EJERCICIO N6
59
Matrices de rigidez de cada barra Barra 1 E 2.10E+07 Tnf/m2 A 0.02 m2 L 0.6946 m Iz 6.67E-05 m4 phi 80.00 ° Matriz de rigidez en coordenadas locales 26 27 28 1 604664.56 0.00 0.00 -604664.56 0.00 50130.84 17410.44 0.00 k'= 0.00 17410.44 8062.19 0.00 -604664.56 0.00 0.00 604664.56 0.00 -50130.84 -17410.44 0.00 0.00 17410.44 4031.10 0.00 Matriz de transformación L= 0.174 0.985 0.000 0.000 -0.985 0.174 0.000 0.000 0.000 0.000 1.000 0.000 0.000 0.000 0.000 0.174 0.000 0.000 0.000 -0.985 0.000 0.000 0.000 0.000 Matriz de rigidez en coordenadas globales 26 27 28 1 66852.073 94830.851 -17145.936 -66852.073 94830.851 587943.317 3023.291 -94830.851 k= -17145.936 3023.291 8062.194 17145.936 -66852.073 -94830.851 17145.936 66852.073 -94830.851 -587943.317 -3023.291 94830.851 -17145.936 3023.291 4031.097 17145.936 Fuerzas de fijación en coordenadas locales 0.000 26 1.389 27 0.159 28 0.000 1 1.389 2 -0.159 3 F F '= Fuerzas de fijación en coordenadas globales F F = L T .F F '
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Transcript of EJERCICIO N6
Matrices de rigidez de cada barraBarra 1
E 2.10E+07 Tnf/m2A 0.02m2L 0.6946mIz 6.67E-05 m4phi 80.00 °
Matriz de rigidez en coordenadas locales26 27 28 1 2604664.56 0.00 0.00 -604664.56 0.00
0.00 50130.84 17410.44 0.00 -50130.84k'= 0.00 17410.44 8062.19 0.00 -17410.44
-604664.56 0.00 0.00 604664.56 0.000.00 -50130.84 -17410.44 0.00 50130.840.00 17410.44 4031.10 0.00 -17410.44
Matriz de transformaciónL= 0.174 0.985 0.000 0.000 0.000
-0.985 0.174 0.000 0.000 0.0000.000 0.000 1.000 0.000 0.0000.000 0.000 0.000 0.174 0.9850.000 0.000 0.000 -0.985 0.1740.000 0.000 0.000 0.000 0.000
Matriz de rigidez en coordenadas globales26 27 28 1 2
66852.073 94830.851 -17145.936 -66852.073 -94830.85194830.851 587943.317 3023.291 -94830.851 -587943.317
k= -17145.936 3023.291 8062.194 17145.936 -3023.291-66852.073 -94830.851 17145.936 66852.073 94830.851-94830.851 -587943.317 -3023.291 94830.851 587943.317-17145.936 3023.291 4031.097 17145.936 -3023.291
Fuerzas de fijación en coordenadas locales
0.000 26
1.389 270.159 280.000 11.389 2-0.159 3
FF'=
Fuerzas de fijación en coordenadas globales FF = LT.FF'
-1.368 26
0.241 270.159 28-1.368 10.241 2-0.159 3
Fuerzas de fijación en g.d.l. libres Fuerzas de fijación en g.d.l. restringidos
-2.571 1 -1.368 26
0.936 2 0.241 270.000 3 0.159 28-2.096 4 1.368 291.759 5 0.241 300.000 6-1.368 72.370 80.000 9-0.475 102.695 110.000 120.475 132.695 140.000 151.368 162.370 170.000 182.096 191.759 200.000 212.571 220.936 230.000 24-0.159 25
MATRIZ DE RIGIDEZ TOTAL DE LA ESTRUCTURA (COORDENADAS GLOBALES)
1 2 3 4 5255616.339 334950.995 2068.053 -188764.266 -240120.144334950.995 1053974.443 5681.929 -240120.144 -466031.1252068.053 5681.929 16124.388 15077.883 -8705.220
