Tugas Anstruk 3

142
Home work Metode Elemen Hingga - 1 SUANTORO WICAKSONO (07 / 260420 / PTK / 4744) Tabel Data Elemen : Elemen Nodal A I E G i j 1 5 1 0.2025 0.0034 20000000 7692308 2 6 2 3 7 3 4 8 4 5 2 1 0.165 0.00415 6 2 3 7 3 4 8 1 4 m 2 m 4 kN/m 2 100 kN 5 m 8 m 4 m 10 kN 10 kN/m 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 x y z 0,45 0,,45 z y 0,55 0,3 z y z

Transcript of Tugas Anstruk 3

Page 1: Tugas Anstruk 3

Home work Metode Elemen Hingga - 1SUANTORO WICAKSONO (07 / 260420 / PTK / 4744)

Tabel Data Elemen :

ElemenNodal A I E G

i j1 5 1

0.2025 0.0034

20000000 7692308

2 6 23 7 34 8 45 2 1

0.165 0.004156 2 37 3 48 1 4

m2 m4 kN/m2

100 kN

5 m 8 m

4 m

10 kN

10 kN/m

1

2

3

45

6

7

8

1

2

3

4

5

6

7

8

x

y

z

0,45

0,,45

z

y

0,55

0,3

z

y

z

Page 2: Tugas Anstruk 3

Home work Metode Elemen Hingga - 1SUANTORO WICAKSONO (07 / 260420 / PTK / 4744)

Elemen 1, 2, 3, 4 :

x

y

z

x

z

yi

j

Page 3: Tugas Anstruk 3

Home work Metode Elemen Hingga - 1SUANTORO WICAKSONO (07 / 260420 / PTK / 4744)

Matriks kekakuannya :

0 0 0 0 0 0 0 0 0 0L L

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 0L L

0 0 0 0 0 0 0 0L L

0 0 0 0 0 0 0 0L L

0 0 0 0 0 0 0 0 0 0L L

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 0L L

0 0 0 0 0 0 0 0L L

0 0 0 0 0 0 0 0L L

EAx - EAx

12EIx 6EIx 12EIx 6EIx

L2 L2 L2 L2

12EIx - 6EIx 12EIx - 6EIx

L2 L2 L2 L2

GIx - GIx

- 6EIx 4EIx 6EIx 2EIx

L2 L2

6EIx 4EIx - 6EIx 2EIx

L2 L2

- EAx EAx

12EIx - 6EIx 12EIx - 6EIx

L2 L2 L2 L2

12EIx 6EIx 12EIx 6EIx

L2 L2 L2 L2

- GIx GIx

- 6EIx 2EIx 6EIx 4EIx

L2 L2

6EIx 2EIx - 6EIx 4EIx

L2 L2

[k l(e )]=

Page 4: Tugas Anstruk 3

Home work Metode Elemen Hingga - 1SUANTORO WICAKSONO (07 / 260420 / PTK / 4744)

1012500 0 0 0 0 0 -1012500 0 0 0 0 00 51000 0 0 0 25500 0 51000 0 0 0 255000 0 51000 0 -25500 0 0 0 51000 0 -25500 00 0 0 6538.462 0 0 0 0 0 -6538.462 0 00 0 -25500 0 68000 0 0 0 25500 0 34000 00 25500 0 0 0 68000 0 -25500 0 0 0 34000

-1012500 0 0 0 0 0 1012500 0 0 0 0 00 51000 0 0 0 -25500 0 51000 0 0 0 -255000 0 51000 0 25500 0 0 0 51000 0 25500 00 0 0 -6538.462 0 0 0 0 0 6538.462 0 00 0 -25500 0 34000 0 0 0 25500 0 68000 00 25500 0 0 0 34000 0 -25500 0 0 0 68000

Matriks transformasi :

dengan :

[R ]=[λ x μx νx

−λ x . μx . cosα−ν x . sinα

√ λx2+νx

2√( λx2+νx2) . cosα

−νx .μx . cos α− λx .sinα

√ λx2+ν x2λx . μx . sinα−ν x . cos α

√ λx2+νx2

−√( λx2+ν x2) . sinαμx .νx . sinα−λx . cosα

√ λx2+ν x2]

[k l(e )]=

[T (e ) ]=[ [R ] [ 0 ] [ 0 ] [ 0 ][ 0 ] [R ] [ 0 ] [ 0 ][ 0 ] [ 0 ] [R ] [ 0 ][ 0 ] [ 0 ] [ 0 ] [R ] ]

Page 5: Tugas Anstruk 3

Home work Metode Elemen Hingga - 1SUANTORO WICAKSONO (07 / 260420 / PTK / 4744)

= 4

= 0

= 0

= 1

= 0

= 0.5

= 0.5

= 0

0

1

cos α =

sin α =

L=√(X j−X i )2+(Y j−Y i )

2+(Z j−Z i )2

λx=cosθxX=X j−X iL

μx=cosθxY=Y j−Y iL

νx=cosθxZ=Z j−Z iL

cos β=λx

√ λx2+νx2

sin β=νx

√ λx2+ν x2cos γ=√ λx2+ν x2sin γ=μx

Page 6: Tugas Anstruk 3

Home work Metode Elemen Hingga - 1SUANTORO WICAKSONO (07 / 260420 / PTK / 4744)

0 0 1 0 0 0 0 0 0 0 0 0-2 0 0 0 0 0 0 0 0 0 0 00 -0.5 0 0 0 0 0 0 0 0 0 00 0 0 0 0 1 0 0 0 0 0 00 0 0 -2 0 0 0 0 0 0 0 00 0 0 0 -0.5 0 0 0 0 0 0 00 0 0 0 0 0 0 0 1 0 0 00 0 0 0 0 0 -2 0 0 0 0 00 0 0 0 0 0 0 -0.5 0 0 0 00 0 0 0 0 0 0 0 0 0 0 10 0 0 0 0 0 0 0 0 -2 0 00 0 0 0 0 0 0 0 0 0 -0.5 0

0 -2 0 0 0 0 0 0 0 0 0 00 0 -0.5 0 0 0 0 0 0 0 0 01 0 0 0 0 0 0 0 0 0 0 00 0 0 0 -2 0 0 0 0 0 0 00 0 0 0 0 -0.5 0 0 0 0 0 00 0 0 1 0 0 0 0 0 0 0 00 0 0 0 0 0 0 -2 0 0 0 00 0 0 0 0 0 0 0 -0.5 0 0 00 0 0 0 0 0 1 0 0 0 0 00 0 0 0 0 0 0 0 0 0 -2 00 0 0 0 0 0 0 0 0 0 0 -0.50 0 0 0 0 0 0 0 0 1 0 0

[T( e ) ]=

[k g(e )]=[T (e )]T [k l(e ) ] [T (e )]

[T (e ) ]T =

Page 7: Tugas Anstruk 3

Home work Metode Elemen Hingga - 1SUANTORO WICAKSONO (07 / 260420 / PTK / 4744)

0 -102000 0 0 0 -51000 0 -102000 0 0 0 -510000 0 -25500 0 12750 0 0 0 -25500 0 12750 0

1012500 0 0 0 0 0 -1012500 0 0 0 0 00 0 51000 0 -136000 0 0 0 -51000 0 -68000 00 -12750 0 0 0 -34000 0 12750 0 0 0 -170000 0 0 6538 0 0 0 0 0 -6538 0 00 -102000 0 0 0 51000 0 -102000 0 0 0 510000 0 -25500 0 -12750 0 0 0 -25500 0 -12750 0

-1012500 0 0 0 0 0 1012500 0 0 0 0 00 0 51000 0 -68000 0 0 0 -51000 0 -136000 00 -12750 0 0 0 -17000 0 12750 0 0 0 -340000 0 0 -6538 0 0 0 0 0 6538 0 0

204000 0 0 0 25500 0 204000 0 0 0 25500 00 12750 0 -25500 0 0 0 12750 0 -25500 0 00 0 1012500 0 0 0 0 0 -1012500 0 0 00 -25500 0 272000 0 0 0 25500 0 136000 0 0

25500 0 0 0 17000 0 -25500 0 0 0 8500 00 0 0 0 0 6538 0 0 0 0 0 -6538

204000 0 0 0 -25500 0 204000 0 0 0 -25500 00 12750 0 25500 0 0 0 12750 0 25500 0 00 0 -1012500 0 0 0 0 0 1012500 0 0 00 -25500 0 136000 0 0 0 25500 0 272000 0 0

25500 0 0 0 8500 0 -25500 0 0 0 17000 00 0 0 0 0 -6538 0 0 0 0 0 6538

[T (e ) ]T [k l(e ) ]=

[k g(e )]=

Page 8: Tugas Anstruk 3

Home work Metode Elemen Hingga - 1SUANTORO WICAKSONO (07 / 260420 / PTK / 4744)

beban nodal ekivalen :

* 0 *

0

0

0

0

=0

0

0

0

0

0

0

Fi

Gi

Hi

Mxi

Myi

Mzi

Fj

Gj

Hj

Mxj

Myj

Mzj

{ f (e )}¿= {F (e ) }¿=

Page 9: Tugas Anstruk 3

Home work Metode Elemen Hingga - 1SUANTORO WICAKSONO (07 / 260420 / PTK / 4744)

