Uji Sap2000 Dengan Metode Kekakuan Langsung

8/18/2019 Uji Sap2000 Dengan Metode Kekakuan Langsung

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MEKANIKA REKAYASA V

Data beban

P1 = 15

P2 = 20

q1 = 60

q2 = 50

Properties penampang

Bahan / material :

E = 2.35E+07

Batang 1 :

0.20m

0.45m

0.09 m2

E = 2.35E+07 t/m2

1.52E-03 m4

5 m

Batang 2 : Batang 3 :

0.40 m 0.40 m

t/m2

b1 =

h1 =

1 =

!1 =

"1 =

b2 = b

3 =

versi lengkap

P1

q1

q2

P2

5,0 m

1,0 m

3,0 m

2,0 m

2,0 m

2

1

3

1 2

43


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0.40 m 0.40 m

0.16 m2 0.16 m2

E = 2.35E+07 t/m2 E = 2.35E+07 t/m2

2.13E-03 m4 2.13E-03 m4

4 m 4 m

PENYELESAIAN :

STEP 1 : Discretize an !"oba" Degrees o# $reeom %D&$'

Defined DOF

after boundary conditions

h2 = h

3 =

2 =

3 =

!2 = !

3 =

"2 = "

3 =

5,0 m

4,0 m2

1

3

1 2

43

1 21

2

3

4

5

6

#

1 d1

d2

d3 d6

#


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3

5,0 m

4,0 m

437

8

9

10

11

12

$

gl%bal a&i'

5,0 m

3

$

gl%bal a&i'

j=1 1

2

3

k=2 4

5

61

LOCALAXIS

j=1

1

2

3

4

5

6

k=3

2

LOCAL

j=2

1

2

3

4

5

6

k=4

3


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D&$ ses(ai s(mb( g"oba" str()t(r an tent()an *eban ata( Momen paa Titi) +oint Str()t(r a"am Ara, S(mb( !"oba"-S(mb( Str()t(r

()* Beban / %men

1

1 ,1 15

2 ,2 0

3 ,3 0

2

4 ,4 0

5 ,5 0

6 ,6 0

3

7 7 0

09 9 0

4

10 10 0

11 11 0

12 12 0

Nomor .oint (nt() setiap e"ement

+oint

ng ng

1 1 2

2 1 3

3 2 4

Disp"acement titi) s(mb( g"oba" str()t(r paa tiap e"ement

E"ement . )

1 1 2 3 4 5 6 == l%bal a&i'

2 1 2 3 7 9 == l%bal a&i'

3 4 5 6 10 11 12 == l%bal a&i'

%.titi%int

(i'.l%bal &i'

E"ement

%i'

11

Y

P1

5,0 m

4,0 m2

1

3

1 2

43


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5

== l%bal a&i'

== l%bal a&i'

Meng,it(ng ni"ai /0 an / berasar)an )oorinat

Element

1 0 4 5 4

2 0 4 0 0

3 5 4 5 0

Batang 1

5 - 0 = 1 8& = 1

5

4 - 4 = 0 8 = 0

5

Batang 2

0 - 0 = 0 8& = 0

4

0 - 4 = -1 8 = -1

4

Batang 3

5 - 5 = 0 8& = 0

4

0 - 4 = -1 8 = -1

4

Re)ap E"emen a"am Matri)s Ke)a)(an *atang

Batang EA / L 4.EI / L 2.EI / L 6.EI / L^2 12.EI / L^3 Sudut (deg) 8& 8

1 4.23E+05 2.6E+04 1.43E+04 .57E+03 3.43E+03 0 1 0

&

&

= %' α = & - &

/ "

1 =

= 'in α = -

/ "

1 =

= %' α = & - &

/ "

2 =

= 'in α = - / "2 =

= %' α = & - &

/ "

3 =

= 'in α = -

/ "

3 =

5,0 m

2

3


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2 9.40E+05 5.01E+04 2.51E+04 1.E+04 9.40E+03 270 -1.3772E-016 -1

3 9.40E+05 5.01E+04 2.51E+04 1.E+04 9.40E+03 270 -1.3772E-016 -1

4

5

Meng,it(ng !aa an Momen 2.(ng %A)ibat beban "(ar i sepan.ang bentang engan (.(ng i)e)ang-i.epit' %DALAM ARA3 S2M*2 L&KAL' :

ELEMENT 41

!aa an Momen 2.(ng paa E"ement 41:

;a = 0 ;b = 0


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ELEMENT 45


;a = 0 ;b = 0


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;a = 0 ;b = 0


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Re)ap !aa 2.(ng *atang %S(mb( Lo)a"'

%. Btgng iri ng anan

Beban FX(j) Beban FY(j) Beban MZ(j) Beban FX() Beban FY() Beban MZ()

1 0 150 125 0 150 -125

2 0 -1.75 -20.333333333 0 -1.25 45.333333333

3 0 16.75 11.25 0 3.125 -3.75

4 >E*? >E*? >E*? >E*? >E*? >E*?

5

Tent()an parameter ang ib(t(,)an :

a. @mb gl%bal 'trtr Aa,a tiaA element

b. ()* 'e'ai 'mb gl%bal 'trtr

. e'e'aian 'b l%al element ,engan ()* arah gl%bal

,.

.

"%al &i' 1 2 3 4 5 6

Element e 1 ,1 ,2 ,3 ,4 ,5 ,6 C=== ()* 'e'

Element e 2 ,2 ,1 ,3 7 9 C=== ()* 'e'

Element e 3 ,5 ,4 ,6 11 10 12 C=== ()* 'e'

Element 1"%al a&i' 1 2 3 4 5 6

l%bal a&i' 1 2 3 4 5 6

()* ,1 ,2 ,3 ,4 ,5 ,6

Element 2

"%al a&i' 1 2 3 4 5 6

l%bal a&i' 2 1 3 7 9

()* ,2 ,1 ,3 0 0 0

Element 3

"%al a&i' 1 2 3 4 5 6

l%bal a&i' 5 4 6 11 10 12

atri' Dran'%rma'i F>G ,an F>DG tiaA element

e'e'aian S* L&KAL element ,engan S* !L&*AL an D&$ ara, g"oba"


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()* ,5 ,4 ,6 0 0 0ARA P!RPI"#AA" S$MB$ LO%AL


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11

,.

E"ement 1:

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

1 0 0 0 0 0

0 1 0 0 0 0

F>G = 0 0 1 0 0 0

0 0 0 1 0 0

0 0 0 0 1 0

0 0 0 0 0 1

1 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 1 0

0 0 0 0 0 1

E"ement 5:

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

-1.3772E-016 -1 0 0 0 0

1 -1.37723E-016 0 0 0 0

F>G = 0 0 1 0 0 0

0 0 0 -1.3772E-016 -1 0

atri' Dran'%rma'i F>G ,an F>DG tiaA element

%' α1

'in α1

- 'in α1

%' α1

%' α1

'in α1

- 'in α1

%' α1

F>GD =

%' α1

'in α1

- 'in α1

%' α1

%' α1

'in α1

- 'in α1

%' α1


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0 0 0 1 -1.3772E-016 0

0 0 0 0 0 1

-1.3772E-016 1 0 0 0 0

-1 -1.37723E-016 0 0 0 0

0 0 1 0 0 0

0 0 0 -1.3772E-016 1 0

0 0 0 -1 -1.3772E-016 0

0 0 0 0 0 1

E"ement 6:

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

-1.3772E-016 -1 0 0 0 01 -1.37723E-016 0 0 0 0

F>G = 0 0 1 0 0 0

0 0 0 -1.3772E-016 -1 0

0 0 0 1 -1.3772E-016 0

0 0 0 0 0 1

-1.3772E-016 1 0 0 0 0

-1 -1.37723E-016 0 0 0 0

0 0 1 0 0 0

0 0 0 -1.3772E-016 1 0

0 0 0 -1 -1.3772E-016 0

0 0 0 0 0 1

F>GD =

%' α1

'in α1

- 'in α1

%' α1

%' α1

'in α1

- 'in α1

%' α1

F>GD =


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7778 DALAM S2M*2 L&KAL

@11 @12 @13 @14 @15 @16

@21 @22 @23 @24 @25 @26

9SM 7 @31 @32 @33 @34 @35 @36

@41 @42 @43 @44 @45 @46

@51 @52 @53 @54 @55 @56

@61 @62 @63 @64 @65 @66

3it(ng matri)s )e)a)(an batang 1 9SM1

j=1 1

2

3

k=2 4

5

61

SM11 SM41

H

SM32

SM52SM22

SM62H

SM63

SM33

SM53SM23

θ

SM11

SM25 SM5

SM35

SM26 SM5

θ


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ARA3 PERPINDA3AN PADA S2M*2 L&KAL *ATAN! DITRANS$&RMASI KE S2M*2 !L&*AL STR2KT2R

1 21

2

3

4

5

61

ARA P!RPI"#AA" S$MB$ &LOBAL

$

#

gl%bal a&i'

SMS11 SMS41

H

SMS32

SMS52SMS22

SMS62H

SMS63

SMS33

SMS53SMS23

θ

SMS11

SMS25 S

SMS35

SMS36

SMS26 S

θ


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Batang = 1

Elemen ,alam matri' eaan batang :