-188764.266 -240120.144 15077.883 564308.846 513174.697-240120.144 -466031.125 -8705.220 513174.697 745281.936-15077.883 8705.220 4031.097 3886.668 4631.951
0 0 0 -375544.580 -273054.5530 0 0 -273054.553 -279250.811
FF=
PFf= PF
s=
0 0 0 -11191.215 13337.1700 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 0
-66852.073 -94830.851 -17145.936 0 0-94830.851 -587943.317 3023.291 0 017145.936 -3023.291 4031.097 0 0
0 0 0 0 00 0 0 0 0
Fuerzas aplicadas a la estructura (g.d.l. libres)
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00 110.00 120.00 130.00 140.00 150.00 160.00 170.00 180.00 190.00 200.00 21
Pf=
0.00 220.00 230.00 240.00 25
RESULTADOS
-6.8541333E-06 1-1.2087797E-05 21.05977053E-05 3-1.9337652E-05 4-2.0027768E-05 57.24366653E-06 6-3.0328355E-05 7-2.7357657E-05 8-3.7644577E-06 9
-4.0349335E-05 10-3.8219651E-05 11-1.5205813E-05 12-5.3469422E-05 13-5.0980349E-05 14-1.9807292E-05 15-6.9771584E-05 16-5.7475356E-05 17-1.1120775E-05 18-7.9505996E-05 19-4.8747872E-05 201.56991274E-05 21-6.3336582E-05 22-2.4364719E-05 236.33106506E-05 240.00013186425 25
0.05470660735 268.0301948342 27
0.12044478005 28-0.05470660735 297.96997307617 30
Desplazamientos globales (g.d.l. libres) = Kff-1. (Pf - PFf)
Df=
Reacciones en los apoyos (g.d.l. restringidos) = Ksf . Df + PFs
Fs=
BARRA 1
0.00000000 260.00000000 27
0.00000000 28-0.00000685 1-0.00001209 20.00001060 3
0.00000000 260.00000000 27
0.00000000 28-0.00001309 10.00000465 20.00001060 3
7.91769783359 261.34055320821 270.12044478005 28-7.91769783359 11.43784679179 2-0.15423484162 3
Desplazamientos locales en cada barra: D' = L. D
D=
D'=
Fuerzas locales (internas) en cada barra: F' = k' . D'+FF'
Barra 2
E 2.10E+07 Tnf/m2A 0.02m2L 0.6946mIz 6.67E-05 m4phi 60.00 °
Matriz de rigidez en coordenadas locales3 1 2 3 40.00 26 604664.56 0.00 0.00 -604664.56
17410.44 27 0.00 50130.84 17410.44 0.004031.10 28 k'= 0.00 17410.44 8062.19 0.00
0.00 1 -604664.56 0.00 0.00 604664.56-17410.44 2 0.00 -50130.84 -17410.44 0.008062.19 3 0.00 17410.44 4031.10 0.00
Matriz de transformación0.000 L= 0.500 0.866 0.000 0.0000.000 -0.866 0.500 0.000 0.0000.000 0.000 0.000 1.000 0.0000.000 0.000 0.000 0.000 0.5000.000 0.000 0.000 0.000 -0.8661.000 0.000 0.000 0.000 0.000
Matriz de rigidez en coordenadas globales3 1 2 3 4
-17145.936 26 188764.266 240120.144 -15077.883 -188764.2663023.291 27 240120.144 466031.125 8705.220 -240120.1444031.097 28 k= -15077.883 8705.220 8062.194 15077.88317145.936 1 -188764.266 -240120.144 15077.883 188764.266-3023.291 2 -240120.144 -466031.125 -8705.220 240120.1448062.194 3 -15077.883 8705.220 4031.097 15077.883
Fuerzas de fijación en coordenadas locales
0.000 1
1.389 20.159 30.000 41.389 5-0.159 6
FF'=
Fuerzas de fijación en coordenadas globales FF = LT.FF'
-1.203 1
0.695 20.159 3-1.203 40.695 5-0.159 6
