kd 4 asmm frame & grid

8/18/2019 Kd 4 Asmm Frame & Grid

1/47

PLANE FRAME

E 2100000 kg/cm2 21000000 t/m2

A 30 cm2 0.003 m2

I 2000 CM4 0.00002 m4

p1

p2

62.5

p3 5

Langkah 1 : Diskretisasi dan D.O.F

D3y D4y

D3x

D4x

3 #3 4

#1 #2

1 2

Langkah 2 : matriks kekakuan elemen sumbu lokal

Elm! #1 "13$

E 21000000 c%& 0

A 0.003 &'! 1

I 0.00002 c%&2 0

L 5 &'!2 1

&()(t *0

)1x )1y +1, )3x )3y

12600 0 0 12600 0

0 40.32 100.- 0 40.32

k1 0 100.- 336 0 100.-

12600 0 0 12600 0

0 40.32 100.- 0 40.32

0 100.- 16- 0 100.-

Elm! #2 "24$

E 21000000 c%& 0

A 0.003 &'! 1

I 0.00002 c%&2 0


2/47

L 5 &'!2 1

&()(t *0

)2x )2y +2, )4x )4y

12600 0 0 12600 0

0 40.32 100.- 0 40.32

k2 0 100.- 336 0 100.-

12600 0 0 12600 00 40.32 100.- 0 40.32

0 100.- 16- 0 100.-

Elm! #3 "34$

E 21000000 c%& 1

A 0.003 &'! 0

I 0.00002 c%&2 1

L 6 &'!2 0

&()(t 0

)3x )3y +3, )4x )4y

10500 0 0 10500 0

0 23.333333333 0 0 23.333333333

k3 0 0 2-0 0 0

10500 0 0 10500 0

0 23.333333333 0 0 23.333333333

0 0 140 0 0


3/47


4/47

0.01-6441 2.54032E005 0.0024*3 0.01-5*652 2.5403E005

2.5E005 .*34060E005 1.1E005 2.5403E005 2.44-02-E00-

& 1 0.0024*3 1.10161E005 0.0020466 0.0024-21 1.101613E005

0.01-5*65 2.54032E005 0.0024-3 0.01-644103 2.5403E005

2.-E005 2.44-02-E00- 1.10E005 2.540E005 .*34060E005

0.0024-3 1.10161E005 5.6E005 0.0024*2-46 1.101613E005


5/47

p1 4 t%!

p2 2 t%!

p3 1 t%!

3

L1 5 2.5 2.5L2 5

L3 6 3 3

Langkah 3 : Matriks Kekakuan Eleme

Elm! #1 "13$

+3,

0 )1x 0 1

100.- )1y 1 0

16- +1, "$1 0 0

0 )3x 0 0

100.- )3y 0 0

336 +3, 0 0

D1x D1y

40.32 0

0 12600

"$1 100.- 0


6/47

40.32 0

0 12600

+4, 100.- 0

0 )2x

100.- )2y Elm! #2 "24$

16- +2,

0 )4x 0.0E700 1100.- )4y 1 0.0E700

336 +4, "$2 0 0

0 0

0 0

0 0

D2x D2y

40.32 0

0 12600

"$2 100.- 0

+4, 40.32 0

0 )3x 0 12600

0 )3y 100.- 0

140 +3,

0 )4x Elm! #3"34$

0 )4y

2-0 +4, 1.0E700 0

0 1.0E700

"$3 0 0

0 0

0 0

0 0

D3x D3y

10500 0

0 23.33333

"$3 0 0

10500 0

0 23.33333

0 0

Langkah : !erakitan Matriks Kekak

D3x D3y

10540.32 0

0 12623.33

& 100.- 0

10500 0

0 23.33333

0 0


7/47

Langkah "a: S#an Loading Sumbu Lo

Elm! #1 "13$

0 81

0.5 82

0.625 830 84

0.5 85

0.625 86

Elm! #2 "24$

0 81

0 82

0 83

0 84

0 85

0 86

Elm! #3 "34$

0 81

11 82

c+' +(m(& 12 83

0 84

11 85

12 86

Langkah "$ : !erakitan s#an loading

0.5 D3x

11 D3y

9F%: 11.35 R3,

0 D4x


8/47

11 D4y

12 R4,

Langkah % : !erakitan &oint loading g

2 D3x

0 D3y9F: 0 R3,

0 D4x

0 D4y

0 R4,

Langkah ' : Global Dis#la$ement (F

0.0024-3 D3x 0.0451313 m

1.1E005 D3y 0.000-1105 m

5.6E005 R3, 0.0301--6 +)

