analisa struktur iv oca selesai

8/11/2019 Analisa Struktur IV Oca Selesai

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Elemen 1

1 0 0 0[T] = 0 1 0 0

0 0 1 00 0 0 1

1 0 0 0[TT] = 0 1 0 0

0 0 1 00 0 0 1

1 0 -1 0k = 0 0 0 0 33333.33 =

-1 0 1 00 0 0 0

1 0 -1 0K = 0 0 0 0

-1 0 1 00 0 0 0

[K] = ( [ T ]T.[k ] ). [T]

33333.333 0.000 -33333.333 0.0000.000 0.000 0.000 0.000 [T] =====

-33333.333 0.000 33333.333 0.0000.000 0.000 0.000 0.000

Member 1Perpindahan akhir member dan gaya akhir member

[K] =

Matriks Kekakuan dalam sistem koordinat global

[K] =


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0.000 0.000 0.000 0.000 [T] =====

33333.333 0.000 -33333.333 0.0000.000 0.000 0.000 0.000

u = T v Q = ku0 7 0 7

[v] = 0 8 [u 1] = 0 8 [Q 1] =0 1 0 1

-0.424264069 2 0.424264069 2

Elemen 3

0.707106781 0.707106781 0 0[T] = -0.707106781 0.707106781 0 0

0 0 0.707106781 0.7071067810 0 -0.707106781 0.707106781

0.707106781 -0.707106781 0 0[TT] = 0.707106781 0.707106781 0 0

0 0 0.707106781 -0.707106780 0 0.707106781 0.707106781

1 0 -1 0k = 0 0 0 0 23570.23 =

-1 0 1 00 0 0 0

1 0 -1 0K = 0 0 0 0

Perpindahan akhir member dan gaya akhir member

[K] =[K] =


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#REF! #REF! #REF! #REF! #REF!

#REF! #REF! #REF! #REF! #REF!

Member 1 2 3 4 5

1 #REF! #REF! #REF! #REF!2 #REF! #REF! #REF! #REF!3 #REF! #REF! #REF! #REF!4 #REF! #REF! #REF! #REF!5 #REF! #REF!6 #REF! #REF! #REF!7 #REF! #REF! #REF! #REF!8 #REF! #REF! #REF!

Cek Gaya-Gaya member

2cmkg 2cm

0 y F

0 x F


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33333.33333 0 -33333.3333 00 0 0 0

-33333.33333 0 33333.33333 00 0 0 0

7 8 1 233333.3 0.0 -33333.3 0.0

0.0 0.0 0.0 0.0-33333.3 0.0 33333.3 0.0

0.0 0.0 0.0 0.0


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0.0 0.0 0.0 0.0-33333.3 0.0 33333.3 0.0

0.0 0.0 0.0 0.0

F = T T Q0 7 00 8 [F1] = 00 1 0

0 2 0

23570.22604 0 -23570.226 00 0 0 0-23570.22604 0 23570.22604 0

0 0 0 0


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-23570.22604 0 23570.22604 00 0 0 0

5 6 3 411785.1 -11785.1 -11785.1 11785.1

-11785.1 11785.1 11785.1 -11785.1-11785.1 11785.1 11785.1 -11785.111785.1 -11785.1 -11785.1 11785.1

F = T T Q7071.067812 5 -5000

0 6 [F1] = 5000-7071.067812 3 5000

0 4 -5000


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MATRIK KEKAKUAN STRUKTUR SECARA KESELURUHAN

1 2 3 4 5 6690228.5714 0 0 -671428.5714 0 0

0 1888769.679 1534693.878 0 -8769.6793 1534693.878 0 1534693.878 1360761905 0 -1534693.878 179047619

-671428.5714 0 0 1361657.143 0 0 0 -8769.6793 -1534693.878 0 1897539.359 0 0 1534693.878 179047619 0 0 1718857143 0 0 0 -671428.5714 0 0

0 0 0 0 -8769.6793 -1534693.878 0 0 0 0 1534693.878 179047619 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

-9400 0 1880000 0 0 0 0 -940000 0 0 0 0

-1880000 0 250666666.7 0 0 0 0 0 0 -9400 0 1880000 0 0 0 0 -940000 0

0 0 0 -1880000 0 250666666.7 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 0

S


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15 16 17 18 19 20 21-1880000 0 0 0 0 0 0

0 0 0 0 0 0 0250666666.7 0 0 0 0 0 0

0 -9400 0 -1880000 0 0 0 0 0 -940000 0 0 0 0 0 1880000 0 250666666.7 0 0 0 0 0 0 0 -9400 0 -1880000

0 0 0 0 0 -940000 0 0 0 0 0 1880000 0 250666666.7 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -671428.5714 0 0 0 0 0

1534693.878 0 -8769.6793 1534693.878 0 0 0 1360761905 0 -1534693.878 179047619 0 0 0

0 1361657.143 0 0 -671428.5714 0 0 -1534693.878 0 1897539.359 0 0 -8769.6793 1534693.878

179047619 0 0 1718857143 0 -1534693.878 179047619 0 -671428.5714 0 0 1361657.143 0 0 -0 0 -8769.6793 -1534693.878 0 1897539.359 0 0 0 1534693.878 179047619 0 0 1718857143 0 0 0 0 -671428.5714 0 0 0 0 0 0 0 -8769.6793 -1534693.878 0 0 0 0 0 1534693.878 179047619

1880000 0 0 0 0 0 0 0 0 0 0 0 0 0

250666666.7 0 0 0 0 0 0 0 -9400 0 1880000 0 0 0 0 0 -940000 0 0 0 0 0 -1880000 0 250666666.7 0 0 0 0 0 0 0 -9400 0 1880000 0 0 0 0 0 -940000 0 0 0 0 0 -1880000 0 250666666.7 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0


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Nama : Fatma NIM : 0341110008Tugas : Mekanika Rekayasa VI

X Y Z1 300 600 02 0 300 03 300 300 04 600 300 05 300 0 06 300 300 300

Posisi Masing-Masing Titik

Titik Koordinat

Panjang Batang, dan Nilai Fungsi Cosinus dari Sudut yang Terbentuk

3 m

3 m

3 m

2

5

3

4

1

6

18

17z

y

8000 kg 6

3

2

8000 kg

6

5 4

3

2

8

79

6 5

4

3

2

1 1

x

11

12

101

16

45

9

87

151314


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Matriks Kekakuan Elemen dalam Sistem Koordinat Lokal

1 -1

-1 1

E = 2100000A = 100

1 300 700000 700000 -700000 494974.75 -494974.72 300 700000 -700000 700000 -494974.7 494974.753 300 700000

4 300 700000 700000 -700000 494974.75 -494974.75 300 700000 -700000 700000 -494974.7 494974.756 424.264069 4949757 424.264069 494975 700000 -700000 494974.75 -494974.78 424.264069 494975 -700000 700000 -494974.7 494974.759 424.264069 494975

700000 -700000 494974.75 -494974.7-700000 700000 -494974.7 494974.75

700000 -700000-700000 700000

Matriks Kekakuan Elemen dalam Koordinat Global

10 11 12 1 2 3

700000 -700000 700000 0 0 -700000 0 0 100 0 0 0 0 0 0 0 11

[K 1] = 0 0 x [T] ==== [K 1] = 0 0 0 0 0 0 12

-700000 700000 -700000 0 0 700000 0 0 10 0 0 0 0 0 0 0 20 0 0 0 0 0 0 0 3

1 2 3 13 14 15

700000 -700000 700000 0 0 -700000 0 0 10 0 0 0 0 0 0 0 2

[K 2] = 0 0 x [T] ==== [K 2] = 0 0 0 0 0 0 3

[K] = [T T][k][T]

[k 6] =

[k 7] =

[k 8] =

[k 9] =

[k 1] =

[k 2] =

[k 3] =

[k 4] =

[k 5] =

[k] =

Member L

11

11

L EA

k

L

EA

2cm

2cmkg


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10 11 12 4 5 6

350000 -350000 247487.37 0 247487.37 -247487.4 0 -247487.4 100 0 0 0 0 0 0 0 11

[K 6] = 350000 -350000 x [T] ==== [K 6] = 247487.37 0 247487.37 -247487.4 0 -247487.4 12

-350000 350000 -247487.4 0 -247487.4 247487.37 0 247487.37 40 0 0 0 0 0 0 0 5

-350000 350000 -247487.4 0 -247487.4 247487.37 0 247487.37 6

13 14 15 4 5 6

-350000 350000 247487.37 0 -247487.4 -247487.4 0 247487.37 130 0 0 0 0 0 0 0 14

[K 7] = 350000 -350000 x [T] ==== [K 7] = -247487.4 0 247487.37 247487.37 0 -247487.4 15350000 -350000 -247487.4 0 247487.37 247487.37 0 -247487.4 4

0 0 0 0 0 0 0 0 5-350000 350000 247487.37 0 -247487.4 -247487.4 0 247487.37 6

7 8 9 4 5 6

0 0 0 0 0 0 0 0 7-350000 350000 0 247487.37 -247487.4 0 -247487.4 247487.37 8

[K 8] = 350000 -350000 x [T] ==== [K 8] = 0 -247487.4 247487.37 0 247487.37 -247487 .4 90 0 0 0 0 0 0 0 4

350000 -350000 0 -247487.4 247487.37 0 247487.37 -247487.4 5-350000 350000 0 247487.37 -247487.4 0 -247487.4 247487.37 6

