18 análisis matricial-de-las-estructuras-por-el-método-de-la-rigidez
armadura método matricial
392
EJE 1 AREA 0.003 m2 EA 20000000 tn/m2 NUDO FUERZAS APLICADAS X Y 1 5 2 2 7 -6 3 5 4 4 5 2 5 7 -6 6 7 -6 7 7 -6 8 7 -6 9 0 0 10 0 0 11 0 0 12 0 0 DATOS DE LAS BARRAS BARRAS INICIO FIN AREA 1 12 1 0 0 -2 5 12 2 1 2 1 2 3 4 5 6 7 8 9 10 11 12 13 1
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método matricial de una armadura idealizada en el programa ftool, con la que se pide calcular los desplazamientos , fuerzas internas, diagramas de cortantes y flectores. Se aplica el metodo paso a paso para obtener las matrices locales de cada elemento y las matriz ensamblada de la estructura general. Una vez obtenida la matriz se divide entre los libres y restringidos, para hallar desplazamientos se multiplica la inversa de la matriz de los libres pos las fuerzas en los nudos de la armadura . Para hallar las reacciones se multiplica la matriz debajo de los libres por los desplazamientos. Para hallas las fuerzas internas de cada barra se procede a multiplicar su matriz de cada elemento por los desplazamientos de la estructura en general, solo se toman los desplazamientos que afectan a ese elemento ....
Transcript of armadura método matricial
EJE 1
AREA 0.003 m2EA 20000000 tn/m2
NUDO FUERZAS APLICADASX Y
1 5 22 7 -63 5 44 5 25 7 -66 7 -67 7 -68 7 -69 0 0
10 0 011 0 012 0 0
DATOS DE LAS BARRASBARRAS INICIO FIN AREA
1 12 10 0 -2 5 12
2 1 2
1
2
3
4
5
6
7
8
9
10
11
12
13
1
-2 5 0 73 1 3
-2 5 2 54 12 3
0 0 2 55 12 11
0 0 2 06 3 2
2 5 2 77 11 3
2 0 2 58 2 4
2 7 9 79 3 5
2 5 9 510 3 6
2 -5 6 -411 11 6
2 0 6 412 11 10
2 0 5 013 10 6
5 0 6 414 6 7
6 4 9 415 10 9
5 0 9 016 5 4
9 5 9 717 5 8
-9 5 -11 418 7 8
9 4 11 419 9 7
9 0 9 420 8 4
11 4 9 721 9 8
9 0 11 4
1A -0.371390676 0 At
0.928476691 00 -0.3713906760 0.928476691 k_
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110344.82759 -10344.82759 K4137.931034 -4137.931034-10344.82759 10344.82759
2A 0.447213595 0 At
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b 1 0.666666667d 2
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1718
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6 7 8
9101112
0.447213595 0.4472135954 15000
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1850.539016 1850.539016 -1850.539016 -1850.539016-4626.34754 -4626.34754 4626.34754 4626.34754
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1 0 0 0
60 0 1 0
15000 -15000-15000 15000
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A1 0 0
0 0 K 00 0 00 0 0
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A 0 0 At 00 0 00 00 0 k_ 0
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A1 0 00 0 K 00 0 00 0 0
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A 0 0 At 00 0 00 00 0 k_ 0
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EJE 4