0.0024*3 D4x 0.044-1-6-- m

1.10E005 D4y 0.000*34*-2 m

0.0020466 R4, 0.01-**3531 +)

Langkah : Menghitung Dis#la$emen

Elm! #1

0 D1x

0 D1y

9D1$ 0 R1,

0.0451313 D3x

0.000-1105 D3y

0.0301--6 R3,

Elm! #2

0 D2x

0 D2y

9D2$ 0 R2,

0.044-1-6-- D4x

0.000*34*-2 D4y

0.01-**3531 R4,

Elm! #3

0.0451313 D3x

0.000-1105 D3y

9D3: 0.0301--6 R3,

0.044-1-6-- D4x

0.000*34*-2 D4y

0.01-**3531 R4,


9/47

n Sumbu Global

40.32

0 0 0 0

0 0 0 0

1 0 0 0

0 0 1 0

0 1 0 0

0 0 0 1

R1, D3x D3y R3,

100.- 40.32 0 100.- D1x

0 0 12600 0 D1y

336 100.- 0 16- R1,


10/47


11/47

kal Langkah "b : S#an Load

84 Elm! #1 "13$

85 86

0.5 0.5

0 0

1 t%! 0.625 0.6250.5 0.5

0 0

83 0.625 0.625

82

81

84 Elm! #2 "24$

85 86

0 0

0 0

0 0

0 0

0 0

83 0 0

82

81

Elm! #3 "34$

82 p1 85 0 0

84 11 11

81 8 12 12

83 86 0 0

11 11

12 12

global


12/47

2.5 D3x

11 D3y

9F: 7 9F%: 11.35 R3,

lobal 0 D4x

11 D4y

12 R4,

)*(Fo)+ ,Ks-.,D-

t Sumbu Lokal (d) + ,/-.(D) Langkah 0 : Gaa atan

Elm! #1

0 )1x 10.21*231*6

0 )1y 1.221633*1

9)1: 0 +1, 98:1 0.51-245165

0.000-1105 )3x 10.21*231*6

0.0451313 )3y 1.221633*1

0.0301--6 +3, 5.5-**41*

Elm! #2

0 )2x 11.-06-04

0 )2y 3.21633*1

9)2: 0 +2, 98:2 .0-636-**

0.000*34*-2 )4x 11.-06-04

0.044-1-6-- )4y 3.21633*1

0.01-**3531 +4, 10.-**55006

Elm! #3

0.0451313 )3x 3.21633*1

0.000-1105 )3y 0.-06-044

9)3: 0.0301--6 +3, 98:3 5.-505-21

0.044-1-6-- )4x 3.21633*1

0.000*34*-2 )4y 0.-06-044

0.01-**3531 +4, 1.10044**43


13/47

0 1 0 0 0 0

1 0 0 0 0 0

"$ 0 0 1 0 0 0

0 0 0 0 1 0

0 0 0 1 0 0

0 0 0 0 0 1

0 40.32 100.- 0 40.32 100.-

12600 0 0 12600 0 0

"$ x k' 0 100.- 336 0 100.- 16-


14/47

0 40.32 100.- 0 40.32 100.-

12600 0 0 12600 0 0

0 100.- 16- 0 100.- 336

0 1 0 0 0 01 0 0 0 0 0

"$ 0 0 1 0 0 0

0 0 0 0 1 0

0 0 0 1 0 0

0 0 0 0 0 1

0 40.32 100.- 0 40.32 100.-

12600 0 0 12600 0 0

"$ x k' 0 100.- 336 0 100.- 16-

0 40.32 100.- 0 40.32 100.-

12600 0 0 12600 0 0

0 100.- 16- 0 100.- 336

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

10500 0 0 10500 0 0

0 23.33333333 0 0 23.33333 0

"$ x k' 0 0 2-0 0 0 140

10500 0 0 10500 0 0