16 17 18 4 5 6

0 0 0 0 0 0 0 0 16350000 -350000 0 247487.37 247487.37 0 -247487.4 -247487.4 17

[K 9] = 350000 -350000 x [T] ==== [K 9] = 0 247487.37 247487.37 0 -247487.4 -247487 .4 180 0 0 0 0 0 0 0 4

-350000 350000 0 -247487.4 -247487.4 0 247487.37 247487.37 5-350000 350000 0 -247487.4 -247487.4 0 247487.37 247487.37 6

Matrik Kekakuan Struktur dari Masing-Masing Batang

[S1] = 700000 0 0 0 0 0 1

0 0 0 0 0 0 20 0 0 0 0 0 30 0 0 0 0 0 40 0 0 0 0 0 50 0 0 0 0 0 6

[S2] = 700000 0 0 0 0 0 1


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[S7] = 0 0 0 0 0 0 10 0 0 0 0 0 20 0 0 0 0 0 30 0 0 247487.4 0 -247487.4 40 0 0 0 0 0 50 0 0 -247487.4 0 247487.37 6

[S8] = 0 0 0 0 0 0 10 0 0 0 0 0 20 0 0 0 0 0 30 0 0 0 0 0 40 0 0 0 247487.37 -247487.4 50 0 0 0 -247487.4 247487.37 6

[S9] = 0 0 0 0 0 0 10 0 0 0 0 0 20 0 0 0 0 0 30 0 0 0 0 0 40 0 0 0 247487.37 247487.37 50 0 0 0 247487.37 247487.37 6

Matriks Kekakuan Struktur secara keseluruhan

1400000 0 0 0 0 0 10 1400000 0 0 0 0 2

[S] = 0 0 700000 0 0 -700000 30 0 0 494974.7 0 0 40 0 0 0 494974.75 0 50 0 -700000 0 0 1689949.5 6

Invers Matriks Struktur Secara Keseluruhan Gaya yang Bekerja Terhadap Konstruksi

7.1429E-07 0 0 0 0 0 1 0 1

[S-1] = 0 7.14E-07 0 0 0 0 2 [P] = 0 20 0 2.439E-06 0 0 1.01E-06 3 0 30 0 0 2.02E-06 0 0 4 0 40 0 0 0 2.02E-06 0 5 0 50 0 1.01E-06 0 0 1.01E-06 6 -8000 6

Perpindahan Titik Nodal yang Timbul[d] = [S -1]*[P]


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Member 3 Member 40 7 Q = k u 0 1 Q = k u0 8 0 2

[v3] = 0 9 [Q 3] = 0 [v4] = -0.008081 3 [Q 4] = 0

0 1 0 0 16 00 2 0 17

-0.0080812 3 F = T T Q 0 18 F = T T Q0 7 0 1

[u] = [T][v] 0 8 [u] = [T][v] 0 2[F 3] = 0 9 [F 4] = 0 3

[u 3] = 0 0 1 [u 4] = 0 0 160 0 2 0 0 17

0 3 0 18


[v5] = -0.0080812 3 [Q 5] = 0 [v6]= 0 12 [Q 6] = 2828.42710 4 0 0 4 -2828.4270 5 0 5

-0.0080812 6 F = T T Q -0.008081 6 F = T T Q0 1 2000 10

[u] = [T][v] 0 2 [u] = [T][v] 0 11[F 5] = 0 3 [F 6] = 2000 12

[u 5] = -0.0080812 0 4 [u 6] = 0 -2000 4-0.0080812 0 5 -0.005714 0 5

0 6 -2000 6


[v7] = 0 15 [Q 7] = 2828.427 [v8] = 0 9 [Q 8] = 2828.42710 4 -2828.427 0 4 -2828.4270 5 0 5

-0.0080812 6 F = T T Q -0.008081 6 F = T T Q-2000 13 0 7

[u] = [T][v] 0 14 [u] = [T][v] -2000 8[F 7] = 2000 15 [F 8] = 2000 9

[u 7] = 0 2000 4 [u 8] = 0 0 4-0.0057143 0 5 -0.005714 2000 5

-2000 6 -2000 6

Member 90 16 Q = k u


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1 2 3 4 5 6 7 8 91 0 0 0 0 0 02 0 0 0 0 0 03 0 0 0 0 0 0

4 0 -2000 2000 0 0 05 0 0 0 2000 -2000 06 0 -2000 -2000 -2000 -2000 -80007 0 0 08 0 -2000 -20009 0 2000 2000

10 0 2000 200011 0 0 012 0 2000 200013 0 -2000 -2000

14 0 0 015 0 2000 200016 0 0 017 0 2000 200018 0 2000 2000F 0 0 0 0 0 0 0 0 0 0

Member


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2.02E-05 1.84E-07 2.41E-08 2.04E-05 7.13E-08 -8.1E-09 2.1E-05 -2E-08-1.6E-09 3.09E-09 -1E-10 -1.5E-09 2.07E-08 8.18E-10 -3.5E-09 1.03E-06

-7E-09 -3E-10 1.02E-11 -7E-09 -8.7E-10 -6.3E-11 -7E-09 3.23E-111.98E-05 1.82E-07 2.35E-08 2E-05 7.03E-08 -8E-09 2.05E-05 -2.2E-084.81E-08 3.9E-11 7.18E-11 4.85E-08 -1.9E-09 -7.5E-11 5.03E-08 1.83E-08-1.2E-08 -2.5E-10 -6.4E-12 -1.2E-08 -1.5E-12 1.79E-11 -1.2E-08 -9.6E-105.07E-06 1.88E-07 -3.1E-09 4.98E-06 4.77E-08 -4.2E-09 4.93E-06 -2.1E-08-3.4E-08 -1.1E-06 1.39E-09 -3.3E-08 -8E-09 8.62E-10 -3.2E-08 1.1E-093.08E-08 -9.6E-10 -1.5E-10 2.87E-08 9.16E-10 2.61E-11 2.75E-08 -6.2E-115.56E-06 1.83E-07 -1.8E-09 5.48E-06 4.9E-08 -5.6E-09 5.43E-06 -2E-082.25E-08 -4.1E-08 1.05E-09 1.73E-08 1E-06 2.41E-11 1.25E-08 3.23E-081.82E-08 9.52E-10 6.08E-11 1.87E-08 8.03E-11 -1.1E-10 1.77E-08 7.03E-105.88E-06 1.81E-07 -1.2E-09 5.8E-06 5.01E-08 -5.5E-09 5.77E-06 -1.9E-08-1.3E-08 3.9E-09 -5.4E-11 -1.3E-08 3.23E-08 6.69E-10 -1.7E-08 1.01E-061.78E-08 1.01E-10 1.48E-11 1.79E-08 -6.7E-10 1.56E-11 1.86E-08 -1E-116.04E-06 1.81E-07 -8.4E-10 5.96E-06 5.01E-08 -5.5E-09 5.94E-06 -1.7E-081.28E-07 9.48E-10 1.39E-10 1.29E-07 -2.5E-09 -8.5E-11 1.33E-07 2.87E-082.66E-08 1.88E-10 3.5E-11 2.68E-08 1.15E-10 -1.6E-11 2.76E-08 -8.7E-10

-5E-07 1.07E-08 6.28E-10 -5E-07 1.52E-09 8.58E-10 -4.9E-07 -8.7E-10-4.1E-08 -1.1E-06 1.38E-09 -4E-08 -5.2E-09 8.62E-10 -3.9E-08 1E-09

3.69E-09 1.71E-09 5.2E-11 4.29E-09 5.98E-10 -2.9E-11 4.57E-09 -4.8E-11-4.7E-07 1E-08 2.56E-10 -4.7E-07 7.51E-09 9.63E-10 -4.7E-07 -9.2E-101.94E-08 -4.4E-08 1.08E-09 1.47E-08 9.99E-07 2.54E-11 1.02E-08 3.53E-088.11E-09 7.01E-10 -3.1E-11 7.72E-09 8.93E-11 2.4E-11 7.91E-09 4.18E-10-4.6E-07 1.31E-08 7.36E-11 -4.6E-07 1.33E-08 8.27E-10 -4.6E-07 4.72E-09-1.2E-08 3.91E-09 -5.8E-11 -1.2E-08 3.52E-08 6.84E-10 -1.6E-08 1E-068.79E-09 3.34E-10 -5E-12 8.62E-09 -3.9E-10 -2.2E-11 8.32E-09 -4.9E-11-4.7E-07 1.43E-08 -3.4E-11 -4.7E-07 1.33E-08 8.07E-10 -4.8E-07 1.06E-081.37E-07 1.36E-09 1.27E-10 1.37E-07 -2.6E-09 -1E-10 1.41E-07 3.14E-08

8.21E-09 3.93E-10 -1.6E-11 7.93E-09 7.12E-11 -1.1E-11 7.59E-09 -5.3E-10


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9 10 11 12 13 14 15 16 170 0 0 0 -9400 0 -1880000 0 00 0 0 0 0 -940000 0 0 00 0 0 0 1880000 0 250666667 0 00 0 0 0 0 0 0 -9400 0