Elemen 6,8 :

Matriks kekakuannya :

412500 0 0 0 0 0 -412500 0 0 0 0 00 15562.5 0 0 0 7781.25 0 15562.5 0 0 0 7781.250 0 15562.5 0 -7781.25 0 0 0 15562.5 0 -7781.25 00 0 0 3990.385 0 0 0 0 0 -3990.385 0 00 0 -7781.25 0 41500 0 0 0 7781.25 0 0 00 7781.25 0 0 0 41500 0 -7781.25 0 0 0 0

-412500 0 0 0 0 0 412500 0 0 0 0 00 15562.5 0 0 0 -7781.25 0 15562.5 0 0 0 -7781.250 0 15562.5 0 7781.25 0 0 0 15562.5 0 7781.25 00 0 0 -3990.385 0 0 0 0 0 3990.385 0 00 0 -7781.25 0 0 0 0 0 7781.25 0 41500 00 7781.25 0 0 0 0 0 -7781.25 0 0 0 41500

karena sumbu lokal sama dengan sumbu global

beban nodal ekivalen :

= -(1/2 x 150) = -75 kN

= +(1/8 x 150 x 8) = +150 kNm

= -(1/2 x 100) = -75 kN

h8

my8

h7

x

y

zy

z

i

j

150 kN

x

[k l(e )]=

[k g(e )]=[kl(e ) ]

Page 10: Tugas Anstruk 3

Home work Metode Elemen Hingga - 1SUANTORO WICAKSONO (07 / 260420 / PTK / 4744)

= -(1/8 x 100 x 5) = -150 kNmmy7

Page 11: Tugas Anstruk 3

Home work Metode Elemen Hingga - 1SUANTORO WICAKSONO (07 / 260420 / PTK / 4744)

* 0 * * 0 *

0 0

= -75 0

0 0

= +150 0

=0

=0

0 0

0 0

= -75 0

0 0

= -150 0

0 0

Elemen 5,7 :

F8 F5

G8 G5

H8 H5

Mx8 Mx5

My8 My5

Mz8 Mz5

F7 F6

G7 G6

H7 H6

Mx7 Mx6

My7 My6

Mz7 Mz6

x

y

z

i

j

25 kN/m x

y

z

{ f 5 }¿= {F5 }¿={ f 6 }¿={F6 }¿=

Page 12: Tugas Anstruk 3

Home work Metode Elemen Hingga - 1SUANTORO WICAKSONO (07 / 260420 / PTK / 4744)

Matriks kekakuannya :

412500 0 0 0 0 0 -412500 0 0 0 0 00 15562.5 0 0 0 7781.25 0 15562.5 0 0 0 7781.250 0 15562.5 0 -7781.25 0 0 0 15562.5 0 -7781.25 00 0 0 3990.385 0 0 0 0 0 -3990.385 0 00 0 -7781.25 0 41500 0 0 0 7781.25 0 0 00 7781.25 0 0 0 41500 0 -7781.25 0 0 0 0

-412500 0 0 0 0 0 412500 0 0 0 0 00 15562.5 0 0 0 -7781.25 0 15562.5 0 0 0 -7781.250 0 15562.5 0 7781.25 0 0 0 15562.5 0 7781.25 00 0 0 -3990.385 0 0 0 0 0 3990.385 0 00 0 -7781.25 0 0 0 0 0 7781.25 0 41500 00 7781.25 0 0 0 0 0 -7781.25 0 0 0 41500

Matriks transformasi :

= 8

= 1

= 0

= 0

[k l(e )]=

L=√(X j−X i )2+(Y j−Y i )

2+(Z j−Z i )2

λx=cosθxX=X j−X iL

μx=cosθxY=Y j−Y iL

νx=cosθxZ=Z j−Z iL

Page 13: Tugas Anstruk 3

Home work Metode Elemen Hingga - 1SUANTORO WICAKSONO (07 / 260420 / PTK / 4744)

= 0.5

= 0

= 0.5

= 0

0

1

cos α =

sin α =

cos β=λx

√ λx2+νx2

sin β=νx

√ λx2+ν x2cos γ=√ λx2+ν x2sin γ=μx

Page 14: Tugas Anstruk 3

Home work Metode Elemen Hingga - 1SUANTORO WICAKSONO (07 / 260420 / PTK / 4744)

1 0 0 0 0 0 0 0 0 0 0 00 0 -2 0 0 0 0 0 0 0 0 00 -0.5 0 0 0 0 0 0 0 0 0 00 0 0 1 0 0 0 0 0 0 0 00 0 0 0 0 -2 0 0 0 0 0 00 0 0 0 -0.5 0 0 0 0 0 0 00 0 0 0 0 0 1 0 0 0 0 00 0 0 0 0 0 0 0 -2 0 0 00 0 0 0 0 0 0 -0.5 0 0 0 00 0 0 0 0 0 0 0 0 1 0 00 0 0 0 0 0 0 0 0 0 0 -20 0 0 0 0 0 0 0 0 0 -0.5 0

1 0 0 0 0 0 0 0 0 0 0 00 0 -0.5 0 0 0 0 0 0 0 0 00 -2 0 0 0 0 0 0 0 0 0 00 0 0 1 0 0 0 0 0 0 0 00 0 0 0 0 -0.5 0 0 0 0 0 00 0 0 0 -2 0 0 0 0 0 0 00 0 0 0 0 0 1 0 0 0 0 00 0 0 0 0 0 0 0 -0.5 0 0 00 0 0 0 0 0 0 -2 0 0 0 00 0 0 0 0 0 0 0 0 1 0 00 0 0 0 0 0 0 0 0 0 0 -0.50 0 0 0 0 0 0 0 0 0 -2 0

[T( e ) ]=

[k g(e )]=[T (e )]T [k l(e ) ] [T (e )]

[T (e ) ]T =

Page 15: Tugas Anstruk 3

Home work Metode Elemen Hingga - 1SUANTORO WICAKSONO (07 / 260420 / PTK / 4744)

412500 0 0 0 0 0 -412500 0 0 0 0 00 0 -7781 0 3891 0 0 0 -7781 0 3891 00 -31125 0 0 0 -15563 0 -31125 0 0 0 -155630 0 0 3990 0 0 0 0 0 -3990 0 00 -3891 0 0 0 -20750 0 3891 0 0 0 00 0 15563 0 -83000 0 0 0 -15563 0 0 0

-412500 0 0 0 0 0 412500 0 0 0 0 00 0 -7781 0 -3891 0 0 0 -7781 0 -3891 00 -31125 0 0 0 15563 0 -31125 0 0 0 155630 0 0 -3990 0 0 0 0 0 3990 0 00 -3891 0 0 0 0 0 3891 0 0 0 -207500 0 15563 0 0 0 0 0 -15563 0 -83000 0

412500 0 0 0 0 0 -412500 0 0 0 0 00 3891 0 0 0 -7781 0 3891 0 0 0 -77810 0 62250 0 7781 0 0 0 62250 0 7781 00 0 0 3990 0 0 0 0 0 -3990 0 00 0 7781 0 10375 0 0 0 -7781 0 0 00 -7781 0 0 0 166000 0 7781 0 0 0 0

-412500 0 0 0 0 0 412500 0 0 0 0 00 3891 0 0 0 7781 0 3891 0 0 0 77810 0 62250 0 -7781 0 0 0 62250 0 -7781 00 0 0 -3990 0 0 0 0 0 3990 0 00 0 7781 0 0 0 0 0 -7781 0 10375 00 -7781 0 0 0 0 0 7781 0 0 0 166000

beban nodal ekivalen :

= -(1/2 x 25 x 8) -100 kN

-133.33 kNm

= -(1/2 x 10 x 8) -100 kN

= +133.33 kNm

h6

my6 = -(1/12 x 25 x 82)

h7

my7 = +(1/12 x 10 x 82)

[T (e ) ]T [k l(e ) ]=

[k g(e )]=

Page 16: Tugas Anstruk 3

Home work Metode Elemen Hingga - 1SUANTORO WICAKSONO (07 / 260420 / PTK / 4744)

* 0 * * 0 *

0 0

-100 0

0 0

-133.33 0

=0

=0

0 0

0 0

-100 0

0 0

= +133.33 0

0 0

* 0 *

0

-100

-133.33

0

=0

0

0

-100

= +133.33

0

0

f6 F5

g6 G5

h6 H5

mx6 Mx5

my6 My5

mz6 Mz5

f7 F8

g7 G8

h7 H8

mx7 Mx8

my7 My8

mz7 Mz8

F6

G6

H6

Mx6

My6

Mz6

F7

G7

H7

Mx7

My7

Mz7

{ f 7 }¿=

{F7 }¿=

{ f 8 }¿= {F8}¿=

Page 17: Tugas Anstruk 3

Home work Metode Elemen Hingga - 1SUANTORO WICAKSONO (07 / 260420 / PTK / 4744)

Matriks Struktur Keseluruhan :

