POrtal 2D BUku Matlab Hal.85

8/19/2019 POrtal 2D BUku Matlab Hal.85

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PENYELESAIAN UAS "MEKANIKA REKAYASA V" (reguler)Semester Gasal 2005/200 ! gl# 2$ %a&uar' 200

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

Defined Dafter boun

PENYELESAIAN

Pr- ert'es e&am a&gBahan / material :

E = 2.10E+06 kg/cm2

Batang 1 :b = 25 cmh = 25 cm

625 cm2E = 2.10E+06 kg/cm2

3.26E+04 cm4

250 cm

A =

I =L1 =


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0 egree!

Batang 3 :b = 25 cmh = 25 cm

625 cm2E = 2.10E+06 kg/cm2

3.26E+04 cm4

250 cm

0 egree!

Re3a Eleme& ,alam Matr'3s Ke3a3ua& 4ata&gBatang EA / L 4.EI / L 2.EI / L 6.EI / L^2 12.EI / L^3 Sudut (deg)

1 5.24E+06 1.0"E+0" 5.46E+0# 6.55E+06 5.24E+04 02 4.3$E+06 ".10E+0# 4.55E+0# 4.55E+06 3.03E+04 2$03 5.24E+06 1.0"E+0" 5.46E+0# 6.55E+06 5.24E+04 0

ata .e.a&

%1 = 0 kg%2 = 0 kg& = 0.1 kg/cm' = 25 kg.cm

Ga a ,a& M-me& U6u&g a,a Eleme&t 7$(a = 0 kg (b = 0 kg)a = 3.66211E+013 kg )b = 3.66210"E+013 kg'a = 6.25 kg.cm 'b = *6.25 kg.cm

Ga a ,a& M-me& U6u&g a,a Eleme&t 72(a = 0 (b = 0

)a = 0 )b = 0'a = 0 .m 'b = 0 .m

Ga a ,a& M-me& U6u&g a,a Eleme&t 78(a = 0 (b = 0)a = 15 )b = 15'a = $50 .m 'b = *$50 .m

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

,-. Btgng kiri i ng kanan

Beban FX(i) Beban FY(i) Beban MZ(i) Beban FX( ) Beban FY( ) Beban MZ( )1 0 3.$E+013 6.25 0 3.66210"E+013 *6.252 0 0 0 0 0 0

theta 1 =

A =

I =L3 =

theta 3 =


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3 0 15 $50 0 15 *$50

4e.a& atau M-me& a,a 't'3 %-'&t Stru3tur ,alam Ara9 Sum.u Gl-.al/Sum.u,-. itik : 1 2

i!. b l-bal : 1 2 3 4 5 6Beban/'-men : 0 0 0 0 0 0

e&tu3a& arameter a&g ,'.utu93a&

a. mb gl-bal !tr kt r a a tia elementb. 78 !e! ai ! mb gl-bal !tr kt r c. 9e!e! aian !b l-kal element engan 78 arah gl-bal

.

a. i! lacement titik ! mb gl-bal !tr kt r a a tia element

Eleme&t ' 61 1 2 3 4 52 4 5 6 $ #3 4 5 6 10 11

b. 78 !e! ai ! mb gl-bal !tr kt r

l-bal a i! 1 2 3 4 578 1 2 3 1 2

c.

L-cal A i! 1 2 3 4Element ke 1 1 2 3 1Element ke 2 1 2 3 !Element ke 3 1 2 3 10

Element ;1L-cal a i! 1 2 3 4 5l-bal a i! 1 2 3 4 5

78 0 0 0 1 2

Element ;2L-cal a i! 1 2 3 4 5l-bal a i! 5 4 6 $ #

78 2 1 3 0 0

Element ;3L-cal a i! 1 2 3 4 5l-bal a i! 4 5 6 10 11

78 1 2 3 0 0

'atrik! ran!? an > ? tia element

9e!e! aian S4 L1KAL element engan S4 GL14AL ,a& 1 ara9 gl-


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.