6 7 8 9 10 11 12 13-15077.883 0 0 0 0 0 0 08705.220 0 0 0 0 0 0 04031.097 0 0 0 0 0 0 03886.668 -375544.580 -273054.553 -11191.215 0 0 0 04631.951 -273054.553 -279250.811 13337.170 0 0 0 016124.388 11191.215 -13337.170 4031.097 0 0 0 011191.215 915341.013 451278.255 5236.494 -539796.433 -178223.702 -5954.721 0-13337.170 451278.255 394249.769 3023.291 -178223.702 -114998.958 16360.461 0
FF=
4031.097 5236.494 3023.291 16124.388 5954.721 -16360.461 4031.097 00 -539796.433 -178223.702 5954.721 ### 178223.702 5954.721 -604664.5550 -178223.702 -114998.958 -16360.461 178223.702 165129.794 1049.978 0.0000 -5954.721 16360.461 4031.097 5954.721 1049.978 16124.388 0.0000 0 0 0 -604664.555 0.000 0.000 ###0 0 0 0 0.000 -50130.836 -17410.439 -178223.7020 0 0 0 0.000 17410.439 4031.097 5954.7210 0 0 0 0 0 0 -539796.4330 0 0 0 0 0 0 178223.7020 0 0 0 0 0 0 5954.7210 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 0
Df=
BARRA 2
-0.00000685 1-0.00001209 2
0.00001060 3-0.00001934 4-0.00002003 50.00000724 6
-0.00001390 1-0.00000011 2
0.00001060 3-0.00002701 40.00000673 50.00000724 6
7.93197479 11.35687813 20.15423484 3-7.93197479 41.42152187 5-0.17668561 6
Desplazamientos locales en cada barra: D' = L. D
D=
D'=
Fuerzas locales (internas) en cada barra: F' = k' . D'+FF'
Barra 3
E 2.10E+07 Tnf/m2A 0.02m2L 0.6946mIz 6.67E-05 m4phi 40.00 °
Matriz de rigidez en coordenadas locales5 6 4 5 60.00 0.00 1 604664.56 0.00 0.00
-50130.84 17410.44 2 0.00 50130.84 17410.44-17410.44 4031.10 3 k'= 0.00 17410.44 8062.19
0.00 0.00 4 -604664.56 0.00 0.0050130.84 -17410.44 5 0.00 -50130.84 -17410.44-17410.44 8062.19 6 0.00 17410.44 4031.10
Matriz de transformación0.000 0.000 L= 0.77 0.643 0.0000.000 0.000 -0.643 0.766 0.0000.000 0.000 0.000 0.000 1.0000.866 0.000 0.000 0.000 0.0000.500 0.000 0.000 0.000 0.0000.000 1.000 0.000 0.000 0.000
Matriz de rigidez en coordenadas globales5 6 4 5 6
-240120.144 -15077.883 1 375544.580 273054.553 -11191.215-466031.125 8705.220 2 273054.553 279250.811 13337.170-8705.220 4031.097 3 k= -11191.215 13337.170 8062.194240120.144 15077.883 4 -375544.580 -273054.553 11191.215466031.125 -8705.220 5 -273054.553 -279250.811 -13337.170-8705.220 8062.194 6 -11191.215 13337.170 4031.097
Fuerzas de fijación en coordenadas locales
0.000 4
1.389 50.159 60.000 71.389 8-0.159 9
FF'=
Fuerzas de fijación en coordenadas globales FF = LT.FF'
-0.893 4
1.064 50.159 6-0.893 71.064 8-0.159 9
14 15 16 17 18 19 20 210 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 0
FF=
0 0 0 0 0 0 0 00.000 0.000 0 0 0 0 0 0
-50130.836 17410.439 0 0 0 0 0 0-17410.439 4031.097 0 0 0 0 0 0-178223.702 5954.721 -539796.433 178223.702 5954.721 0 0 0165129.794 -1049.978 178223.702 -114998.958 16360.461 0 0 0-1049.978 16124.388 -5954.721 -16360.461 4031.097 0 0 0
178223.702 -5954.721 915341.013 -451278.255 5236.494 -375544.580 273054.553 11191.215-114998.958 -16360.461 -451278.255 394249.769 -3023.291 273054.553 -279250.811 13337.17016360.461 4031.097 5236.494 -3023.291 16124.388 -11191.215 -13337.170 4031.097