1534693.9 0 0 0 0 0 0 0 -940000179047619 0 0 0 0 0 0 1880000 0

0 -671428.6 0 0 0 0 0 0 00 0 -8769.679 1534693.9 0 0 0 0 0

1.719E+09 0 -1534694 179047619 0 0 0 0 00 690228.57 0 0 0 0 0 0 0

-1534694 0 1888769.7 -1534694 0 0 0 0 0179047619 0 -1534694 1.361E+09 0 0 0 0 0

0 0 0 0 690228.57 0 0 -671428.6 0

0 0 0 0 0 1888769.7 1534693.9 0 -8769.6790 0 0 0 0 1534693.9 1.361E+09 0 -15346940 0 0 0 -671428.6 0 0 1361657.1 00 0 0 0 0 -8769.679 -1534694 0 1897539.40 0 0 0 0 1534693.9 179047619 0 0

1880000 0 0 0 0 0 0 -671428.6 00 0 0 0 0 0 0 0 -8769.679

250666667 0 0 0 0 0 0 0 1534693.90 -9400 0 1880000 0 0 0 0 0

0 0 -940000 0 0 0 0 0 00 -1880000 0 250666667 0 0 0 0 00 0 0 0 -9400 0 1880000 0 00 0 0 0 0 -940000 0 0 00 0 0 0 -1880000 0 250666667 0 00 0 0 0 0 0 0 -9400 0


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-3.7E-09 2.05E-05 2.11E-07 -9.7E-09 -5.5E-07 2.73E-08 5.28E-08 -5E-07 9.69E-081.3E-11 -5.7E-09 1.84E-08 -9.9E-10 -5.9E-10 1E-09 -2.3E-11 -7.2E-10 3.24E-08

6.18E-10 -6.9E-09 4.87E-10 -7.7E-11 9.06E-10 -8.1E-11 -6.4E-11 6.39E-10 -7.6E-10-3.6E-09 2.16E-05 2.12E-07 -1E-08 -5.5E-07 2.65E-08 5.24E-08 -5E-07 9.61E-087.41E-10 5.14E-08 1.05E-06 8.97E-10 4.73E-09 1.24E-11 4.54E-11 4.41E-09 -2.8E-09-7.9E-11 -1.3E-08 5.25E-10 7.95E-10 1.26E-09 1.64E-11 -8.5E-11 8.52E-10 -1.1E-10-2.3E-09 4.92E-06 2.97E-07 -6.5E-09 -1.1E-06 -1.1E-08 6.28E-08 -2.2E-06 9.6E-08-7.4E-11 -3.2E-08 -1.3E-09 4.43E-11 4.62E-09 -6.3E-09 -5.4E-10 6.84E-09 -8.4E-09

-1E-11 2.69E-08 2.36E-10 -1E-11 -1.3E-09 -2.2E-10 9.16E-10 -9.4E-10 2.09E-09-3.5E-09 5.43E-06 2.88E-07 -8.1E-09 -1.1E-06 -1.1E-08 6.16E-08 -7.3E-07 9.47E-08-6.7E-10 1.25E-08 -2.8E-09 2.31E-11 -2.7E-09 -8E-09 1.97E-09 -2.6E-09 2.03E-061.93E-11 1.74E-08 1.02E-10 -1.4E-11 5.99E-10 -7E-11 -6.8E-11 5.11E-10 7.89E-11-4.8E-09 5.77E-06 2.81E-07 -9.8E-09 -1.1E-06 -9.7E-09 6.09E-08 -7.3E-07 9.36E-083.41E-12 -2.2E-08 2.88E-08 -7.3E-10 -4.3E-10 7.39E-10 -1.6E-10 -5.1E-10 5.59E-08

-1E-10 1.8E-08 8.25E-10 2.44E-11 3.56E-10 5.68E-11 4.85E-11 3.54E-10 -1.6E-09-4.6E-09 5.96E-06 2.78E-07 -1.2E-08 -1.1E-06 -9.2E-09 6.06E-08 -7.3E-07 9.34E-086.1E-10 1.35E-07 1.04E-06 6.39E-10 5.97E-09 1.2E-10 3.34E-10 6.43E-09 -4.5E-09

2.82E-11 2.94E-08 1.01E-09 -1.7E-10 4.98E-10 3.12E-11 5.03E-11 4.58E-10 2.28E-108.4E-10 -4.9E-07 9.26E-09 1.15E-09 -1.1E-06 2.51E-09 8.7E-10 -1.1E-06 3.33E-09

-6.3E-11 -3.9E-08 -2E-09 6.21E-11 4.41E-09 -6.3E-09 -5.3E-10 8.01E-09 -2.8E-09

-4.1E-12 4.77E-09 7.19E-10 -1.8E-11 5.46E-10 4.84E-11 -2E-10 -3.1E-09 1.1E-098.47E-10 -4.7E-07 7.01E-09 1.2E-09 -1.1E-06 2.01E-09 2.78E-09 -1.1E-06 1.6E-08-6.8E-10 1.02E-08 -2.9E-09 3.16E-11 -2.4E-09 -7.9E-09 1.8E-09 -4.6E-09 2.01E-06-1.9E-11 7.97E-09 5.58E-10 -1.5E-11 -2.1E-10 -5.1E-12 1.8E-10 9.25E-10 1.88E-109.56E-10 -4.7E-07 1.29E-09 1.33E-09 -1.1E-06 1.47E-09 3.84E-09 -1.1E-06 2.82E-088.94E-12 -2.1E-08 3.15E-08 -7.5E-10 -4.7E-10 7.3E-10 -1.3E-10 -4.3E-10 6.19E-082.49E-11 8.61E-09 1.01E-09 -3.7E-11 -2.8E-11 -3.8E-11 1.01E-10 6.27E-10 -7.4E-108.36E-10 -4.9E-07 -2.4E-09 1.66E-09 -1.1E-06 1.27E-09 4.26E-09 -1.1E-06 2.81E-086.05E-10 1.43E-07 1.04E-06 6.32E-10 5.88E-09 7.89E-11 4.65E-10 7.19E-09 -4.7E-09

-3E-11 6.94E-09 1.18E-09 3.31E-11 -1.1E-10 -4.1E-11 1.41E-10 7.98E-10 1.23E-10


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18 19 20 21 22 23 24 25 260 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0

-1880000 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0

250666667 0 0 0 0 0 0 0 00 -9400 0 -1880000 0 0 0 0 00 0 -940000 0 0 0 0 0 00 1880000 0 250666667 0 0 0 0 00 0 0 0 -9400 0 -1880000 0 00 0 0 0 0 -940000 0 0 00 0 0 0 1880000 0 250666667 0 00 0 0 0 0 0 0 -940000 0

1534693.9 0 0 0 0 0 0 0 -9400179047619 0 0 0 0 0 0 0 -18800000 -671428.6 0 0 0 0 0 0 00 0 -8769.679 1534693.9 0 0 0 0 0

1.719E+09 0 -1534694 179047619 0 0 0 0 00 1361657.1 0 0 -671428.6 0 36 0 0

-1534694 0 1897539.4 0 0 -8769.679 1534693.9 0 0179047619 0 0 1.719E+09 0 -1534694 179047619 0 0

0 -671428.6 0 0 690228.57 0 0 0 0

0 0 -8769.679 -1534694 0 1888769.7 -1534694 0 00 0 1534724.9 179047619 0 -1534694 1.361E+09 0 00 0 0 0 0 0 0 412257.14 00 0 0 0 0 0 0 0 942959.770 0 0 0 0 0 0 1880000 517959.18

1880000 0 0 0 0 0 0 -402857.1 0


28/116

4.32E-08 -4.5E-07 -4.5E-08 4.22E-08 -4.1E-07 4.46E-07 5.95E-08 -3.6E-05 2.66E-087.27E-10 3.45E-10 1.01E-06 1.47E-11 1.63E-09 2.9E-08 -8.4E-10 -2.2E-08 -2.3E-10-2.1E-11 -1.5E-10 4.6E-11 -1.4E-10 3.14E-10 9.32E-11 -2.5E-11 5.74E-08 8.8E-12

4.28E-08 -4.4E-07 -5E-08 4.15E-08 -3.8E-07 4.48E-07 6.12E-08 -3.6E-05 2.57E-081.21E-11 3.35E-09 2.88E-08 7.28E-10 2.61E-09 1.04E-06 8.83E-10 8.25E-09 1.06E-10-7.2E-11 -4.1E-11 -6.7E-10 -3.2E-11 -1.6E-09 -1E-10 -2.5E-10 8.39E-08 2.66E-114.78E-08 -2.9E-06 -4.9E-08 4.7E-08 -3.2E-06 6.11E-07 6.29E-08 -6.6E-05 -2.9E-08

-3E-10 9.72E-09 9.72E-10 -1.7E-10 1.08E-08 -2.6E-09 -2.8E-10 2.73E-07 -6.1E-10-5.2E-11 -7.4E-10 -1.9E-10 6.07E-11 -6.1E-10 5.08E-10 6.8E-11 -3.8E-08 1.91E-094.67E-08 -1.4E-06 -4.8E-08 4.6E-08 -1.7E-06 5.98E-07 6.15E-08 -6.4E-05 -2.9E-083.38E-11 -2.8E-09 5.59E-08 -1.6E-09 -2.7E-09 -4.9E-09 1.57E-10 -1.4E-08 9.65E-096.83E-10 6.98E-10 1.57E-09 -5E-11 7.66E-10 1.91E-10 5.39E-11 -2E-08 -8.9E-114.62E-08 1.83E-08 -4.8E-08 4.52E-08 -3E-07 5.89E-07 6.05E-08 -6.3E-05 -2.7E-081.58E-09 -1E-09 2.03E-06 7.45E-12 -1.4E-09 4.96E-08 -2E-09 2.11E-09 -6.1E-10-4.8E-11 2.21E-10 -7.3E-12 6.83E-10 3.89E-10 1.79E-09 -5.7E-11 -2E-08 2.87E-114.61E-08 5.32E-09 -4.8E-08 4.51E-08 1.16E-06 5.86E-07 5.98E-08 -6.3E-05 -2.6E-08