Element 1:

> = 0 0 0

0 0 0

0 0 1 0 00 0 0

0 0 00 0 0 0 0

Element 2:

> = 0 0 0

0 0 00 0 1 0 0

0 0 00 0 00 0 0 0 0

Element 3:

> = 0 0 0

0 0 00 0 1 0 0

0 0 0

0 0 00 0 0 0 0

:::; ALAM SUM4U L1KALBatang = 1

Elemen alam matrik! kekak an batang :EA / L 4.EI / L 2.EI / L 6.EI / L@2 12.EI / [email protected]+06 1.0"E+0" 5.46E+0# 6.55E+06 5.24E+04

= c-! theta = 1

= !in theta = 0

L-cal a i! 1 2 3 4 51 5240000 0 0 *5240000 02 0 52400 6550000 0 *52400

3 0 6550000 1.1E+00" 0 *65500004 *5240000 0 0 5240000 05 0 *52400 *6550000 0 524006 0 6550000 5.5E+00# 0 *6550000


Elemen alam matrik! kekak an batang :

'atrik! ran!? an > ? tia element

c-! α 1 !in α 1 * !in α 1 c-! α 1

c-! α 1 !in α 1 * !in α 1 c-! α 1

c-! α 1 !in α 1 * !in α 1 c-! α 1

c-!α

1 !inα

1

* !in α 1 c-! α 1

c-! α 1 !in α 1 * !in α 1 c-! α 1

c-! α 1 !in α 1

* !in α 1 c-! α 1

' 1? =


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EA / L 4.EI / L 2.EI / L 6.EI / L@2 12.EI / [email protected]$E+06 ".10E+0# 4.55E+0# 4.55E+06 3.03E+04

= c-! theta = *2E*016 = !in theta = *1

L-cal a i! 1 2 3 4 51 436666$ 0 0 *4366666.666$ 02 0 30324.0$ 454#611 0 *30324.0$

3 0 454#611 ".1E+00# 0 *454#6114 *436666$ 0 0 4366666.6666$ 05 0 *30324.0$ *454#611 0 30324.0$6 0 454#611 4.5E+00# 0 *454#611


Elemen alam matrik! kekak an batang :EA / L 4.EI / L 2.EI / L 6.EI / L@2 12.EI / [email protected]+06 1.0"E+0" 5.46E+0# 6.55E+06 5.24E+04

= c-! theta = 1 = !in theta = 0

L-cal a i! 1 2 3 4 51 5240000 0 0 *5240000 0

2 0 52400 6550000 0 *524003 0 6550000 1.1E+00" 0 *65500004 *5240000 0 0 5240000 05 0 *52400 *6550000 0 524006 0 6550000 5.5E+00# 0 *6550000

78 1 2 3 1 2l-bal a i! 1 2 3 4 5

1 2 3 1 24 5 6 1 2

4 10510324 $."$E*010 454#611 *5240000 05 $."$E*010 44$146$ 0 0 *524006 454#611 0 3.1E+00" 0 65500001 *5240000 0 0 5240000 0

2 0 *52400 6550000 0 524003 0 *6550000 5.5E+00# 0 6550000$ *30324.0$ *#E*010 *454#611 0 0# *#E*010 *436666$ #.36E*010 0 0" 454#611 *#E*010 4.5E+00# 0 0

10 *5240000 0 0 0 011 0 *52400 *6550000 0 0

' 2? =

' 3? =

' ? =


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12 0 6550000 5.5E+00# 0 0


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1 2 0 21 3 0 32 4 0 1

A = 2 5 0 22 6 0 33 $ 0 $

3 # 0 #3 " 0 "

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

C-int b l-bal 781 1 1 01 2 2 *3.66211E+0131 3 3 *6.252 4 1 0

Ac = 2 5 2 *3.66211E+013 +2 6 3 6.253 $ $ 03 # # 03 " " 0

i! lacement / eeacti-n!:

ADA* ADA ALA' C , ELE'E,

4ata&g $

e


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0 5240000 0 03.$E+013 0 52400 6550000

6.25 + 0 6550000 1.1E+00"0 *5240000 0 0

3.$E+013 0 *52400 *6550000*6.25 0 6550000 5.5E+00#

4ata&g 2

e


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F ary conditions

45

Batang 2 : 1b = 25 cm 0.$0$10$h = 25 cm 0.$0$10$

625 m2E = 2.10E+06t/m2

3.26E+04m4

300 cm

A =

I =L2 =

versi buku matlab


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2$0 egree!

1 0*2E*016 *1

1 0

theta 2 =


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tru3tur 3 4

$ # " 10 11 120 0 0 0 0 0

6 ==F l-bal a i!" ==F l-bal a i!

12 ==F l-bal a i!

6 $ # " 10 11 123 $ # " 10 11 12

5 62 3 G=== 78 !e! ai !b gl-bal

' " G=== 78 !e! ai !b gl-bal11 12 G=== 78 !e! ai !b gl-bal

66

3

6 raian !b gl-bal :" raian !b 4 = 1. + 2.0 raian !b 5 = 1. + 2.

raian !b $ = 4. + 5.raian !b # = 4. + 5.

