Ejercicio de Aplicacion en Estructura Discreta - Terrones Vera Christian
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Análisis Matricial. Datos. Dimensiones y Cargas de la Estructura. Enumeración de Grados de libertad y Elementos.
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DESARROLLO DE UNA ESTRUCTURA DISCRETA POR EL MÉTODO MATRICIAL
Transcript of Ejercicio de Aplicacion en Estructura Discreta - Terrones Vera Christian
Anlisis Matricial.Datos.Dimensiones y Cargas de la Estructura.
Enumeracin de Grados de libertad y Elementos.
Sistema de Coordenadas y Numeracin de los Nudos.
Tabla de Datos.
Atbka
ElementoNudoL (cm)A (cmE (Tn/cm)I (cm)SenCosAE/L12EI/L6EI/L4EI/L2EI/L
Inicial Final
112316,2289002106750071,5650,9490,316597,6705,379850,5179301,143389650,57167
223316,2289002106750071,5650,9490,316597,6705,379850,5179301,143389650,57167
33440012002101600000016306,31260336000168000
454316,22890021067500108,4350,949-0,316597,6705,379850,5179301,143389650,57167
52560015002103125000015253,6461093,75437500218750
665316,22890021067500108,4350,949-0,316597,6705,379850,5179301,143389650,57167
Matriz de Rigidez de los Elementos de Coordenadas Globales a Locales.
Elemento 1
597,670477800-597,670477800
05,3790343850,50-5,3790343850,5
K'=0850,5179301,14330-850,589650,57167
-597,670477800597,670477800
0-5,3790343-850,505,3790343-850,5
0850,589650,571670-850,5179301,1433
0,3162277660,94868330000
-0,9486832980,316227770000
R=001000
0000,3162277660,9486832980
000-0,9486832980,3162277660
000001
1895670-189-5670
-5,1031,701850,55,103-1,701850,5
K'R=-806,855145268,951715179301,1433806,855145-268,95171589650,57167
-189-56701895670
5,103-1,701-850,5-5,1031,701-850,5
-806,855145268,95171589650,57167806,855145-268,951715179301,1433
64,60817865177,687433-806,855145-64,60817865-177,687433-806,85514513
177,687433538,441333268,951715-177,687433-538,4413334268,95171514
K=RK'R=-806,855145268,951715179301,1433806,855145-268,95171589650,5716715
-64,60817865-177,687433806,85514564,60817865177,687433806,8551451
-177,687433-538,441333-268,951715177,687433538,4413334-268,9517152
-806,855145268,95171589650,57167806,855145-268,951715179301,14333
131415123
Elemento 2
597,670477800-597,670477800
05,3790343850,50-5,3790343850,5
K'=0850,5179301,14330-850,589650,57167
-597,670477800597,670477800
0-5,3790343-850,505,3790343-850,5
0850,589650,571670-850,5179301,1433
00,9486832980000
-0,94868329800000
R=001000
00000,9486832980
000-0,94868329800
000001
1895670-189-5670
-5,1031,701850,55,103-1,701850,5
K'R=-806,855145268,951715179301,1433806,855145-268,95171589650,57167
-189-56701895670
5,103-1,701-850,5-5,1031,701-850,5
-806,855145268,95171589650,57167806,855145-268,951715179301,1433
64,60817865177,687433-806,855145-64,60817865-177,687433-806,8551451
177,687433538,4413334268,951715-177,687433-538,4413334268,9517152
K=RK'R=-806,855145268,951715179301,1433806,855145-268,95171589650,571673
-64,60817865-177,687433806,85514564,60817865177,687433806,8551454
-177,687433-538,4413334-268,951715177,687433538,4413334-268,9517155
-806,855145268,95171589650,57167806,855145-268,951715179301,14336
123456
Elemento 3
63000-63000
06,312600-6,31260
K'=012603360000-1260168000
-6300063000
0-6,3-126006,3-1260
012601680000-1260336000
100000
010000
R=001000
000100
000010
000001
63000-63000
06,312600-6,31260
K'R=012603360000-1260168000
-6300063000
0-6,3-126006,3-1260
012601680000-1260336000
63000-630004
06,312600-6,312605
K=RK'R=012603360000-12601680006
-63000630007
0-6,3-126006,3-12608
012601680000-12603360009
456789
Elemento 4
597,670477800-597,670477800
05,3790343850,50-5,3790343850,5
K'=0850,5179301,14330-850,589650,57167
-597,670477800597,670477800
0-5,3790343-850,505,3790343-850,5
