8/18/2019 Perhitungan Matrix Untuk Soal Nomor 2

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Perhitungan Matrix untuk soal nomor 2.

U2 U3 V3 U4 V4

82417582418

1.6 -0.6 -0.05 -0.8 0.95 U2

-0.6 1.6 0.65 -0.2 -0.05 U3

-0.05 0.65 2.9 0.05 1.1 V3

-0.8 -0.2 0.05 1.6 -0.65 U4

0.95 -0.05 1.1 -0.65 2.9 V4

[K] [d] [F]

1.31868E+11

-

49450549451 -4120879121

-

65934065934 78296703297 d1-50

-

49450549451 1.31868E+11 53571428571

-

16483516484 -4120879121 d2-50

-4120879121 53571428571 2.39011E+11 4120879121 90659340659 d3 = 100

-

65934065934

-

16483516484 4120879121 1.31868E+11

-

53571428571 d40

78296703297 -4120879121 90659340659

-

53571428571 2.39011E+11 d5-100

8/18/2019 Perhitungan Matrix Untuk Soal Nomor 2

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[K]-1  [F] [d]

1.58299E-11 6.79532E-12 -9.8159E-14 7.39704E-12 -3.37332E-12 -50 -8.0375E-10

6.79532E-12 1.18441E-11

-2.66625E-

12 5.00688E-12 1.11726E-13-50

-1.2098E-

09

-9.8159E-14

-2.66625E-

12 5.78101E-12

-1.60566E-

12 -2.5665E-12100

=

9.7297E-

10

7.39704E-12 5.00688E-12

-1.60566E-

12 1.23836E-11 1.04783E-120

-8.8554E-

10

-3.37332E-

12 1.11726E-13 -2.5665E-12 1.04783E-12 6.49924E-12-100

-7.4349E-

10

[B]

0.5

-1 0 -1 0 1 0 -1 0

0 -2 0 -2 0 2 0 2

-2 -1 -2 1 2 1 2 -1

[D]

329670329670

1 0.3 0

0.3 1 0

0 0 0.35

8/18/2019 Perhitungan Matrix Untuk Soal Nomor 2

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[B]

-0.5 0 -0.5 0 0.5 0 -0.5 0

0 -1 0 -1 0 1 0 1

-1 -0.5 -1 0.5 1 0.5 1 -0.5

Stresses = [D] * [B] * [d]

[D] * [B]

-

1.64835E+11

-

98901098901

-

1.64835E+11

-

98901098901 1.6484E+11 9.8901E+10 -1.6484E+11 9.8901E+10

-49450549451 -3.2967E+11

-49450549451 -3.2967E+11 4.9451E+10 3.2967E+11 -4.9451E+10 3.2967E+11

-

1.15385E+11

-

57692307692

-

1.15385E+11 57692307692 1.1538E+11 5.7692E+10 1.15385E+11

-

5.7692E+10

[D] * [B] *[d]

101.737712

99.36430784

-50

[d]

0

0-8.03747E-10

0

-1.20977E-09

9.72971E-10

-8.85545E-10

-7.43495E-10

8/18/2019 Perhitungan Matrix Untuk Soal Nomor 2

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Perhitungan Matrix untuk soal nomor 3.

[K] * [t] = [F]

[t] = [K]-1

* [F]

[k] [F] [t]

1 0 0 0 30 t1

0 11.098 -3.194 0 590.62 = t2

0 -3.194 11.098 -3.194 494.8 t3

0 0 -3.194 6.334 290.59 t4

[K]-1  [F] [t]

1 0 0 0 30 30

0 0.099773 0.033589 0.016938 590.62 = 80.47019

0 0.033589 0.116711 0.058853 494.8 94.68947

0 0.016938 0.058853 0.187556 290.59 93.62617