Contoh Struktur Grid-revisi

8/19/2019 Contoh Struktur Grid-revisi

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Data-data struktur gridIx 100,000 mm4Iy 50,000,000 mm4G 76,925 N/mm2E 200,000 N/mm2

Ix (mm4) Iy (mm4) G(N/mm2) E(N/mm2) L (mm) GIx/L 4EIy/L 6EIy/L^2 12EI

100,000 50,000,000 76925 200000 5000 1538500 8000000000 2400000

300,000 200,000,000 76925 200000 8000 2884687.5 20000000000 3750000

1538500 0 0 -1538500 0 00 8000000000 -2400000 0 4000000000 2400000

[K] lokal-1 0 -2400000 960 0 -2400000 -960-1538500 0 0 1538500 0 0

0 4000000000 -2400000 0 8000000000 2400000

0 2400000 -960 0 2400000 960

1 0 0 0 0 00 1 0 0 0 0

[T] el-1 0 0 1 0 0 00 0 0 1 0 00 0 0 0 1 00 0 0 0 0 1

Eleme -1(1-2)Eleme -2(2-3)

α 0


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w1 w2

1538500 0 0 -1538500 0 00 8000000000 -2400000 0 4000000000 24000000 -2400000 960 0 -2400000 -960 w1

[K] !lo"al-1 -1538500 0 0 1538500 0 00 4000000000 -2400000 0 8000000000 24000000 2400000 -960 0 2400000 960 w2

2884687.5 0 0 -2884687.5 0 0

0 20000000000 -3750000 0 10000000000 37500000 -3750000 938 0 -3750000 -938

[K] lokal-2 -2884687.5 0 0 2884687.5 0 00 10000000000 -3750000 0 20000000000 37500000 3750000 -938 0 3750000 938

0 1 0 0 0 0-1 0 0 0 0 0

[T] el-2 0 0 1 0 0 0 [T]#T el-2 0 0 0 0 1 00 0 0 -1 0 00 0 0 0 0 1

w2 w320000000000 0 3750000 10000000000 0 -3750000

0 2884687.5 0 0 -2884687.5 0 -2.03750000 0 937.5 3750000 0 -937.5 w2

[K] !lo"al-2 10000000000 0 3750000 20000000000 0 -37500000 -2884687.5 0 0 2884687.5 0 -1.0

-3750000 0 -937.5 -3750000 0 937.5 w3

!u"u ga matriks #$% & ' #*%w1 w2

x1 y1 x2 y2

x1 y1

x2 y2

% 90

x2 y2 x3 y3 x2 y2

x3 y3

x1 y1 x2 y2 x3


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&x1 1538500 0 0 -1538500 0 0 0&y1 0 8000000000 -2400000 0 4000000000 2400000 0'1 0 -2400000 960 0 -2400000 -960 0

&x2 -1538500 0 0 20001538500 0 3750000 2500000000&y2 0 4000000000 -2400000 0 8002884687.5 2400000 0 -961562.5'2 0 2400000 -960 3750000 2400000 1897.5 937500

&x3 0 0 0 2500000000 0 937500 5000000000&y3 0 0 0 0 -961562.5 0 0 9'3 0 0 0 -937500 0 -234.375 -937500

+, strai matrik dis la.eme da matrik gayaw1 w2

x1 1538500 0 0 -1538500 0 0 0y1 0 8000000000 -2400000 0 4000000000 2400000 0!1 0 -2400000 960 0 -2400000 -960 00 -1538500 0 0 5001538500 0 937500 25000000000 0 4000000000 -2400000 0 8000961562.5 2400000 0 -961562.5

- 000 0 2400000 -960 937500 2400000 1194.375 937500x3 0 0 0 2500000000 0 937500 5000000000y3 0 0 0 0 -961562.5 0 0!3 0 0 0 -937500 0 -234.375 -937500

x1 y1 x2 y2 x3


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e-arrageme matriks , er-allw1 w3

x1 1538500 0 0 0 0 0 -1538500y1 0 8000000000 -2400000 0 0 0 0 4000000!1 0 -2400000 960 0 0 0 0 -2x3 0 0 0 5000000000 0 -937500 2500000000y3 0 0 0 0 961562.5 0 0 -9!3 0 0 0 -937500 0 234.375 -9375000 -1538500 0 0 2500000000 0 -937500 50015385000 0 4000000000 -2400000 0 -961562.5 0 0 800096156