NUDO FUERZAS APLICADASX Y
1 1 02 0 03 0 -24 0 05 0 0
0.003 4 x0.00075
ENSAMBLANDO MATRICES1 2 3 4
16711.76196947 -12998.037087 -16711.761969 12998.037087-12998.0370874 53796.7844013 12998.037087 -10109.584401
0 12998.0370874 16711.761969 -12998.03708712998.03708736 -10109.584401 -12998.037087 44088.517735
0 0 0 00 -43687.2 0 -33978.933333
1 2
Kuu7.3685132E-005 1.780333E-005
F5
1.7803333E-005 0.00002289 5
D0.0004574423 1 R 2.64466725820.0002034667 2 3.8888888889
3 04 -8.888888888956
EJE 4
A 0.03 m2E 10193680 tn/m2
DATOS DE LAS BARRASBARRAS INICIO FIN
1 3 10 0 0 7
BARRAS INICIO FIN
2 1 20 7 9 0
BARRAS INICIO FIN
3 3 20 0 0 9
ENSAMBLANDO MATRICES5 60 0 10 -43687.2 20 0 30 -33978.933333 40 0 50 77666.133333 6
3456
DATOS DE LAS BARRASE tn/m2 AREA m2 LONGITUD CX CY
10193680.0000 0.03 7 0 1
E tn/m2 AREA m2 LONGITUD CX CY
10193680 0.03 11.40175425 0.789352217 -0.613940614
E tn/m2 AREA m2 LONGITUD CX CY
10193680 0.03 9 0 1
ENSAMBLANDO MATRICES
DATOS DE LAS BARRASK
43687.20000
K
26821.346370749
K
33978.933333333
1K_ 43687.2 -43687.2
-43687.2 43687.2
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-26821.34637 26821.34637
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K16711.762 -12998.04-12998.04 10109.584
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1AT 0 1 0 0
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43687.2 -43687.20 0
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0 43687.2 2
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3 4-16711.76 12998.037 1 K 26821.3463712998.037 -10109.58 2 CX 0.78935221716711.762 -12998.04 3 CY -0.613940614
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VALORES
VALORES
3K_ 33978.93333 -33978.93333 AT 0 1
-33978.93333 33978.93333 0 0
A0 0
OP0 0
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K0 0 0 0 50 33978.933 0 -33978.93 60 0 0 0 30 -33978.93 0 33978.933 4
30 00 1
K 33978.93333CX 0CY 1
VALORES
1K_ 12600 -12600 AT-12600 12600
A1 0
OP2 00 10 2
K#REF! #REF! #REF!#REF! #REF! #REF!#REF! #REF! #REF!#REF! #REF! #REF!
2
K_ 26821.3464 -26821.3464-26821.3464 26821.3464
A0.78935222 0-0.61394061 0
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K0 0
34484.5882 -26821.34640 0
K-34484.5882 26821.3464
11 2 0 00 0 1 2
12600 #REF!25200-12600-25200#REF! K 12600#REF! CX 1#REF! CY 2#REF!
5
K_
A
K
2 6
AT 0.78935222 -0.61394061 0 0 K_0 0 0.78935222 -0.61394061
OP34484.5882 -34484.5882
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0 0 K 26821.3464
K-34484.5882 26821.3464 CX 0.789352220 0 CY -0.61394061
VALORES
VALORES
34484.5882 -26821.3464K
5
0 0 AT 0 0 00 0 0 0 00 0
OP0 0
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6
0 0 AT 0 0 00 0 0 0 00 0
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0 0 0 00 0 0 00 0 0 00 0 0 0 K0 0 0 0 CX0 0 0 0 CY
VALORES
VALORES
0 0 0 0
5
0 30 K_ 33978.9333
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A010