E / " 4.E! / " 2.E! / " 6.E! / "I2 12.E! / "I3

4.23E+05 2.6E+04 1.43E+04 .57E+03 3.43E+03

8& = %' theta = 1

8 = 'in theta = 0

"%al a&i' 1 2 3 4 5 6

1 423000 0 0 -423000 0 0

2 0 3426.3 565.75 0 -3426.3 565.75

3 0 565.75 2552.5 0 -565.75 14276.254 -423000 0 0 423000 0 0

5 0 -3426.3 -565.75 0 3426.3 -565.75

6 0 565.75 14276.25 0 -565.75 2552.5

,1 ,2 ,3 ,4 ,5 ,6

l%bal a&i' 1 2 3 4 5 6

1 423000 0 0 -423000 0 0

2 0 3426.3 565.75 0 -3426.3 565.75

3 0 565.75 2552.5 0 -565.75 14276.25

4 -423000 0 0 423000 0 0

5 0 -3426.3 -565.75 0 3426.3 -565.75

6 0 565.75 14276.25 0 -565.75 2552.5

F@1G =

F@@1

G =



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@11 @12 @13 @14 @15 @16

@21 @22 @23 @24 @25 @269SM 7 @31 @32 @33 @34 @35 @36

@41 @42 @43 @44 @45 @46

@51 @52 @53 @54 @55 @56

@61 @62 @63 @64 @65 @66


S M 1 1

H

S M

3 2

S M 2 2

H

S M

3 3

S M 2

3

S M 1 1

S M 2 5

S M 3 5

j = 1

1

2

3

k =

3

4

5

6

2

ARA P!RPI"#AA" S$MB$ LO%AL

α =270


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S M 4 1

S M

5 2

S M

6

2

S M

6 3

S M

5 3

θ

S M 4 4

H

S M 6 5

S M 5 5

H

1

3

1

2

3

7

8

9

2

$

#


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gl%bal a&i'

S M S 2 2

S M S 8 2

H

S M S 3 1

S M S 7 1

S M S 1 1

S M S 9 1

H

S M S 9 3

S M S 3 3

S M S 7 3

S M S 1 3

θ S M

S 2

8

S M

S 9

7

S M

S 1 7

S M

S 7 7

S M S 3

7 H


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Batang = 2


E / " 4.E! / " 2.E! / " 6.E! / "I2 12.E! / "I3

9.40E+05 5.01E+04 2.51E+04 1.E+04 9.40E+03

8& = %' theta = -1.37723E-016

8 = 'in theta = -1

"%al a&i' 1 2 3 4 5 6

1 940000 0 0 -940000 0 0

2 0 9400 100 0 -9400 100

3 0 100 50133.333333 0 -100 25066.666667

4 -940000 0 0 940000 0 0

5 0 -9400 -100 0 9400 -100

6 0 100 25066.666667 0 -100 50133.333333

F@2G =



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,1 ,2 ,3 7 9

l%bal a&i' 1 2 3 7 9

1 9400 1.71015E-010 100 -9400 -1.7101E-010 100

2 1.71015E-010 940000 -3.45492E-012 -1.7101E-010 -940000 -3.45492E-012

3 100 -3.454919E-012 50133.333333 -100 3.454919E-012 25066.666667

7 -9400 -1.71015E-010 -100 9400 1.71015E-010 -100

-1.7101E-010 -940000 3.45492E-012 1.71015E-010 940000 3.45492E-012

9 100 -3.454919E-012 25066.666667 -100 3.454919E-012 50133.333333


@11 @12 @13 @14 @15 @16

F@@2

G =


j = 2

1

2

3

k = 4

4

5

6

3

ARA P!RPI"#AA" S$MB$ LO%AL

α =270


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@21 @22 @23 @24 @25 @26

9SM 7 @31 @32 @33 @34 @35 @36

@41 @42 @43 @44 @45 @46

@51 @52 @53 @54 @55 @56

@61 @62 @63 @64 @65 @66


2 4

5

6

3

S M 1 1

S M 4

1

H

S M

3 2

S M

5 2

S M 2 2

S M

6 2

H

S M

6 3

S M

3 3

S M

5 3

S M 2

3

θ

S

M 4 4

S M 1 4

H

S M 6 5

S M 2

5

S M 5 5

S M 3 5

H


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4 10

11

12$

#

gl%bal a&i'

S M S 5 5

S M S 1 1 ' 5

H

S M S 6 4

S M S 1 0

' 4

S M S 4 4

S M S 1 2 ' 4

H

S M S 1 2 ' 6

S M S 6 6

S M S 1 0 ' 6

S M S

4 6

θ

S M

S 1 1 ' 1 1

S M

S 5

' 1 1 H

S M

S 1 2 ' 1

0

S

M S 4 ' 1

0

S M

S 1

0 ' 1

0

S M

S 6

' 1 0

H


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Batang = 3


E / " 4.E! / " 2.E! / " 6.E! / "I2 12.E! / "I3

9.40E+05 5.01E+04 2.51E+04 1.E+04 9.40E+03

8& = %' theta = -1.37723E-016

8 = 'in theta = -1

"%al a&i' 1 2 3 4 5 6

1 940000 0 0 -940000 0 0

2 0 9400 100 0 -9400 100

3 0 100 50133.333333 0 -100 25066.666667

4 -940000 0 0 940000 0 0

5 0 -9400 -100 0 9400 -100

6 0 100 25066.666667 0 -100 50133.333333

,4 ,5 ,6 10 11 12

l%bal a&i' 4 5 6 10 11 12

4 9400 1.71015E-010 100 -9400 -1.7101E-010 100

F@3G =


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5 1.71015E-010 940000 -3.45492E-012 -1.7101E-010 -940000 -3.45492E-012

6 100 -3.454919E-012 50133.333333 -100 3.454919E-012 25066.666667

10 -9400 -1.71015E-010 -100 9400 1.71015E-010 -100

11 -1.7101E-010 -940000 3.45492E-012 1.71015E-010 940000 3.45492E-012

12 100 -3.454919E-012 25066.666667 -100 3.454919E-012 50133.333333

F@@3

G =

MATRIKS KEKAK2AN STR2KT2R 9SMS

5,0 m

1 2

43

d1

d2

d3

d

d6

5,0 m

4,0 m

1 2

43

1

2

3

4

5

6

7

8

9

10

11

12

SMS11

1

H

AKIBAT

DEFROMASI d1


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2

AKIBAT DEFROMASI

d5

4,0 m

1 2

H

SMS32

SMS5SMS22

H

1SMS22

H

AKIBAT

DEFROMASI d2

HSMS31

SMS71

SMS11

SMS91

H

2

1

3

5,0 m

4,0 m

1 2

43


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29

5,0 m

4,0 m

1 2

43

θ

θ

SMS33

SMS23

θ

1

SMS93

SMS33

SMS73

SMS13

θ

2

AKIBAT

DEFROMASI d3

5,0 m

43

SMS82

2


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5,0 m

4,0 m

21

3 4

H

1

3

2

SMS10

SMS4

3

SSMS11

H1

4,0 m

21

H

1

2

SMS6

SMS25 SMS55

SMS35 H

1

AKIBAT

DEFROMASI d4


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5,0 m

3 4

3


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rtan 'e'ai 'mb gl%bal/'trtr ,engan ()* ang ,i,ahlan

()* : ,1 ,2 ,3 ,4 ,5 ,6 7

(i'.l%bal a&i' : 1 2 3 4 5 6 7

,1 ,2 ,3 ,4 ,5 ,6 7

1 2 3 4 5 6 7

1 432400 1.71015E-010 100 -423000 0 0 -9400 -1.71015E-010

2 1.71015E-010 943426.3 565.75 0 -3426.3 565.75 -1.7101E-010 -940000

3 100 565.75 765.33333 0 -565.75 14276.25 -100 3.454919E-012

4 -423000 0 0 432400 1.71015E-010 100 0 0

5 0 -3426.3 -565.75 1.71015E-010 943426.3 -565.75 0 0F@@G =

1

5,0 m

4,0 m

21

3 4

θ

θ

1

3

2

SMS36

SMS6

SMS26 SMS56

θ

1

AKIBAT

DEFROMASI d6


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6 0 565.75 14276.25 100 -565.75 765.33333 0 0

7 -9400 -1.71015E-010 -100 0 0 0 9400 1.71015E-010

-1.7101E-010 -940000 3.45492E-012 0 0 0 1.71015E-010 940000

9 100 -3.454919E-012 25066.666667 0 0 0 -100 3.454919E-012

10 0 0 0 -9400 -1.7101E-010 -100 0 0

11 0 0 0 -1.7101E-010 -940000 3.45492E-012 0 0

12 0 0 0 100 -3.45492E-012 25066.666667 0 0

3it(ng Matri)s *eban +oint- Noa"

Noa" #orces:

a; < A)ibat beban i sepan.ang bentang %)e(a (.(ng i)e)ang'

E"ement: 1

"%al a&i'

0 1

150 2

= 125 30 4

150 5

-125 6

Dran'%rma'i 'b l%al e gl%bal ==

1 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 1 0

F"G1

AMS 1 ! "# . AM

L 1

F@G1


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0 0 0 0 0 1

l%bal a&i'

1 0

2 150

= 3 125

4 0

5 150

6 -125

E"ement: 5

"%al a&i'

0 1

-1.75 2

= -20.3333333 3

0 4

-1.25 5

45.33333333 6

F@G1

F"G2

j=1 1

2

3 6LOCALAXIS

1

q1

VA

MA

1

1

2

3 6&LOBAL

AXIS

1


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-1.3772E-016 1 0 0 0 0

-1 -1.3772E-016 0 0 0 0

= 0 0 1 0 0 0

0 0 0 -1.3772E-016 1 0

0 0 0 -1 -1.3772E-016 0

0 0 0 0 0 1

l%bal a&i'

