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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
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