0 0 0 1 0 0 -50000 0

0 0 0 0 1 0 0 -34*.2222

0 0 0 0 0 1 0 1041.66*

50000 0 0 -50000 0 0 1 0

0 34*.2222 1041.66* 0 -34*.2222 1041.66* 0 1

0 1041.66* 4166.66* 0 -1041.66* 203.333 0 0

-50000 0 0 50000 0 0 0 0

0 -34*.2222 -1041.66* 0 34*.2222 -1041.66* 0 0

0 1041.66* 203.333 0 -1041.66* 4166.66* 0 0

=R> =SM> =R>


32/81

0.*0*10* -0.*0*10* 0 0 0 0 *0*10.6 0

0.*0*10* 0.*0*10* 0 0 0 0 0 ,2.0,2

0 0 1 0 0 0 0 203.333

0 0 0 0.*0*10* -0.*0*10* 0 -*0*10.6 00 0 0 0.*0*10* 0.*0*10* 0 0 -,2.0,2

0 0 0 0 0 1 0 203.333

0.*0*10* 0.*0*10* 0 0 0 0 *0*10.6 0

-0.*0*10* 0.*0*10* 0 0 0 0 0 ,2.0,2

0 0 1 0 0 0 0 203.333

0 0 0 0.*0*10* 0.*0*10* 0 -*0*10.6 0

0 0 0 -0.*0*10* 0.*0*10* 0 0 -,2.0,2

0 0 0 0 0 1 0 203.333

=R> =SM> =R>

=R> =SM> =R>


33/81


34/81

- >@

- >@

- >@

- >@

80.009 ida7 >@...)e7 agi..

0.00 ida7 >@...)e7 agi..


35/81

1K

',a3 1K###e3 Lag'##

',a3 1K###e3 Lag'##

1K

',a3 1K###e3 Lag'##

',a3 1K###e3 Lag'##

80.009 ida7 >@...)e7 agi.. 80.009 ida7 >@...)e7 agi..

0.00 ida7 >@...)e7 agi..

- >@

- >@

- >@

',a3 1K###e3 Lag'##

',a3 1K###e3 Lag'##

',a3 1K###e3 Lag'##

',a3 1K###e3 Lag'##

',a3 1K###e3 Lag'##

',a3 1K###e3 Lag'##

0.00 ida7 >@...)e7 agi..

80.009 ida7 >@...)e7 agi..

0.00 ida7 >@...)e7 agi..

- >@

- >@

- >@


36/81

',a3 1K###e3 Lag'##

',a3 1K###e3 Lag'##

',a3 1K###e3 Lag'##

',a3 1K###e3 Lag'##

',a3 1K###e3 Lag'##

',a3 1K###e3 Lag'##


37/81


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39/81


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0 -50000 0 0 1 0 0 0

1041.66* 0 -34*.2222 1041.66* 0 1 0 0

4166.66* 0 -1041.66* 203.333 0 0 1 00 50000 0 0 0 0 0 1

-1041.66* 0 34*.2222 -1041.66* 0 0 0 0

203.333 0 -1041.66* 4166.66* 0 0 0 0

0 0 0 0 50000 0 0 -50000

0 0 0 0 0 34*.2222 1041.66* 0

1 0 0 0 = 0 1041.66* 4166.66* 0

0 1 0 0 -50000 0 0 50000

0 0 1 0 0 -34*.2222 -1041.66* 0

0 0 0 1 0 1041.66* 203.333 0


41/81

0 -*0*10.6 0 0 1 1 0 0

203.333 0 -,2.0,2 203.333 -1 1 0 0

5,2.55* 0 -203.333 2,46.2* 0 0 1 0

0 *0*10.6 0 0 0 0 0 1-203.333 0 ,2.0,2 -203.333 0 0 0 -1

2,46.2* 0 -203.333 5,2.55* 0 0 0 0

0 -*0*10.6 0 0 1 -1 0 0

203.333 0 -,2.0,2 203.333 1 1 0 0

5,2.55* 0 -203.333 2,46.2* 0 0 1 0

0 *0*10.6 0 0 0 0 0 1

-203.333 0 ,2.0,2 -203.333 0 0 0 1

2,46.2* 0 -203.333 5,2.55* 0 0 0 0


42/81


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49/81

0 0

0 0

0 00 0

1 0

0 1

0 0 - - - - - -

-34*.2222 1041.66* - - - - - -

-1041.66* 203.333 - - - - - -

0 0 - - - - - -

34*.2222 -1041.66* - - - - - -

-1041.66* 4166.66* - - - - - -


50/81

0 0 50000 -6,4.4444 -14*3.13, -50000 6,4.4444 -14*3.13,

0 0 50000 6,4.4444 14*3.13, -50000 -6,4.4444 14*3.13,

0 0 0 203.333 5,2.55* 0 -203.333 2,46.2*

1 0 -50000 6,4.4444 14*3.13, 50000 -6,4.4444 14*3.13,1 0 -50000 -6,4.4444 -14*3.13, 50000 6,4.4444 -14*3.13,

0 1 0 203.333 2,46.2* 0 -203.333 5,2.55*

0 0 50000 6,4.4444 14*3.13, -50000 -6,4.4444 14*3.13,

0 0 -50000 6,4.4444 14*3.13, 50000 -6,4.4444 14*3.13,

0 0 0 203.333 5,2.55* 0 -203.333 2,46.2*

-1 0 -50000 -6,4.4444 -14*3.13, 50000 6,4.4444 -14*3.13,

1 0 50000 -6,4.4444 -14*3.13, -50000 6,4.4444 -14*3.13,

0 1 0 203.333 2,46.2* 0 -203.333 5,2.55*


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0.*0*10* 0.*0*10* 0 0 0 0 3546.3,

-0.*0*10* 0.*0*10* 0 0 0 0 3464.2,

0 0 1 0 0 0 = -14*3.13,

0 0 0 0.*0*10* 0.*0*10* 0 -3546.3,0 0 0 -0.*0*10* 0.*0*10* 0 -3464.2,

0 0 0 0 0 1 -14*3.13,

0.*0*10* -0.*0*10* 0 0 0 0 3546.3,

0.*0*10* 0.*0*10* 0 0 0 0 -3464.2,

0 0 1 0 0 0 = 14*3.13,

0 0 0 0.*0*10* -0.*0*10* 0 -3546.3,

0 0 0 0.*0*10* 0.*0*10* 0 3464.2,

0 0 0 0 0 1 14*3.13,


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- - -

- - -

- - -

- - -- - -

- - -

- - -

- - -

- - -

- - -

- - -

- - -


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portal 7 frame 2d metode kekakuan

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