6120

al


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0 >? = 1 0 0 0 0 0

0 0 1 0 0 0 0

0 0 0 1 0 0 00 0 0 0 1 0 0

0 0 0 0 0 1 01 0 0 0 0 0 1

0 >? = *2E*016 *1 0 0 0 0

0 1 *2E*016 0 0 0 00 0 0 1 0 0 0

0 0 0 0 *2E*016 *1 00 0 0 0 1 *2E*016 01 0 0 0 0 0 1

0 >? = 1 0 0 0 0 0

0 0 1 0 0 0 00 0 0 1 0 0 0

0 0 0 0 1 0 0

0 0 0 0 0 1 01 0 0 0 0 0 1

1 2 3 16 l-bal a i! 1 2 3 4

0 1 5240000 0 0 *52400006550000 2 0 52400 6550000 0

5.5E+00# 3 0 6550000 1.1E+00" 00 4 *5240000 0 0 5240000

*6550000 5 0 *52400 *6550000 01.1E+00" 6 0 6550000 5.5E+00# 0

' 1 ? =


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1 2 3 $

6 l-bal a i! 4 5 6 $0 4 30324.0$ $."$E*010 454#611 *30324.0$

454#611 5 $."$E*010 436666$ *#E*010 *#E*010

4.5E+00# 6 454#611 *#E*010 ".1E+00# *454#6110 $ *30324.0$ *#E*010 *454#611 30324.0$

*454#611 # *#E*010 *436666$ #.36E*010 $."$E*010".1E+00# " 454#611 *#E*010 4.5E+00# *454#611

10510324 $."$E*010 454#611$."$E*010 44$146$ 0

454#611 0 3.1E+00"

1 2 3 10

6 l-bal a i! 4 5 6 100 4 5240000 0 0 *5240000

6550000 5 0 52400 6550000 05.5E+00# 6 0 6550000 1.1E+00" 0

0 10 *5240000 0 0 5240000*6550000 11 0 *52400 *6550000 01.1E+00" 12 0 6550000 5.5E+00# 0

3 $ # " 10 11 126 $ # " 10 11 12

3 $ # " 10 11 12 G=== itata lang ma3 $ # " 10 11 120 *30324.0$ *#E*010 454#611 *5240000 0 0 4 1

*6550000 *#E*010 *436666$ *#E*010 0 *52400 6550000 5 25.5E+00# *454#611 #.36E*010 4.5E+00# 0 *6550000 5.5E+00# 6 3

0 0 0 0 0 0 0 1 1

6550000 0 0 0 0 0 0 2 21.1E+00" 0 0 0 0 0 0 3 3

0 30324.0$ $."$E*010 *454#611 0 0 0 $ $0 $."$E*010 436666$ #.36E*010 0 0 0 # #0 *454#611 #.36E*010 ".1E+00# 0 0 0 " "0 0 0 0 5240000 0 0 10 100 0 0 0 0 52400 *6550000 11 11

' 2 ? =

' 3 ? =


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0 0 0 0 0 *6550000 1.1E+00" 12 12

ran!


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ata lang Ac :0 0 1 00 *4E+013 2 *4E+0130 *6.25 3 6.250 0 1 00 = *4E+013 Ac = 2 *4E+0130 6.25 3 *6.250 0 $ 00 0 # 00 0 " 0

e


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*5240000 0 0 0 0 0.00132"0 *52400 6550000 0 3.$E+013 4.3E+011

0 *6550000 5.5E+00# 0 = 6.25 + 5.4E+0135240000 0 0 *3E*010 0 *0.00132"

0 52400 *6550000 *#1#""51 3.$E+013 *4E+0110 *6550000 1.1E+00" 2.02E*00" *6.25 5.4E+013

e


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1 0 0 0 0 0

0 1 0 0 0 0

0 0 1 0 0 00 0 0 1 0 0

0 0 0 0 1 00 0 0 0 0 1

*2E*016 1 0 0 0 0

*1 *2E*016 0 0 0 00 0 1 0 0 0

0 0 0 *2E*016 1 00 0 0 *1 *2E*016 00 0 0 0 0 1

1 0 0 0 0 0

0 1 0 0 0 00 0 1 0 0 0

0 0 0 1 0 0

0 0 0 0 1 00 0 0 0 0 1

2 35 6

0 0*52400 6550000

*6550000 545#333330 0

52400 *6550000*6550000 1.0"E+00"

>? =

>? =

>? =


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# "