1 -1.75

2 3.445730E-015

= 3 -20.33333333

7 -1.25

1.493150E-014

9 45.333333333

AMS 2 ! "# . AM

L 2

F@G2

F@G2

j=1

1

2

3

4

5

6

k=3

2

V A

V B

q2

1

3

M B

M A

2

1

2

3

7

8

9

1

3

LOCALAXIS &LOBAL AXIS


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36

E"ement: 6

"%al a&i'

0 1

16.75 2

= 11.25 3

0 4

3.125 5

-3.75 6


-1.3772E-016 1 0 0 0 0

-1 -1.3772E-016 0 0 0 0

= 0 0 1 0 0 0

0 0 0 -1.3772E-016 1 0

0 0 0 -1 -1.3772E-016 0

0 0 0 0 0 1

l%bal a&i'

4 16.75

5 -3.10116E-015

= 6 11.2510 3.125

11 -5.742E-016

12 -3.75

F"G3

AMS 3 ! "# . AM

L 3

F@G3

F@G3

V A

M A

j=2 2

3

2 4

5

6


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37

S(s(n matri)s beban e)i=a"en

%int @b l%bal Element 1 Element 2 Element 3

1 1 0 -1.75 0

1 2 150 3.445730E-015 0

1 3 125 -20.33333333 0

2 4 0 0 16.75

-e = 2 5 150 + 0 + -3.10116E-015 =

2 6 -125 0 11.253 7 0 -1.25 0

3 0 1.493150E-014 0

3 9 0 45.333333333 0

4 10 0 0 3.125

4 11 0 0 -5.742E-016

4 12 0 0 -3.75

5 13 0 0 0

5 14 0 0 0

5 15 0 0 0

6 16 0 0 0

6 17 0 0 0

6 1 0 0 0

LOCALAXIS

3

V B

M B

1

4

5

6

k=4

3

&LOBAL AXIS

4 10

11

12

3


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3

1.75 1 ,1

-150 2 ,2

-104.16666667 3 ,3

-16.75 4 ,4

e = -150 5 ,5

113.75 6 ,6

1.25 7 7

-1.49315E-014

-45.33333333 9 9

-3.125 10 10

5.7423E-016 11 113.75 12 12

0 13 /

0 14 /

0 15 /

0 16 /

0 17 /

0 1 /

b; < A)ibat *eban i .oint %)e(a (.(ng i)e)ang'

%int @b l%bal ()*

2

31

,e%rme, 'haAe

n,e%rme, 'haAe

P1

11

2

31

2

3

5

6

1

4

2

3

5

6

1

4


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39

1 1 15 ,1

1 2 0 ,2

1 3 0 ,3

2 4 0 ,4

= 2 5 0 ,5

2 6 0 ,6

3 7 0 7

3 0

3 9 0 9

4 10 0 10

4 11 0 11

4 12 0 125 13 / /

5 14 / /

5 15 / /

6 16 / /

6 17 / /

6 1 / /

c; < *eban )ombinasi ata( gab(ngan %Ae > A.'

%int @b l%bal ()*

1 1 ,1 1.75 15 33.75

1 2 ,2 -150 0 -150

1 3 ,3 -104.16666667 0 -104.16666667

2 4 ,4 -16.75 0 -16.75

= 2 5 ,5 -150 + 0 = -1502 6 ,6 113.75 0 113.75

3 7 7 1.25 0 1.25

3 -1.49315E-014 0 -1.493150E-014

3 9 9 -45.33333333 0 -45.33333333

4 10 10 -3.125 0 -3.125

4 11 11 5.7423E-016 0 5.7423E-016

4 12 12 3.75 0 3.75

5 13 / 0 / /

5 14 / 0 / /

5 15 / 0 / /

6 16 / 0 / /

6 17 / 0 / /

5,0 m

2

3


40/473

40

6 1 / 0 / /


41/473

41

Data lang : (i'Alaement / (e%rma'i @trtr

,1 33.75

,2 -150

,3 -104.166666667

,4 -16.75 ,1 =

= ,5 -150 ,2 =

,6 113.75 ,3 =

7 1.25 ,4 =

-1.493150E-014 ,5 =

9 -45.333333333 ,6 =

10 -3.125 ,7 =

11 5.7423E-016 , =

12 3.75 ,9 =

0 / ,10 =

0 / ,11 =

0 / ,12 =

0 / ,13 =

0 /

0 /

$F ! S

FF%1.A

F&

(* =

4,0 m

1 2

43

d1

d2

d3

d4

d5

d6

2

1

3

5,0 m

1

3

2

1

3


42/473

42

>eati%n':

#-# (" E"EE

*atang: 1

(e%rma'i 'trtr ,alam arah @B ")B" ,i batang 1J 'bb :

Dentan n%. @b gl%bal ,ahl

1 ,1 0.001403759

2 ,2 -0.000155603

3 ,3 -0.001930752

4 ,4 0.001269327

5 ,5 -0.0001635466 ,6 0.001491773

(e%rma'i 'trtr ,alam arah @B ")" ,i batang 1J 'bb :

1 0 0 0 0 0 0.001403759

0 1 0 0 0 0 -0.0001556032

0 0 1 0 0 0 & -0.001930751

0 0 0 1 0 0 0.001269327

0 0 0 0 1 0 -0.0001635457

0 0 0 0 0 1 0.001491773

F(@G1 =

M 1 = R . DMS 1

∆M 1 !

5,0 m

,e%rme,n,e%rme, 'haAe


43/473

43

'b l%al ()*

0.001403759 1 ,1 ,1

-0.0001556032 2 ,2 ,2

-0.001930751 3 ,3 ,3

0.001269327 4 ,4 ,4

-0.0001635457 5 ,5 ,5

0.001491773 6 ,6 ,6

aa ng batang

∆M 1 !

d1 d4

d5

d

6

d2

d3 #O( = &LOBALAXIS

1

j=1 1

2

3

k=2 4

5

6

LOCALAXIS

1

1 2

d1 d4

d5

d6

d2

d3#O( = &LOBAL

AXIS

1

1 2

1 2

q1

VA VB

MA MB

1


44/473

44

-0.001930751 0.001491773

0.001403759

-0.0001556032 -0.0001635457

(e%rma'i ban gaa

etetaAan +- 'e'ai 'mb l%al

0 423000 0 0 -423000 0 0

150 0 3426.3 565.75 0 -3426.3 565.75

125 + 0 565.75 2552.5 0 -565.75 14276.25

0 -423000 0 0 423000 0 0

150 0 -3426.3 -565.75 0 3426.3 -565.75

-125 0 565.75 14276.25 0 -565.75 2552.5

'b l%al ()* / 'b gl%bal

0 56.5254549 56.52545491 1 ,1

150 -3.732961971 146.26703029 2 ,2125 + -33.7622032 = 91.2371796761 3 ,3

0 -56.5254549 -56.5254549 4 ,4

150 3.7329619712 153.732961971 5 ,5

-125 15.0901046 -109.9019953 6 ,6

91.2371796761 -109.9019953

56.52545 -56.5254549

AM 1 = AML 1 + SM 1 . M 1

F1G =

F1G =

j=1 1

2

3

k=2 4

5

6

LOCALAXIS

1


45/473

45

146.26703029 153.732961971

etetaAan +- 'e'ai 'mb l%al

*atang: 5



1 ,1 0.001403759

2 ,2 -0.000155603

3 ,3 -0.001930752

7 7 0

09 9 0


-1.3772E-016 -1 0 0 0 0 0.001403759

1 -1.37723E-016 0 0 0 0 -0.0001556032

0 0 1 0 0 0 & -0.001930751

0 0 0 -1.3772E-016 -1 0 0

0 0 0 1 -1.3772E-016 0 0

0 0 0 0 0 1 0

'b l%al ()*

0.0001556032 1 ,20.001403759 2 ,1

-0.001930751 3 ,3

0 4

0 5 7

0 6 9

F(@G2 =

M 2 = R . DMS 2

∆M 2 !

∆M 2 !

j=1 2

3

d1

d2

1


46/473

46

aa ng batang

-0.001930751

0

(e%rma'i ba

etetaAan +-

V A

V B

q2

1

3

M B

M A

1

4

5

6

k=3

2

LOCALAXIS

2

d3

7

8

93

#O( =&LOBALAXIS

j=1

1

2

3

4

5

6

k=3

2

LOCALAXIS

2

d1

d2

d3

7

8

9

1

3

#O( =&LOBALAXIS

j=

k=

2

LOCAL

AXIS


47/473

47

0 940000 0 0 -940000 0 0

-1.75 0 9400 100 0 -9400 100

-20.33333333 + 0 100 50133.3333333 0 -100 25066.6666667

0 -940000 0 0 940000 0 0

-1.25 0 -9400 -100 0 9400 -100

45.333333333 0 100 25066.6666667 0 -100 50133.3333333


0 146.2670303 146.26703029 1 ,2

-1.75 -23.10254549 -41.5254549 2 ,1

-20.33333333 + -70.4034634 = -91.237179676 3 ,3

0 -146.26703 -146.2670303 4

-1.25 23.10254549 -5.147454511 5 7

45.333333333 -22.00633561 23.26997719 6 9

-91.237179676

23.26997719

*atang: 6



4 ,4 0.001269327

5 ,5 -0.000163546

6 ,6 0.001491773

AM 2 = AML 2 + SM 2 . M 2

F2G =

F2G =

F(@G3 =

j=1

1

2

3

4

5

6

k=3

2

LOCAL AXIS


48/473

4

10 10 0

11 11 0

12 12 0


-1.3772E-016 -1 0 0 0 0 0.001269327

1 -1.37723E-016 0 0 0 0 -0.0001635457

0 0 1 0 0 0 & 0.001491773

0 0 0 -1.3772E-016 -1 0 0

0 0 0 1 -1.3772E-016 0 00 0 0 0 0 1 0

'b l%al ()*

0.0001635457 1 ,5

0.001269327 2 ,4

0.001491773 3 ,6

0 4 11

0 5 10

0 6 12

M 3 = R . DMS 3

∆M 3 !