0 0 -375544.580 273054.553 -11191.215 564308.846 -513174.697 3886.6680 0 273054.553 -279250.811 -13337.170 -513174.697 745281.936 -4631.9510 0 11191.215 13337.170 4031.097 3886.668 -4631.951 16124.3880 0 0 0 0 -188764.266 240120.144 -15077.8830 0 0 0 0 240120.144 -466031.125 -8705.2200 0 0 0 0 15077.883 8705.220 4031.0970 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 0
BARRA 3
-0.00001934 4-0.00002003 5
0.00000724 6-0.00003033 7-0.00002736 8-0.00000376 9
-0.00002769 4-0.00000291 5
0.00000724 6-0.00004082 7-0.00000146 8-0.00000376 9
7.9398073 41.37710154 50.17668561 6-7.9398073 71.40129846 8-0.1850892 9
Desplazamientos locales en cada barra: D' = L. D
D=
D'=
Fuerzas locales (internas) en cada barra: F' = k' . D'+FF' Fuerzas locales (internas) en cada barra: F' = k' . D'+FF'
Barra 4
E 2.10E+07A 0.02L 0.6946Iz 6.67E-05phi 20.00
Matriz de rigidez en coordenadas locales7 8 9 7
-604664.56 0.00 0.00 4 604664.560.00 -50130.84 17410.44 5 0.000.00 -17410.44 4031.10 6 k'= 0.00
604664.56 0.00 0.00 7 -604664.560.00 50130.84 -17410.44 8 0.000.00 -17410.44 8062.19 9 0.00
Matriz de transformación0.000 0.000 0.000 L= 0.9400.000 0.000 0.000 -0.3420.000 0.000 0.000 0.0000.766 0.643 0.000 0.000-0.643 0.766 0.000 0.0000.000 0.000 1.000 0.000
Matriz de rigidez en coordenadas globales7 8 9 7
-375544.580 -273054.553 -11191.215 4 539796.433-273054.553 -279250.811 13337.170 5 178223.70211191.215 -13337.170 4031.097 6 k= -5954.721375544.580 273054.553 11191.215 7 -539796.433273054.553 279250.811 -13337.170 8 -178223.70211191.215 -13337.170 8062.194 9 -5954.721
Fuerzas de fijación en coordenadas locales
0.000
1.3890.1590.0001.389-0.159
FF'=
Fuerzas de fijación en coordenadas globales FF = LT.FF' Fuerzas de fijación en coordenadas globales FF = LT.FF'
-0.475
1.3050.159-0.4751.305-0.159
22 23 24 25 26 27 28 290 0 0 0 -66852.073 -94830.851 17145.936 00 0 0 0 -94830.851 -587943.317 -3023.291 00 0 0 0 -17145.936 3023.291 4031.097 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 0
FF=
0 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 0
-188764.266 240120.144 15077.883 0 0 0 0 0240120.144 -466031.125 8705.220 0 0 0 0 0-15077.883 -8705.220 4031.097 0 0 0 0 0255616.339 -334950.995 2068.053 17145.936 0 0 0 -66852.073-334950.995 ### -5681.929 3023.291 0 0 0 94830.851
2068.053 -5681.929 16124.388 4031.097 0 0 0 -17145.93617145.936 3023.291 4031.097 8062.194 0 0 0 -17145.936
0 0 0 0 66852.073 94830.851 -17145.936 00 0 0 0 94830.851 587943.317 3023.291 00 0 0 0 -17145.936 3023.291 8062.194 0
-66852.073 94830.851 -17145.936 -17145.936 0 0 0 66852.07394830.851 -587943.317 -3023.291 -3023.291 0 0 0 -94830.851
BARRA 4
-0.00003033-0.00002736
-0.00000376-0.00004035-0.00003822-0.00001521
-0.00003786-0.00001533