- 000 0 2400000 -960 937500 0 -234.375 937500 240000

Dis la.eme ,dal-2

0 5001538500 0 9375000 0 8000961562.5 2400000

- 000 937500 2400000 1194.375 2

3.17550078E-010 1.88213839E-010 -6.27455E-007 0 05003 (a)1.88213839E-010 4.26183578E-010 -1.00412E-006 0 & 0500 (a)

2 -6.2745487E-007 -1.0041160E-006 0.0033474557 - 000 -165 3 mm

eaksi erletaka grid ( ,dal-1 da ,dal-3)

x1 -1538500 0 0 -472 N-mm -y1 0 4000000000 2400000 0.003137274 -2007 147 N-mm!1 0 -2400000 -960 0.00502058 & 4017 Nx3 2500000000 0 937500 -16.73727837 - 747013 N-mmy3 0 -961562.5 0 -4727 N-mm -!3 -937500 0 -234.375 972 N

x1 y1 x3 y3 x2

x2 y2

x2 y2


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Gaya dalam ada eleme -1

mx1 1 0 0 0 0 0 1538500my1 0 1 0 0 0 0 0 8000000000*1 0 0 1 0 0 0 0 -240000

mx2 0 0 0 1 0 0 -1538500my2 0 0 0 0 1 0 0 4000000000*2 0 0 0 0 0 1 0 240000

Gaya dalam ada eleme -2

mx2 0 1 0 0 0 0 5000000000 0my2 -1 0 0 0 0 0 0 961562.*2 0 0 1 0 0 0 937500

mx3 0 0 0 0 1 0 2500000000 0my3 0 0 0 -1 0 0 0 -961562.*3 0 0 0 0 0 1 -937500

mx2 0 1 0 0 0 0 -4826.69659587my2 -1 0 0 0 0 0 4827.601515343*2 0 0 1 0 0 0 -981.60491023 &

mx3 0 0 0 0 1 0 -7848012.58524my3 0 0 0 -1 0 0 -4827.60151534*3 0 0 0 0 0 1 981.6049102298

{ } [ ] [ ] { } U k f e g )(T=


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2EIy/L

4000000000

10,000,000,000


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

0 0 -2884687.5 0-3750000 -10000000000 0 3750000

937.5 3750000 0 -937.50 0 2884687.5 0

-3750000 -20000000000 0 3750000-937.5 -3750000 0 937.5


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1

2

3

000

2000

x1 y1

x2 y2

x3 y3

x2 y2


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000000

2

x2 y2


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-1538500 0 0 0 -472 N-mm0 4000000000 2400000 0 -2007 147 N-mm -20807 kN-m0 -2400000 -960 0 & 4017 N

1538500 0 0 0.00313727 472 N-mm0 8000000000 2400000 0.00502058 -4727 N-mm0 2400000 960 -16.737278 -4017 N

2500000000 0 -937500 0.003137270 -961562.5 0 0.00502058

937500 0 -234.375 -16.7372785000000000 0 -937500 0

0 961562.5 0 0-937500 0 234.375 0

N-mmN-mm

NN-mmN-mm 5747 kN-mN

m y24828 N-mm

h

408

m x1 4827 N-mm

h1=

4018Nm

y1

20.087.1

48N-mm

1

m y2 4821


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N-mm

2

N-mm

m x3 4827 N-mm

m y3 7.848.013 N-mm3=982N

3


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Data-data struktur gridIx 200,000 mm4Iy 125,000 mm4G 70 kN/mm2

E 210 kN/mm2

N,de Ix (mm4) Iy (mm4) G(N/mm2) E(N/mm2)

Eleme -1 1-2 200,000 125,000 70 210Eleme -2 2-3 200,000 125,000 70 210Eleme -3 3-4 200,000 125,000 70 210