U1

V1

W1

= ; = =0 F5

0 G5

0 H5

0 Mx5

U1 F1 F1 F1

V1 G1 G1 G1

W1 H1 H1 H1

θx1 Mx1 θx1 Mx1 Mx1

θy1 My1 θy5 My1 My1

θz1 Mz1 θz5 Mz1 Mz1

U2 F2 U6 F2 F2

V2 G2 V6 G2 G2

W2 H1 W6 H1 H1

θx2 Mx2 θx6 Mx2 Mx2

θy2 My2 θy6 My2 My2

θz2 Mz2 θz6 Mz2 Mz2

U3 F3 U7 F3 F3

V3 G3 V7 G3 G3

W3 H3 W7 H3 H3

θx3 Mx3 θx7 Mx3 Mx3

θy3 My3 θy7 My3 My3

θz3 Mz3 θz7 Mz3 Mz3

U4 F4 U8 F4 F4

V4 G4 V8 G4 G4

W4 H4 W8 H4 H4

θx4 Mx4 θx8 Mx4 Mx4

θy4 My4 θy8 My4 My4

[K]48x48

θz4 Mz4[K]48x48

θz8 Mz4 Mz4

U5 F5 U5

V5 G5 V5

W5 H5 W5

θx5 Mx5 θx5

Page 18: Tugas Anstruk 3

Home work Metode Elemen Hingga - 1SUANTORO WICAKSONO (07 / 260420 / PTK / 4744)

0 My5

0 Mz5

0 F6

0 G6

0 H6

0 Mx6

0 My6

0 Mz6

0 F7

0 G7

0 H7

0 Mx7

0 My7

0 Mz7

0 F8

0 G8

0 H8

0 Mx8

0 My8

0 Mz8

θy5 My5 θy5

θz5 Mz5 θz5

U6 F6 U6

V6 G6 V6

W6 H6 W6

θx6 Mx6 θx6

θy6 My6 θy6

θz6 Mz6 θz6

U7 F7 U7

V7 G7 V7

W7 H7 W7

θx7 Mx7 θx7

θy7 My7 θy7

θz7 Mz7 θz7

U8 F8 U8

V8 G8 V8

W8 H8 W8

θx8 Mx8 θx8

θy8 My8 θy8

θz8 48 x 1 Mz8 48 x 1 θz8 48 x 1 48 x 1 48 x 1

Page 19: Tugas Anstruk 3

Home work Metode Elemen Hingga - 1SUANTORO WICAKSONO (07 / 260420 / PTK / 4744)

=

karena ~ = 0, maka :

=

=

[K11] 6x6 [K12] 6x6 [K13] 6x6 [K14] 6x6 [K15] 6x6 [K16] 6x6 [K17] 6x6 [K18] 6x6 {U1} 6x1 {F1} 6x1

[K21] 6x6 [K22] 6x6 [K23] 6x6 [K24] 6x6 [K25] 6x6 [K26] 6x6 [K27] 6x6 [K28] 6x6 {U2} 6x1 {F2} 6x1

[K31] 6x6 [K32] 6x6 [K33] 6x6 [K34] 6x6 [K35] 6x6 [K36] 6x6 [K37] 6x6 [K38] 6x6 {U3} 6x1 {F3} 6x1

[K41] 6x6 [K42] 6x6 [K43] 6x6 [K44] 6x6 [K45] 6x6 [K46] 6x6 [K47] 6x6 [K48] 6x6 {U4} 6x1 {F4} 6x1

[K51] 6x6 [K52] 6x6 [K53] 6x6 [K54] 6x6 [K55] 6x6 [K56] 6x6 [K57] 6x6 [K58] 6x6 {U5} 6x1 {F5} 6x1

[K61] 6x6 [K62] 6x6 [K63] 6x6 [K64] 6x6 [K65] 6x6 [K66] 6x6 [K67] 6x6 [K68] 6x6 {U6} 6x1 {F6} 6x1

[K71] 6x6 [K72] 6x6 [K73] 6x6 [K74] 6x6 [K75] 6x6 [K76] 6x6 [K77] 6x6 [K78] 6x6 {U7} 6x1 {F7} 6x1

[K81] 6x6 [K82] 6x6 [K83] 6x6 [K84] 6x6 [K85] 6x6 [K86] 6x6 [K87] 6x6 [K88] 6x6 48 x 48 {U8} 6x1 48 x 1 {F8} 6x1 48 x 1

{U1} 6x1 {U4} 6x1

[K55] 6x6 [K56] 6x6 [K57] 6x6 [K58] 6x6 {U5} 6x1 {F5} 6x1

[K65] 6x6 [K66] 6x6 [K67] 6x6 [K68] 6x6 {U6} 6x1 {F6} 6x1

[K75] 6x6 [K76] 6x6 [K77] 6x6 [K78] 6x6 {U7} 6x1 {F7} 6x1

[K85] 6x6 [K86] 6x6 [K87] 6x6 [K88] 6x6 24 x 24 {U8} 6x1 24 x 1 {F8} 6x1 24 x 1

{U5} 6x1 [K55] 6x6 [K56] 6x6 [K57] 6x6 [K58] 6x6 -1 {F5} 6x1

{U6} 6x1 [K65] 6x6 [K66] 6x6 [K67] 6x6 [K68] 6x6 {F6} 6x1

{U7} 6x1 [K75] 6x6 [K76] 6x6 [K77] 6x6 [K78] 6x6 {F7} 6x1

{U8} 6x1 24 x 1 [K85] 6x6 [K86] 6x6 [K87] 6x6 [K88] 6x6 24 x 24 {F8} 6x1 24 x 1

Page 20: Tugas Anstruk 3

Home work Metode Elemen Hingga - 1SUANTORO WICAKSONO (07 / 260420 / PTK / 4744)

1029000 0 0 0 -25500 0 -412500 0 0 0 0 0 0

0 32203 0 25500 0 0 0 15562.5 0 0 0 7781.25 0

0 0 1090313 0 0 0 0 0 15562.5 0 -7781.25 0 0

0 25500 0 279981 0 0 0 0 0 -3990.385 0 0 0

-25500 0 0 0 68875 0 0 0 7781.25 0 0 0 0

0 0 0 0 0 214038 0 -7781.25 0 0 0 0 0

-412500 0 0 0 0 0 1029000 0 0 0 -25500 0 -412500

0 15562.5 0 0 0 -7781.25 0 32203 0 25500 0 -15563 0

0 0 15562.5 0 7781.25 0 0 0 1090313 0 15563 0 0

0 0 0 -3990.385 0 0 0 25500 0 279981 0 0 0

0 0 -7781.25 0 0 0 -25500 0 15563 0 68875 0 0

=0 7781.25 0 0 0 0 0 -15563 0 0 0 214038 0

0 0 0 0 0 0 -412500 0 0 0 0 0 1029000

0 0 0 0 0 0 0 3891 0 0 0 7781 0

0 0 0 0 0 0 0 0 62250 0 -7781 0 0

0 0 0 0 0 0 0 0 0 -3990 0 0 0

0 0 0 0 0 0 0 0 7781 0 0 0 -25500

0 0 0 0 0 0 0 -7781 0 0 0 0 0

-412500 0 0 0 0 0 0 0 0 0 0 0 -412500

0 3891 0 0 0 7781 0 0 0 0 0 0 0

0 0 62250 0 -7781 0 0 0 0 0 0 0 0

0 0 0 -3990 0 0 0 0 0 0 0 0 0

0 0 7781 0 0 0 0 0 0 0 0 0 0

0 -7781 0 0 0 0 0 0 0 0 0 0 0

U5

V5

W5

θx5

θy5

θz5

U6

V6

W6

θx6

θy6

θz6

U7

V7

W7

θx7

θy7

θz7

U8

V8

W8

θx8

θy8

θz8 24 x 1

Page 21: Tugas Anstruk 3

Home work Metode Elemen Hingga - 1SUANTORO WICAKSONO (07 / 260420 / PTK / 4744)