∆M 3 !

j=2

1

2

3

5

6

k=4

3

2

4

d4

d5

d6

10

11

1

3


49/473

49

4 #O( = &LOBALAXIS

2


50/473

50

aa ng batang

3

0.0001635457

0

0

(e%rma'i ba

etetaAan +-

0 940000 0 0 -940000 0 0

16.75 0 9400 100 0 -9400 100

11.25 + 0 100 50133.3333333 0 -100 25066.66666670 -940000 0 0 940000 0 0

3.125 0 -9400 -100 0 9400 -100

-3.75 0 100 25066.6666667 0 -100 50133.3333333


0 153.73296197 153.732961971 1 ,5 ,5

16.75 39.97754549 56.52545491 2 ,4 ,4

11.25 + 9.65199532 = 109.90199532 3 ,6 ,6

0 -153.732962 -153.73296197 4 11 11

3.125 -39.97754549 -36.5254549 5 10 10

-3.75 61.25192424 57.501924242 6 12 12

AM 3 = AML 3 + SM 3 . M 3

F3G =

F3G =

3

P2

V A

V B

M A

M B

LOCALAXIS

j=2

1

2

3

4

5

6

k=4

3

#O( = &LOBALAXIS

2

4

d4

d5

d6

10

11

12

3

j=2

k=4

3


51/473

51

109.90199532

57.501924242

SELESAI

j=2

1

2

4

5

6

k=4

3

LOCAL AXIS


52/473

52

/m

/m


53/473

53

2 d4

d5


54/473

54

4,0 m


55/473

55

2


56/473

56

4,0 m3

4 X


57/473

57


58/473

5


59/473

59


60/473

60

i 'b gl%bal

i 'b gl%bal

i 'b gl%bal


61/473

61


62/473

62


63/473

63


64/473

64


65/473

65

SM44

SM65

H

SM66


66/473

66


67/473

67

SMS44

H

SMS65

MS55

H

SMS66

MS56


68/473

6


69/473


70/473

70

S M

3 6

S M 2

6


71/473

71

S M

6

6

S M

5 6

θ


72/473

72

S M

S 8 8

S M S 3 9

S M S 9 9

S M S 1 9

S M S 7 9

θ


73/473

73


74/473

74


75/473

75

S M

3 6

S M

6

6

S M 2

6

S M

5 6

θ


76/473

76

' S M S 1 2 ' 1 2

S M S 4 ' 1 2

S M S 1 0 ' 1 2

θ


77/473

77


78/473

7

4,0 m

d4

5

SMS41

2


79/473

79

2

SMS62

2

4

3


80/473

0

2

4

3

SMS63

SMS53

4

3


81/473


82/473

2

SMS11'5


83/473

3

9 10

9 10

9 10

9 10

100 0

-3.454919E-012 0

25066.6666667 0

0 -9400

0 -1.71015E-010

26

SMS12'6

SMS66

SMS10'6

SMS46

θ

3


84/473

4

0 -100

-100 0

3.454919E-012 0

50133.3333333 0

0 9400

0 1.71015E-010

0 -100

0

150

& 125

0

150


85/473

-125

k=2 4

5

VB

MB

4

5


86/473

6

0

-1.75

& -20.333333333

0

-1.25

45.333333333


87/473

7

0

16.75

& 11.25

0

3.125

-3.75


88/473

-1.75

150

104.166666667

16.75

150

-113.75-1.25

1.493150E-014

45.333333333

3.125

-5.7423E-016

-3.75

0

0

0

0

0

0


89/473

5

6

4

4,0 m

2

5

6

4

2

3

5

6

1

4

2

3

5

6

1

4


90/473


91/473

91


92/473

92

0.001403759

-0.0001556032

-0.001930751

0.001269327

-0.0001635457

0.001491773

/

/

/

/

/

/

/

2


93/473

'haAe


94/473

94


95/473

95

0.001269327

0.001403759

-0.0001556032

& -0.001930751

0.001269327

-0.0001635457

0.001491773


96/473

96


97/473

97

0.001403759

0.0001556032

0

0

n gaa

'e'ai 'mb l%al

3


98/473

9

0.0001556032

0.001403759

& -0.001930751

0

0

0

146.26703029

-41.52545491

-5.1474545109

-146.2670303


99/473

99


100/473

100


101/473

101

0.001269327

0

n gaa

'e'ai 'mb l%al

0.0001635457

0.001269327

& 0.0014917730

0

0

153.732961971


102/473

102

56.52545491

-36.52545491

-153.73296197


103/473

Data beban

P1 = 50 P2 = 100

q1 = 0 /m

q2 = 0 /m

Properties penampang

Bahan / material :

%. Element E b m h m

1 25000000 0.5 0.5

2 25000000 0.4 0.4

3 25000000 0.5 0.5

4 25000000 0.4 0.4

5 25000000 0.5 0.5

6 25000000 0.4 0.4

7 25000000 0.5 0.5

25000000 0.4 0.4

9 25000000 0.4 0.4

10 25000000 0.4 0.4

PENYELESAIAN :

STEP 1 : Discretize an !"oba" Degrees o# $reeom %D&$'


104/473

D&$ ses(ai s(mb( g"oba" str()t(r an tent()an *eban ata( Momen

%.titi %int ()*

1

1 1 0 Dran'. $

2 2 0 Dran'. #

3 ,1 0 >%t. K

24 ,2 50 Dran'. $5 ,3 0 Dran'. #

6 ,4 0 >%t. K

3

7 ,5 0 Dran'. $

,6 0 Dran'. #

9 ,7 0 >%t. K

4

10 10 0 Dran'. $

11 11 0 Dran'. #

12 , 0 >%t. K

5

13 ,9 0 Dran'. $

14 ,10 0 Dran'. #15 ,11 0 >%t. K

6

16 ,12 0 Dran'. $

17 ,13 0 Dran'. #

1 ,14 0 >%t. K

7

19 19 0 Dran'. $

20 20 0 Dran'. #

21 ,15 0 >%t. K

22 22 0 Dran'. $

23 23 0 Dran'. #

24 ,16 0 >%t. K

9

25 ,17 50 Dran'. $

26 ,1 -100 Dran'. #

27 ,19 0 >%t. K

(i'.l%bal &i'

Beban /%men

rahBeban/%men


105/473

10

2 ,20 0 Dran'. $

29 ,21 -100 Dran'. #

30 ,22 0 >%t. K

Nomor .oint (nt() setiap e"ement

E"ement %i'+oint

Sudut (deg)ng ng

1 1 2 90

2 2 3 0

3 3 4 270

4 3 5 0

5 5 7 270

6 5 6 0

7 6 270

3 9 90

9 9 10 0

10 10 5 270

Disp"acement titi) s(mb( g"oba" str()t(r paa tiap e"ement

E"ement .

1 1 2 3 4

2 4 5 6 7

3 7 9 10

4 7 9 13

5 13 14 15 16

6 13 14 15 19

7 19 20 21 22

7 9 25

9 25 26 27 2

10 2 29 30 13

Re)ap E"emen a"am Matri)s Ke)a)(an *atang

Batang EA / L 4.EI / L 2.EI / L 6.EI / L^2

1 1562500 13020.333 65104.166667 42.125

2 666666.6667 35555.5556 17777.77777 .9

3 1562500 13020.333 65104.166667 42.125

4 666666.6667 35555.5556 17777.77777 .9

5 1562500 13020.333 65104.166667 42.1256 666666.6667 35555.5556 17777.77777 .9

7 1562500 13020.333 65104.166667 42.125

1000000 53333.3333 26666.666667 20000

9 666666.6667 35555.5556 17777.77777 .9

10 1000000 53333.3333 26666.666667 20000

Meng,it(ng !aa an Momen 2.(ng %A)ibat beban "(ar i sepan.ang

ELEMENT 41

arena ti,a a,a gaa ,i'eAanang bentang reeb%, ma

!aa an Momen 2.(ng paa E"ement 41 :


106/473

2nit : -m

;a


107/473

ELEMENT 4B

arena ti,a a,a gaa ,i'eAanang bentang reeb%, ma

!aa an Momen 2.(ng paa E"ement 4B :

2nit : -m;a


108/473


109/473

E"ement 6 :

0 0

0 0

> = 0 0 1 0

0 0 0

0 0 00 0 0 0

-1.3E-016 -1 0 0

1 -1.3E-016 0 0

F>G = 0 0 1 0

0 0 0 -1.3772E-016

0 0 0 1

0 0 0 0

-1.3E-016 1 0 0-1 -1.3E-016 0 0

0 0 1 0

0 0 0 -1.3772E-016

0 0 0 -1

0 0 0 0

E"ement ? :

0 0

0 0

> = 0 0 1 0

0 0 0

0 0 0

0 0 0 0

1 0 0 0

0 1 0 0

F>G = 0 0 1 0

0 0 0 1

0 0 0 0

0 0 0 0

1 0 0 0

0 1 0 0

0 0 1 0

0 0 0 1

0 0 0 0

0 0 0 0

E"ement @ :

0 0

0 0

%' α1

'in α1

- 'in α1

%' α1

%' α1

- 'in α1

F>GD =

%' α1

'in α1

- 'in α1

%' α1

%' α1

- 'in α1

F>GD =

%' α1 'in α1

- 'in α1

%' α1


110/473

> = 0 0 1 0

0 0 0

0 0 0

0 0 0 0

-1.3E-016 -1 0 0

1 -1.3E-016 0 0

F>G = 0 0 1 0

0 0 0 -1.3772E-016

0 0 0 1

0 0 0 0

-1.3E-016 1 0 0

-1 -1.3E-016 0 0

0 0 1 0

0 0 0 -1.3772E-016

0 0 0 -10 0 0 0

E"ement :