0 00
K0
0 000
6
0 40 K_ 0
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A000
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0 0
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3-33978.9333 AT 0 1 0 033978.9333 0 0 0 1
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-43687.2 0 43687.2
40 AT 0 0 0 00 0 0 0 00
OP0 0
0 0 00 0 00 0 00 0 0 K 00 0 0 CX 0
VALORES
VALORES
0 0 0 CY 00 0 0
VALORES
7K_ 0 0 AT 0 0
0 0 0 0
A0 0
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0 0 0 00 0 0 00 0 0 0
K0 0 0 00 0 0 00 0 0 00 0 0 0
VALORES
70 00 0
K 0CX 0CY 0
A 0.03 m2E 21000000 tn/m2
DATOS DE LAS BARRASBARRAS INICIO FIN
1 1 20 4 2
BARRAS INICIO FIN
2 2 32 7 4
BARRAS INICIO FIN
3 3 44 4 6
BARRAS INICIO FIN
4 4 56 7 8
BARRAS INICIO FIN
5 5 6
5 8 4 10BARRAS INICIO FIN
6 6 710 7 12
BARRAS INICIO FIN
7 8 712 0 12
BARRAS INICIO FIN
8 9 80 0 12
BARRAS INICIO FIN
9 9 10 0 0
DATOS DE LAS BARRASFIN E tn/m2 AREA m2 LONGITUD CX CY2
21000000 0.03 3.605551275 0.554700196 0.8320502947
FIN E tn/m2 AREA m2 LONGITUD CX CY3
21000000 0.03 3.605551275 0.554700196 -0.8320502944
FIN E tn/m2 AREA m2 LONGITUD CX CY4
21000000 0.03 3.605551275 0.554700196 0.8320502947
FIN E tn/m2 AREA m2 LONGITUD CX CY5
21000000 0.03 3.605551275 0.554700196 -0.8320502944
FIN E tn/m2 AREA m2 LONGITUD CX CY6
21000000 0.03 3.605551275 0.554700196 0.832050294
721000000 0.03 3.605551275 0.554700196 0.832050294
FIN E tn/m2 AREA m2 LONGITUD CX CY7
21000000 0.03 3.605551275 0.554700196 -0.8320502944
FIN E tn/m2 AREA m2 LONGITUD CX CY7
21000000 0.03 4 0 14
FIN E tn/m2 AREA m2 LONGITUD CX CY
8 21000000 0.03 12 1 00
FIN E tn/m2 AREA m2 LONGITUD CX CY1
21000000 0.03 4 0 14
DATOS DE LAS BARRASK
1747311 1 174731 1 1 1747311 0 2 1 0 2
K 1 -1 174731
174730.561810951 -1 174731 2 0 32 0 3 1 1 174731
K 3 0 4
174730.561810951 1 174731 1 -1 1747313 0 4 4 0 5
K 1 1 174731
174730.561810951 -1 174731 5 0 64 0 5 1 -1 174731
K 6 0 7
174730.561810951 1 174731 0 1 157500
174730.561810955 0 6 8 0 7
K 1 0 52500
174730.561810951 -1 174731 9 0 86 0 7 0 1 157500
K 9 0 1
1575000 1 157500 0 0 08 0 7 0 0 0
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525001 0 52500 0 0 0
9 0 8 0 0 0
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K
1K_ 174731 -174730.56181095
1-174730.56181095 174730.561810947
A 1 0
21 00 0.5547001962
3 0 0.8320502943
1 2
4 K 53763.249788 80644.87468280644.874682 120967.31202
5 -53763.249788 -80644.874682-80644.874682 -120967.31202
6
7
7
8
9
10
11
12
13
14
15
16
17
18
19
20
MATRIX GLOBAL1 2 3
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F
0 10 20 3
-10 40 50 60 7
-10 8
F 0 90 100 11
-10 120 130 140 150 160 170 18
1AT 0.5547001962 0.8320502943 0
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3 4-53763.249788 -80644.874682 1 VALORES-80644.874682 -120967.31202 253763.249788 80644.874682 380644.874682 120967.31202 4