1.91E-06 0 -5.87E-10 0 7.11E-07 0 1.15E-06 0 -1.37E-08 0 4.29E-07 0 9.3E-07

0 5.55E-05 0 -5E-06 0 -6.16E-07 0 -3.38E-05 0 2.99E-06 0 -5E-06 0

-5.87E-10 0 9.22E-07 0 -4.69E-09 0 2.22E-09 0 -1.48E-08 0 1.09E-07 0 -5.87E-10

0 -5E-06 0 4.02E-06 0 5.61E-08 0 2.99E-06 0 -2.13E-07 0 4.47E-07 0

7.11E-07 0 -4.69E-09 0 1.48E-05 0 4.29E-07 0 -1.1E-07 0 1.84E-07 0 3.48E-07

0 -6.16E-07 0 5.61E-08 0 4.79E-06 0 1.58E-06 0 -1.44E-07 0 1.15E-07 0

1.15E-06 0 2.22E-09 0 4.29E-07 0 1.91E-06 0 -1.65E-08 0 7.12E-07 0 1.15E-06

0 -3.38E-05 0 2.99E-06 0 1.58E-06 0 5.71E-05 0 -5.14E-06 0 5.99E-06 0

-1.37E-08 0 -1.48E-08 0 -1.1E-07 0 -1.65E-08 0 9.25E-07 0 -2.23E-07 0 -1.37E-08

0 2.99E-06 0 -2.13E-07 0 -1.44E-07 0 -5.14E-06 0 4.04E-06 0 -5.35E-07 0

4.29E-07 0 1.09E-07 0 1.84E-07 0 7.12E-07 0 -2.23E-07 0 1.49E-05 0 4.29E-07

=0 -5E-06 0 4.47E-07 0 1.15E-07 0 5.99E-06 0 -5.35E-07 0 5.43E-06 0

9.3E-07 0 -5.87E-10 0 3.48E-07 0 1.15E-06 0 -1.37E-08 0 4.29E-07 0 1.91E-06

0 1.54E-05 0 -1.34E-06 0 6.16E-07 0 -1.68E-05 0 1.44E-06 0 -3.8E-06 0

5.87E-10 0 3.24E-09 0 4.69E-09 0 3.4E-09 0 -5.44E-08 0 1.18E-07 0 5.87E-10

0 -1.34E-06 0 1.18E-07 0 -5.61E-08 0 1.44E-06 0 -7.24E-08 0 3.35E-07 0

3.48E-07 0 -4.69E-09 0 1.53E-07 0 4.29E-07 0 -1.1E-07 0 1.84E-07 0 7.11E-07

0 -6.16E-07 0 5.61E-08 0 1.15E-07 0 1.58E-06 0 -1.44E-07 0 1.15E-07 0

1.15E-06 0 -3.4E-09 0 4.29E-07 0 9.3E-07 0 -1.09E-08 0 3.46E-07 0 1.15E-06

0 -1.68E-05 0 1.44E-06 0 -1.58E-06 0 1.38E-05 0 -1.19E-06 0 2.84E-06 0

1.37E-08 0 -5.44E-08 0 1.1E-07 0 1.09E-08 0 1.14E-10 0 -3.82E-09 0 1.37E-08

0 1.44E-06 0 -7.24E-08 0 1.44E-07 0 -1.19E-06 0 1.04E-07 0 -2.48E-07 0

4.29E-07 0 -1.18E-07 0 1.84E-07 0 3.46E-07 0 3.82E-09 0 1.02E-07 0 4.29E-07

0 3.8E-06 0 -3.35E-07 0 1.15E-07 0 -2.84E-06 0 2.48E-07 0 -5.28E-07 0

U5

V5

W5

θx5

θy5

θz5

U6

V6

W6

θx6

θy6

θz6

U7

V7

W7

θx7

θy7

θz7

U8

V8

W8

θx8

θy8

θz8 24 x 1

Page 22: Tugas Anstruk 3

Home work Metode Elemen Hingga - 1SUANTORO WICAKSONO (07 / 260420 / PTK / 4744)

#VALUE! #VALUE! #VALUE!

#VALUE! #VALUE! #VALUE!

#VALUE! #VALUE! #VALUE!

#VALUE! #VALUE! #VALUE!

#VALUE! #VALUE! #VALUE!

#VALUE! #VALUE! #VALUE!

#VALUE! #VALUE! #VALUE!

#VALUE! #VALUE! #VALUE!

#VALUE! #VALUE! #VALUE!

#VALUE! #VALUE! #VALUE!

#VALUE! #VALUE! #VALUE!

=#VALUE! #VALUE! #VALUE!

#VALUE! #VALUE! #VALUE!

#VALUE! #VALUE! #VALUE!

#VALUE! #VALUE! #VALUE!

#VALUE! #VALUE! #VALUE!

#VALUE! #VALUE! #VALUE!

#VALUE! #VALUE! #VALUE!

#VALUE! #VALUE! #VALUE!

#VALUE! #VALUE! #VALUE!

#VALUE! #VALUE! #VALUE!

#VALUE! #VALUE! #VALUE!

#VALUE! #VALUE! #VALUE!

#VALUE! #VALUE! #VALUE!

=

U5

V5

W5

θx5

θy5

θz5

U6

V6

W6

θx6

θy6

θz6

U7

V7

W7

θx7

θy7

θz7

U8

V8

W8

θx8

θy8

θz8 24 x 1 24 x 1

{F1} 6x1 [K15] 6x6 [K16] 6x6 [K17] 6x6 [K18] 6x6 {U5} 6x1

{F2} 6x1 [K25] 6x6 [K26] 6x6 [K27] 6x6 [K28] 6x6 {U6} 6x1

{F3} 6x1 [K35] 6x6 [K36] 6x6 [K37] 6x6 [K38] 6x6 {U7} 6x1

Page 23: Tugas Anstruk 3

Home work Metode Elemen Hingga - 1SUANTORO WICAKSONO (07 / 260420 / PTK / 4744)

204000 0 0 0 25500 0 0 0 0 0 0 0 0

0 12750 0 -25500 0 0 0 0 0 0 0 0 0

0 0 -1012500 0 0 0 0 0 0 0 0 0 0

0 25500 0 136000 0 0 0 0 0 0 0 0 0

-25500 0 0 0 8500 0 0 0 0 0 0 0 0

0 0 0 0 0 -6538 0 0 0 0 0 0 0

0 0 0 0 0 0 204000 0 0 0 25500 0 0

0 0 0 0 0 0 0 12750 0 -25500 0 0 0

0 0 0 0 0 0 0 0 -1012500 0 0 0 0

0 0 0 0 0 0 0 25500 0 136000 0 0 0

0 0 0 0 0 0 -25500 0 0 0 8500 0 0

=0 0 0 0 0 0 0 0 0 0 0 -6538 0

0 0 0 0 0 0 0 0 0 0 0 0 204000

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 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 -25500

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 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 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

{F4} 6x1 24 x 1 [K45] 6x6 [K46] 6x6 [K47] 6x6 [K48] 6x6 24 x 24 {U8} 6x1 24 x 1

F1

G1

H1

Mx1

My1

Mz1

F2

G2

H1

Mx2

My2

Mz2

F3

G3

H3

Mx3

My3

Mz3

F4

G4

H4

Mx4

My4

Mz4 24 x 1

Page 24: Tugas Anstruk 3

Home work Metode Elemen Hingga - 1SUANTORO WICAKSONO (07 / 260420 / PTK / 4744)

#VALUE! #VALUE! #VALUE!

#VALUE! #VALUE! #VALUE!

#VALUE! #VALUE! #VALUE!

#VALUE! #VALUE! #VALUE!

#VALUE! #VALUE! #VALUE!

#VALUE! #VALUE! #VALUE!

#VALUE! #VALUE! #VALUE!

#VALUE! #VALUE! #VALUE!

#VALUE! #VALUE! #VALUE!

#VALUE! #VALUE! #VALUE!

#VALUE! #VALUE! #VALUE!

=#VALUE! #VALUE! #VALUE!

#VALUE! #VALUE! #VALUE!

#VALUE! #VALUE! #VALUE!

#VALUE! #VALUE! #VALUE!

#VALUE! #VALUE! #VALUE!

#VALUE! #VALUE! #VALUE!

#VALUE! #VALUE! #VALUE!

#VALUE! #VALUE! #VALUE!

#VALUE! #VALUE! #VALUE!

#VALUE! #VALUE! #VALUE!

#VALUE! #VALUE! #VALUE!

#VALUE! #VALUE! #VALUE!

#VALUE! #VALUE! #VALUE!

F1

G1

H1

Mx1

My1

Mz1

F2

G2

H1

Mx2

My2

Mz2

F3

G3

H3

Mx3

My3

Mz3

F4

G4

H4

Mx4

My4

Mz4 24 x 1 24 x 1

Page 25: Tugas Anstruk 3

Home work Metode Elemen Hingga - 1SUANTORO WICAKSONO (07 / 260420 / PTK / 4744)

Hasil Analisis :

Nodal U V W1 0 0 0 0 0 02 0 0 0 0 0 03 0 0 0 0 0 04 0 0 0 0 0 05 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!6 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!7 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!8 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!

Reaksi dan gaya luar pada nodal (dalam satuan KN dan meter) :

Nodal F G H1 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!2 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!3 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!4 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!5 0 10 0 0 0 06 0 0 0 0 0 07 0 0 0 0 0 08 0 0 0 0 0 0

Displacement pada nodal (dalam satuan meter dan radian) :

θx θy θz

Mx My Mz

Page 26: Tugas Anstruk 3

Home work Metode Elemen Hingga - 1SUANTORO WICAKSONO (07 / 260420 / PTK / 4744)

Gaya-gaya Batang :

Elemen 1 :

0 0 1 0 0 0 0 0 0 0 0 0

-2 0 0 0 0 0 0 0 0 0 0 0

0 -0.5 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 1 0 0 0 0 0 0

0 0 0 -2 0 0 0 0 0 0 0 0

=0 0 0 0 -0.5 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 1 0 0 0

0 0 0 0 0 0 -2 0 0 0 0 0

0 0 0 0 0 0 0 -0.5 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 1

0 0 0 0 0 0 0 0 0 -2 0 0

0 0 0 0 0 0 0 0 0 0 -0.5 0

0 0 1012500 0 0 0 0 0 -1012500 0 0 0

-408000 0 0 0 -51000 0 -408000 0 0 0 -51000 0

0 -6375 0 12750 0 0 0 -6375 0 12750 0 0

0 0 0 0 0 6538.462 0 0 0 0 0 -6538.462

0 51000 0 -544000 0 0 0 -51000 0 -272000 0 0

=-12750 0 0 0 -8500 0 12750 0 0 0 -4250 0

0 0 -1012500 0 0 0 0 0 1012500 0 0 0

-408000 0 0 0 51000 0 -408000 0 0 0 51000 0

0 -6375 0 -12750 0 0 0 -6375 0 -12750 0 0

0 0 0 0 0 -6538.462 0 0 0 0 0 6538.462

0 51000 0 -272000 0 0 0 -51000 0 -544000 0 0

-12750 0 0 0 -4250 0 12750 0 0 0 -8500 0

f1

g1

h1

mx1

my1

mz1

f5

g5

h5

mx5

my5

mz5

f1

g1

h1

mx1

my1

mz1

f5

g5

h5

mx5

my5

mz5

{ f e }=[T e ] [k ge ] {U e }

Page 27: Tugas Anstruk 3

Home work Metode Elemen Hingga - 1SUANTORO WICAKSONO (07 / 260420 / PTK / 4744)

#VALUE!