0 0

0 0

> = 0 0 1 0

0 0 0

0 0 0

0 0 0 0

1 0 0 0

0 1 0 0

F>G = 0 0 1 0

0 0 0 1

0 0 0 0

0 0 0 0

1 0 0 0

0 1 0 00 0 1 0

0 0 0 1

0 0 0 0

0 0 0 0

E"ement B :

0 0

0 0

> = 0 0 1 0

0 0 0

0 0 0

%' α1

- 'in α1

F>GD =

%' α1

'in α1

- 'in α1

%' α1

%' α1

- 'in α1

F>GD =

%' α1

'in α1

- 'in α1

%' α1

%' α1

- 'in α1


111/473

0 0 0 0

-1.3E-016 -1 0 0

1 -1.3E-016 0 0

F>G = 0 0 1 0

0 0 0 -1.3772E-016

0 0 0 10 0 0 0

-1.3E-016 1 0 0

-1 -1.3E-016 0 0

0 0 1 0

0 0 0 -1.3772E-016

0 0 0 -1

0 0 0 0

E"ement C :0 0

0 0

> = 0 0 1 0

0 0 0

0 0 0

0 0 0 0

6.1257E-017 1 0 0

-1 6.126E-017 0 0

F>G = 0 0 1 0

0 0 0 6.125742E-017

0 0 0 -1

0 0 0 0

6.1257E-017 -1 0 0

1 6.126E-017 0 0

0 0 1 0

0 0 0 6.125742E-017

0 0 0 1

0 0 0 0

E"ement :

0 0

0 0

> = 0 0 1 0

0 0 0

0 0 0

0 0 0 0

1 0 0 0

0 1 0 0

F>GD =

%' α1

'in α1

- 'in α1

%' α1

%' α1

- 'in α1

F>GD =

%' α1

'in α1

- 'in α1

%' α1

%' α1

- 'in α1


112/473

F>G = 0 0 1 0

0 0 0 1

0 0 0 0

0 0 0 0

1 0 0 0

0 1 0 00 0 1 0

0 0 0 1

0 0 0 0

0 0 0 0

E"ement 1 :

0 0

0 0

> = 0 0 1 0

0 0 0

0 0 0

0 0 0 0

-1.3E-016 -1 0 0

1 -1.3E-016 0 0

F>G = 0 0 1 0

0 0 0 -1.3772E-016

0 0 0 1

0 0 0 0

-1.3E-016 1 0 0

-1 -1.3E-016 0 0

0 0 1 0

0 0 0 -1.3772E-016

0 0 0 -1

0 0 0 0

7778 DALAM

Batang = 1


E / " 4.E! / " 2.E! / " 6.E! / "I2

1562500 13020.333 65104.166667 42.125

8& = %' theta = 6.12574E-017

8 = 'in theta = 1

"%al a&i' 1 2 3

1 1562500 0 0

2 0 24414.0625 42.1253 0 42.125 13020.333333

4 -1562500 0 0

F>GD =

%' α1

'in α1

- 'in α1

%' α1

%' α1

- 'in α1

F>GD =


F@1G =


113/473

5 0 -24414.0625 -42.125

6 0 42.125 65104.1666667

1 2 ,1

l%bal a&i' 1 2 3

1 24414.0625 9.42192E-011 -42.125

2 9.422E-011 1562500 2.99105E-0123 -42.125 2.99109E-012 13020.333333

4 -24414.0625 -9.4219E-011 42.125

5 -9.422E-011 -1562500 -2.99109E-012

6 -42.125 2.99109E-012 65104.1666667

7778 DALAM

Batang = 2


E / " 4.E! / " 2.E! / " 6.E! / "I2666666.6667 35555.5556 17777.77777 .9

8& = %' theta = 1

8 = 'in theta = 0

"%al a&i' 1 2 3

1 666666.667 0 0

2 0 2962.962963 .9

3 0 .9 35555.5555556

4 -666666.667 0 05 0 -2962.962963 -.9

6 0 .9 17777.777777

,2 ,3 ,4

l%bal a&i' 4 5 6

4 666666.667 0 0

5 0 2962.962963 .9

6 0 .9 35555.5555556

7 -666666.667 0 0

0 -2962.962963 -.99 0 .9 17777.777777

7778 DALAM

Batang = 3


E / " 4.E! / " 2.E! / " 6.E! / "I2

1562500 13020.333 65104.166667 42.125

8& = %' theta = -1.377E-016

8 = 'in theta = -1

"%al a&i' 1 2 3

F@@1

G =


F@2G =

F@@2

G =



114/473

1 1562500 0 0

2 0 24414.0625 42.125

3 0 42.125 13020.333333

4 -1562500 0 0

5 0 -24414.0625 -42.125

6 0 42.125 65104.1666667

,5 ,6 ,7

l%bal a&i' 7 9

7 24414.0625 2.265E-010 42.125

2.27E-010 1562500 -.97326E-012

9 42.125 -.9733E-012 13020.333333

10 -24414.0625 -2.266E-010 -42.125

11 -2.27E-010 -1562500 .973255E-012

12 42.125 -.9733E-012 65104.1666667

7778 DALAM

Batang = 4


E / " 4.E! / " 2.E! / " 6.E! / "I2

666666.6667 35555.5556 17777.77777 .9

8& = %' theta = 1

8 = 'in theta = 0

"%al a&i' 1 2 31 666666.667 0 0

2 0 2962.962963 .9

3 0 .9 35555.5555556

4 -666666.667 0 0

5 0 -2962.962963 -.9

6 0 .9 17777.777777

,5 ,6 ,7

l%bal a&i' 7 9

7 666666.667 0 0 0 2962.962963 .9

9 0 .9 35555.5555556

13 -666666.667 0 0

14 0 -2962.962963 -.9

15 0 .9 17777.777777

7778 DALAM

Batang = 5

Elemen ,alam matri' eaan batang :E / " 4.E! / " 2.E! / " 6.E! / "I2

1562500 13020.333 65104.166667 42.125

F@3G =

F@@3

G =

3it(ng matri)s )e)a)(an batang ? 9SM?