-0.00000376-0.00005099-0.00002211-0.00001521
Desplazamientos locales en cada barra: D' = L. D
D=
D'=
Fuerzas locales (internas) en cada barra: F' = k' . D'+FF' Fuerzas locales (internas) en cada barra: F' = k' . D'+FF'
Barra 5
Tnf/m2 Em2 Am Lm4 Iz° phi
Matriz de rigidez en coordenadas locales Matriz de rigidez en coordenadas locales8 9 10 11 120.00 0.00 -604664.56 0.00 0.00 7
50130.84 17410.44 0.00 -50130.84 17410.44 817410.44 8062.19 0.00 -17410.44 4031.10 9 k'=
0.00 0.00 604664.56 0.00 0.00 10-50130.84 -17410.44 0.00 50130.84 -17410.44 1117410.44 4031.10 0.00 -17410.44 8062.19 12
Matriz de transformación0.342 0.000 0.000 0.000 0.000 L=0.940 0.000 0.000 0.000 0.0000.000 1.000 0.000 0.000 0.0000.000 0.000 0.940 0.342 0.0000.000 0.000 -0.342 0.940 0.0000.000 0.000 0.000 0.000 1.000
Matriz de rigidez en coordenadas globales Matriz de rigidez en coordenadas globales8 9 10 11 12
178223.702 -5954.721 -539796.433 -178223.702 -5954.721 7114998.958 16360.461 -178223.702 -114998.958 16360.461 816360.461 8062.194 5954.721 -16360.461 4031.097 9 k=-178223.702 5954.721 539796.433 178223.702 5954.721 10-114998.958 -16360.461 178223.702 114998.958 -16360.461 1116360.461 4031.097 5954.721 -16360.461 8062.194 12
Fuerzas de fijación en coordenadas locales Fuerzas de fijación en coordenadas locales
7
89101112
FF'=
Fuerzas de fijación en coordenadas globales FF = LT.FF' Fuerzas de fijación en coordenadas globales FF = LT.FF'
7
89101112
300 10 20 30 40 50 60 70 8
FF=
0 90 100 110 120 130 140 150 160 170 180 190 200 21
94830.851 22-587943.317 23-3023.291 24-3023.291 25
0 260 270 28
-94830.851 29587943.317 30
BARRA 5
78
9101112
78
9101112
7.94025063 71.39878421 80.1850892 9
-7.94025063 101.37961579 11-0.17843201 12
Desplazamientos locales en cada barra: D' = L. D Desplazamientos locales en cada barra: D' = L. D
D=
D'=
Fuerzas locales (internas) en cada barra: F' = k' . D'+FF'
2.10E+07 Tnf/m20.02m2
0.6946m6.67E-05 m4
0.00 °
Matriz de rigidez en coordenadas locales10 11 12 13 14 15
604664.56 0.00 0.00 -604664.56 0.00 0.00 100.00 50130.84 17410.44 0.00 -50130.84 17410.44 110.00 17410.44 8062.19 0.00 -17410.44 4031.10 12
-604664.56 0.00 0.00 604664.56 0.00 0.00 130.00 -50130.84 -17410.44 0.00 50130.84 -17410.44 140.00 17410.44 4031.10 0.00 -17410.44 8062.19 15
Matriz de transformación1.000 0.000 0.000 0.000 0.000 0.0000.000 1.000 0.000 0.000 0.000 0.0000.000 0.000 1.000 0.000 0.000 0.0000.000 0.000 0.000 1.000 0.000 0.0000.000 0.000 0.000 0.000 1.000 0.0000.000 0.000 0.000 0.000 0.000 1.000
Matriz de rigidez en coordenadas globales10 11 12 13 14 15
604664.555 0.000 0.000 -604664.555 0.000 0.000 100.000 50130.836 17410.439 0.000 -50130.836 17410.439 110.000 17410.439 8062.194 0.000 -17410.439 4031.097 12
-604664.555 0.000 0.000 604664.555 0.000 0.000 130.000 -50130.836 -17410.439 0.000 50130.836 -17410.439 140.000 17410.439 4031.097 0.000 -17410.439 8062.194 15