# "*#E*010 454#611.1

*436666$ *#.36E*010

#.36E*010 454#61111$."$E*010 *454#611

436666$ #.36E*010#.36E*010 "0"$22222

10510324 $."$E*010 454#611 * * *$."$E*010 44$146$ 0 * * *454#611.1 0 3.1E+00" * * *

11 12

11 120 0

*52400 6550000*6550000 545#33333

0 052400 *6550000

*6550000 1.0"E+00"

ek: 79n al

;;; 0.00 ;;; 0.00 ;;; *

;;; * ;;;


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l-bal a i!0 1 0

3.$E+013 2 3.$E+013

6.25 = 3 6.250 4 0

3.$E+013 5 3.$E+013*6.25 6 *6.25

l-bal a i!0 4 00 5 0

0 = 6 00 $ 00 # 00 " 0


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0 *0 ;;;0 6.25

ek: 790 0.00

*0.00021 ;;;0.0005#" 0.00

!b l-kal 780 0 1 1 *0 0 2 2 *

0 = 0 3 3 **3E*010 *3E*010 4 1 *

*#1#""51 *#1#""51 5 2 *2.02E*00" 2.02E*00" 6 3 *


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!b l-kal 78 / !b gl-bal ek :0.00132"3 1 1 *0.0005 0.003.$1E+013 2 2 0.035#46 ;;;

= 5.36E+013 3 3 4.6$6"52 ;;;*0.00132" 4 1 0.0005 0.003.62E+013 5 2 0.004154 ;;;5.36E+013 6 3 1.661524 ;;;

!b l-kal 78*3E*010 #1#""51 1 1 ;;;

*#1#""51 1.25E*00" 2 2 0.00

2.02E*00" = 2.02E*00" 3 3 *0 0 4 $ *

0 0 5 # *0 0 6 " *

!b l-kal 78 / !b gl-bal ek :3.5#E+013 1 1 0.002"3$ ;;;0.00"230# 2 2 *0.002"3$ 0.00

= 1.#44266# 3 3 *1.661524 1.66

*3.6E+013 4 $ *0.002"3$ ;;;*0.00"231 5 # 0.002"3$ 0.000."24"$"5 6 " *5E*016 0.00


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1 0 0 0 0 0 5240000 00 1 0 0 0 0 0 52400

0 0 1 0 0 0 0 65500000 0 0 1 0 0 *5240000 00 0 0 0 1 0 0 *524000 0 0 0 0 1 0 6550000

=R> =SM> =R>


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*2E*016 1 0 0 0 0 436666$ 0

*1 *2E*016 0 0 0 0 0 30324.0$0 0 1 0 0 0 0 454#6110 0 0 *1.#4E*016 1 0 *436666$ 00 0 0 *1 *2E*016 0 0 *30324.0$0 0 0 0 0 1 0 454#611

0 0 0 0 0 0 5240000 00 0 0 0 0 0 0 524000 0 0 0 0 0 0 65500000 0 0 0 0 0 *5240000 00 0 0 0 0 0 0 *524000 0 0 0 0 0 0 6550000

=R> =SM> =R>

=R> =SM> =R>


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',a3 1K###De3 Lag'## 1.32"E*00"',a3 1K###De3 Lag'## ;;;

',a3 1K###De3 Lag'## ;;;',a3 1K###De3 Lag'## *1.33E*00"',a3 1K###De3 Lag'## ;;;',a3 1K###De3 Lag'## ;;;

',a3 1K###De3 Lag'## ;;;',a3 1K###De3 Lag'## 0.0000

',a3 1K###De3 Lag'## 0.0000

',a3 1K###De3 Lag'## ;;;',a3 1K###De3 Lag'## 0.0000',a3 1K###De3 Lag'## 0.0000


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0 *5240000 0 0 1 0 0 06550000 0 *52400 6550000 0 1 0 0

1.1E+00" 0 *6550000 5.5E+00# 0 0 1 00 5240000 0 0 0 0 0 1

*6550000 0 52400 *6550000 0 0 0 05.5E+00# 0 *6550000 1.1E+00" 0 0 0 0


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0 *436666$ 0 0 0 *1 0 0

454#611 0 *30324.0$ 454#611 1 0 0 0".1E+00# 0 *454#611 4.5E+00# 0 0 1 0

0 436666$ 0 0 0 0 0 0*454#611 0 30324.0$ *454#611 0 0 0 14.5E+00# 0 *454#611 ".1E+00# 0 0 0 0

0 *5240000 0 0 0 0 0 06550000 0 *52400 6550000 0 0 0 01.1E+00" 0 *6550000 5.5E+00# 0 0 0 0

0 5240000 0 0 0 0 0 0*6550000 0 52400 *6550000 0 0 0 05.5E+00# 0 *6550000 1.1E+00" 0 0 0 0


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0 0 5240000 0 0 *5240000 0 00 0 0 52400 6550000 0 *52400 6550000