F@4G =

F@@4

G =

3it(ng matri)s )e)a)(an batang @ 9SM@


115/473

8& = %' theta = -1.377E-016

8 = 'in theta = -1

"%al a&i' 1 2 3

1 1562500 0 0

2 0 24414.0625 42.1253 0 42.125 13020.333333

4 -1562500 0 0

5 0 -24414.0625 -42.125

6 0 42.125 65104.1666667

,9 ,10 ,11

l%bal a&i' 13 14 15

13 24414.0625 2.265E-010 42.125

14 2.27E-010 1562500 -.97326E-012

15 42.125 -.9733E-012 13020.33333316 -24414.0625 -2.266E-010 -42.125

17 -2.27E-010 -1562500 .973255E-012

1 42.125 -.9733E-012 65104.1666667

7778 DALAM

Batang = 6


E / " 4.E! / " 2.E! / " 6.E! / "I2

666666.6667 35555.5556 17777.77777 .9

8& = %' theta = 1

8 = 'in theta = 0

"%al a&i' 1 2 3

1 666666.667 0 0

2 0 2962.962963 .9

3 0 .9 35555.5555556

4 -666666.667 0 0

5 0 -2962.962963 -.96 0 .9 17777.777777

,9 ,10 ,11

l%bal a&i' 13 14 15

13 666666.667 0 0

14 0 2962.962963 .9

15 0 .9 35555.5555556

19 -666666.667 0 0

20 0 -2962.962963 -.9

21 0 .9 17777.777777

7778 DALAM

F@5G =

F@@5G =

3it(ng matri)s )e)a)(an batang 9SM

F@6G =

F@@6

G =

3it(ng matri)s )e)a)(an batang B 9SMB


116/473

Batang = 7


E / " 4.E! / " 2.E! / " 6.E! / "I2

1562500 13020.333 65104.166667 42.125

8& = %' theta = -1.377E-0168 = 'in theta = -1

"%al a&i' 1 2 3

1 1562500 0 0

2 0 24414.0625 42.125

3 0 42.125 13020.333333

4 -1562500 0 0

5 0 -24414.0625 -42.125

6 0 42.125 65104.1666667

19 20 ,15

l%bal a&i' 19 20 21

19 24414.0625 2.265E-010 42.125

20 2.27E-010 1562500 -.97326E-012

21 42.125 -.9733E-012 13020.333333

22 -24414.0625 -2.266E-010 -42.125

23 -2.27E-010 -1562500 .973255E-012

24 42.125 -.9733E-012 65104.1666667

7778 DALAM

Batang =


E / " 4.E! / " 2.E! / " 6.E! / "I2

1000000 53333.3333 26666.666667 20000

8& = %' theta = 6.12574E-017

8 = 'in theta = 1

"%al a&i' 1 2 3

1 1000000 0 0

2 0 10000 20000

3 0 20000 53333.3333333

4 -1000000 0 0

5 0 -10000 -20000

6 0 20000 26666.6666667

,5 ,6 ,7

l%bal a&i' 7 9

7 10000 6.0644E-011 -20000

6.064E-011 1000000 1.22514E-012

9 -20000 1.22515E-012 53333.3333333

25 -10000 -6.0645E-011 20000

F@7G =

F@@7

G =

3it(ng matri)s )e)a)(an batang C 9SMC

F@G =

F@@

G =


117/473

26 -6.064E-011 -1000000 -1.22515E-012

27 -20000 1.22515E-012 26666.6666667

7778 DALAM

Batang = 9

Elemen ,alam matri' eaan batang :E / " 4.E! / " 2.E! / " 6.E! / "I2

666666.6667 35555.5556 17777.77777 .9

8& = %' theta = 1

8 = 'in theta = 0

"%al a&i' 1 2 3

1 666666.667 0 0

2 0 2962.962963 .9

3 0 .9 35555.55555564 -666666.667 0 0

5 0 -2962.962963 -.9

6 0 .9 17777.777777

,17 ,1 ,19

l%bal a&i' 25 26 27

25 666666.667 0 0

26 0 2962.962963 .9

27 0 .9 35555.5555556

2 -666666.667 0 029 0 -2962.962963 -.9

30 0 .9 17777.777777

7778 DALAM

Batang = 10


E / " 4.E! / " 2.E! / " 6.E! / "I2

1000000 53333.3333 26666.666667 20000

8& = %' theta = -1.377E-016

8 = 'in theta = -1

"%al a&i' 1 2 3

1 1000000 0 0

2 0 10000 20000

3 0 20000 53333.3333333

4 -1000000 0 0

5 0 -10000 -20000

6 0 20000 26666.6666667

,20 ,21 ,22

l%bal a&i' 2 29 30

3it(ng matri)s )e)a)(an batang 9SM

F@9G =

F@@9

G =


F@10

G =


118/473

2 10000 1.1935E-010 20000

29 1.19E-010 1000000 -3.67545E-012

30 20000 -3.6754E-012 53333.3333333

13 -10000 -1.193E-010 -20000

14 -1.19E-010 -1000000 3.675445E-012

15 20000 -3.6754E-012 26666.6666667

I$ERR&R%VL&

rtan 'e'ai 'mb gl%bal/'trtr ,engan ()* ang ,i,ahlan

()* : 1 2 ,1

(i'.l%bal a&i' : 1 2 3

(itata lang manal == ,1 ,2 ,3

3 4 5

3 13020.333 42.125 -2.99109E-012

4 42.125 69100.72917 9.42191E-011

5 -2.991E-012 9.42192E-011 1565462.96296

6 65104.1667 42.125 .9

7 0 -666666.6667 0

0 0 -2962.962963

9 0 0 .9

12 0 0 0

13 0 0 0

14 0 0 0

15 0 0 016 0 0 0

17 0 0 0

1 0 0 0

21 0 0 0

24 0 0 0

25 0 0 0

26 0 0 0

27 0 0 0

2 0 0 0

29 0 0 0

30 0 0 0

1 -42.125 -24414.0625 -9.42192E-011

2 2.991E-012 -9.4219E-011 -1562500

10 0 0 0

11 0 0 0

19 0 0 0

20 0 0 0

22 0 0 0

23 0 0 0

3it(ng Matri)s *eban +oint- Noa"Noa" #orces:

a; < A)ibat beban i sepan.ang bentang %)e(a (.(ng i)

F@@10

G =

MATRIKS KEKAK2AN STR2KT2R 9SMS

F@@G =


119/473

E"ement: 1

0

0

= 0

0

0

0


6.125742E-017

1

= 0

0

0

0

l%bal a&i'

1

2

= 3

4

5

6

E"ement: 5

0

0

= 0

0

0

0


1

0

= 0

0

0

0

l%bal a&i'

4

F"G1

F@G1

F@G1

F"G1

F@G1


120/473

5

= 6

7

9

E"ement: 6

0

0

= 0

0

0

0


-1.3772E-016

-1

= 0

0

0

0

l%bal a&i'

7

= 9

10

11

12

E"ement: ?

0

0

= 0

0

0

0


1

0

= 00

0

F@G1

F"G1

F@G1

F@G1

F"G1

F@G1


121/473

0

l%bal a&i'

7

= 9

1314

15

E"ement: @

0

0

= 0

0

00


-1.3772E-016

-1

= 0

0

0

0

l%bal a&i'

13

14

= 15

16

17

1

E"ement:

0

0

= 0

0

0

0


1

0

F@G1

F"G1

F@G1

F@G1

F"G1


122/473

= 0

0

0

0

l%bal a&i'

1314

= 15

19

20

21

E"ement: B

0

0

= 0

0

0

0


-1.3772E-016

-1

= 0

0

0

0

l%bal a&i'

19

20

= 21

22

23

24

E"ement: C

0

0

= 0

0

0

0

F@G1

F@G1

F"G1

F@G1

F@G1

F"G1


123/473


6.125742E-017

1

= 0

0

0

0

l%bal a&i'

7

= 9

25

26

27

E"ement:

0

0

= 0

0

0

0


1

0

= 0

0

0

0

l%bal a&i'

25

26

= 27

2

29

30

E"ement: 1

0

0

= 0

F@G1

F@G1

F"G1

F@G1

F@G1

F"G1


124/473


125/473

9 27 0

10 2 0

10 29 0

10 30 0

e = 0 1 1

0 2 20 3 ,1

0 4 ,2

0 5 ,3

0 6 ,4

0 7 ,5

0 ,6

0 9 ,7

0 10 10

0 11 11

0 12 ,

0 13 ,9

0 14 ,10

0 15 ,11

0 16 ,12

0 17 ,13

0 1 ,14

0 19 19

0 20 20

0 21 ,15

0 22 22

0 23 230 24 ,16

0 25 ,17

0 26 ,1

0 27 ,19

0 2 ,20

0 29 ,21

0 30 ,22

b; < A)ibat *eban i .oint %)e(a (.(ng i)e)ang'

%int @b l%bal

1 1 0

1 2 0

1 3 0

2 4 50

= 2 5 0

2 6 0

3 7 0

3 0

3 9 0

4 10 04 11 0

4 12 0


126/473

5 13 0

5 14 0

5 15 0

6 16 0

6 17 0

6 1 0

7 19 07 20 0

7 21 0

22 0

23 0

24 0

9 25 50

9 26 -100

9 27 0

10 2 0

10 29 -100

10 30 0

c; < *eban )ombinasi ata( gab(ngan %Ae > A.'

%int @b l%bal ()*

1 1 1

1 2 2

1 3 ,1

2 4 ,2

= 2 5 ,3

2 6 ,43 7 ,5

3 ,6

3 9 ,7

4 10 10

4 11 11

4 12 ,

5 13 ,9

5 14 ,10

5 15 ,11

6 16 ,126 17 ,13

6 1 ,14

7 19 19

7 20 20

7 21 ,15

22 22

23 23

24 ,16

9 25 ,17

9 26 ,1

9 27 ,1910 2 ,20

10 29 ,21


127/473

10 30 ,22

Data lang : (i'Alaement /

,1 0

,2 50

,3 0

,4 0

= ,5 0

,6 0

,7 0

, 0

,9 0

,10 0

,11 0

,12 0

,13 0,14 0

,15 0

,16 0

,17 50

,1 -100

,19 0

,20 0

,21 -100

,22 0

1 02 0

10 0

11 0

19 0

20 0

22 0

23 0

9.949272E-006

-1.2714E-006

1.76516E-00

-3.5467E-006

-.52254E-007

-1.92105E-00

4.636491E-007

.777072E-00

= -4.275E-007

.47391E-007

4.6914E-00

-0.000000234

.47391E-0074.6914E-00

-0.000000063


128/473


129/473


130/473

Defined DOF

after boundary conditions

aa Titi) +oint Str()t(r a"am Ara, S(mb( !"oba"-S(mb( Str()t(r

TA*LE: +oint /oorinates

+oint /oorSs /oorTpe HorRDe&t De&t De&t m

1 ")B" 8arte'ian -9

2 ")B" 8arte'ian -9

3 ")B" 8arte'ian -3

4 ")B" 8arte'ian -3

5 ")B" 8arte'ian 3

6 ")B" 8arte'ian 9

7 ")B" 8arte'ian 3

")B" 8arte'ian 9

9 ")B" 8arte'ian -310 ")B" 8arte'ian 3

TA*LE: /onnecti=it < $rame

$rame +ointI +oint+ Is/(r=e

De&t De&t De&t #e'/%

1 1 2 %

2 2 3 %

3 4 3 %

4 3 5 %

5 7 5 %

6 5 6 %

7 6 %


131/473

3 9 %

9 9 10 %

10 5 10 %

)

5 6 == l%bal a&i'

9 == l%bal a&i'

11 12 == l%bal a&i'

14 15 == l%bal a&i'

17 1 == l%bal a&i'

20 21 == l%bal a&i'

23 24 == l%bal a&i'

26 27 == l%bal a&i'

29 30 == l%bal a&i'

14 15 == l%bal a&i'