0 23.33333333 0 0 23.33333 0

0 0 140 0 0 2-0


15/47

ing Sumbu Global

84

85 86

D1x

D1y

R1, 1 t%!D3x

D3y

R3, 83

82

81

84

85 86

D2x

D2y

R2,

D4x

D4y

R4, 83

82

81

+'&; k%l%m

D3x 82 p1 85

D3y 84

R3, 81 8

D4x 83 86

D4y

R4,


16/47

g Sumbu Lokal () + ,k-.(d)4(5)

0 10.21*232 t

0.5 0.2163 t

0.625 0.10654- t.m

0 10.21*23 t

0.5 1.21634 t

0.625 6.214*42 t.m

0 11.-06- t

0 3.21634 t

0 .0-636* t.m

0 11.-0 t

0 3.2163 t

0 10.-**55 t.m

0 3.21634 t

11 10.21*232 t

12 6.214*41- t.m

0 3.2163 t

11 11.-06- t

12 10.-**55 t.m


17/47


18/47


19/47


20/47


21/47

?


D3y

3 R3x

D1y D2y R3, D2y

R1x #2

1

R1, #1 2 R2x 1 #1 2

R2, R2,

Langkah 2 : matriks kekakuan elemen sumbu lokal dan global

Elm! #1

E 200000000 N/m2 c%& 1

< -0000000 N/m2 &'! 0I 0.000166 m4

@ 0.000046 m4

L 4 m4

)1y +1x +1, )2y +2x

6225 0 12450 6225 0

0 *20 0 0 *20

k1.l%cl 12450 0 33200 12450 0

6225 0 12450 6225 0

0 *20 0 0 *20

12450 0 16600 12450 0

1 0 0 0 0

0 1 0 0 0

1 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 01. 0 0 1 0 0

0 0 0 1 0


22/47

0 0 0 0 1

0 0 0 0 0

6225 0 12450 6225 0

0 *20 0 0 *20

.k 12450 0 33200 12450 0

6225 0 12450 6225 00 *20 0 0 *20

12450 0 16600 12450 0

D1y R1x R1, D2y R2x

6225 0 12450 6225 0

0 *20 0 0 *20

1.gl%l 12450 0 33200 12450 0

6225 0 12450 6225 0

0 *20 0 0 *20

12450 0 16600 12450 0

Elm! #2 "23$

E 200000000 N/m2 c%& 0

< -0000000 N/m2 &'! 1

I 0.000166 m4

@ 0.000046 m4

L 3 m4

)2y +2x +2, )3y +3x

1455.556 0 22133.33 1455.56 0

0 1226.66 0 0 1226.66

k2.l%cl 22133.333 0 44266.6 22133.33 0

1455.556 0 22133.33 1455.56 0

0 1226.66 0 0 1226.66

22133.333 0 22133.33 22133.33 0

1 0 0 0 0

0 0 1 0 0

2 0 1 0 0 0

0 0 0 1 0

0 0 0 0 0

0 0 0 0 1

1 0 0 0 0

0 0 1 0 0

2. 0 1 0 0 0

0 0 0 1 0

0 0 0 0 0

0 0 0 0 1

1455.556 0 22133.33 1455.56 0

22133.333 0 44266.6 22133.33 0


23/47


24/47

20 N

10 N/m

4 m

3

#2

R2x

Langkah : S#an Lo

Elm! #1

5

0

98%:1 5

+2, 5

12450 )1y 0

0 +1x 5

16600 +1,

12450 )2y Elm! #2

0 +2x

33200 +2, 00

0 98%:1 0

0 0

0 0

0 0

0

1 Langkah " : Global

0 %'!t l!g& 20

0 00 0

0 9F:


25/47

0

1 Langkah %a : Sol7e

12450 D2y

0 R2x

16600 R2,

124500 D2y

33200 R2x

R2,

R2,

12450 D1y Langkah %b : Eleme

0 R1x

16600 R1, Elm! #1

12450 D2y )1

0 R2x )2

33200 R2, )3

)4

)5

)6

Elm! #2

)1

)2

+3, )3

22133.33 )2y )4

0 +2x )5

22133.33 +2, )6

22133.33 )3y

0 +3x Langkah ' : sol7e el

44266.6 +3, k% )( )(!y )' c+'

Elm! #1

0 81

0 82

0 83

0 84

1 85

0 86

0

0 Elm! #2

0 81

0 82

1 83

0 84

85

22133.33 86

22133.33


26/47

0

22133.33


27/47

ding Sumbu Lokal dan Global

81 5 D1y

82 0 R1x

83 9F%:1.gl%l 5 R1,

84 5 D2y

85 0 R2x

86 5 R2,

9F%: Bl

81 0 D2y82 0 R2x

83 9F%:1.gl%l 0 R2,

84 0 D3y

85 0 R3x

86 0 R3,

6uation (F)*(Fo)+ ,Ks-.,D-

5 20*-0.555556 22133.33 12450

7 0 22133.333333 451-6.6 05 12450 0 34426.6

9F :


28/47

lobal E6uation (F)*(Fo)+ ,Ks-.,D-

0.00014053 -.6-*6E005 6.415655E005 25

-.6-*6E005 6.46*415E005 3.14252E005 > 0

6.415655E005 3.14252E005 5.224-1E005 5

0.0041143501 m

0.0020152*1 +)

0.001342602 +)

t 8odal Dis#la$ement (d) + ,/-. (D)

0 0 m D1y

0 0 +) R1x

1 x 0 0 +) R1,

0.0041143501 0.0041143501 m D2y

0.0020152*1 0.0020152*1 +) R2x

0.001342602 0.001342602 +) R2,

0.0041143501 0.0041143501 m D2y

0.0020152*1 0.001342602 +) R2x

2 x 0.001342602 0.0020152*1 +) R2,

0 0 m D3y

0 0 +) R3x

0 0 +) R3,

ement or$es () + ,k-.(d)4(o)

yg lm! &m yg k&l(+(!

-.-*55-561- 5 13.-*55*

1.-540623 0 1.-5406-

2-.*35333*21 5 33.*3533

-.-*55-561- 5 3.-*55-6

1.-540623 0 1.-5406-

6.6400-664 5 1.6400*

k1.9):1 98%:1

16.10441432- 0 16.10441

1.6400-664 0 1.6400*

1.-540623 0 1.-5406-

16.10441432- 0 16.10441

1.6400-664 0 1.6400*

46.45*15262 0 46.45*1-

k2.9):2 98%:2


29/47

: .9D:9F%: !y pk y!g t')k )'+)(k&'

-.-*55-561- 5 13.-*55*

1.-540623 0 1.-5406-

2-.*35333*21 5 33.*3533

25 5 20 0 0 0

5 5 0

16.10441432- 0 16.10441

46.45*15262 0 46.45*1-

1.6400-664 0 1.6400*


30/47

t+&l&'

p(!t'+

m%m!

5 D1y t+&l&'

0 R1x p(!t'+

5 R1, m%m!

5 D2y

0 R2x

5 R2,

0 D3y0 R3x

0 R3,

D2y

R2xR2,

D


31/47

0 D1y

0 R1x

0 R1,

0.004114 D2y

D 0.002015 R2x

0.001343 R2,

0 D3y

0 R3x

0 R3,

N

N.m

N.m

N

N.m

N.m

N

N.m

N.m

N

N.m

N.m


32/47

R1G

R3G


33/47


34/47


35/47


36/47

L2

p1 p2

100 200 c

?