#VALUE!

#VALUE!

#VALUE!

#VALUE!

=#VALUE!

#VALUE!

#VALUE!

#VALUE!

#VALUE!

#VALUE!

#VALUE!

Elemen 2 :

0 0 1012500 0 0 0 0 0 -1012500 0 0 0

-408000 0 0 0 -51000 0 -408000 0 0 0 -51000 0

0 -6375 0 12750 0 0 0 -6375 0 12750 0 0

0 0 0 0 0 6538.462 0 0 0 0 0 -6538.462

0 51000 0 -544000 0 0 0 -51000 0 -272000 0 0

=-12750 0 0 0 -8500 0 12750 0 0 0 -4250 0

0 0 -1012500 0 0 0 0 0 1012500 0 0 0

-408000 0 0 0 51000 0 -408000 0 0 0 51000 0

0 -6375 0 -12750 0 0 0 -6375 0 -12750 0 0

0 0 0 0 0 -6538.462 0 0 0 0 0 6538.462

0 51000 0 -272000 0 0 0 -51000 0 -544000 0 0

-12750 0 0 0 -4250 0 12750 0 0 0 -8500 0

#VALUE!

f1

g1

h1

mx1

my1

mz1

f5

g5

h5

mx5

my5

mz5

f2

g2

h2

mx2

my2

mz2

f6

g6

h6

mx6

my6

mz6

f2

Page 28: Tugas Anstruk 3

Home work Metode Elemen Hingga - 1SUANTORO WICAKSONO (07 / 260420 / PTK / 4744)

#VALUE!

#VALUE!

#VALUE!

#VALUE!

=#VALUE!

#VALUE!

#VALUE!

#VALUE!

#VALUE!

#VALUE!

#VALUE!

Elemen 3 :

0 0 1012500 0 0 0 0 0 -1012500 0 0 0

-408000 0 0 0 -51000 0 -408000 0 0 0 -51000 0

0 -6375 0 12750 0 0 0 -6375 0 12750 0 0

0 0 0 0 0 6538.462 0 0 0 0 0 -6538.462

0 51000 0 -544000 0 0 0 -51000 0 -272000 0 0

=-12750 0 0 0 -8500 0 12750 0 0 0 -4250 0

0 0 -1012500 0 0 0 0 0 1012500 0 0 0

-408000 0 0 0 51000 0 -408000 0 0 0 51000 0

0 -6375 0 -12750 0 0 0 -6375 0 -12750 0 0

0 0 0 0 0 -6538.462 0 0 0 0 0 6538.462

0 51000 0 -272000 0 0 0 -51000 0 -544000 0 0

-12750 0 0 0 -4250 0 12750 0 0 0 -8500 0

#VALUE!

#VALUE!

#VALUE!

g2

h2

mx2

my2

mz2

f6

g6

h6

mx6

my6

mz6

f3

g3

h3

mx3

my3

mz3

f7

g7

h7

mx7

my7

mz7

f3

g3

h3

Page 29: Tugas Anstruk 3

Home work Metode Elemen Hingga - 1SUANTORO WICAKSONO (07 / 260420 / PTK / 4744)

#VALUE!

#VALUE!

=#VALUE!

#VALUE!

#VALUE!

#VALUE!

#VALUE!

#VALUE!

#VALUE!

Elemen 4 :

0 0 1012500 0 0 0 0 0 -1012500 0 0 0

-408000 0 0 0 -51000 0 -408000 0 0 0 -51000 0

0 -6375 0 12750 0 0 0 -6375 0 12750 0 0

0 0 0 0 0 6538.462 0 0 0 0 0 -6538.462

0 51000 0 -544000 0 0 0 -51000 0 -272000 0 0

=-12750 0 0 0 -8500 0 12750 0 0 0 -4250 0

0 0 -1012500 0 0 0 0 0 1012500 0 0 0

-408000 0 0 0 51000 0 -408000 0 0 0 51000 0

0 -6375 0 -12750 0 0 0 -6375 0 -12750 0 0

0 0 0 0 0 -6538.462 0 0 0 0 0 6538.462

0 51000 0 -272000 0 0 0 -51000 0 -544000 0 0

-12750 0 0 0 -4250 0 12750 0 0 0 -8500 0

#VALUE!

#VALUE!

#VALUE!

#VALUE!

#VALUE!

mx3

my3

mz3

f7

g7

h7

mx7

my7

mz7

f4

g4

h4

mx4

my4

mz4

f8

g8

h8

mx8

my8

mz8

f4

g4

h4

mx4

my4

Page 30: Tugas Anstruk 3

Home work Metode Elemen Hingga - 1SUANTORO WICAKSONO (07 / 260420 / PTK / 4744)

=#VALUE!

#VALUE!

#VALUE!

#VALUE!

#VALUE!

#VALUE!

#VALUE!

Elemen 5 :

412500 0 0 0 0 0 -412500 0 0 0 0 0

0 15562.5 0 0 0 7781.25 0 15562.5 0 0 0 7781.25

0 0 15562.5 0 -7781.25 0 0 0 15562.5 0 -7781.25 0

0 0 0 3990.385 0 0 0 0 0 -3990.385 0 0

0 0 -7781.25 0 41500 0 0 0 7781.25 0 0 0

=0 7781.25 0 0 0 41500 0 -7781.25 0 0 0 0

-412500 0 0 0 0 0 412500 0 0 0 0 0

0 15562.5 0 0 0 -7781.25 0 15562.5 0 0 0 -7781.25

0 0 15562.5 0 7781.25 0 0 0 15562.5 0 7781.25 0

0 0 0 -3990.385 0 0 0 0 0 3990.385 0 0

0 0 -7781.25 0 0 0 0 0 7781.25 0 41500 0

0 7781.25 0 0 0 0 0 -7781.25 0 0 0 41500

#VALUE!

#VALUE!

#VALUE!

#VALUE!

#VALUE!

=#VALUE!

#VALUE!

mz4

f8

g8

h8

mx8

my8

mz8

f5

g5

h5

mx5

my5

mz5

f6

g6

h6

mx6

my6

mz6

f1

g1

h1

mx1

my1

mz1

f5

Page 31: Tugas Anstruk 3

Home work Metode Elemen Hingga - 1SUANTORO WICAKSONO (07 / 260420 / PTK / 4744)

#VALUE!

#VALUE!

#VALUE!

#VALUE!

#VALUE!

Elemen 6 :

412500 0 0 0 0 0 -412500 0 0 0 0 0

0 15562.5 0 0 0 7781.25 0 15562.5 0 0 0 7781.25

0 0 15562.5 0 -7781.25 0 0 0 15562.5 0 -7781.25 0

0 0 0 3990.385 0 0 0 0 0 -3990.385 0 0

0 0 -7781.25 0 41500 0 0 0 7781.25 0 0 0

=0 7781.25 0 0 0 41500 0 -7781.25 0 0 0 0

-412500 0 0 0 0 0 412500 0 0 0 0 0

0 15562.5 0 0 0 -7781.25 0 15562.5 0 0 0 -7781.25

0 0 15562.5 0 7781.25 0 0 0 15562.5 0 7781.25 0

0 0 0 -3990.385 0 0 0 0 0 3990.385 0 0

0 0 -7781.25 0 0 0 0 0 7781.25 0 41500 0

0 7781.25 0 0 0 0 0 -7781.25 0 0 0 41500

#VALUE!

#VALUE!

#VALUE!

#VALUE!

#VALUE!

=#VALUE!

#VALUE!

#VALUE!

#VALUE!

g5

h5

mx5

my5

mz5

f8

g8

h8

mx8

my8

mz8

f7

g7

h7

mx7

my7

mz7

f8

g8

h8

mx8

my8

mz8

f7

g7

h7

Page 32: Tugas Anstruk 3

Home work Metode Elemen Hingga - 1SUANTORO WICAKSONO (07 / 260420 / PTK / 4744)

#VALUE!

#VALUE!

#VALUE!