0850,589650,571670-850,5179301,1433
00,94868330000
-0,94868329800000
R=001000
000010
000-100
000001
-1895670189-5670
-5,103-1,701850,55,1031,701850,5
K'R=-806,855145-268,951715179301,1433806,855145268,95171589650,57167
189-5670-1895670
5,1031,701-850,5-5,103-1,701-850,5
-806,855145-268,95171589650,57167806,855145268,951715179301,1433
64,60817865-177,687433-806,855145-64,60817865177,687433-806,85514510
-177,687433538,441333-268,951715177,687433-538,4413334-268,95171511
K=RK'R=-806,855145-268,951715179301,1433806,855145268,95171589650,5716712
-64,60817865177,687433806,85514564,60817865-177,687433806,8551457
177,687433-538,441333268,951715-177,687433538,4413334268,9517158
-806,855145-268,95171589650,57167806,855145268,951715179301,14339
101112789
Elemento 5
52500-52500
03,6458333331093,750-3,6458333331093,75
K'=01093,754375000-1093,75218750
-5250052500
0-3,645833333-1093,7503,645833333-1093,75
01093,752187500-1093,75437500
100000
010000
R=001000
000100
000010
000001
52500-52500
03,6458333331093,750-3,6458333331093,75
K'R=01093,754375000-1093,75218750
-5250052500
0-3,645833333-1093,7503,645833333-1093,75
01093,752187500-1093,75437500
52500-525001
03,6458333331093,750-3,6458333331093,752
K=RK'R=01093,754375000-1093,752187503
-525005250010
0-3,645833333-1093,7503,645833333-1093,7511
01093,752187500-1093,7543750012
123101112
Elemento 6
597,670477800-597,670477800
05,3790343850,50-5,3790343850,5
K'=0850,5179301,14330-850,589650,57167
-597,670477800597,670477800
0-5,3790343-850,505,3790343-850,5
0850,589650,571670-850,5179301,1433
-0,3162277660,9486832980000
-0,948683298-0,3162277660000
R=001000
000-0,3162277660,9486832980
000-0,948683298-0,3162277660
000001
-1895670189-5670
-5,103-1,701850,55,1031,701850,5
K'R=-806,855145-268,951715179301,1433806,855145268,95171589650,57167
189-5670-1895670
5,1031,701-850,5-5,103-1,701-850,5
-806,855145-268,95171589650,57167806,855145268,951715179301,1433
64,60817865-177,687433-806,855145-64,60817865177,687433-806,85514516
-177,687433538,4413334-268,951715177,687433-538,4413334-268,95171517
K=RK'R=-806,855145-268,951715179301,1433806,855145268,95171589650,5716718
-64,60817865177,687433806,85514564,60817865-177,687433806,85514510
177,687433-538,4413334268,951715-177,687433538,4413334268,95171511
-806,855145-268,95171589650,57167806,855145268,951715179301,143312
161718101112
Matriz de Rigidez de la Estructura.
123456789101112131415161718
1654,216355,3750-64,608-177,687-806,855000-52500-64,608-177,687806,855000
2355,3751080,5291093,750-177,687-538,441268,9520000-3,6461093,75-177,687-538,441-268,952000
301093,750796102,287806,855-268,95289650,5720000-1093,75218750-806,855268,95289650,572000
4-64,608-177,687806,855694,608177,687806,855-63000000000000
5-177,687-538,441-268,952177,687544,741991,0480-6,31260000000000
6-806,855268,95289650,572806,855991,048515301,1430-1260168000000000000
7000-63000694,608-177,687806,855-64,608177,687806,855000000
80000-6,3-1260-177,687544,741-991,048177,687-538,441268,952000000
900001260168000806,855-991,048515301,143-806,855-268,95289650,572000000
10-52500000-64,608177,687-806,855654,216-355,3750000-64,608177,687806,855
110-3,646-1093,750000177,687-538,441-268,952-355,3751080,529-1093,75000177,687-538,441268,952
1201093,750218750,000000806,855268,95289650,5720-1093,750796102,287000177,687-268,95289650,572
13-64,608-177,687-806,85500000000064,608177,687-806,855000
14-177,687-538,441268,952000000000177,687538,441268,952000
15806,855-268,95289650,572000000000-806,855268,952179301,143000
16000000000-64,608177,687-806,85500064,608-177,687-806,855
17000000000177,687-538,441-268,952000-177,687538,441-268,952
18000000000806,855268,95289650,572000-806,855-268,952179301,143
Matriz .