MATRIX GLOBAL4 5 6 7
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D
102002297.999307 1-0.0002843246 2
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15161718
10
0.8320502943
Cx 1Cy 1K 174731
MATRIX GLOBAL8 9 10 11
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R
0 13236931228.07949 2
0 344.7811256324 4
#N/A 5#N/A 6#N/A 7#N/A 8
R #N/A 9#N/A 10#N/A 11#N/A 12#N/A 13#N/A 14
15161718
MATRIX GLOBAL12 13 14 15
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-101.088227199 -334986.73329294 2.334487009E-010-1480799.0254309 -70422.244212551 6.345138970E-006
22.5721124873 4.6383299129 -9.67183977E-011-1480716.5852044 152905.336868107 6.344918859E-006-107.7918220268 -781680.47352316 3.112758130E-011
-1480629.6759147 674028.744770013 6.344833628E-006-69.8808948602 -967585.30365637 8.477117861E-011
-1480604.4019633 550092.191345331 6.344869390E-006-22.00782927 -2915746.0904661 -4.37360949E-010
-1480636.3173404 1848866.04922121 6.345217479E-0062222342.59802095 -5690805.9890908 -4.97119173E-010
940.0865570417 -1173.8832042594 6.345177640E-006
MATRIX GLOBAL16 17 18 19 20
0.0000000 0.0000000 0.00000000.0000000 0.0000000 -157500.00000000.0000000 0.0000000 0.00000000.0000000 0.0000000 0.00000000.0000000 0.0000000 0.00000000.0000000 0.0000000 0.00000000.0000000 0.0000000 0.00000000.0000000 0.0000000 0.00000000.0000000 0.0000000 0.00000000.0000000 0.0000000 0.00000000.0000000 0.0000000 0.00000000.0000000 0.0000000 0.00000000.0000000 0.0000000 0.0000000
-157500.0000000 0.0000000 0.00000000.0000000 -52500.0000000 0.0000000
157500.0000000 0.0000000 0.00000000.0000000 52500.0000000 0.00000000.0000000 0.0000000 157500.0000000
2K_
A
K
MATRIX GLOBAL21 22 23 24
123456789
10111213
1415161718192021222324
2174731 -174730.5618 AT 0.554700196 -0.832050294 0
-174730.5618 174730.5618 0 0 0.5547001961 0 OP 96923.07692 -96923.07692-1 0 -145384.6154 145384.61540 0.554700196 -96923.07692 96923.076920 -0.832050294 145384.6154 -145384.6154
3 4 5 653763.25 -80644.87 -53763.25 80644.875 3 VALORES-80644.87 120967.31 80644.875 -120967.3 4-53763.25 80644.875 53763.25 -80644.87 580644.875 -120967.3 -80644.87 120967.31 6
20
-0.832050294
Cx 1Cy -1K 174731
3K_ 174731 -174730.5618 AT 0.554700196 0.832050294
-174730.5618 174730.5618 0 0
A 1 0 OP 96923.07692 -96923.076921 0 145384.6154 -145384.61540 0.554700196 -96923.07692 96923.076920 0.832050294 -145384.6154 145384.6154
5 6 7 8
K 53763.25 80644.875 -53763.25 -80644.87 580644.875 120967.31 -80644.87 -120967.3 6-53763.25 -80644.87 53763.25 80644.875 7-80644.87 -120967.3 80644.875 120967.31 8
30 0
0.554700196 0.832050294
VALORES Cx 1Cy 1K 174731
4K_ 174731 -174730.5618 AT 0.554700196
-174730.5618 174730.5618 0
A 1 0 OP 96923.07692-1 0 -145384.61540 0.554700196 -96923.076920 -0.832050294 145384.6154
7 8 9 10