1.7E-10 7.04E-09 4.95E-08 1.75E-09 7.4E-09 2.09E-06 2.23E-09 -2.1E-07 1.58E-105.66E-11 3.06E-10 -2E-09 -5.7E-11 -4.5E-11 2.28E-09 9.16E-10 -2.8E-08 4.66E-111.19E-09 -1.1E-06 -1.4E-09 1.08E-09 -1.1E-06 1.54E-08 1.44E-09 -2.1E-06 -2.3E-09-3.2E-10 1.3E-08 7.88E-10 -3.1E-10 1.49E-08 -4.1E-09 -4.2E-10 4.31E-07 1.06E-06

1.75E-10 -5.1E-09 -9.1E-11 1E-10 -6E-09 1.48E-09 1.48E-10 -1.7E-07 -1.7E-096.82E-10 -1.1E-06 -1.6E-09 7.58E-10 -1.1E-06 1.07E-08 1.02E-09 -4.1E-06 -5E-106.06E-11 -6.9E-09 6.19E-08 -1.5E-09 -6.7E-09 -5.1E-09 1.31E-10 -3.9E-08 1.2E-08-1.4E-10 -9.5E-10 7.75E-10 1.34E-10 -1.6E-09 1.17E-09 1.07E-10 -1.2E-07 -6.4E-101.64E-09 -1.1E-06 1.02E-08 -2.2E-10 -1.1E-06 -1.2E-09 -6.6E-11 -5.3E-06 -1.5E-091.45E-09 -3.1E-09 2.02E-06 -1.3E-11 -5.8E-09 5.51E-08 -1.8E-09 1.54E-08 -8.7E-101.32E-10 2.51E-09 -1.3E-10 -1.4E-10 1.39E-09 2.06E-09 1.81E-10 -1.2E-07 -2.2E-111.95E-09 -1E-06 2.28E-08 2.81E-10 -1E-06 -9E-09 -2E-09 -5.8E-06 -1.9E-09

3E-10 9.95E-09 5.5E-08 1.76E-09 1.17E-08 2.08E-06 2.2E-09 -3.6E-07 9.33E-11

9.66E-11 2.83E-09 -1E-09 1.73E-10 6.52E-09 2.37E-09 -2E-10 -1.5E-07 -8.9E-11


29/116

27 28 29 30 31 32 33 34 350 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0

1880000 0 0 0 0 0 0 0 0250666667 0 0 0 0 0 0 0 00 -9400 0 -1880000 0 0 0 0 00 0 -940000 0 0 0 0 0 00 1880000 0 250666667 0 0 0 0 00 0 0 0 -9400 0 -1880000 0 00 0 0 0 0 -940000 0 0 00 0 0 0 1880000 0 250666667 0 00 0 0 0 0 0 0 -9400 0

0 0 0 0 0 0 0 0 -9400000 0 0 0 0 0 0 1880000 0

1880000 -402857.1 0 0 0 0 0 0 0517959.18 0 -2959.767 517959.18 0 0 0 0 0622190476 0 -517959.2 60428571 0 0 0 0 0

0 815114.29 0 1880000 -402857.1 0 0 0 0


30/116


31/116

360 10 20 30 40 50 60 70 80 90 100 110 120 13

0 140 150 160 170 180 190 200 21

-1880000 22

0 23250666667 24

0 250 260 270 28


32/116

7.44E-08 7-4.4E-10 8-1.5E-10 9

7.36E-08 105.01E-10 11-1.3E-10 121.44E-07 13

-6E-10 147.58E-11 151.44E-07 16-6.1E-11 173.38E-11 181.45E-07 19-9.1E-10 201.12E-10 211.48E-07 221.47E-09 23-2.8E-10 242.19E-09 25-9.7E-10 26

3.7E-10 279.48E-10 286E-11 29

3.08E-10 30-2E-09 31

-1.9E-09 321.33E-10 33-7.3E-09 342.73E-09 35

2.18E-09 36


33/116

Nama : Fatma NIM : 0341110008Tugas : Mekanika Rekayasa IV

Jumlah Derajat Kebebasan

NDOF 3 NJ - R 3 4 - 66

Vektor Beban Nodal

0 10 2 0 30 40 50 6

P =

3 m

3 m

q = 2 t/m

1 2

3 4

1 2

3 3

21

43

213 m

3 m

Model AnalitisRangka


34/116

4 300 3003 0 3004 300 300

3003 1 0


35/116

Matriks Kekakuan Elemen Dalam Sistem Koordinat Global

E 2100000 kg/cm 2 b 10 cmA 200 cm 2 h 10 cm

I 833.3333333 cm 4

Member L EI/L3 AL2/I Cos Sin

1 300 64.81481481 21600 0 12 300 64.81481481 21600 0 13 300 64.81481481 21600 1 0

7 8 9 1 2 3777.7777778 0 -116666.6667 -777.7777778 0 -116666.6667 7

0 1400000 0 0 -1400000 0 8-116666.6667 0 23333333.33 116666.6667 0 11666666.67 9-777.7777778 0 116666.6667 777.7777778 0 116666.6667 1

0 -1400000 0 0 1400000 0 2-116666.6667 0 11666666.67 116666.6667 0 23333333.33 3

10 11 12 4 5 6777.7777778 0 -116666.6667 -777.7777778 0 -116666.6667 100 1400000 0 0 -1400000 0 11

-116666.6667 0 23333333.33 116666.6667 0 11666666.67 12-777.7777778 0 116666.6667 777.7777778 0 116666.6667 4

0 -1400000 0 0 1400000 0 5116666 6667 0 11666666 67 116666 6667 0 23333333 33 6

K 1 =

K 2 =

22

2222

2222

222

2222

2

22

2222

2222

222

2222

2

3

466266

612.12612.12

6.12126.1212

266466

612.12612.12

6.12126.1212

][

LCos LSin L LCos LSin L

Cos LCosSin I

ALSinCos

I AL

Cos LCosSin I

ALSinCos

I AL

Sin LSinCos I

ALSinCos

I AL

Sin LSinCos I

ALSinCos

I AL

LCos LSin L LCos LSin L

Cos LCosSin I

ALSinCos

I AL

Cos LCosSin I

ALSinCos

I AL

Sin LSinCos I AL

SinCos I AL

Sin LSinCos I AL

SinCos I AL

L EI

K


36/116


37/116

10 11 12 4 5 61400000 0 0 -1400000 0 0 10

0 777.7777778 116666.6667 0 -777.7777778 116666.6667 110 116666.6667 23333333.33 0 -116666.6667 11666666.67 12

-1400000 0 0 1400000 0 0 40 -777.7777778 -116666.6667 0 777.7777778 -116666.6667 50 116666.6667 11666666.67 0 -116666.6667 23333333.33 6

1 2 3 4 5 61400000 0 0 -1400000 0 0 1

0 777.7777778 116666.6667 0 -777.7777778 116666.6667 2

0 116666.6667 23333333.33 0 -116666.6667 11666666.67 3-1400000 0 0 1400000 0 0 4

0 -777.7777778 -116666.6667 0 777.7777778 -116666.6667 50 116666.6667 11666666.67 0 -116666.6667 23333333.33 6

Member Global Fixed-End Force Vector (F f )

Member Cos Sin1 0 12 0 13 1 0

Elemen 1FS b = FS e = 0

FM b = - FM e = 0FA b = FA e = 0

0 70 80 9

k 3 = K 3=

F =

k 2 =

kg

e

ee

ee

b

bb

bb

f

FM

Cos FS Sin FA

Sin FS Cos FA

FM Cos FS Sin FA

Sin FS Cos FA

F


38/116

Elemen 3FS b = FS e =

1/2 q L = 3000 kg

FM b = - FM e = 1/12 qL

2 = 150000 kg.cmFA b = FA e = 0

0 1-3000 2

150000 30 4

-3000 5

-150000 6Struktur Fixed-End Force (P f )

0 1-3000 2

150000 30 4

-3000 5-150000 6

Joint Displacement (Perpindahan Titik Nodal)

Invers matriks kekakuan struktur0.000918808 3.06074E-07 -1.83908E-06 0.000918451 -3.06074E-07 -1.83789E-063.06074E-07 7.14229E-07 -2.04049E-09 3.06074E-07 5.66803E-11 -2.04049E-09

-1.83908E-06 -2.04049E-09 2.65443E-08 -1.83789E-06 2.04049E-09 -2.03114E-090.000918451 3.06074E-07 -1.83789E-06 0.000918808 -3.06074E-07 -1.83908E-06

-3.06074E-07 5.66803E-11 2.04049E-09 -3.06074E-07 7.14229E-07 2.04049E-09-1.83789E-06 -2.04049E-09 -2.03114E-09 -1.83908E-06 2.04049E-09 2.65443E-08