Fuerzas de fijación en coordenadas locales
0.000 10
1.389 110.159 120.000 131.389 14-0.159 15
Fuerzas de fijación en coordenadas globales FF = LT.FF'
0.000 10
1.389 110.159 120.000 131.389 14-0.159 15
-0.00004035 10-0.00003822 11
-0.00001521 12-0.00005347 13-0.00005098 14-0.00001981 15
-0.00004035 10-0.00003822 11
-0.00001521 12-0.00005347 13-0.00005098 14-0.00001981 15
7.93325131 101.41931088 110.17843201 12-7.93325131 131.35908912 14-0.15751699 15
Desplazamientos locales en cada barra: D' = L. D
Fuerzas locales (internas) en cada barra: F' = k' . D'+FF'
Barra 6
E 2.10E+07 Tnf/m2A 0.02m2L 0.6946mIz 6.67E-05 m4phi -20.00 °
Matriz de rigidez en coordenadas locales13 14 15 16 17 18
604664.56 0.00 0.00 -604664.56 0.00 0.00 130.00 50130.84 17410.44 0.00 -50130.84 17410.44 14
k'= 0.00 17410.44 8062.19 0.00 -17410.44 4031.10 15-604664.56 0.00 0.00 604664.56 0.00 0.00 16
0.00 -50130.84 -17410.44 0.00 50130.84 -17410.44 170.00 17410.44 4031.10 0.00 -17410.44 8062.19 18
Matriz de transformaciónL= 0.94 -0.342 0.000 0.000 0.000 0.000
0.342 0.940 0.000 0.000 0.000 0.0000.000 0.000 1.000 0.000 0.000 0.0000.000 0.000 0.000 0.940 -0.342 0.0000.000 0.000 0.000 0.342 0.940 0.0000.000 0.000 0.000 0.000 0.000 1.000
Matriz de rigidez en coordenadas globales13 14 15 16 17 18
539796.433 -178223.702 5954.721 -539796.433 178223.702 5954.721 13-178223.702 114998.958 16360.461 178223.702 -114998.958 16360.461 14
k= 5954.721 16360.461 8062.194 -5954.721 -16360.461 4031.097 15-539796.433 178223.702 -5954.721 539796.433 -178223.702 -5954.721 16178223.702 -114998.958 -16360.461 -178223.702 114998.958 -16360.461 175954.721 16360.461 4031.097 -5954.721 -16360.461 8062.194 18
Fuerzas de fijación en coordenadas locales
0.000 13
1.389 140.159 150.000 161.389 17-0.159 18
FF'=
Fuerzas de fijación en coordenadas globales FF = LT.FF'
0.475 13
1.305 140.159 150.475 161.305 17-0.159 18
FF=
BARRA 6
-0.00005347 13-0.00005098 14
-0.00001981 15-0.00006977 16-0.00005748 17-0.00001112 18
-0.00003281 13-0.00006619 14
-0.00001981 15-0.00004591 16-0.00007787 17-0.00001112 18
7.91965357 131.43620573 140.15751699 15-7.91965357 161.34219427 17-0.12486681 18
Desplazamientos locales en cada barra: D' = L. D
D=
D'=
Fuerzas locales (internas) en cada barra: F' = k' . D'+FF'
Barra 7
E 2.10E+07 Tnf/m2A 0.02m2L 0.6946mIz 6.67E-05 m4phi -40.00 °
Matriz de rigidez en coordenadas locales16 17 18 19 20
604664.56 0.00 0.00 -604664.56 0.000.00 50130.84 17410.44 0.00 -50130.84
k'= 0.00 17410.44 8062.19 0.00 -17410.44-604664.56 0.00 0.00 604664.56 0.00
0.00 -50130.84 -17410.44 0.00 50130.840.00 17410.44 4031.10 0.00 -17410.44
Matriz de transformaciónL= 0.766 -0.643 0.000 0.000 0.000
0.643 0.766 0.000 0.000 0.0000.000 0.000 1.000 0.000 0.0000.000 0.000 0.000 0.766 -0.6430.000 0.000 0.000 0.643 0.7660.000 0.000 0.000 0.000 0.000