0 0 0 6550000 1.1E+00" 0 *6550000 5.5E+00#0 0 *5240000 0 0 5240000 0 01 0 0 *52400 *6550000 0 52400 *65500000 1 0 6550000 5.5E+00# 0 *6550000 1.1E+00"


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0 0 *#E*010 30324.0$ 454#611 #.02E*010 *30324.0$ 454#611

0 0 *436666$ *6E*012 *#E*010 436666$ 5.5$E*012 *#E*0100 0 0 454#611 ".1E+00# 0 *454#611 4.5E+00#*1 0 #.02E*010 *30324.0$ *454#611 *#E*010 30324.0$ *454#6110 0 436666$ 5.5$E*012 #.36E*010 *436666$ *6E*012 #.36E*0100 1 0 454#611 4.5E+00# 0 *454#611 ".1E+00#

0 0 ;)AL EH ;)AL EH ;)AL EH ;)AL EH ;)AL EH ;)AL EH0 0 ;)AL EH ;)AL EH ;)AL EH ;)AL EH ;)AL EH ;)AL EH0 0 ;)AL EH ;)AL EH ;)AL EH ;)AL EH ;)AL EH ;)AL EH0 0 ;)AL EH ;)AL EH ;)AL EH ;)AL EH ;)AL EH ;)AL EH0 0 ;)AL EH ;)AL EH ;)AL EH ;)AL EH ;)AL EH ;)AL EH0 0 ;)AL EH ;)AL EH ;)AL EH ;)AL EH ;)AL EH ;)AL EH


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1 0 0 0 0 0 52400000 1 0 0 0 0 0

0 0 1 0 0 0 = 00 0 0 1 0 0 *52400000 0 0 0 1 0 00 0 0 0 0 1 0


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*2E*016 *1 0 0 0 0 30324.0$

1 *2E*016 0 0 0 0 $."$E*0100 0 1 0 0 0 = 454#6110 0 0 *2E*016 *1 0 *30324.0$0 0 0 1 *2E*016 0 *#E*0100 0 0 0 0 1 454#611

0 0 0 0 0 0 ;)AL EH0 0 0 0 0 0 ;)AL EH0 0 0 0 0 0 = ;)AL EH0 0 0 0 0 0 ;)AL EH0 0 0 0 0 0 ;)AL EH0 0 0 0 0 0 ;)AL EH


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0 0 *5240000 0 0 * * *52400 6550000 0 *52400 6550000 * * *

6550000 1.1E+00" 0 *6550000 5.5E+00# * * *0 0 5240000 0 0 * * *

*52400 *6550000 0 52400 *6550000 * * *6550000 5.5E+00# 0 *6550000 1.1E+00" * * *


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$."$E*010 454#611 *30324.0$ *#E*010 454#611 * * *

436666$ *#E*010 *#E*010 *436666$ *#E*010 * * **#E*010 ".1E+00# *454#611 #.36E*010 4.5E+00# * * **#E*010 *454#611 30324.0$ $."$E*010 *454#611 * * *

*436666$ #.36E*010 $."$E*010 436666$ #.36E*010 * * **#E*010 4.5E+00# *454#611 #.36E*010 ".1E+00# * * *

;)AL EH ;)AL EH ;)AL EH ;)AL EH ;)AL EH ;)AL EH ;)AL EH ;)AL EH;)AL EH ;)AL EH ;)AL EH ;)AL EH ;)AL EH ;)AL EH ;)AL EH ;)AL EH;)AL EH ;)AL EH ;)AL EH ;)AL EH ;)AL EH ;)AL EH ;)AL EH ;)AL EH;)AL EH ;)AL EH ;)AL EH ;)AL EH ;)AL EH ;)AL EH ;)AL EH ;)AL EH;)AL EH ;)AL EH ;)AL EH ;)AL EH ;)AL EH ;)AL EH ;)AL EH ;)AL EH;)AL EH ;)AL EH ;)AL EH ;)AL EH ;)AL EH ;)AL EH ;)AL EH ;)AL EH


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* * ** * *

* * ** * ** * ** * *


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* * *

* * ** * ** * ** * ** * *

;)AL EH ;)AL EH ;)AL EH;)AL EH ;)AL EH ;)AL EH;)AL EH ;)AL EH ;)AL EH;)AL EH ;)AL EH ;)AL EH;)AL EH ;)AL EH ;)AL EH;)AL EH ;)AL EH ;)AL EH


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POrtal 2D BUku Matlab Hal.85

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Transcript of POrtal 2D BUku Matlab Hal.85