0 0 0

Ff3 = Q f3 =

P f =

S-1 =

P P f = S . dd = S -1 . (P P f )

kg

kg


39/116

Perpindahan Ujung Elemen dalam Koordinat Global (v)

Elemen 1

0 7 00 8 00 9 0d1 1 0.000178547 cmd2 2 6.430714286 cmd3 3 642.9421299 rad

Elemen 20 10 00 11 00 12 0d4 4 -0.000178547 cmd5 5 6.430714286 cmd6 6 642.9507025 rad

Elemen 30 1 0.000178547 cm

0 2 6.430714286 cm0 3 642.9421299 radd4 4 -0.000178547 cmd5 5 6.430714286 cmd6 6 642.9507025 rad

Matriks Transformasi (T)

Member Cos Sin

1 0 12 0 13 1 0

v1 =

v3 =

v2 =

0000000000010000000000

CosSin

SinCos

CosSinSinCos

T


40/116

Elemen 31 0 0 0 0 00 1 0 0 0 0

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

Transpose Matriks Transformasi (T T)

0 -1 0 0 0 0

1 0 0 0 0 00 0 1 0 0 00 0 0 0 -1 00 0 0 1 0 00 0 0 0 0 1

0 -1 0 0 0 01 0 0 0 0 00 0 1 0 0 0

0 0 0 0 -1 00 0 0 1 0 00 0 0 0 0 1

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

Perpindahan Ujung Elemen Dala Koordinat Lokal (u)

u = T. v

TT1 =

TT2 =

TT3 =

T3 =


41/116

Elemen 3u3 = T 3. v3

0.000178547 1 cm6.430714286 2 cm642.9421299 3 rad-0.000178547 4 cm6.430714286 5 cm642.9507025 6 rad

Member Local Fixed-End Force Vector (Q f )

Elemen 1FS b = FS e = 0

FM b = - FM e = 0FA b = FA e = 0

0 70 80 90 10 20 3

Elemen 2FS b = FS e = 0FM b = - FM e = 0FA b = FA e = 0

u3 =

Q f1 = kg

e

e

e

b

b

b

f

FM

FS

FA

FM

FS FA

Q


42/116

Member Lokal End Force (Gaya Ujung Elemen Dalam Koordinat Lokal)

Elemen 1Q1 = k 1.u1 + Q f1

-9003000 -9003000 775009915.29 75009915.29 8

7500991536 7500991536 99003000 9003000 1

-75009915.29 -75009915.29 215001983051 15001983051 3


-9003000 -9003000 1075010915.15 75010915.15 117501091508 7501091508 12

9003000 9003000 4-75010915.15 -75010915.15 515002183037 15002183037 6


499.9305652 499.9305652 1150020830.4 150017830.4 222503074559 22503224559 3-499.9305652 -499.9305652 4-150020830.4 -150023830.4 522503174573 22503024573 6

Member Global End Force (Gaya Ujung Elemen Dalam Koordinat Global)Elemen 1

F1 = TT

1.Q1-75009915 29 7 0

Q1 = + Q f1

Q2 = + Q 2

Q3 = + Q 3

kg

kg

kg


43/116

Elemen 3F3 = T

T3.Q3

499.9305652 1 0150017830.4 2 -6000 600022503224559 3 45006249132-499.9305652 4-150023830.4 522503024573 6

Support Reaction (Reaksi Tumpuan)

-75009915.29 7-9003000 8

7500991536 9-75010915.15 10

-9003000 117501091508 12

Cek Keseimbangan Gaya Elemen

-75009915.29 -75010915.15 75010415.22 159020830.4 84010415.22

0 0 -3000 -6000 -9000

0 0 150000 -150000 0

R =

F3 =

kg kg

kg kg

cmkg .

cmkg .

0 M

kg

0 x F

0 y F


44/116

Plane Frame

No. titik 1 2 3 4 5 6X cm 0 400 800 0 400 800Y cm 400 400 400 0 0 0

No. Elemen 1 2 3 4 5Titik awal 1 2 4 5 6

Koordinat X cm 0 400 0 400 800

Koordinat Y cm 400 400 0 0 0

No. dof (Horizontal) 1 4 10 13 16

No. dof (Vertical) 2 5 11 14 17No. dof (Momen) 3 6 12 15 18

Titik akhir 2 3 1 2 3Koordinat X cm 400 800 0 400 800

Koordinat Y cm 400 400 400 400 400

No. dof (Horizontal) 4 7 1 4 7

No dof (Vertical) 5 8 2 5 8

Koordinat Titik Simpul

Data Elemen WF 100 x 100


45/116


46/116

A11 114975 114975 114975 114975 114975

A12 0 0 0 0 0

(k) A13 0 0 0 0 0

A14 -114975 -114975 -114975 -114975 -114975

A15 0 0 0 0 0A16 0 0 0 0 0

A21 0 0 0 0 0

A22 150.81 150.81 150.81 150.81 150.81

A23 30161.25 30161.25 30161.25 30161.25 30161.25

A24 0 0 0 0 0

A25 -150.81 -150.81 -150.81 -150.81 -150.81

A26 30161.25 30161.25 30161.25 30161.25 30161.25A31 0 0 0 0 0

A32 30161.25 30161.25 30161.25 30161.25 30161.25

A33 8043000 8043000 8043000 8043000 8043000

A34 0 0 0 0 0

A35 -30161.25 -30161.25 -30161.25 -30161.25 -30161.25

A36 4021500 4021500 4021500 4021500 4021500

A41 -114975 -114975 -114975 -114975 -114975A42 0 0 0 0 0

A43 0 0 0 0 0

A44 114975 114975 114975 114975 114975

A45 0 0 0 0 0

A46 0 0 0 0 0

A51 0 0 0 0 0

A52 -150.81 -150.81 -150.81 -150.81 -150.81A53 -30161.25 -30161.25 -30161.25 -30161.25 -30161.25

A54 0 0 0 0 0

A55 150.81 150.81 150.81 150.81 150.81

A56 -30161 25 -30161 25 -30161 25 -30161 25 -30161 25

Matriks KekakuanElemen Koordinat Lokal


47/116

1 2 3 4 5Panjang cm 400.0 400.0 400.0 400.0 400.0Berat 0.0 0.0 0.0 0.0 0.0Beban lantai 0.0 0.0 0.0 0.0 0.0Beban dinding 0.0 0.0 0.0 0.0 0.0B.terbagi rata kg/cm 40.0 40.0 0.0 0.0 0.0B.terpusat P1 kg 0.0 0.0 0.0 0.0 0.0B.terpusat P2 kg 0.0 0.0 0.0 0.0 0.0Jarak P1 ke a cm 0.0 0.0 0.0 0.0 0.0Jarak P2 ke a cm 0.0 0.0 0.0 0.0 0.0Momen akb. b.terbagi rata kg.cm 533333.3 533,333.3 0.0 0.0 0.0Momen akb. b.terbagi rata kg.cm -533333.3 -533333.3 0.0 0.0 0.0Momen akibat P1 dan P2 kg.cm 0.0 0.0 0.0 0.0 0.0Momen akibat P1 dan P2 kg.cm 0.0 0.0 0.0 0.0 0.0Momen Mab total kg.cm 533,333.3 533,333.3 0.0 0.0 0.0Momen Mba total kg.cm -533333.3 -533333.3 0.0 0.0 0.0Reaksi ab kg 8,000.0 8,000.0 0.0 0.0 0.0Reaksi ba kg 8,000.0 8,000.0 0.0 0.0 0.0FA b (gaya aksial ) kg 0.0 0.0 0.0 0.0 0.0FS b (gaya lintang ujung awal) kg 8,000.0 8,000.0 0.0 0.0 0.0FMb (momen ujung awal) kg.cm 533,333.3 533,333.3 0.0 0.0 0.0FA e (gaya aksial) kg 0.0 0.0 0.0 0.0 0.0FS e (gaya lintang ujung akhir) kg 8,000.0 8,000.0 0.0 0.0 0.0FM e (monen ujung akhir) kg.cm -533333.3 -533333.3 0.0 0.0 0.0

1 2 3 4 5

F f 0 0 0 0 08,000.0 8,000.0 0 0 0

533333 3 533333 3 0 0 0

DATA BEBAN PADA ELEMEN

Vektor Gaya ElemenKoordinat Global


48/116

El 1


49/116

Elemen 1

1 0 0 0 0 0

0 1 0 0 0 00 0 1 0 0 0

0 0 0 1 0 0

0 0 0 0 1 0

0 0 0 0 0 1

1 0 0 0 0 0

0 1 0 0 0 00 0 1 0 0 0

0 0 0 1 0 0

0 0 0 0 1 0

0 0 0 0 0 1

114975 0 0 -114975 0 0

0 150.80625 30161.25 0 -150.80625 30161.250 30161.25 8043000 0 -30161.25 4021500

-114975 0 0 114975 0 0

0 -150.80625 -30161.25 0 150.80625 -30161.25

0 30161.25 4021500 0 -30161.25 8043000

114975 0 0 -114975 0 0

0 150.80625 30161.25 0 -150.80625 30161.250 30161 25 8043000 0 30161 25 4021500

[K]= ( [T]T.[k] ). [T]