7000 0 0 -7000 00 52500 -39.375 0 26250

[K] lokal-1 0 -39.375 0.039375 0 -39.375-7000 0 0 7000 0

0 26250 -39.375 0 52500

0 39.375 -0.039375 0 39.375

0 -1 0 0 0[T] el-1 1 0 0 0 0

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

0 1 0 0 0

-1 0 0 0 0[T]#T el-1 0 0 1 0 0

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

w1

52500 0 -39.375 26250 0

0 7000 0 0 -7000

[K] !lo"al-1 -39.375 0 0.039375 -39.375 0

26250 0 -39.375 52500 0

α -90

x1 y1 x2 y2

1

2

0,5 kN


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0 -7000 0 0 7000

39.375 0 -0.039375 39.375 0

Eleme -1 sama de ga eleme -3w4

52500 0 -39.375 26250 00 7000 0 0 -7000

[K] !lo"al-3 -39.375 0 0.039375 -39.375 026250 0 -39.375 52500 0

0 -7000 0 0 700039.375 0 -0.039375 39.375 0

w2

7000 0 0 -7000 00 52500 -39.375 0 26250

[K] lokal-2 0 -39.375 0.039375 0 -39.375-7000 0 0 7000 0

0 26250 -39.375 0 525000 39.375 -0.039375 0 39.375

!u"u ga matriks #$% & ' #*%w1

&x1 52500 0 -39.375 26250 0

&y1 0 7000 0 0 -7000'1 -39.375 0 0.039375 -39.375 0

&x2 26250 0 -39.375 59500 0&y2 0 -7000 0 0 59500'2 39.375 0 -0.039375 39.375 -39.375

&x3 0 0 0 -7000 0&y3 0 0 0 0 26250'3 0 0 0 0 39.375

&x4 0 0 0 0 0&y4 0 0 0 0 0

'4 0 0 0 0 0

w1

&x1 52500 0 -39.375 26250 0&y1 0 7000 0 0 -7000'1 -39.375 0 0.039375 -39.375 00 26250 0 -39.375 59500 00 0 -7000 0 0 59500

-50 39.375 0 -0.039375 39.375 -39.3750 0 0 0 -7000 00 0 0 0 0 26250

x4 y4 x3 y3

x2 y2 x3 y3

α 0

x1 y1 x2 y2

x1 y1 x2 y2


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&x4 0 0 0 0 0&y4 0 0 0 0 0'4 0 0 0 0 0

w2

0 59500 0 39.375 -7000 00 0 59500 -39.375 0 26250

-50 39.375 -39.375 0.07875 0 -39.3750 -7000 0 0 59500 00 0 26250 -39.375 0 59500

50 0 39.375 -0.039375 39.375 39.375&x4 0 0 0 26250 0&y4 0 0 0 0 -7000'4 0 0 0 -39.375 0

&x1 26250 0 39.375 0 0&y1 0 -7000 0 0 0'1 -39.375 0 -0.039375 0 0

0 59500 0 39.375 -7000 00 0 59500 -39.375 0 26250

-50 39.375 -39.375 0.07875 0 -39.375

0 -7000 0 0 59500 00 0 26250 -39.375 0 5950050 0 39.375 -0.039375 39.375 39.375

5.3E-05 -1.2E-05 -5.1E-02 2.3E-05 -1.2E-05-1.2E-05 4.0E-05 2.0E-02 1.2E-05 9.5E-06

w2 -5.1E-02 2.0E-02 7.3E$01 -2.5E-02 2.0E-022.3E-05 1.2E-05 -2.5E-02 5.3E-05 1.2E-05

-1.2E-05 9.5E-06 2.0E-02 1.2E-05 4.0E-05

w3 -2.5E-02 -2.0E-02 2.9E$01 -5.1E-02 -2.0E-02

0.013 (a)-0.020 (a)

w2 & -22.233 mm-0.013 (a)-0.020 (a)

w3 22.233 mm

&x4 0 0 0 26250 0

x2 y2 x3 y3

x2 y2

x3 y3

x2 y2

x3 y3


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'4 0 0 0 -39.375 0&x1 26250 0 39.375 0 0&y1 0 -7000 0 0 0'1 -39.375 0 -0.039375 0 0


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L (mm) GIx/L 4EIy/L 6EIy/L^2 12EIy/L^3

2000 7000 52500 39.375 0.0393752000 7000 52500 39.375 0.0393752000 7000 52500 39.375 0.039375