D3y

3 R3x

D1y D2y R3, D2yR1x #2

1

R1, #1 2 R2x 1 #1 2

R2, R2,

Langkah 2 : matriks kekakuan elemen sumbu lokal dan global

Elm! #1"c$

E 200000 kg/cm2 c%& 1

< -0000 kg/cm2 &'! 0

I 6500 cm4

@ 113*00 cm4

L 300 cm4

)y +x +, )cy +cx

6000 0 *00000 6000 0

0 3033333 0 0 3E700

k1.l%cl *00000 0 1.-E700- *00000 0

6000 0 *00000 6000 0

0 3E700 0 0 3033333

*00000 0 *0000000 *00000 0

1 0 0 0 0

0 1 0 0 0

1 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


37/47

0 1 0 0 0

1. 0 0 1 0 0

0 0 0 1 0

0 0 0 0 1

0 0 0 0 0

6000 0 *00000 6000 00 3033333 0 0 3E700

.k *00000 0 1.-E700- *00000 0

6000 0 *00000 6000 0

0 3E700 0 0 3033333

*00000 0 *0000000 *00000 0

Dy Rx R, Dcy Rcx

6000 0 *00000 6000 0

0 3033333 0 0 3E700

1.gl%l *00000 0 1.-E700- *00000 06000 0 *00000 6000 0

0 3E700 0 0 3033333

*00000 0 *0000000 *00000 0

Elm! #2 "c$

E 200000 kg/cm2 c%& 0.242536

< -0000 kg/cm2 &'! 0.*0143

I 6500 cm4

@ 113*00 cm4

L 412.31056 cm4

)y +x +, )cy +cx

2311.221- 0 4640.6 2311.222 0

0 220**-46 0 0 2E700

k2.l%cl 4640.5* 0 1.3E700- 4641 0

2311.221- 0 4641 2311.222 0

0 2E700 0 0 220**-46

4640.5* 0 654-461* 4641 0

1 0 0 0 0

0 0.242536 0.*0143 0 0

2 0 0.*0143 0.242536 0 0

0 0 0 1 0

0 0 0 0 0.242536

0 0 0 0 0.*0143

1 0 0 0 0

0 0.242536 0.*0143 0 0

2. 0 0.*0143 0.242536 0 0


38/47

0 0 0 1 0

0 0 0 0 0.242536

0 0 0 0 0.*0143

2311.221- 0 4640.6 2311.222 0

462244.3 5360000 1E700- 462244.4 5360000

.k 115561.0* 21440000 316406 115561 2E7002311.221- 0 4641 2311.222 0

462244.3 5360000 6E700 462244.4 5360000

115561.0* 2E700 15--2353 115561 21440000

Dy Rx R, Dcy Rcx

2311.221- 462244 115561.1 2311.222 462244

462244.3 1.2E700- 3E700 462244.4 603325*1

2.gl%l 115561.0* 3E700 2-503*2- 115561 2E700

2311.221- 462244.4 115561 2311.222 462244.4

462244.3 603325*1 2E700 462244.4 1.2E700-115561.0* 2E700 2E700 115561 3E700

Langkah 3 : !erakitan Matriks Kekakuan Struktur Global

l(m R)(k&'

Dy Rx R, Dy Rx

6000 0 *00000 0 0

0 3033333 0 0 0

*00000 0 1.-E700- 0 0

0 0 0 2311.222 462244

Bl 0 0 0 462244 1.2E700-

0 0 0 115561.1 3E700

6000 0 *00000 2311.222 462244.4

0 3E700 0 462244 603325*1

*00000 0 *0000000 115561.1 2E700

&() R)(k&'

Dcy Rcx Rc,

-311.221- 462244.4 1015561 Dcy

+)(k&' 462244.3 1.5E700- 3E700 Rcx

1015561 3E700 2.1E700- Rc,


39/47

2 t%! 2000 kg

1 t%! 1000 kg

300 cm

412.3106 cm

3

#2

R2x

Langkah : S#an Lo

Elm! #1

14-1.4-1

0

98%:1 -----.-*

+c, 51-.51-5

*00000 )y 0

0 +x 44444.44

*0000000 +,

*00000 )cy Elm! #2

0 +cx

1.-E700- +c, 0

0

0 98%:1 0

0 0

0 0

0 0

0

1 Langkah " : Global

0 1000


40/47

0 0

0 0

0 9F:

0

1 Langkah %a : Sol7e

*00000 Dcy0 Rcx

*0000000 Rc,

*00000

0 Dcy

1.-E700- Rcx

Rc,

Rc,

*00000 Dy Langkah %b : Eleme

0 Rx

*0000000 R, Elm! #1*00000 Dcy )1

0 Rcx )2

1.-E700- Rc, )3

)4

)5

)6

Elm! #2

)1

)2

+c, )3

4640.6 )y )4

0 +x )5

654-461* +, )6

4641 )cy

0 +cx Langkah ' : sol7e el

1.3E700- +c,

Elm! #1

0 81

0 82

0 83

0 84

0.*0143 85

0.242536 86

0

0 Elm! #2

0 81


41/47

0 82

0.*0143 83

0.242536 84

85

4640.6 86

6E700

15--23534641


42/47

ding Sumbu Lokal dan Global

9F%: .98%:

81 14-1.4-14-15 Dy

82 0 Rx

83 9F%:1.gl%l -----.-----* R,

84 51-.51-51-52 Dcy

85 0 Rcx

86 44444.444444 Rc,

9F%: .98%: 9F%:Bl

81 0 Dy

82 0 Rx

83 9F%:1.gl%l 0 R,

84 0 Dcy

85 0 Rcx

86 0 Rc,

6uation (F)*(Fo)+ ,Ks-.,D-

51-.51-51-52 -311.221-3-6 462244.4 1015561


43/47

7 0 462244.362 1.5E700- 3E700

44444.444444 1015561.0*1* 3E700 2.1E700-

9F%: &

lobal E6uation (F)*(Fo)+ ,Ks-.,D-

0.0003-24*3 -.503*1E00 1.5-53E006 151-.51* -.503*1E00 -.4-650E00* 3.10034E00* > 0

1.5-53E006 3.10034E00* 0.000000013 44444.44

0.5026665*1 cm

0.001153541* +)

0.0020*34602 +)

t 8odal Dis#la$ement (d) + ,/-. (D)

0 0 cm Dy

0 0 +) Rx

1 x 0 0 +) R,

0.5026665*1 0.5026665*1 cm Dcy

0.001153541* 0.001153541* +) Rcx

0.0020*34602 0.0020*34602 +) Rc,

0 0 cm Dy

0 0 +) Rx

2 x 0 0 +) R,

0.5026665*1 0.5026665*1 cm Dcy

0.001153541* 0.001511* +) Rcx

0.0020*34602 0.001626-3- +) Rc,

ement or$es () + ,k-.(d)4(o)

1131.--531* 14-1.4-14-15 2613.36

35036.*11632 0 35036.*1

263*--.50551 -----.-----* 352-.4

1131.--531* 51-.51-51-52 613.366-

35036.*11632 0 35036.*1

55.0-*-6 44444.444444 31132.65

k1.9):1 98%:1

3-6.63320063 0 3-6.6332


44/47

3-00.-0122 0 3-00.-

132*2.*3102 0 132*2.*

3-6.63320063 0 3-6.6332

3-00.-0122 0 3-00.-

26440.021433 0 26440.02

k2.9):2 98%:2

1131.--531* 14-1.4-14-15 2613.36

35036.*11632 0 35036.*1

263*--.50551 -----.-----* 352-.4

3-6.63320063 0 3-6.6332

11*616.36-62 0 11*616

6**5.*654- 0 6**5.*

151-.51-51-5 51-.51-51-52 1000

.25*6E012 0 .3E01244444.444444 44444.444444 0


45/47

14-1.4-1 Dy

0 Rx

-----.-* R,

0 Dy

0 Rx

0 R,

51-.51-5 Dcy

0 Rcx

44444.44 Rc,

D2y


46/47

R2x

R2,

D

0 Dy

0 Rx

0 R,

0 Dy

D 0 Rx

0 R,

0.50266 Dcy

0.001154 Rcx

0.0020*3 Rc,

kg

kg.cm

kg.cm

kg

kg.cm

kg.cm

kg


47/47

kg.cm

kg.cm

kg

kg.cm

kg.cm

R1G

R2G

kd 4 asmm frame & grid

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