12.EI / L^3 Sudut (deg) 8& 8

24414.0625 90 6.12574E-017 1

2962.96296296 0 1 0

24414.0625 270 -1.3697E-016 -1

2962.96296296 0 1 0

24414.0625 270 -1.3697E-016 -12962.96296296 0 1 0

24414.0625 270 -1.3697E-016 -1

10000 90 6.12323E-017 1

2962.96296296 0 1 0

10000 270 -1.3697E-016 -1

bentang engan (.(ng i)e)ang-i.epit' %DALAM ARA3 S2M*2 L&KAL' :

rea'i ng tereang 'emana = 0


132/473


133/473

rea'i ng tereang 'emana = 0


134/473

0 0

0 0

0 0

0 0

0

0

0 1

0 0

0 0

0 0

1 06.125742E-017 0

0 1

0 0

0 0

0 0

-1 0

6.125742E-017 0

0 1

0 0

0 0

0 0

0

0

0 1

0 0

0 0

0 0

0 0

1 0

0 1

0 0

0 0

0 0

0 0

1 0

0 1

'in α1

%' α1

'in α1

%' α1


135/473

0 0

0 0

0 0

0

00 1

0 0

0 0

0 0

-1 0

-1.3772E-016 0

0 1

0 00 0

0 0

1 0

-1.3772E-016 0

0 1

0 0

0 0

0 0

0

0

0 1

0 0

0 0

0 0

0 0

1 0

0 1

0 0

0 0

0 0

0 0

1 0

0 1

0 0

0 0

'in α1

%' α1

'in α1

%' α1


136/473

0 0

0

0

0 1

0 0

0 0

0 0

-1 0

-1.3772E-016 0

0 1

0 0

0 0

0 0

1 0

-1.3772E-016 00 1

0 0

0 0

0 0

0

0

0 1

0 0

0 0

0 0

0 0

1 0

0 1

0 0

0 00 0

0 0

1 0

0 1

0 0

0 0

0 0

0

0

'in α1

%' α1

'in α1

%' α1

'in α1

%' α1


137/473


138/473

0 0

0 0

1 0

0 1

0 0

0 00 0

0 0

1 0

0 1

0 0

0 0

0 0

0

0

0 1

0 0

0 0

0 0

-1 0

-1.3772E-016 0

0 1

0 0

0 0

0 0

1 0

-1.3772E-016 0

0 1

2M*2 L&KAL

12.E! / "I3

24414.0625

4 5 6

-1562500 0 0

0 -24414.0625 42.1250 -42.125 65104.166667

1562500 0 0

'in α1

%' α1


139/473

0 24414.0625 -42.125

0 -42.125 13020.33333

,2 ,3 ,4

4 5 6

-24414.0625 -9.4219E-011 -42.125

-9.42192E-011 -1562500 2.99109E-01242.125 -2.9911E-012 65104.166667

24414.0625 9.42192E-011 42.125

9.42191E-011 1562500 -2.99109E-012

42.125 -2.9911E-012 13020.33333

2M*2 L&KAL

12.E! / "I32962.96296296

4 5 6

-666666.66667 0 0

0 -2962.962963 .9

0 -.9 17777.77777

666666.666667 0 00 2962.962963 -.9

0 -.9 35555.555556

,5 ,6 ,7

7 9

-666666.66667 0 0

0 -2962.962963 .9

0 -.9 17777.77777

666666.666667 0 0

0 2962.962963 -.90 -.9 35555.555556

2M*2 L&KAL

12.E! / "I3

24414.0625

4 5 6


140/473

-1562500 0 0

0 -24414.0625 42.125

0 -42.125 65104.166667

1562500 0 0

0 24414.0625 -42.125

0 -42.125 13020.33333

10 11 ,

10 11 12

-24414.0625 -2.266E-010 42.125

-2.265E-010 -1562500 -.97326E-012

-42.125 .97326E-012 65104.166667

24414.0625 2.265E-010 -42.125

2.26575E-010 1562500 .97326E-012

-42.125 .97326E-012 13020.33333

2M*2 L&KAL

12.E! / "I3

2962.96296296

4 5 6-666666.66667 0 0

0 -2962.962963 .9

0 -.9 17777.77777

666666.666667 0 0

0 2962.962963 -.9

0 -.9 35555.555556

,9 ,10 ,11

13 14 15

-666666.66667 0 00 -2962.962963 .9

0 -.9 17777.77777

666666.666667 0 0

0 2962.962963 -.9

0 -.9 35555.555556

2M*2 L&KAL

12.E! / "I3

24414.0625


141/473

4 5 6

-1562500 0 0

0 -24414.0625 42.1250 -42.125 65104.166667

1562500 0 0

0 24414.0625 -42.125

0 -42.125 13020.33333

,12 ,13 ,14

16 17 1

-24414.0625 -2.266E-010 42.125

-2.265E-010 -1562500 -.97326E-012

-42.125 .97326E-012 65104.16666724414.0625 2.265E-010 -42.125

2.26575E-010 1562500 .97326E-012

-42.125 .97326E-012 13020.33333

2M*2 L&KAL

12.E! / "I3

2962.96296296

4 5 6

-666666.66667 0 0

0 -2962.962963 .9

0 -.9 17777.77777

666666.666667 0 0

0 2962.962963 -.90 -.9 35555.555556

19 20 ,15

19 20 21

-666666.66667 0 0

0 -2962.962963 .9

0 -.9 17777.77777

666666.666667 0 0

0 2962.962963 -.9

0 -.9 35555.555556

2M*2 L&KAL


142/473

12.E! / "I3

24414.0625

4 5 6

-1562500 0 0

0 -24414.0625 42.125

0 -42.125 65104.166667

1562500 0 0

0 24414.0625 -42.125

0 -42.125 13020.33333

22 23 ,16

22 23 24

-24414.0625 -2.266E-010 42.125

-2.265E-010 -1562500 -.97326E-012

-42.125 .97326E-012 65104.166667

24414.0625 2.265E-010 -42.125

2.26575E-010 1562500 .97326E-012

-42.125 .97326E-012 13020.33333

2M*2 L&KAL

12.E! / "I3

10000

4 5 6

-1000000 0 0

0 -10000 20000

0 -20000 26666.666667

1000000 0 0

0 10000 -20000

0 -20000 53333.333333

,17 ,1 ,19

25 26 27

-10000 -6.0645E-011 -20000

-6.0644E-011 -1000000 1.22515E-012

20000 -1.2251E-012 26666.666667

10000 6.0644E-011 20000


143/473

6.06445E-011 1000000 -1.22515E-012

20000 -1.2251E-012 53333.333333

2M*2 L&KAL

12.E! / "I3

2962.96296296

4 5 6

-666666.66667 0 0

0 -2962.962963 .9

0 -.9 17777.77777666666.666667 0 0

0 2962.962963 -.9

0 -.9 35555.555556

,20 ,21 ,22

2 29 30

-666666.66667 0 0

0 -2962.962963 .9

0 -.9 17777.77777

666666.666667 0 00 2962.962963 -.9

0 -.9 35555.555556

2M*2 L&KAL

12.E! / "I3

10000

4 5 6

-1000000 0 0

0 -10000 20000

0 -20000 26666.666667

1000000 0 0

0 10000 -20000

0 -20000 53333.333333

,9 ,10 ,11

13 14 15


144/473

-10000 -1.193E-010 20000

-1.1935E-010 -1000000 -3.67545E-012

-20000 3.67545E-012 26666.666667

10000 1.1935E-010 -20000

1.19345E-010 1000000 3.67545E-012

-20000 3.67545E-012 53333.333333

K2P%FDCGFDF?:F+F@?GMAT/3%EFBGFDF?C:F+F?CG'G$ALSE'G'>I$ERR&R%VL&&K2P%F

,2 ,3 ,4 ,5 ,6 ,7

4 5 6 7 9

,4 ,5 ,6 ,7 , ,9

6 7 9 12 13

65104.1666667 0 0 0 0 0

42.125 -666666.6667 0 0 0 0

.9 0 -2962.962963 .9 0 0

165763.9 0 -.9 17777.77777 0 0

0 1367747.396 3.43302E-010 22.125 42.125 -666666.66667

-.9 3.43302E-010 256425.9259 1.22515E-012 -.97326E-012 0

17777.777777 22.125 1.22515E-012 254652.7777 65104.1666667 0

0 42.125 -.97326E-012 65104.166667 13020.333333 0

0 -666666.6667 0 0 0 1367747.3953

0 0 -2962.962963 -.9 0 4.645921E-010

0 0 .9 17777.77777 0 22.1250 0 0 0 0 -24414.0625

0 0 0 0 0 -2.265E-010

0 0 0 0 0 42.125

0 0 0 0 0 0

0 0 0 0 0 0

0 -10000 -6.0644E-011 20000 0 0

0 -6.0645E-011 -1000000 -1.2251E-012 0 0

0 -20000 1.22515E-012 26666.666667 0 0

0 0 0 0 0 -10000

0 0 0 0 0 -1.1935E-010

0 0 0 0 0 -20000

-42.125 0 0 0 0 0

2.99105E-012 0 0 0 0 0

0 -24414.0625 -2.265E-010 -42.125 -42.125 0

0 -2.266E-010 -1562500 .97326E-012 .973255E-012 0

0 0 0 0 0 -666666.66667

0 0 0 0 0 0

0 0 0 0 0 0

0 0 0 0 0 0

)ang'


145/473

"%al a&i'

1

2

3

4

5

6

-1 0 0 0 0

6.125742E-017 0 0 0 0

0 1 0 0 0 &

0 0 6.12574E-017 -1 0

0 0 1 6.12574E-017 0

0 0 0 0 1

0

0

0

0

0

0

"%al a&i'

1

2

3

4

5

6

0 0 0 0 0

1 0 0 0 0

0 1 0 0 0 &

0 0 1 0 0

0 0 0 1 0

0 0 0 0 1

0

AMS 1 ! "# . AM

L 1

AMS 1 ! "# . AM

L 1


146/473

0

0

0

0

0

"%al a&i'

1

2

3

4

5

6

1 0 0 0 0

-1.3772E-016 0 0 0 0

0 1 0 0 0 &

0 0 -1.3772E-016 1 0

0 0 -1 -1.377E-016 0

0 0 0 0 1

0

0

0

0

0

0

"%al a&i'

1

2

3

4

5

6

0 0 0 0 0

1 0 0 0 0

0 1 0 0 0 &0 0 1 0 0

0 0 0 1 0

AMS 1 ! "# . AM

L 1

AMS 1 ! "# . AM

L 1


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0 0 0 0 1

0

0

0

00

0

"%al a&i'