123456789101112
0,0738988-0,0239962-0,00000990,0603710-0,01945790,00009140,06036800,01945780,00008890,07295500,0236845-0,00000951
-0,02399620,00964430,0000015-0,01878600,0078981-0,0000330-0,0187846-0,0060399-0,0000319-0,0236845-0,00768380,00000052
-0,00000990,00000150,0000015-0,00007790,0000243-0,0000003-0,0000769-0,00002240,0000002-0,0000095-0,0000005-0,00000033
0,0603710-0,0187860-0,00007790,1273830-0,04029730,00007030,12659110,04003420,00007210,06036800,0187846-0,00007694
-0,01945790,00789810,0000243-0,04029730,0164271-0,0000284-0,0400342-0,0126231-0,0000300-0,0194578-0,00603990,00002245
KLL=0,0000914-0,0000330-0,00000030,0000703-0,00002840,00000240,00007210,0000300-0,00000060,00008890,00003190,00000026
0,0603680-0,0187846-0,00007690,1265911-0,04003420,00007210,12738300,04029730,00007030,06037100,0187860-0,00007797
0,0194578-0,0060399-0,00002240,0400342-0,01262310,00003000,04029730,01642710,00002840,01945790,0078981-0,00002438
0,0000889-0,00003190,00000020,0000721-0,0000300-0,00000060,00007030,00002840,00000240,00009140,0000330-0,00000039
0,0729550-0,0236845-0,00000950,0603680-0,01945780,00008890,06037100,01945790,00009140,07389880,0239962-0,000009910
0,0236845-0,0076838-0,00000050,0187846-0,00603990,00003190,01878600,00789810,00003300,02399620,0096443-0,000001511
-0,00000950,0000005-0,0000003-0,00007690,00002240,0000002-0,0000779-0,0000243-0,0000003-0,0000099-0,00000150,000001512
Calculo de Vectores de Carga en los Elementos.Elemento 5.
Calculo del Vector P en Coordenadas Globales.f1=0Tn001
f2=9Tn9-92
f3=900,000Tn-cmF=900,000P=-R F=-900,0003
f10=0Tn0010
f11=9Tn9-911
f12=-900,000Tn-cm-900,000900,00012
Voladizo.
Calculo del Vector P en Coordenadas Globales.f10=0Tn00
f11=4,5TnF=4,5P=-4,5
f12=337,5Tn-cm337,5-337,5
Elemento 3.
Calculo del Vector P en Coordenadas Globales.f1=0Tn001
f2=4Tn4-42
f3=266,667Tn-cmF=266,6666667P=-R F=-266,6666673
f10=0Tn0010
f11=4Tn4-411
f12=-266,667Tn-cm-266,6666667266,66666712
Voladizo.
Calculo del Vector P en Coordenadas Globales.f10=0Tn00
f11=3TnF=3P=-3
f12=225Tn-cm225-225
Resumen de Acciones en los Nudos.
Determinacin de los Desequilibrantes en los Nudos .
310,3442973331
-92-0,1319151722
-900,0003-0,0017905753
540,6255343714
-45-0,2296886585
Q=-266,66666676DL=KLL Q=9,8316E-056
070,6166957777
-780,1414576798
41,6666666790,0003430219
0100,3346370210
-13,5110,06523760411
562,500120,00075799612
Calculo del Vector de Reacciones en los Apoyos .123456789101112
-64,608-177,687-806,85500000000013
-177,687-538,441268,95200000000014
Kr=806,855-268,95289650,57200000000015
000000000-64,608177,687-806,85516
000000000177,687-538,441-268,95217
000000000806,855268,95289650,57218
2,63997925413
9,36969375114
Qr=Kr DL152,750828515
-10,6399792516
24,1303062517
355,504172618
Calculo en Coordenadas Globales del Vector .