[T] =

[T]T=

[k] =


Elemen 1


50/116

Elemen 1

u = T vd1 1 0.0087373 0.0087373 1

d2 2 -0.0609568 -0.0609568 2

d3 3 -0.0333505 -0.0333505 3

d4 4 -3.553E-15 cm -3.553E-15 4

d5 5 -0.1564079 cm -0.1564079 5

d6 6 3.469E-18 rad 3.469E-18 6

Q = kuk.u 1004.5745 Q f 0 Q 1004.5745 1

-991.49748 8000 7008.5025 2

-265358.97 533333.33 267974.36 3

-1004.5745 0 -1004.5745 4991.49748 8000 8991.4975 5

-131240.02 -533333.33 -664573.36 6

F = T T Q

F 1004.5745 1 kg7008.5025 2 kg267974.36 3 kg.cm-1004.5745 4 kg8991 4975 5 kg

u1 =

Gaya Ujung Elemen dalam koordinat Global


Gaya Ujung Elemen dalam koordinat lokal

v1 =


51/116


52/116

Elemen 2


53/116

Elemen 2

1 0 0 0 0 0

0 1 0 0 0 00 0 1 0 0 0

0 0 0 1 0 0

0 0 0 0 1 0

0 0 0 0 0 1

1 0 0 0 0 0

0 1 0 0 0 00 0 1 0 0 0

0 0 0 1 0 0

0 0 0 0 1 0

0 0 0 0 0 1

114975 0 0 -114975 0 0

0 150.80625 30161.25 0 -150.80625 30161.250 30161.25 8043000 0 -30161.25 4021500

-114975 0 0 114975 0 0

0 -150.80625 -30161.25 0 150.80625 -30161.25

0 30161.25 4021500 0 -30161.25 8043000

[K]= ( [T]T.[k] ). [T]

114975 0 0 -114975 0 0

0 150.80625 30161.25 0 -150.80625 30161.250 30161 25 8043000 0 30161 25 4021500

[T] =

[T]T =

[k] =


Elemen 2


54/116


u = T v0 4 -3.553E-15 -3.553E-15 4

0 5 -0.1564079 -0.1564079 5

0 6 3.469E-18 3.469E-18 6

d1 7 -0.0087373 cm -0.0087373 7

d2 8 -0.0609568 cm -0.0609568 8

d3 9 0.0333505 rad 0.0333505 9

Q = kuk.u 1004.5745 Q f 0 Q 1004.5745 4

991.49748 0 991.49748 5

131240.02 0 131240.02 6

-1004.5745 0 -1004.5745 7-991.49748 0 -991.49748 8

265358.97 0 265358.97 9

F = T T Q

F 1004.5745 4 kg991.49748 5 kg131240.02 6 kg.cm-1004.5745 7 kg-991 49748 8 kg

u1 =



v2 =


55/116


56/116

Elemen 3


57/116

0 1 0 0 0 0

-1 0 0 0 0 00 0 1 0 0 0

0 0 0 0 1 0

0 0 0 -1 0 0

0 0 0 0 0 1

0 -1 0 0 0 0

1 0 0 0 0 00 0 1 0 0 0

0 0 0 0 -1 0

0 0 0 1 0 0

0 0 0 0 0 1

114975 0 0 -114975 0 0

0 150.80625 30161.25 0 -150.80625 30161.250 30161.25 8043000 0 -30161.25 4021500

-114975 0 0 114975 0 0

0 -150.80625 -30161.25 0 150.80625 -30161.25

0 30161.25 4021500 0 -30161.25 8043000

[K]= ( [T]T.[k] ). [T]

0 -150.80625 -30161.25 0 150.80625 -30161.25

114975 0 0 -114975 0 00 30161 25 8043000 0 30161 25 4021500

[T]T =

[k] =


[T] =

Elemen 3


58/116


u = T v0 10 0 0 10

0 11 0 0 11

0 12 0 0 12

d1 1 0.0087373 cm -0.0609568 1

d2 2 -0.0609568 cm -0.0087373 2

d3 3 -0.0333505 rad -0.0333505 3

Q = kuk.u 7008.5025 Q f 0 Q 7008.5025 10

-1004.5745 0 -1004.5745 11

-133855.42 0 -133855.42 12

-7008.5025 0 -7008.5025 11004.5745 0 1004.5745 2

-267974.36 0 -267974.36 3

F = T T Q

F 1004.5745 10 kg7008.5025 11 kg-133855.42 12 kg.cm-1004.5745 1 kg-7008 5025 2 kg

u1 =



v3 =


59/116


60/116

Elemen 4


61/116

0 1 0 0 0 0

-1 0 0 0 0 00 0 1 0 0 0

0 0 0 0 1 0

0 0 0 -1 0 0

0 0 0 0 0 1

0 -1 0 0 0 0

1 0 0 0 0 00 0 1 0 0 0

0 0 0 0 -1 0

0 0 0 1 0 0

0 0 0 0 0 1

114975 0 0 -114975 0 0

0 150.80625 30161.25 0 -150.80625 30161.250 30161.25 8043000 0 -30161.25 4021500

-114975 0 0 114975 0 0

0 -150.80625 -30161.25 0 150.80625 -30161.25

0 30161.25 4021500 0 -30161.25 8043000

[K]= ( [T]T

.[k] ). [T]

0 -150.80625 -30161.25 0 150.80625 -30161.25

114975 0 0 -114975 0 00 30161 25 8043000 0 30161 25 4021500

[T] =

[T]T =

[k] =


Elemen 4


62/116


u = T v0 13 0 0 13

0 14 0 0 14

0 15 0 0 15

d1 4 -3.553E-15 cm -0.1564079 4

d2 5 -0.1564079 cm 3.553E-15 5

d3 6 3.469E-18 rad 3.469E-18 6

Q = kuk.u 17982.995 Q f 0 Q 17982.995 13

-4.311E-13 0 -4.311E-13 14

-9.32E-11 0 -9.32E-11 15

-17982.995 0 -17982.995 44.311E-13 0 4.311E-13 5

-7.925E-11 0 -7.925E-11 6

F = T T Q

F 4.31E-13 13 kg17982.995 14 kg-9.32E-11 15 kg.cm

-4.311E-13 4 kg-17982 995 5 kg

u1 =



v4 =


63/116


64/116

Elemen 5


65/116

0 1 0 0 0 0

-1 0 0 0 0 00 0 1 0 0 0

0 0 0 0 1 0

0 0 0 -1 0 0

0 0 0 0 0 1

0 -1 0 0 0 0

1 0 0 0 0 00 0 1 0 0 0

0 0 0 0 -1 0

0 0 0 1 0 0

0 0 0 0 0 1

114975 0 0 -114975 0 0

0 150.80625 30161.25 0 -150.80625 30161.250 30161.25 8043000 0 -30161.25 4021500

-114975 0 0 114975 0 0

0 -150.80625 -30161.25 0 150.80625 -30161.25

0 30161.25 4021500 0 -30161.25 8043000

[K]= ( [T]T

.[k] ). [T]

0 -150.80625 -30161.25 0 150.80625 -30161.25

114975 0 0 -114975 0 00 30161 25 8043000 0 30161 25 4021500

[T] =

[T]T =

[k] =



66/116


67/116


68/116

Matrik Kekakuan Struktur dari Masing-Masing Member


69/116

1 2 3 4 5 6 7 8 9

114975 0 0 -114975 0 0 0 0 0 1

0 150.806 30161.3 0 -150.806 30161.3 0 0 0 20 30161.3 8043000 0 -30161.3 4021500 0 0 0 3

-114975 0 0 114975 0 0 0 0 0 4

0 -150.806 -30161.3 0 150.806 -30161.3 0 0 0 5

0 30161.3 4021500 0 -30161.3 8043000 0 0 0 60 0 0 0 0 0 0 0 0 7

0 0 0 0 0 0 0 0 0 8

0 0 0 0 0 0 0 0 0 9

1 2 3 4 5 6 7 8 9

0 0 0 0 0 0 0 0 0 1

0 0 0 0 0 0 0 0 0 20 0 0 0 0 0 0 0 0 30 0 0 114975 0 0 -114975 0 0 4

0 0 0 0 150.806 30161.3 0 -150.806 30161.3 50 0 0 0 30161.3 8043000 0 -30161.3 4021500 6

0 0 0 -114975 0 0 114975 0 0 7

0 0 0 0 -150.806 -30161.3 0 150.806 -30161.3 8

0 0 0 0 30161.3 4021500 0 -30161.3 8043000 9

1 2 3 4 5 6 7 3 9

150.806 0 30161.3 0 0 0 0 0 0 10 114975 0 0 0 0 0 0 0 2

30161.3 0 8043000 0 0 0 0 0 0 3

0 0 0 0 0 0 0 0 0 40 0 0 0 0 0 0 0 0 5

S 1 =

S 2 =

S 3 =

Jumlah 1 2 3 4 5Elemen

Vektor Gaya Struktur Koordinat Global dari Elemen


70/116

0.0 0.0 0.0 0.0 0.0 0.0 1

8000.0 8000.0 0.0 0.0 0.0 0.0 2

533333 533333 0.0 0.0 0.0 0.0 30.0 0.0 0.0 0.0 0.0 0.0 4

16000.0 8000.0 8000.0 0.0 0.0 0.0 5

0 -533333 533333 0.0 0.0 0.0 6

0.0 0.0 0.0 0.0 0.0 0.0 7

8000.0 0.0 8000.0 0.0 0.0 0.0 8-533333 0.0 -533333 0.0 0.0 0.0 9

0.0 1

0.0 20.0 3

0.0 40.0 5

0.0 60.0 7

0.0 80.0 9

0.0 1

-8000.0 2-533333 3

0.0 4

-16000 50 6

P - P f

Vektor Gaya Struktur Koordinat Global pada Joint

P


P f

P Pf = S . dd = S-1 . (P Pf)