Elemen 7 :

1 0 0 0 0 0 0 0 0 0 0 0

0 0 -2 0 0 0 0 0 0 0 0 0

0 -0.5 0 0 0 0 0 0 0 0 0 0

0 0 0 1 0 0 0 0 0 0 0 0

0 0 0 0 0 -2 0 0 0 0 0 0

=0 0 0 0 -0.5 0 0 0 0 0 0 0

0 0 0 0 0 0 1 0 0 0 0 0

0 0 0 0 0 0 0 0 -2 0 0 0

0 0 0 0 0 0 0 -0.5 0 0 0 0

0 0 0 0 0 0 0 0 0 1 0 0

0 0 0 0 0 0 0 0 0 0 0 -2

0 0 0 0 0 0 0 0 0 0 -0.5 0

412500 0 0 0 0 0 -412500 0 0 0 0 0

0 0 -124500 0 -15562.5 0 0 0 -124500 0 -15562.5 0

0 -1945.313 0 0 0 3890.625 0 -1945.313 0 0 0 3890.625

0 0 0 3990.385 0 0 0 0 0 -3990.385 0 0

0 15562.5 0 0 0 -332000 0 -15562.5 0 0 0 0

=0 0 -3890.625 0 -5187.5 0 0 0 3890.625 0 0 0

-412500 0 0 0 0 0 412500 0 0 0 0 0

0 0 -124500 0 15562.5 0 0 0 -124500 0 15562.5 0

0 -1945.313 0 0 0 -3890.625 0 -1945.313 0 0 0 -3890.625

0 0 0 -3990.385 0 0 0 0 0 3990.385 0 0

0 15562.5 0 0 0 0 0 -15562.5 0 0 0 -332000

mx7

my7

mz7

f6

g6

h6

mx6

my6

mz6

f7

g7

h7

mx7

my7

mz7

f6

g6

h6

mx6

my6

mz6

f7

g7

h7

mx7

my7

Page 33: Tugas Anstruk 3

Home work Metode Elemen Hingga - 1SUANTORO WICAKSONO (07 / 260420 / PTK / 4744)

0 0 -3890.625 0 0 0 0 0 3890.625 0 -5187.5 0

#VALUE!

#VALUE!

#VALUE!

#VALUE!

#VALUE!

=#VALUE!

#VALUE!

#VALUE!

#VALUE!

#VALUE!

#VALUE!

#VALUE!

Elemen 8 :

412500 0 0 0 0 0 -412500 0 0 0 0 0

0 0 -124500 0 -15562.5 0 0 0 -124500 0 -15562.5 0

0 -1945.313 0 0 0 3890.625 0 -1945.313 0 0 0 3890.625

0 0 0 3990.385 0 0 0 0 0 -3990.385 0 0

0 15562.5 0 0 0 -332000 0 -15562.5 0 0 0 0

=0 0 -3890.625 0 -5187.5 0 0 0 3890.625 0 0 0

-412500 0 0 0 0 0 412500 0 0 0 0 0

0 0 -124500 0 15562.5 0 0 0 -124500 0 15562.5 0

0 -1945.313 0 0 0 -3890.625 0 -1945.313 0 0 0 -3890.625

0 0 0 -3990.385 0 0 0 0 0 3990.385 0 0

0 15562.5 0 0 0 0 0 -15562.5 0 0 0 -332000

0 0 -3890.625 0 0 0 0 0 3890.625 0 -5187.5 0

#VALUE!

mz7

f6

g6

h6

mx6

my6

mz6

f7

g7

h7

mx7

my7

mz7

f5

g5

h5

mx5

my5

mz5

f88

g8

h8

mx8

my8

mz8

f5

Page 34: Tugas Anstruk 3

Home work Metode Elemen Hingga - 1SUANTORO WICAKSONO (07 / 260420 / PTK / 4744)

#VALUE!

#VALUE!

#VALUE!

#VALUE!

=#VALUE!

#VALUE!

#VALUE!

#VALUE!

#VALUE!

#VALUE!

#VALUE!

ElemenNodal i Normal Shear Shear Bending Bending TorsionalNodal j Force Force y Force z Moment x Moment y Moment

11 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!5 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!

22 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!6 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!

33 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!7 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!

44 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!8 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!

55 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!6 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!

68 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!7 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!

76 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!7 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!

85 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!8 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!

g5

h5

mx5

my5

mz5

f88

g8

h8

mx8

my8

mz8

Rekapitulasi Gaya-gaya Batang (satuan dalam Kn dan meter) :

Page 35: Tugas Anstruk 3

Home work Metode Elemen Hingga - 1SUANTORO WICAKSONO (07 / 260420 / PTK / 4744)

0 0 0 0 0 -412500 0 0 0 0 0 F5

0 0 0 0 0 0 3891 0 0 0 -7781 G5

0 0 0 0 0 0 0 62250 0 7781 0 H5

0 0 0 0 0 0 0 0 -3990 0 0 Mx5

0 0 0 0 0 0 0 -7781 0 0 0 My5

0 0 0 0 0 0 7781 0 0 0 0 Mz5

0 0 0 0 0 0 0 0 0 0 0 F6

3891 0 0 0 -7781 0 0 0 0 0 0 G6

0 62250 0 7781 0 0 0 0 0 0 0 H6

0 0 -3990 0 0 0 0 0 0 0 0 Mx6

0 -7781 0 0 0 0 0 0 0 0 0 My6

7781 0 0 0 0 0 0 0 0 0 0 Mz6

0 0 0 -25500 0 -412500 0 0 0 0 0 F7

32203 0 25500 0 0 0 15563 0 0 0 -7781 G7

0 1090313 0 0 0 0 0 15563 0 7781 0 H7

25500 0 279981 0 0 0 0 0 -3990 0 0 Mx7

0 0 0 68875 0 0 0 -7781 0 0 0 My7

0 0 0 0 214038 0 7781 0 0 0 0 Mz7

0 0 0 0 0 1029000 0 0 0 -25500 0 F8

15563 0 0 0 7781 0 32203 0 25500 0 15563 G8

0 15563 0 -7781 0 0 0 1090313 0 -15563 0 H8

0 0 -3990 0 0 0 25500 0 279981 0 0 Mx8

0 7781 0 0 0 -25500 0 -15563 0 68875 0 My8

-7781 0 0 0 0 0 15563 0 0 0 214038 Mz8

-1

24 x 24 24 x 1

Page 36: Tugas Anstruk 3

Home work Metode Elemen Hingga - 1SUANTORO WICAKSONO (07 / 260420 / PTK / 4744)

0 5.87E-10 0 3.48E-07 0 1.15E-06 0 1.37E-08 0 4.288E-07 0 F5

1.54E-05 0 -1.34E-06 0 -6.16E-07 0 -1.68E-05 0 1.443E-06 0 3.802E-06 G5

0 3.24E-09 0 -4.69E-09 0 -3.4E-09 0 -5.44E-08 0 -1.18E-07 0 H5

-1.34E-06 0 1.18E-07 0 5.609E-08 0 1.443E-06 0 -7.24E-08 0 -3.35E-07 Mx5

0 4.69E-09 0 1.53E-07 0 4.29E-07 0 1.096E-07 0 1.835E-07 0 My5

6.16E-07 0 -5.61E-08 0 1.146E-07 0 -1.58E-06 0 1.436E-07 0 1.146E-07 Mz5

0 3.4E-09 0 4.29E-07 0 9.3E-07 0 1.089E-08 0 3.463E-07 0 F6

-1.68E-05 0 1.44E-06 0 1.577E-06 0 1.377E-05 0 -1.19E-06 0 -2.84E-06 G6

0 -5.44E-08 0 -1.1E-07 0 -1.09E-08 0 1.143E-10 0 3.821E-09 0 H6

1.44E-06 0 -7.24E-08 0 -1.44E-07 0 -1.19E-06 0 1.044E-07 0 2.476E-07 Mx6

0 1.18E-07 0 1.84E-07 0 3.46E-07 0 -3.82E-09 0 1.017E-07 0 My6

-3.8E-06 0 3.35E-07 0 1.146E-07 0 2.841E-06 0 -2.48E-07 0 -5.28E-07 Mz6

0 5.87E-10 0 7.11E-07 0 1.15E-06 0 1.37E-08 0 4.288E-07 0 F7

5.55E-05 0 -5E-06 0 6.159E-07 0 -3.38E-05 0 2.986E-06 0 5.034E-06 G7

0 9.22E-07 0 4.69E-09 0 -2.22E-09 0 -1.48E-08 0 -1.09E-07 0 H7

-5E-06 0 4.02E-06 0 -5.61E-08 0 2.986E-06 0 -2.13E-07 0 -4.47E-07 Mx7

0 4.69E-09 0 1.48E-05 0 4.29E-07 0 1.096E-07 0 1.835E-07 0 My7

6.16E-07 0 -5.61E-08 0 4.787E-06 0 -1.58E-06 0 1.436E-07 0 1.146E-07 Mz7

0 -2.22E-09 0 4.29E-07 0 1.91E-06 0 1.651E-08 0 7.12E-07 0 F8

-3.38E-05 0 2.99E-06 0 -1.58E-06 0 5.714E-05 0 -5.14E-06 0 -5.99E-06 G8

0 -1.48E-08 0 1.1E-07 0 1.65E-08 0 9.252E-07 0 2.23E-07 0 H8

2.99E-06 0 -2.13E-07 0 1.436E-07 0 -5.14E-06 0 4.036E-06 0 5.348E-07 Mx8

0 -1.09E-07 0 1.84E-07 0 7.12E-07 0 2.23E-07 0 1.486E-05 0 My8

5.03E-06 0 -4.47E-07 0 1.146E-07 0 -5.99E-06 0 5.348E-07 0 5.429E-06 Mz824 x 24 24 x 1

Page 37: Tugas Anstruk 3

Home work Metode Elemen Hingga - 1SUANTORO WICAKSONO (07 / 260420 / PTK / 4744)

0 0 0 0 0 0 0 0 0 0 0 #VALUE!