Matriz de rigidez en coordenadas globales16 17 18 19 20
375544.580 -273054.553 11191.215 -375544.580 273054.553-273054.553 279250.811 13337.170 273054.553 -279250.811
k= 11191.215 13337.170 8062.194 -11191.215 -13337.170-375544.580 273054.553 -11191.215 375544.580 -273054.553273054.553 -279250.811 -13337.170 -273054.553 279250.81111191.215 13337.170 4031.097 -11191.215 -13337.170
Fuerzas de fijación en coordenadas locales
0.000 16
1.389 170.159 180.000 191.389 20-0.159 21
FF'=
Fuerzas de fijación en coordenadas globales FF = LT.FF'
0.893 16
1.064 170.159 180.893 191.064 20-0.159 21
FF=
BARRA 7
-0.00006977 16-0.00005748 17
-0.00001112 18-0.00007951 19-0.00004875 200.00001570 21
-0.00001650 16-0.00008888 17
-0.00001112 18-0.00002957 19-0.00008845 200.00001570 21
7.9010975 161.447431 17
0.12486681 18-7.9010975 191.330969 20
-0.08441956 21
Desplazamientos locales en cada barra: D' = L. D
D=
D'=
Fuerzas locales (internas) en cada barra: F' = k' . D'+FF'
Barra 8
E 2.10E+07 Tnf/m2A 0.02m2L 0.6946mIz 6.67E-05 m4phi -60.00 °
Matriz de rigidez en coordenadas locales21 19 20 21 22
0.00 16 604664.56 0.00 0.00 -604664.5617410.44 17 0.00 50130.84 17410.44 0.004031.10 18 k'= 0.00 17410.44 8062.19 0.00
0.00 19 -604664.56 0.00 0.00 604664.56-17410.44 20 0.00 -50130.84 -17410.44 0.008062.19 21 0.00 17410.44 4031.10 0.00
Matriz de transformación0.000 L= 0.500 -0.866 0.000 0.0000.000 0.866 0.500 0.000 0.0000.000 0.000 0.000 1.000 0.0000.000 0.000 0.000 0.000 0.5000.000 0.000 0.000 0.000 0.8661.000 0.000 0.000 0.000 0.000
Matriz de rigidez en coordenadas globales21 19 20 21 22
11191.215 16 188764.266 -240120.144 15077.883 -188764.26613337.170 17 -240120.144 466031.125 8705.220 240120.1444031.097 18 k= 15077.883 8705.220 8062.194 -15077.883-11191.215 19 -188764.266 240120.144 -15077.883 188764.266-13337.170 20 240120.144 -466031.125 -8705.220 -240120.1448062.194 21 15077.883 8705.220 4031.097 -15077.883
Fuerzas de fijación en coordenadas locales
0.000 19
1.389 200.159 210.000 221.389 23-0.159 24
FF'=
Fuerzas de fijación en coordenadas globales FF = LT.FF'
1.203 19
0.695 200.159 211.203 220.695 23-0.159 24
FF=
BARRA 8
-0.00007951 19-0.00004875 20
0.00001570 21-0.00006334 22-0.00002436 230.00006331 24
0.00000246 19-0.00009323 20
0.00001570 21-0.00001057 22-0.00006703 230.00006331 24
7.87982122 191.45163275 200.08441956 21-7.87982122 221.32676725 23-0.04105377 24
Desplazamientos locales en cada barra: D' = L. D
D=
D'=
Fuerzas locales (internas) en cada barra: F' = k' . D'+FF'
Barra 9
E 2.10E+07 Tnf/m2A 0.02m2L 0.6946mIz 6.67E-05 m4phi -80.00 °
Matriz de rigidez en coordenadas locales23 24 22 23 24
0.00 0.00 19 604664.56 0.00 0.00-50130.84 17410.44 20 0.00 50130.84 17410.44-17410.44 4031.10 21 k'= 0.00 17410.44 8062.19
0.00 0.00 22 -604664.56 0.00 0.0050130.84 -17410.44 23 0.00 -50130.84 -17410.44-17410.44 8062.19 24 0.00 17410.44 4031.10