71/116


72/116

1 2 3 4 5 6 7 8 9

0 0 0 0 0 0 0 0 0


73/116

0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0

0 0 0 150.8063 0 30161.25 0 0 00 0 0 0 114975 0 0 0 0

0 0 0 30161.25 0 8043000 0 0 0

0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0

1 2 3 4 5 6 7 8 90 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 00 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0

0 0 0 0 0 0 150.8063 0 30161.250 0 0 0 0 0 0 114975 0

0 0 0 0 0 0 30161.25 0 8043000

Matrik Kekakuan Struktur Secara Keseluruhan1 2 3 4 5 6 7 8 9

115125.8 0 30161.25 -114975 0 0 0 0 0

0 115125.8 30161.25 0 -150.8063 30161.25 0 0 030161.25 30161.25 16086000 0 -30161.25 4021500 0 0 0

-114975 0 0 230100.8 0 30161.25 -114975 0 0

0 -150.8063 -30161.25 0 115276.6 0 0 -150.8063 30161.250 30161 25 4021500 30161 25 0 24129000 0 30161 25 4021500

S 4 =

S 5 =

S =


74/116


75/116


76/116

1

2


77/116

2

3

45

6

7

89

1

2

3

456

78

9

1

2

3

4

56

Nama : Maskura Sadila

Nim : 1204101010110

Analisa Struktur IV


78/116

No. titik 1 2 3 4 5 6X cm 0 500 0 500 0 500Y cm 1000 1000 500 500 0 0

Data Elemen

No. Elemen 1 2 3 4 5 6

Titik awal 1 3 4 3 5 6

Koordinat X cm 0 0 500 0 0 500

Koordinat Y cm 1000 500 500 500 0 0

No. dof (Horizontal) 1 7 10 7 13 16

No. dof (Vertical) 2 8 11 8 14 17No. dof (Momen) 3 9 12 9 15 18

Titik akhir 2 1 2 4 3 4

Koordinat X cm 500 0 500 500 0 500

Koordinat Y cm 1000 1000 1000 500 500 500

No. dof (Horizontal) 4 1 4 10 7 10

No dof (Vertical) 5 2 5 11 8 11

WF 100 x 100

Analisa Struktur IV

Plane Frame

Koordinat Titik Simpul


79/116

A11 91980 91980 91980 91980 91980 91980

A12 0 0 0 0 0 0

(k) A13 0 0 0 0 0 0

Matriks KekakuanElemen Koordinat Lokal


80/116

A14 -91980 -91980 -91980 -91980 -91980 -91980

A15 0 0 0 0 0 0

A16 0 0 0 0 0 0

A21 0 0 0 0 0 0

A22 77.21 77.21 77.21 77.21 77.21 77.21

A23 19303.2 19303.2 19303.2 19303.2 19303.2 19303.2

A24 0 0 0 0 0 0

A25 -77.21 -77.21 -77.21 -77.21 -77.21 -77.21

A26 19303.2 19303.2 19303.2 19303.2 19303.2 19303.2

A31 0 0 0 0 0 0

A32 19303.2 19303.2 19303.2 19303.2 19303.2 19303.2

A33 6434400 6434400 6434400 6434400 6434400 6434400

A34 0 0 0 0 0 0

A35 -19303.2 -19303.2 -19303.2 -19303.2 -19303.2 -19303.2

A36 3217200 3217200 3217200 3217200 3217200 3217200

A41 -91980 -91980 -91980 -91980 -91980 -91980

A42 0 0 0 0 0 0

A43 0 0 0 0 0 0

A44 91980 91980 91980 91980 91980 91980

A45 0 0 0 0 0 0

A46 0 0 0 0 0 0

A51 0 0 0 0 0 0

A52 -77.21 -77.21 -77.21 -77.21 -77.21 -77.21

A53 -19303.2 -19303.2 -19303.2 -19303.2 -19303.2 -19303.2

A54 0 0 0 0 0 0

A55 77.21 77.21 77.21 77.21 77.21 77.21

A56 -19303 2 -19303 2 -19303 2 -19303 2 -19303 2 -19303 2

1 2 3 4 5 6Panjang cm 500.0 500.0 500.0 500.0 500.0 500.0Berat 0.0 0.0 0.0 0.0 0.0 0.0

Data Beban Pada Elemen


81/116

Beban lantai 0.0 0.0 0.0 0.0 0.0 0.0

Beban dinding 0.0 0.0 0.0 0.0 0.0 0.0B.terbagi rata kg/cm 50.0 0.0 0.0 50.0 0.0 0.0B.terpusat P1 kg 0.0 0.0 0.0 0.0 0.0 0.0B.terpusat P2 kg 0.0 0.0 0.0 0.0 0.0 0.0Jarak P1 ke a cm 0.0 0.0 0.0 0.0 0.0 0.0Jarak P2 ke a cm 0.0 0.0 0.0 0.0 0.0 0.0Momen akb. b.terbagi rata kg.cm 1041667 0.0 0.0 1041667 0.0 0.0Momen akb. b.terbagi rata kg.cm -1041667 . 0.0 -1041667 0.0 0.0Momen akibat P1 dan P2 kg.cm 0.0 0.0 0.0 0.0 0.0 0.0Momen akibat P1 dan P2 kg.cm 0.0 0.0 0.0 0.0 0.0 0.0Momen Mab total kg.cm 1041667 0.0 0.0 1,041,667 0.0 0.0Momen Mba total kg.cm -1041667 0.0 0.0 -1,041,667 0.0 0.0Reaksi ab kg 12,500.0 0.0 0.0 12,500.0 0.0 0.0Reaksi ba kg 12,500.0 0.0 0.0 12,500.0 0.0 0.0FA b (gaya aksial ) kg 0.0 0.0 0.0 0.0 0.0 0.0FS b (gaya lintang ujung awal) kg 12,500.0 0.0 0.0 12,500.0 0.0 0.0FMb (momen ujung awal) kg.cm 1,041,667 0.0 0.0 1041667 0.0 0.0FA e (gaya aksial) kg 0.0 0.0 0.0 0 0.0 0.0FS e (gaya lintang ujung akhir) kg 12,500.0 0.0 0.0 12500 0.0 0.0FM e (monen ujung akhir) kg.cm -1041666.7 . 0.0 -1041667 0.0 0.0

1 2 3 4 5 6

F f 0 0 0 0 0 012500.0 0.0 0 12500 0 0

1041666 7 0 0 0 1041667 0 0

Vektor Gaya ElemenKoordinat Global


82/116

Elemen 1


83/116

1 0 0 0 0 0

0 1 0 0 0 00 0 1 0 0 0

0 0 0 1 0 0

0 0 0 0 1 0

0 0 0 0 0 1

1 0 0 0 0 00 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

91980 0 0 -91980 0 0

0 77.2128 19303.2 0 -77.2128 19303.2

0 19303.2 6434400 0 -19303.2 3217200

-91980 0 0 91980 0 0

0 -77.2128 -19303.2 0 77.2128 -19303.2

0 19303.2 3217200 0 -19303.2 6434400

91980 0 0 -91980 0 0

0 77.2128 19303.2 0 -77.2128 19303.20 19303 2 6434400 0 19303 2 3217200

[T]T=

[k] =

[T] =

[K]= ( [T]T.[k] ). [T]


Elemen 1



84/116

u = T vd1 1 0.014556 0.0145561 1

d2 2 -0.407697 -0.4076973 2

d3 3 -0.092554 -0.0925545 3

d4 4 -0.014556 cm -0.0145561 4

d5 5 -0.407697 cm -0.4076973 5

d6 6 0.092554 rad 0.0925545 6

Q = k uk.u 2677.7422 Q f 0 Q 2677.7422 1

1.137E-12 12500 12500 2

-297766.18 1041666.67 743900.48 3

-2677.7422 0 -2677.7422 4

-1.137E-12 12500 12500 5

297766.18 -1041666.7 -743900.48 6

F = T T QF 2678 1 kg

12500 2 kg743900 3 kg.cm-2678 4 kg12500 5 kg



v1 = u1 =


85/116


86/116

Elemen 2

0 1 0 0 0 0


87/116

0 1 0 0 0 0

-1 0 0 0 0 00 0 1 0 0 0

0 0 0 0 1 0

0 0 0 -1 0 0

0 0 0 0 0 1

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

91980 0 0 -91980 0 0

0 77.2128 19303.2 0 -77.2128 19303.2

0 19303.2 6434400 0 -19303.2 3217200

-91980 0 0 91980 0 0

0 -77.2128 -19303.2 0 77.2128 -19303.2

0 19303.2 3217200 0 -19303.2 6434400

[K]= ( [T]T.[k] ). [T]