K 53763.25 -80644.87 -53763.25 80644.875-80644.87 120967.31 80644.875 -120967.3-53763.25 80644.875 53763.25 -80644.8780644.875 -120967.3 -80644.87 120967.31
4-0.832050294 0 0
0 0.554700196 -0.832050294-96923.07692145384.615496923.07692-145384.6154
7 VALORES Cx 18 Cy -19 K 17473110
5K_ 174731 -174730.5618 AT
-174730.5618 174730.5618
A 1 0 OP1 00 0.5547001960 0.832050294
9 10 11
K 53763.25 80644.875 -53763.2580644.875 120967.31 -80644.87-53763.25 -80644.87 53763.25-80644.87 -120967.3 80644.875
50.554700196 0.832050294 0 0
0 0 0.554700196 0.83205029496923.07692 -96923.07692145384.6154 -145384.6154-96923.07692 96923.07692-145384.6154 145384.6154
12-80644.87 9 VALORES Cx 1
-120967.3 10 Cy 1
80644.875 11 K 174731120967.31 12
6K_ 174731 -174730.5618
-174730.5618 174730.5618
A 1 0-1 00 0.5547001960 -0.832050294
0 1
K 53763.25 -80644.87-80644.87 120967.31-53763.25 80644.87580644.875 -120967.3
6AT 0.554700196 -0.832050294 0 0
0 0 0.554700196 -0.832050294
OP 96923.07692 -96923.07692-145384.6154 145384.6154-96923.07692 96923.07692145384.6154 -145384.6154
13 14-53763.25 80644.875 0 VALORES Cx 1
80644.875 -120967.3 1 Cy -1
53763.25 -80644.87 13 K 174731-80644.87 120967.31 14
7K_ 157500
-157500
A 0100
15
K 0000
7-157500 AT 0 1 0 0157500 0 0 0 1
0 OP 0 00 157500 -1575000 0 01 -157500 157500
16 13 140 0 0 15 VALORES Cx
157500 0 -157500 16 Cy
0 0 0 13 K-157500 0 157500 14
7
01
157500
8K_
A
K
852500 -52500 AT 1 0 0-52500 52500 0 0 1
1 0 OP 52500 -525000 0 0 00 1 -52500 525000 0 0 0
17 18 15 1652500 0 -52500 0 17 VALORES
0 0 0 0 18-52500 0 52500 0 15
0 0 0 0 16
800
Cx 1Cy 0K 52500
9K_ 157500 -157500 AT 0 1
-157500 157500 0 0
A 0 0 OP 0 01 0 157500 -1575000 0 0 00 1 -157500 157500
17 18 1 2
K 0 0 0 0 170 157500 0 -157500 180 0 0 0 10 -157500 0 157500 2
90 00 1
VALORES Cx 0Cy 1K 157500
10K_ 0 0
0 0
A 0 00 00 00 0
-1 0
K 0 00 00 00 0
10AT 0 0 0 0
0 0 0 0
OP 0 00 00 00 0
-1 00 0 -1 VALORES Cx 0
0 0 0 Cy 0
0 0 -1 K 00 0 0
11K_ 0 0 AT
0 0
A 0 0 OP0 00 00 0
-1 0 -1
K 0 0 00 0 00 0 00 0 0
110 0 0 00 0 0 00 00 00 00 0
00 -1 VALORES Cx 0
0 0 Cy 0
0 -1 K 00 0
12K_ 0 0
0 0
A 0 00 00 00 0
-1 0
K 0 00 00 00 0
12AT 0 0 0 0
0 0 0 0
OP 0 00 00 00 0
-1 00 0 -1 VALORES Cx 0
0 0 0 Cy 0
0 0 -1 K 00 0 0
13K_ 0 0 AT 0 0
0 0 0 0
A 0 0 OP 0 00 0 0 00 0 0 00 0 0 0
-1 0 -1 0
K 0 0 0 0 -10 0 0 0 00 0 0 0 -10 0 0 0 0
130 00 0
VALORES Cx 0Cy 0K 0
14K_
A
K
140 0 AT 0 0 00 0 0 0 00 0 OP 0 00 0 0 00 0 0 00 0 0 0
-1 0 -1 00 0 0 0 -1 VALORES0 0 0 0 00 0 0 0 -10 0 0 0 0
1400
Cx 0Cy 0K 0
15K_ 0 0 AT 0 0
0 0 0 0
A 0 0 OP 0 00 0 0 00 0 0 00 0 0 0
-1 0 -1 0
K 0 0 0 0 -10 0 0 0 00 0 0 0 -10 0 0 0 0
150 00 0
VALORES Cx 0Cy 0K 0
16K_ 0 0
0 0
A 0 00 00 00 0
-1 0
K 0 00 00 00 0
16AT 0 0 0 0
0 0 0 0
OP 0 00 00 00 0
-1 00 0 -1 VALORES Cx 0
0 0 0 Cy 0
0 0 -1 K 00 0 0
17K_ 0 0 AT
0 0
A 0 0 OP0 00 00 0
-1 0 -1
K 0 0 00 0 00 0 00 0 0
170 0 0 00 0 0 00 00 00 00 0
00 -1 VALORES Cx 0
0 0 Cy 0
0 -1 K 00 0