Matriz de transformación0.000 0.000 L= 0.17 -0.985 0.0000.000 0.000 0.985 0.174 0.0000.000 0.000 0.000 0.000 1.000-0.866 0.000 0.000 0.000 0.0000.500 0.000 0.000 0.000 0.0000.000 1.000 0.000 0.000 0.000
Matriz de rigidez en coordenadas globales23 24 22 23 24
240120.144 15077.883 19 66852.073 -94830.851 17145.936-466031.125 8705.220 20 -94830.851 587943.317 3023.291-8705.220 4031.097 21 k= 17145.936 3023.291 8062.194-240120.144 -15077.883 22 -66852.073 94830.851 -17145.936466031.125 -8705.220 23 94830.851 -587943.317 -3023.291-8705.220 8062.194 24 17145.936 3023.291 4031.097
Fuerzas de fijación en coordenadas locales
0.000 22
1.389 230.159 240.000 291.389 30-0.159 25
FF'=
Fuerzas de fijación en coordenadas globales FF = LT.FF'
1.368 22
0.241 230.159 241.368 290.241 30-0.159 25
FF=
BARRA 9
-0.00006334 22-0.00002436 23
0.00006331 240.00000000 290.00000000 300.00013186 25
0.00001300 22-0.00006661 23
0.00006331 240.00000000 290.00000000 300.00013186 25
7.85839098 221.44830419 230.04105377 24-7.85839098 291.33009581 30-2.2593E-14 25
Desplazamientos locales en cada barra: D' = L. D
D=
D'=
Fuerzas locales (internas) en cada barra: F' = k' . D'+FF' Fuerzas locales (internas) en cada barra: F' = k' . D'+FF'
29 30 25-604664.56 0.00 0.00 22
0.00 -50130.84 17410.44 230.00 -17410.44 4031.10 24
604664.56 0.00 0.00 290.00 50130.84 -17410.44 300.00 -17410.44 8062.19 25
0.000 0.000 0.0000.000 0.000 0.0000.000 0.000 0.0000.174 -0.985 0.0000.985 0.174 0.0000.000 0.000 1.000
29 30 25-66852.073 94830.851 17145.936 2294830.851 -587943.317 3023.291 23-17145.936 -3023.291 4031.097 2466852.073 -94830.851 -17145.936 29-94830.851 587943.317 -3023.291 30-17145.936 -3023.291 8062.194 25
Fuerzas de fijación en coordenadas globales FF = LT.FF'
Fuerzas locales (internas) en cada barra: F' = k' . D'+FF'
R 2180
N 9TETA 20 0
BARRA X Z TETA1 2 0 Z12 1.879385242 20 Z23 1.532088886 40 Z34 1 60 Z45 0.347296355 80 Z56 -0.34729636 100 Z67 -1 120 Z78 -1.53208889 140 Z89 -1.87938524 160 Z910 -2 180 Z10
31 2 0 Z3132 -0.73624911 111.6 Z3233 -0.85155858 115.2 Z3334 -0.96350735 118.8 Z3435 -1.07165359 122.4 Z3536 -1.1755705 126 Z3637 -1.27484798 129.6 Z3738 -1.36909421 133.2 Z3839 -1.45793725 136.8 Z3940 -1.54102649 140.4 Z4041 -1.61803399 144 Z4142 -1.68865585 147.6 Z4243 -1.75261336 151.2 Z4344 -1.8096541 154.8 Z4445 -1.85955297 158.4 Z4546 -1.90211303 162 Z4647 -1.93716632 165.6 Z4748 -1.9645745 169.2 Z48
49 -1.9842294 172.8 Z4950 -1.99605346 176.4 Z5051 -2 180 Z51
00.6840402871.2855752191.7320508081.9696155061.9696155061.7320508081.2855752190.6840402872.44929E-16
01.8595529721.8096541051.752613361.6886558511.6180339891.5410264861.4579372551.3690942121.2748479791.1755705051.071653590.9635073480.8515585830.7362491050.6180339890.4973797740.374762629
0.2506664670.125581039
0