Elemento 1
131415123
64,6081786177,687433-806,855145-64,60817865-177,687433-806,855145130130132,63997925413
177,687433538,4413334268,951715-177,687433-538,4413334268,951715140140149,36969375114
K=-806,855145268,951715179301,1433806,855145-268,95171589650,5716715d=015p=015q=152,750828515
-64,6081786-177,687433806,85514564,60817865177,687433806,85514510,344297333101-2,6399792541
-177,687433-538,4413334-268,951715177,687433538,4413334-268,9517152-0,131915172202-9,3696937512
-806,855145268,95171589650,57167806,855145-268,951715179301,14333-0,001790575303-7,7752296483
Elemento 2
123456
64,6081786177,687433-806,855145-64,60817865-177,687433-806,85514510,3442973331010,5683145921
177,687433538,4413334268,951715-177,687433-538,4413334268,9517152-0,1319151722022,2178626382
-806,855145268,951715179301,1433806,855145-268,95171589650,571673-0,001790575303-59,024130173
K=-64,6081786-177,687433806,85514564,60817865177,687433806,8551454d=0,6255343714p=04q=-0,5683145924
-177,687433-538,4413334-268,951715177,687433538,4413334-268,9517155-0,229688658505-2,2178626385
-806,855145268,95171589650,57167806,855145-268,951715179301,143369,8316E-05606110,31601636
Elemento 3
456789
63000-6300040,6255343714045,5683145924
06,312600-6,312605-0,2296886585-452,2178626385
K=012603360000-126016800069,8316E-056-266,66666676-110,31601636
-63000630007d=0,6166957777p=07q=-5,5683145927
0-6,3-126006,3-126080,1414576798-485,7821373628
012601680000-126033600090,0003430219266,66666679-602,53892849
Elemento 4
101112789
64,6081786-177,687433-806,855145-64,60817865177,687433-806,855145100,3346370210010-5,56831459210
-177,687433538,4413334-268,951715177,687433-538,4413334-268,951715110,065237604110118,78213736211
K=-806,855145-268,951715179301,1433806,855145268,95171589650,5716712d=0,00075799612p=012q=414,741713112
-64,6081786177,687433806,85514564,60817865-177,687433806,85514570,6166957777075,5683145927
177,687433-538,4413334268,951715-177,687433538,4413334268,95171580,141457679808-8,7821373628
-806,855145-268,95171589650,57167806,855145268,951715179301,143390,000343021909377,53892849
Elemento 5
123101112
52500-5250010,3442973331015,0716646621
03,6458333331093,750-3,6458333331093,752-0,1319151722-927,1518311132
K=01093,754375000-1093,752187503d=-0,0017905753p=-9003q=66,799359823
-5250052500100,3346370210010-5,07166466210
0-3,645833333-1093,7503,645833333-1093,75110,06523760411-91110,8481688911
01093,752187500-1093,75437500120,0007579961290012-1175,70069212
Elemento 6
161718101112
64,6081786-177,687433-806,855145-64,60817865177,687433-806,85514516016016-10,6399792516
-177,687433538,4413334-268,951715177,687433-538,4413334-268,9517151701701724,1303062517
K=-806,855145-268,951715179301,1433806,855145268,95171589650,5716718d=018p=018q=355,504172618
-64,6081786177,687433806,85514564,60817865-177,687433806,855145100,334637021001010,6399792510
177,687433-538,4413334268,951715-177,687433538,4413334268,951715110,06523760411011-24,1303062511
-806,855145-268,95171589650,57167806,855145268,951715179301,1433120,00075799612012423,458978812
Calculo en Coordenadas Locales del Vector .Elemento 100,94868329800002,639979254139,72370671213
-0,94868330,31622776600009,369693751140,45845309714
R=001000q=152,750828515q'=152,750828515
0000,3162277660,9486832980-2,6399792541-9,7237067121
000-0,9486832980,3162277660-9,3696937512-0,4584530972
000001-7,7752296483-7,7752296483
Elemento 200,94868329800000,56831459212,2837660961
-0,94868330,31622776600002,21786263820,1621991862
R=001000q=-59,024130173q'=-59,024130173
0000,3162277660,9486832980-0,5683145924-2,2837660964
000-0,9486832980,3162277660-2,2178626385-0,1621991865
000001110,31601636110,31601636
Elemento 31000005,56831459245,5683145924
0100002,21786263852,2178626385
R=001000q=-110,31601636q'=-110,31601636
000100-5,5683145927-5,5683145927
0000105,78213736285,7821373628
000001-602,53892849-602,53892849
Elemento 400,9486832980000-5,5683145921010,0923227210
-0,9486833-0,31622776600008,782137362112,50541137311
R=001000q=414,741713112q'=414,741713112
000-0,3162277660,94868329805,5683145927-10,092322727
000-0,948683298-0,3162277660-8,7821373628-2,5054113738
000001377,53892849377,53892849
Elemento 51000005,07166466215,0716646621
0100007,15183111327,1518311132
R=001000q=66,799359823q'=66,799359823
000100-5,07166466210-5,07166466210
00001010,848168891110,8481688911
000001-1175,70069212-1175,70069212
Elemento600,9486832980000-10,639979251626,2566753816
-0,9486833-0,316227766000024,13030625172,46329777217
R=001000q=355,504172618q'=355,504172618
000-0,3162277660,948683298010,6399792510-26,2566753810
000-0,948683298-0,3162277660-24,1303062511-2,46329777211
000001423,458978812423,458978812
Coordenadas Locales.