0 -77.2128 -19303.2 0 77.2128 -19303.2

91980 0 0 -91980 0 00 19303 2 6434400 0 19303 2 3217200

[T]T =

[k] =

[T] =


Elemen 2



88/116

u = T vd7 7 0.0 -0.2717982 7

d8 8 -0.2718 0.0096976 8

d9 9 -0.0463 -0.0462627 9

d1 1 0.014556 cm -0.4076973 1

d2 2 -0.407697 cm -0.0145561 2

d3 3 -0.092554 rad -0.0925545 3

Q = kuk.u 12500 Q f 0 Q 12500 7

-2677.7422 0 -2677.7422 8

-594970.59 0 -594970.59 9

-12500 0 -12500 1

2677.7422 0 2677.7422 2

-743900.48 0 -743900.48 3

F = T T QF 2678 7 kg

12500 8 kg-594971 9 kg.cm

-2678 1 kg-12500 2 kg



v2 = u 1 =


89/116


90/116

Elemen 3

0 1 0 0 0 0


91/116

-1 0 0 0 0 00 0 1 0 0 0

0 0 0 0 1 0

0 0 0 -1 0 0

0 0 0 0 0 1

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

91980 0 0 -91980 0 0

0 77.2128 19303.2 0 -77.2128 19303.2

0 19303.2 6434400 0 -19303.2 3217200

-91980 0 0 91980 0 0

0 -77.2128 -19303.2 0 77.2128 -19303.2

0 19303.2 3217200 0 -19303.2 6434400

[K]= ( [T]T.[k] ). [T]

0 -77.2128 -19303.2 0 77.2128 -19303.2

91980 0 0 -91980 0 00 19303 2 6434400 0 19303 2 3217200

[T]T =

[k] =

[T] =



92/116


93/116


94/116


95/116

Elemen 4



96/116

u = T vd7 7 -0.009698 -0.0096976 7

d8 8 -0.271798 -0.2717982 8

d9 9 -0.046263 -0.0462627 9

d10 10 0.009698 cm 0.0096976 10

d11 11 -0.271798 cm -0.2717982 11

d12 12 0.046263 rad 0.0462627 12

Q = kuk.u -1783.9756 Q f 0 Q -1783.9756 7

3.411E-13 12500 12500 8

-148836.29 1041666.7 892830.37 9

1783.9756 0 1783.9756 10

-3.411E-13 12500 12500 11148836.29 -1041666.7 -892830.37 12

F = T T QF -1784 7 kg

12500 8 kg892830 9 kg.cm

1784 10 kg12500 11 kg



u1 =v4 =


97/116


98/116

Elemen 5

0 1 0 0 0 0

1 0 0 0 0 0


99/116

-1 0 0 0 0 00 0 1 0 0 0

0 0 0 0 1 0

0 0 0 -1 0 0

0 0 0 0 0 1

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

91980 0 0 -91980 0 0

0 77.2128 19303.2 0 -77.2128 19303.2

0 19303.2 6434400 0 -19303.2 3217200

-91980 0 0 91980 0 0

0 -77.2128 -19303.2 0 77.2128 -19303.2

0 19303.2 3217200 0 -19303.2 6434400

[K]= ( [T]T.[k] ). [T]

0 -77.2128 -19303.2 0 77.2128 -19303.2

91980 0 0 -91980 0 00 19303 2 6434400 0 19303 2 3217200

[T]T =

[k] =

[T] =


Elemen 5

u = T v



100/116

u T v

d13 13 0 0 13d14 14 0 0 14

d15 15 0 0 15

d7 7 -0.009698 cm -0.2717982 7

d8 8 -0.271798 cm 0.0096976 8

d9 9 -0.046263 rad -0.0462627 9

Q = kuk.u 25000 Q f 0 Q 25000 13

-893.76654 0 -893.76654 14

-149023.49 0 -149023.49 15

-25000 0 -25000 7

893.76654 0 893.76654 8-297859.78 0 -297859.78 9

F = T T QF 894 13 kg

25000 14 kg-149023 15 kg.cm

-894 7 kg-25000 8 kg



u1 =v5 =


101/116


102/116

Elemen 6

0 1 0 0 0 0

-1 0 0 0 0 0


103/116

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 -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

91980 0 0 -91980 0 0

0 77.2128 19303.2 0 -77.2128 19303.2

0 19303.2 6434400 0 -19303.2 3217200-91980 0 0 91980 0 0

0 -77.2128 -19303.2 0 77.2128 -19303.2

0 19303.2 3217200 0 -19303.2 6434400

[K]= ( [T]T.[k] ). [T]

0 -77.2128 -19303.2 0 77.2128 -19303.2

91980 0 0 -91980 0 00 19303 2 6434400 0 19303 2 3217200

[T]T =

[T] =

[k] =


Elemen 6

u = T v



104/116

d16 16 0 0 16d17 17 0 0 17

d18 18 0 0 18

d10 10 0.009698 cm -0.2717982 10

d11 11 -0.271798 cm -0.0096976 11

d12 12 0.046263 rad 0.0462627 12

Q = kuk.u 25000 Q f 0 Q 25000 16

893.767 0 893.76654 17

149023.49 0 149023.49 18

-25000 0 -25000 10

-893.76654 0 -893.76654 11297859.78 0 297859.78 12

F = T T QF -894 16 kg

25000 17 kg149023 18 kg.cm

894 10 kg-25000 11 kg



u1 =v6 =


105/116


106/116


107/116

Vektor Gaya Struktur Koordinat Global dari Elemen

Elemen Jumlah 1 2 3 4 5 6

Pf 0.0 0.0 1


108/116

12500.0 12500.0 21041666.7 1041666.7 3

0.0 0.0 4

12500.0 12500.0 5-1041666.7 -1041666.7 6

0.0 0 7

12500.0 12500.0 8

1041666.7 1041666.7 90.0 0 10

12500.0 12500.0 11

-1041666.7 -1041666.7 12


P 0.0 1

0.0 2

0.0 3

0.0 40.0 5

0.0 6

0 0 7


P - P f 0.0 1 P Pf = S . d


109/116

-12500.0 2-1041666.7 3

0.0 4

-12500.0 5

1041666.7 6

0.0 7

-12500.0 8

-1041666.7 90.0 10

-12500.0 111041666.7 12

0.014556 1 cm

-0.407697 2 cm

-0.092554 3 rad

-0.014556 4 cm

d = -0.407697 5 cm0.092554 6 rad

-0.009698 7 cm

0 271798 8 cm

Mencari Perpindahan Titik Joint

d = S-1 . (P Pf )


110/116


111/116


112/116

1 2 3 4 5 6 7 8 9 10 11 12123

77.2128 0 19303.2 -77.2128 0 19303.2 4

S3 = 0 91980 0 0 -91980 0 5


113/116

S3 0 91980 0 0 91980 0 519303.2 0 6434400 -19303.2 0 3217200 6

789

-77.2128 0 -19303.2 77.2128 0 -19303.2 100 -91980 0 0 91980 0 11

19303.2 0 3217200 -19303.2 0 6434400 12

1 2 3 4 5 6 7 8 9 10 11 121234

S4 = 56

91980 0 0 -91980 0 0 70 77.2128 19303.2 0 -77.2128 19303.2 8

0 19303.2 6434400 0 -19303.2 3217200 9-91980 0 0 91980 0 0 10

0 -77.2128 -19303.2 0 77.2128 -19303.2 110 19303.2 3217200 0 -19303.2 6434400 12


114/116


115/116

1 2 3 4 5 6 7 8 9 10 11 121 -1.2E-17 -1.49E-16 -3.58E-14 1.25E-17 2.04E-17 2.698E-14 1.136E-16 5.204E-18 1.6E-13 -1.13E-16 1.7E-16 10 1 0 0 -2.71E-20 0 -1.11E-16 1.11E-16 0 0 -2.71E-20 0 2

4.263E-14 -1.2E-16 1 0 -1.11E-16 -3.5E-17 3.197E-14 6.939E-17 -1.11E-16 3.2E-14 -1.39E-17 -4.5E-17 34.23E-14 - 4.4E-17 2.02E-16 1 4.5E-17 2.2E-17 -3.226E-13 1.881E-17 3.104E-16 -1.3E-13 -1.84E-17 -6E-17 4

0 4.61E-19 0 2.22E-16 1 -8.7E-19 1.11E-16 3.524E-19 -2.17E-19 5.55E-17 1.11E-16 0 5

-7.11E-14 -5.6E-17 6.94E-17 -2.84E-14 4.16E-17 1 -4.263E-14 6.939E-17 -1.39E-17 -7.1E-15 9.71E-17 1.1E-16 6


116/116

-2.27E-13 0 -2.78E-17 0 0 5.55E-17 1 -5.551E-17 1.11E-16 -1.1E-13 0 -2.2E-16 72.22E-16 1.03E-16 -2.17E-19 -1.11E-16 -1.08E-19 -1.4E-20 1.11E-16 1 -8.13E-19 5.55E-17 -5.42E-20 4.3E-19 8

5.684E-14 2.78E-17 -8.33E-17 4.263E-14 -1.8E-16 -5.2E-17 5 .329E-14 -2 .776E-17 1 8.88E-14 2.78E-17 -2.8E-17 90 0 2.78E-17 -2.27E-13 0 -2.8E-17 0 5.551E-17 -1.11E-16 1 0 2.2E-16 10

6.661E-16 -3.8E-19 2.17E-19 2.22E-16 -1.54E-16 -4.2E-19 1.11E-16 1.626E-19 -3.66E-19 8.33E-17 1 -2.2E-19 11-5.68E-14 0 -5.55E-17 -5.68E-14 0 -1 .4E-17 -8.527E-14 -5.551E-17 2.776E-17 -2.8E-14 5.55E-17 1 12

analisa struktur iv oca selesai

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