1

2

3

4

56

1 0 0 0 0

-1.3772E-016 0 0 0 0

0 1 0 0 0 &

0 0 -1.3772E-016 1 0

0 0 -1 -1.377E-016 0

0 0 0 0 1

0

0

0

0

0

0

"%al a&i'

1

2

3

4

5

6

0 0 0 0 0

1 0 0 0 0

AMS 1 ! "# . AM

L 1

AMS 1 ! "# . AM

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-1 0 0 0 0

6.125742E-017 0 0 0 0

0 1 0 0 0 &

0 0 6.12574E-017 -1 0

0 0 1 6.12574E-017 0

0 0 0 0 1

0

0

0

0

0

0

"%al a&i'

1

2

3

4

5

6

0 0 0 0 0

1 0 0 0 0

0 1 0 0 0 &

0 0 1 0 0

0 0 0 1 0

0 0 0 0 1

0

0

0

0

0

0

"%al a&i'

1

2

3

AMS 1 ! "# . AM

L 1

AMS 1 ! "# . AM

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4

5

6

1 0 0 0 0-1.3772E-016 0 0 0 0

0 1 0 0 0 &

0 0 -1.3772E-016 1 0

0 0 -1 -1.377E-016 0

0 0 0 0 1

0

0

0

0

0

0

Element 2 Element 3 Element 4

0 0 0

0 0 0

0 0 00 0 0

0 + 0 + 0 +

0 0 0

0 0 0

0 0 0

0 0 0

0 0 0

0 0 0

0 0 0

0 0 0

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AMS 1 ! "# . AM

L 1


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0 0 0

0 0 0

0 0 0

0 0 0

()*

1 1

2 1

,1 1

,2 2

,3 2

,4 2

,5 3

,6 3

,7 3

10 411 4

, 4


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,9 5

,10 5

,11 5

,12 6

,13 6

,14 6

19 720 7

,15 7

22

23

,16

,17 9

,1 9

,19 9

,20 10

,21 10

,22 10

0 0 0

0 0 0

0 0 0

0 50 50

0 + 0 = 0

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0 0 0

0 0 0

0 0 0

0 0 0

0 0 0

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0 0 0

0 0 0

0 0 00 0 0

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0 0 0

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0 0 0

0 0 0

0 50 50

0 -100 -100

0 0 00 0 0

0 -100 -100


153/473

0 0 0

e%rma'i @trtr

,1 = -0.000221 1

,2 = 0.000419 2

,3 = 0.00000 2

,4 = 0.00012 2

,5 = 0.000352 3

,6 = -0.000095 3

,7 = -0.00154 3

, = 0.000660 4

,9 = 0.000196 5

,10 = -0.02267 5

,11 = -0.001302 5

,12 = -0.005013 6

,13 = -0.02267 6,14 = -0.001302 6

,15 = 0.0016 7

,16 = -0.00044

,17 = 0.01375 9

,1 = -0.000190 9

,19 = -0.00393 9

,20 = 0.013745 10

,21 = -0.022792 10

,22 = -0.004121 10

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0.000000006 6.3910E-007 -3.949E-00 4.5600E-009 9.057520E-010 -2.730E-00

-7.74216E-007 -3.950E-00 0.00000775 -4.9749E-007 4.16573E-00 -7.17907E-007

0.000002936 4.5600E-009 -4.97491E-007 2.94466E-006 -3.10195E-009 -0.00000030

-4.59307E-009 9.05752E-010 4.1657E-00 -3.1019E-009 6.3211E-007 1.15549E-00

-2.7919E-007 -2.73E-00 -7.17907E-007 -0.00000030 1.15549E-00 5.72949E-006

-9.61405E-007 1.26560E-00 5.45512E-007 -9.5023E-007 -4.61602E-009 -0.000002776

1.471195E-006 2.41526E-009 -2.450E-007 1.47566E-006 -1.600E-009 -1.0111E-007

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-1.0710E-007 -1.3979E-009 -1.653E-00 -1.0940E-007 -5.97235E-00 2.42197E-007

0.00000104 -3.1763E-009 -0.000000312 0.00000103 -2.4070E-007 7.911674E-007

-5.59199E-007 -5.15E-00 -1.27540E-006 -0.000000611 3.742452E-007 1.053777E-005-1.0710E-007 -1.3979E-009 -1.653E-00 -1.0940E-007 -5.97235E-00 2.42197E-007

5.170173E-00 3.646E-009 .73112E-00 5.53725E-00 -0.000000017 -7.35564E-007

$F ! S

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Y Specia"+t !"oba"H !"oba"Y !"oba"m m #e'/% m m m

0 0 % -9 0 0

0 4 % -9 0 4

0 4 % -3 0 4

0 0 % -3 0 0

0 4 % 3 0 4

0 4 % 9 0 4

0 0 % 3 0 0

0 0 % 9 0 0

0 % -3 0 0 % 3 0

Lengt, /entroiH /entroiY /entroi

m m m m

4 -9 0 2

6 -6 0 4

4 -3 0 2

6 0 0 4

4 3 0 2

6 6 0 4

4 9 0 2


157/473

4 -3 0 6

6 0 0

4 3 0 6


158/473


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166/473


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DCGFDF@C:F+F6GMAT/3%EFBGFDF@B:F+F@BG'G$ALSE'G'

10 11 , ,9 ,10 ,11

10 11 12 13 14 15

,10 ,11 ,12 ,13 ,14 ,15

14 15 16 17 1 21

0 0 0 0 0 0

0 0 0 0 0 0

0 0 0 0 0 0

0 0 0 0 0 0

0 0 0 0 0 0

-2962.962963 .9 0 0 0 0

-.9 17777.777777 0 0 0 0

0 0 0 0 0 0

4.645921E-010 22.125 -24414.0625 -2.265E-010 42.125 0

256425.92593 3.675445E-012 -2.265E-010 -1562500 -.97326E-012 .9

3.675445E-012 254652.77777 -42.125 .973255E-012 65104.1666667 17777.777777-2.265E-010 -42.125 24414.0625 2.26575E-010 -42.125 0

-1562500 .973255E-012 2.26575E-010 1562500 .973255E-012 0

-.97326E-012 65104.1666667 -42.125 .973255E-012 13020.333333 0

.9 17777.777777 0 0 0 165763.9

0 0 0 0 0 65104.1666667

0 0 0 0 0 0

0 0 0 0 0 0

0 0 0 0 0 0

-1.1935E-010 20000 0 0 0 0

-1000000 -3.67545E-012 0 0 0 0

3.675445E-012 26666.6666667 0 0 0 0

0 0 0 0 0 0

0 0 0 0 0 0

0 0 0 0 0 0

0 0 0 0 0 0

0 0 0 0 0 42.125

-2962.962963 -.9 0 0 0 -.9

0 0 0 0 0 -42.125

0 0 0 0 0 .973255E-012


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0

0

0

0

0

0

0

0

0

0

0

0


172/473

0

0

0

0

0

0

0

0

00

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173/473

0

0

0

0

0

0

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0

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174/473

0

0

0

0

0

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175/473

0

0

0

0

0

0

0

0

0

0

0

0


176/473

00

0

0

0

0

Element 5 Element 6 Element 7

0 0 0

0 0 0

0 0 00 0 0

0 + 0 + 0 +

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0 0 0

0 0 0

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0 0 00 0 0

0 0 0


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0 0 0

0 0 0

0 0 0

0 0 0


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+oint &(tp(t/ase /aseTpe 21

De&t De&t De&t m

1 (E( "in@tati 0

2 (E( "in@tati 0.010466

3 (E( "in@tati 0.010423

4 (E( "in@tati 0

5 (E( "in@tati 0.01036

6 (E( "in@tati 0.010354

7 (E( "in@tati 0

(E( "in@tati 0

9 (E( "in@tati 0.01793

10 (E( "in@tati 0.01756

.777072E-00 -4.275E-007 .47391E-007 4.6914E-00 -0.000000234 .47391E-007

-9.61405E-007 1.471195E-006 -5.59199E-007 -1.0710E-007 0.00000104 -5.59199E-007

1.265602E-00 2.415260E-009 -5.145E-00 -1.3979E-009 -3.17630E-009 -5.145E-00

5.455125E-007 -2.450E-007 -1.27540E-006 -1.653E-00 -0.000000312 -1.27540E-006

-9.50230E-007 1.475660E-006 -0.000000611 -1.09403E-007 0.00000103 -0.000000611

-4.61602E-009 -1.600E-009 3.742452E-007 -5.97235E-00 -2.4070E-007 3.742452E-007

-0.000002776 -1.0111E-007 1.053777E-005 2.42197E-007 7.911674E-007 1.053777E-005

9.424317E-006 -4.63317E-007 -5.03975E-006 -.033E-00 -7.452E-007 -5.03975E-006

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0.000000347 2.275944E-00 -1.34975E-005 -1.014E-006 -7.1317E-006 -1.34975E-005


180/473

-1.73509E-007 -1.13797E-00 6.7473E-006 9.007409E-007 3.59154E-006 6.7473E-006

4.076456E-006 1.79379E-006 -7.07475E-005 -1.46172E-005 -5.6674E-005 -7.07475E-005

-2.52433E-009 -1.7431E-009 4.51105E-007 -7.5624E-00 -3.0424E-007 4.51105E-007

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- - - - - -

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- - - - - -

0.00 - - - - -

- - - - - -

- - - - - -

- 24J414.06 0.00 4J2.13 - 0.00

- 0.00 1J562J500.00 17J777.7 0.00 -

- 4J2.13 17J777.7 130J20.33 - 0.00

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