039.375

-0.0393750

39.375

0.039375

000001

0 0 52500 -39.375 0 26250

0 -7000 0 0 7000 00 0 -39.375 0.039375 0 -39.3750 0 26250 -39.375 0 525000 7000 0 0 -7000 01 0 39.375 -0.039375 0 39.375

w2

39.375

0

-0.039375 w1

39.375

x1

y1

x2

3

2000 mm

2000 mm

4

0,5 kN

Sb-globalX

Z Y


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0

0.039375 w2

w3

39.3750

-0.039375 w439.375

00.039375 w3

w3

039.375

-0.039375 w2 [K] !lo"al-20

39.3750.039375 w3

w2 w3 w4

39.375 0 0 0 0 0 0

0 0 0 0 0 0 0-0.039375 0 0 0 0 0 0

39.375 -7000 0 0 0 0 0-39.375 0 26250 39.375 0 0 0

0.07875 0 -39.375 -0.039375 0 0 00 59500 0 39.375 26250 0 -39.375

-39.375 0 59500 39.375 0 -7000 0-0.039375 39.375 39.375 0.07875 39.375 0 -0.039375

0 26250 0 39.375 52500 0 -39.3750 0 -7000 0 0 7000 0

0 -39.375 0 -0.039375 -39.375 0 0.039375

w2 w3 w4

39.375 0 0 0 0 0 00 0 0 0 0 0 0

-0.039375 0 0 0 0 0 039.375 -7000 0 0 0 0 0

-39.375 0 26250 39.375 0 0 00.07875 0 -39.375 -0.039375 0 0 0

0 59500 0 39.375 26250 0 -39.375-39.375 0 59500 39.375 0 -7000 0

y2

x4 y4

x3 y3

x2 y2

x3

y3

x3 y3 x4 y4

x3 y3 x4 y4


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0 26250 0 39.375 52500 0 -39.3750 0 -7000 0 0 7000 00 -39.375 0 -0.039375 -39.375 0 0.039375

w3 w4 w1

0 0 0 0 26250 0 -39.37539.375 0 0 0 0 -7000 0

-0.039375 0 0 0 39.375 0 -0.03937539.375 26250 0 -39.375 0 0 039.375 0 -7000 0 0 0 0

0.07875 39.375 0 -0.039375 0 0 039.375 52500 0 -39.375 0 0 0

0 0 7000 0 0 0 0-0.039375 -39.375 0 0.039375 0 0 0

0 0 0 0 52500 0 -39.3750 0 0 0 0 7000 00 0 0 0 -39.375 0 0.039375

039.375

-0.039375 w2

39.37539.3750.07875 w3

-2.5E-02 0-2.0E-02 02.9E$01 -0.5-5.1E-02 0-2.0E-02 0

7.3E$01 0.5

39.375 0.013 530 kN-mm

x4 y4 x1 y1

x2 y2

x3 y3


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-0.039375 -22.233 & 0 kN0 -0.013 -530 kN-mm0 -0.020 143 kN-mm0 22.233 0 kN


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39.375

0-0.039375

39.3750

0.039375


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w1

w2

w3

w4

000

w2

x1

y1

x2 y2

x3 y3

x4 y4

x2 y2

x3 y3


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000

w2

w3

000000

x2 y2

x3 y3


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+"-y

+"-x+"-

+"-y

+"-x+"-


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+, strai matrik dis la.eme da matrik gayaw2

0 5001538500 0 937500 2500000000 00 0 8000961563 2400000 0 -961562.5

- 000 937500 2400000 1194.375 937500 0x3 2500000000 0 937500 5000000000 0y3 0 -961562.5 0 0 961562.5!3 -937500 0 -234.375 -937500 0x1 -1538500 0 0 0 0y1 0 4000000000 2400000 0 0!1 0 -2400000 -960 0 0

0 5001538500 0 9375000 0 8000961563 2400000

-5000 937500 2400000 1194.375 2

x2 y2 x3 y3

x2 y2


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w3 w1

-937500 -1538500 0 00 0 4.0E$009 -2400000

-234.375 0 2400000 -960 2-937500 0 0 0 0

0 0 0 0 0234.375 0 0 0 0

0 1538500 0 0 00 0 8.0E$009 -2400000 00 0 -2400000 960 0

x1 y1

x2 y2

Documents

Contoh Struktur Grid-revisi