0 0 0 0 0 0 0 0 0 0 0 #VALUE!

0 0 0 0 0 0 0 0 0 0 0 #VALUE!

0 0 0 0 0 0 0 0 0 0 0 #VALUE!

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0 0 0 0 0 0 0 0 0 0 0 #VALUE!

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0 0 0 0 0 0 0 0 0 0 0 #VALUE!

0 0 0 0 0 0 0 0 0 0 0 #VALUE!

0 0 0 0 0 0 0 0 0 0 0 #VALUE!

0 0 0 0 0 0 0 0 0 0 0 #VALUE!

0 0 0 0 0 0 0 0 0 0 0 #VALUE!

0 0 0 25500 0 0 0 0 0 0 0 #VALUE!

12750 0 -25500 0 0 0 0 0 0 0 0 #VALUE!

0 -1012500 0 0 0 0 0 0 0 0 0 #VALUE!

25500 0 136000 0 0 0 0 0 0 0 0 #VALUE!

0 0 0 8500 0 0 0 0 0 0 0 #VALUE!

0 0 0 0 -6538 0 0 0 0 0 0 #VALUE!

0 0 0 0 0 204000 0 0 0 25500 0 #VALUE!

0 0 0 0 0 0 12750 0 -25500 0 0 #VALUE!

0 0 0 0 0 0 0 -1012500 0 0 0 #VALUE!

0 0 0 0 0 0 25500 0 136000 0 0 #VALUE!

0 0 0 0 0 -25500 0 0 0 8500 0 #VALUE!

0 0 0 0 0 0 0 0 0 0 -6538 #VALUE!24 x 24 24 x 1

Page 38: Tugas Anstruk 3

Home work Metode Elemen Hingga - 1SUANTORO WICAKSONO (07 / 260420 / PTK / 4744)

204000 0 0 0 25500 0 204000 0 0 0 25500 0 0

0 12750 0 -25500 0 0 0 12750 0 -25500 0 0 0

0 0 1012500 0 0 0 0 0 -1012500 0 0 0 0

0 -25500 0 272000 0 0 0 25500 0 136000 0 0 0

25500 0 0 0 17000 0 -25500 0 0 0 8500 0 0

0 0 0 0 0 6538 0 0 0 0 0 -6538 0

204000 0 0 0 -25500 0 204000 0 0 0 -25500 0 #VALUE!

0 12750 0 25500 0 0 0 12750 0 25500 0 0 #VALUE!

0 0 -1012500 0 0 0 0 0 1012500 0 0 0 #VALUE!

0 -25500 0 136000 0 0 0 25500 0 272000 0 0 #VALUE!

25500 0 0 0 8500 0 -25500 0 0 0 17000 0 #VALUE!

0 0 0 0 0 -6538 0 0 0 0 0 6538 #VALUE!

0

0

0

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Page 39: Tugas Anstruk 3

Home work Metode Elemen Hingga - 1SUANTORO WICAKSONO (07 / 260420 / PTK / 4744)

0

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Page 40: Tugas Anstruk 3

Home work Metode Elemen Hingga - 1SUANTORO WICAKSONO (07 / 260420 / PTK / 4744)

0

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Page 41: Tugas Anstruk 3

Home work Metode Elemen Hingga - 1SUANTORO WICAKSONO (07 / 260420 / PTK / 4744)

0

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Page 42: Tugas Anstruk 3

Home work Metode Elemen Hingga - 1SUANTORO WICAKSONO (07 / 260420 / PTK / 4744)

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Page 43: Tugas Anstruk 3

Home work Metode Elemen Hingga - 1SUANTORO WICAKSONO (07 / 260420 / PTK / 4744)

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Page 44: Tugas Anstruk 3

Home work Metode Elemen Hingga - 1SUANTORO WICAKSONO (07 / 260420 / PTK / 4744)

412500 0 0 0 0 0 -412500 0 0 0 0 0 #VALUE!

0 3891 0 0 0 -7781 0 3891 0 0 0 -7781 #VALUE!

0 0 62250 0 7781 0 0 0 62250 0 7781 0 #VALUE!

0 0 0 3990 0 0 0 0 0 -3990 0 0 #VALUE!

0 0 7781 0 10375 0 0 0 -7781 0 0 0 #VALUE!

0 -7781 0 0 0 166000 0 7781 0 0 0 0 #VALUE!

-412500 0 0 0 0 0 412500 0 0 0 0 0 #VALUE!

0 3891 0 0 0 7781 0 3891 0 0 0 7781 #VALUE!

0 0 62250 0 -7781 0 0 0 62250 0 -7781 0 #VALUE!

0 0 0 -3990 0 0 0 0 0 3990 0 0 #VALUE!

0 0 7781 0 0 0 0 0 -7781 0 10375 0 #VALUE!

0 -7781 0 0 0 0 0 7781 0 0 0 166000 #VALUE!

#VALUE!

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Page 45: Tugas Anstruk 3

Home work Metode Elemen Hingga - 1SUANTORO WICAKSONO (07 / 260420 / PTK / 4744)

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Page 46: Tugas Anstruk 3

1029000 0 0 0 -25500 0 -412500 00 32203.13 0 25500 0 0 0 15562.50 0 1090312.5 0 0 0 0 00 25500 0 279980.8 0 0 0 0

-25500 0 0 0 68875 0 0 00 0 0 0 0 214038.5 0 -7781.25

-412500 0 0 0 0 0 1029000 00 15562.5 0 0 0 -7781.25 0 32203.130 0 15562.5 0 7781.25 0 0 00 0 0 -3990.385 0 0 0 255000 0 -7781.25 0 0 0 -25500 00 7781.25 0 0 0 0 0 -15562.50 0 0 0 0 0 -412500 00 0 0 0 0 0 0 3890.6250 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 -7781.25

-412500 0 0 0 0 0 0 00 3890.625 0 0 0 7781.25 0 00 0 62250 0 -7781.25 0 0 00 0 0 -3990.385 0 0 0 00 0 7781.25 0 0 0 0 00 -7781.25 0 0 0 0 0 0

1 0 0 0 -0.024781 0 -0.400875 00 32203.13 0 25500 0 0 0 15562.50 0 1090312.5 0 0 0 0 00 25500 0 279980.8 0 0 0 00 0 0 0 68243.08 0 -10222.3 00 0 0 0 0 214038.5 0 -7781.250 0 0 0 -10222.3 0 863639.2 00 15562.5 0 0 0 -7781.25 0 32203.130 0 15562.5 0 7781.25 0 0 00 0 0 -3990.385 0 0 0 255000 0 -7781.25 0 0 0 -25500 00 7781.25 0 0 0 0 0 -15562.50 0 0 0 0 0 -412500 00 0 0 0 0 0 0 3890.6250 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 -7781.250 0 0 0 -10222.3 0 -165361 00 3890.625 0 0 0 7781.25 0 00 0 62250 0 -7781.25 0 0 00 0 0 -3990.385 0 0 0 00 0 7781.25 0 0 0 0 0

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Page 47: Tugas Anstruk 3

0 -7781.25 0 0 0 0 0 0

1 0 0 0 -0.024781 0 -0.400875 00 1 0 0.791849 0 0 0 0.4832610 0 1090312.5 0 0 0 0 00 0 0 259788.6 0 0 0 -12323.140 0 0 0 68243.08 0 -10222.3 00 0 0 0 0 214038.5 0 -7781.250 0 0 0 -10222.3 0 863639.2 00 0 0 -12323.14 0 -7781.25 0 24682.380 0 15562.5 0 7781.25 0 0 00 0 0 -3990.385 0 0 0 255000 0 -7781.25 0 0 0 -25500 00 0 0 -6161.572 0 0 0 -19322.870 0 0 0 0 0 -412500 00 0 0 0 0 0 0 3890.6250 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 -7781.250 0 0 0 -10222.3 0 -165361 00 0 0 -3080.786 0 7781.25 0 -1880.1860 0 62250 0 -7781.25 0 0 00 0 0 -3990.385 0 0 0 00 0 7781.25 0 0 0 0 00 0 0 6161.572 0 0 0 3760.371

1 0 0 0 -0.024781 0 -0.400875 00 1 0 0.791849 0 0 0 0.4832610 0 1 0 0 0 0 00 0 0 259788.6 0 0 0 -12323.140 0 0 0 68243.08 0 -10222.3 00 0 0 0 0 214038.5 0 -7781.250 0 0 0 -10222.3 0 863639.2 00 0 0 -12323.14 0 -7781.25 0 24682.380 0 0 0 7781.25 0 0 00 0 0 -3990.385 0 0 0 255000 0 0 0 0 0 -25500 00 0 0 -6161.572 0 0 0 -19322.870 0 0 0 0 0 -412500 00 0 0 0 0 0 0 3890.6250 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 -7781.250 0 0 0 -10222.3 0 -165361 00 0 0 -3080.786 0 7781.25 0 -1880.1860 0 0 0 -7781.25 0 0 00 0 0 -3990.385 0 0 0 00 0 0 0 0 0 0 0

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Page 48: Tugas Anstruk 3

0 0 0 6161.572 0 0 0 3760.371

1 0 0 0 -0.024781 0 -0.400875 00 1 0 0 0 0 0 0.5208220 0 1 0 0 0 0 00 0 0 1 0 0 0 -0.0474350 0 0 0 68243.08 0 -10222.3 00 0 0 0 0 214038.5 0 -7781.250 0 0 0 -10222.3 0 863639.2 00 0 0 0 0 -7781.25 0 24097.830 0 0 0 7781.25 0 0 00 0 0 0 0 0 0 25310.720 0 0 0 0 0 -25500 00 0 0 0 0 0 0 -19615.150 0 0 0 0 0 -412500 00 0 0 0 0 0 0 3890.6250 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 -7781.250 0 0 0 -10222.3 0 -165361 00 0 0 0 0 7781.25 0 -2026.3240 0 0 0 -7781.25 0 0 00 0 0 0 0 0 0 -189.2850 0 0 0 0 0 0 00 0 0 0 0 0 0 4052.647

1 0 0 0 0 0 -0.404587 00 1 0 0 0 0 0 0.5208220 0 1 0 0 0 0 00 0 0 1 0 0 0 -0.0474350 0 0 0 1 0 -0.149793 00 0 0 0 0 214038.5 0 -7781.250 0 0 0 0 0 862108 00 0 0 0 0 -7781.25 0 24097.830 0 0 0 0 0 1165.573 00 0 0 0 0 0 0 25310.720 0 0 0 0 0 -25500 00 0 0 0 0 0 0 -19615.150 0 0 0 0 0 -412500 00 0 0 0 0 0 0 3890.6250 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 -7781.250 0 0 0 0 0 -166892 00 0 0 0 0 7781.25 0 -2026.3240 0 0 0 0 0 -1165.573 00 0 0 0 0 0 0 -189.2850 0 0 0 0 0 0 0

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Page 49: Tugas Anstruk 3

0 0 0 0 0 0 0 4052.647

1 0 0 0 0 0 -0.404587 00 1 0 0 0 0 0 0.5208220 0 1 0 0 0 0 00 0 0 1 0 0 0 -0.0474350 0 0 0 1 0 -0.149793 00 0 0 0 0 1 0 -0.0363540 0 0 0 0 0 862108 00 0 0 0 0 0 0 23814.950 0 0 0 0 0 1165.573 00 0 0 0 0 0 0 25310.720 0 0 0 0 0 -25500 00 0 0 0 0 0 0 -19615.150 0 0 0 0 0 -412500 00 0 0 0 0 0 0 3890.6250 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 -7781.250 0 0 0 0 0 -166892 00 0 0 0 0 0 0 -1743.440 0 0 0 0 0 -1165.573 00 0 0 0 0 0 0 -189.2850 0 0 0 0 0 0 00 0 0 0 0 0 0 4052.647

1 0 0 0 0 0 0 00 1 0 0 0 0 0 0.5208220 0 1 0 0 0 0 00 0 0 1 0 0 0 -0.0474350 0 0 0 1 0 0 00 0 0 0 0 1 0 -0.0363540 0 0 0 0 0 1 00 0 0 0 0 0 0 23814.950 0 0 0 0 0 0 00 0 0 0 0 0 0 25310.720 0 0 0 0 0 0 00 0 0 0 0 0 0 -19615.150 0 0 0 0 0 0 00 0 0 0 0 0 0 3890.6250 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 -7781.250 0 0 0 0 0 0 00 0 0 0 0 0 0 -1743.440 0 0 0 0 0 0 00 0 0 0 0 0 0 -189.2850 0 0 0 0 0 0 0

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Page 50: Tugas Anstruk 3

0 0 0 0 0 0 0 4052.647

1 0 0 0 0 0 0 00 1 0 0 0 0 0 00 0 1 0 0 0 0 00 0 0 1 0 0 0 00 0 0 0 1 0 0 00 0 0 0 0 1 0 00 0 0 0 0 0 1 00 0 0 0 0 0 0 10 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 0

1 0 0 0 0 0 0 00 1 0 0 0 0 0 00 0 1 0 0 0 0 00 0 0 1 0 0 0 00 0 0 0 1 0 0 00 0 0 0 0 1 0 00 0 0 0 0 0 1 00 0 0 0 0 0 0 10 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 0

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Page 51: Tugas Anstruk 3

0 0 0 0 0 0 0 0

1 0 0 0 0 0 0 00 1 0 0 0 0 0 00 0 1 0 0 0 0 00 0 0 1 0 0 0 00 0 0 0 1 0 0 00 0 0 0 0 1 0 00 0 0 0 0 0 1 00 0 0 0 0 0 0 10 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 0

1 0 0 0 0 0 0 00 1 0 0 0 0 0 00 0 1 0 0 0 0 00 0 0 1 0 0 0 00 0 0 0 1 0 0 00 0 0 0 0 1 0 00 0 0 0 0 0 1 00 0 0 0 0 0 0 10 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 0

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0 0 0 0 0 0 0 0

1 0 0 0 0 0 0 00 1 0 0 0 0 0 00 0 1 0 0 0 0 00 0 0 1 0 0 0 00 0 0 0 1 0 0 00 0 0 0 0 1 0 00 0 0 0 0 0 1 00 0 0 0 0 0 0 10 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 0

1 0 0 0 0 0 0 00 1 0 0 0 0 0 00 0 1 0 0 0 0 00 0 0 1 0 0 0 00 0 0 0 1 0 0 00 0 0 0 0 1 0 00 0 0 0 0 0 1 00 0 0 0 0 0 0 10 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 0

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Page 53: Tugas Anstruk 3

0 0 0 0 0 0 0 0

1 0 0 0 0 0 0 00 1 0 0 0 0 0 00 0 1 0 0 0 0 00 0 0 1 0 0 0 00 0 0 0 1 0 0 00 0 0 0 0 1 0 00 0 0 0 0 0 1 00 0 0 0 0 0 0 10 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 0

1 0 0 0 0 0 0 00 1 0 0 0 0 0 00 0 1 0 0 0 0 00 0 0 1 0 0 0 00 0 0 0 1 0 0 00 0 0 0 0 1 0 00 0 0 0 0 0 1 00 0 0 0 0 0 0 10 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 0

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0 0 0 0 0 0 0 0

1 0 0 0 0 0 0 00 1 0 0 0 0 0 00 0 1 0 0 0 0 00 0 0 1 0 0 0 00 0 0 0 1 0 0 00 0 0 0 0 1 0 00 0 0 0 0 0 1 00 0 0 0 0 0 0 10 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 0

1 0 0 0 0 0 0 00 1 0 0 0 0 0 00 0 1 0 0 0 0 00 0 0 1 0 0 0 00 0 0 0 1 0 0 00 0 0 0 0 1 0 00 0 0 0 0 0 1 00 0 0 0 0 0 0 10 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 0

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Page 55: Tugas Anstruk 3

0 0 0 0 0 0 0 0

1 0 0 0 0 0 0 00 1 0 0 0 0 0 00 0 1 0 0 0 0 00 0 0 1 0 0 0 00 0 0 0 1 0 0 00 0 0 0 0 1 0 00 0 0 0 0 0 1 00 0 0 0 0 0 0 10 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 0

1 0 0 0 0 0 0 00 1 0 0 0 0 0 00 0 1 0 0 0 0 00 0 0 1 0 0 0 00 0 0 0 1 0 0 00 0 0 0 0 1 0 00 0 0 0 0 0 1 00 0 0 0 0 0 0 10 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 0

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0 0 0 0 0 0 0 0

1 0 0 0 0 0 0 00 1 0 0 0 0 0 00 0 1 0 0 0 0 00 0 0 1 0 0 0 00 0 0 0 1 0 0 00 0 0 0 0 1 0 00 0 0 0 0 0 1 00 0 0 0 0 0 0 10 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 0

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1 0 0 0 0 0 0 00 1 0 0 0 0 0 00 0 1 0 0 0 0 00 0 0 1 0 0 0 00 0 0 0 1 0 0 00 0 0 0 0 1 0 00 0 0 0 0 0 1 00 0 0 0 0 0 0 10 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 0

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2192.208 0 21575.97 0 150.7966 0 208547.5 0 0.418851

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2230.016 0 21943 0 262.9869 0 208346.6 0 0.421718

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0 0 21879.09 0 264.0441 0 208323 0 0.424079

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0 0 0 0 -24731.43 0 186627.5 0 0.673882

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0 0 0 0 0 0 184191.2 0 0.700311

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