TÉCNICAS DE ESTUDIO Preparación del Examen Durante el Examen Después del examen Trucos Test.
examen
125
ENSAMBLADO DE MATRIZ DE RIGIDEZ Pórtico con carga puntual 1.- Ingr!o " "ato! Barra Di#n!ion! " la !cción Ara M. " inrcia Mo". Ela!tici"a Longitu" Angulo ntr $ b h A f'c E L α m m m ° 1 0.3 0.5 0.15 0.003125 210 2173706.511928 5 0 2 0.4 0.4 0.16 0.0021333333 210 2173706.511928 5 90 '.- Matri( " rigi"( " )arra n coor"na"a! local! *.- EA/L 0 0 (-1) EA/L 0 0 0 0 0 4EI/L 0 2EI/L k (-1) EA/L 0 0 EA/L 0 0 T 0 0 0 2EI/L 0 4EI/L 4 5 6 1 2 3 65211.19535785 0 0 -65211.1953579 0 0 4 0 652.1119535785 1630.279883946 0 -652.111953579 1630.2798839465 0 1630.279883946 5434.266279821 0 -1630.27988395 2717.1331399116 T1 k1 -65211.1953579 0 0 65211.19535785 0 0 1 0 -652.111953579 -1630.27988395 0 652.1119535785 -1630.279883952 0 1630.279883946 2717.133139911 0 -1630.27988395 5434.2662798213 1 2 3 7 8 9 69558.60838171 0 0 -69558.6083817 0 0 1 0 445.1750936429 1112.937734107 0 -445.175093643 1112.9377341072 0 1112.937734107 3709.792447025 0 -1112.93773411 1854.8962235123 T2 k2 -69558.6083817 0 0 69558.60838171 0 0 7 0 -445.175093643 -1112.93773411 0 445.1750936429 -1112.937734118 0 1112.937734107 1854.896223512 0 -1112.93773411 3709.7924470259 I = bh 3 /12 m 2 m 4 k/cm 2 T!/m 2 12EI/L 3 6 EI/L 2 (-1) 12EI/L 3 6 EI/L 2 6EI/L 2 (-1) 6EI/L 2 (-1) 12EI/L 3 (-1) 6 EI/L 2 12EI/L 3 (-1) 6 EI/L 2 6EI/L 2 (-1) 6EI/L 2
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Ejemplo 1ENSAMBLADO DE MATRIZ DE RIGIDEZPrtico con carga puntual1.-Ingreso de datos
BarraDimensiones de la seccinAreaM. de inerciaMod. ElasticidadLongitudAngulo entre x y XbhAI = bh3/12f'cELmmm2m4kg/cm2Tn/m2mrad10.30.50.150.0031252102173706.5119284250020.40.40.160.00213333332102173706.511928425901.5707963268
2.-Matriz de rigidez de barra en coordenadas locales3.-Matriz de transformacin4.-Matriz de rigidez de barra en coordenadas globales5.-Ensamblaje de Matriz de rigidez en coordenadas globales6.-Obteniendo los desplazamientos y recciones en coordenadas globales7.-Obteniendo los desplazamientos en coordenadas locales8.-Obteniendo las fuerzas en coordenadas localesEA/L00(-1) EA/L00cossin0000{u} = [T]T {U]{f} = [k] {u]012EI/L36 EI/L20(-1) 12EI/L36 EI/L2(-1) sincos000006EI/L24EI/L0(-1) 6EI/L22EI/L001000k(-1) EA/L00 EA/L00T000cossin00(-1) 12EI/L3(-1) 6 EI/L2012EI/L3(-1) 6 EI/L2000(-1) sincos006EI/L22EI/L0(-1) 6EI/L24EI/L000001
Barra 1Barra 2Barra 1Barra 245612345612312345678965211.195357852500-65211.195357852500410000010000065211.195357852500-65211.19535785250065211.195357852500-65211.195357852500465656.3704514954-01112.9377341074-65211.195357852500-445.175093642901112.9377341074165656.3704514954-01112.9377341074F10.000Tn0.0000152624-0.0000000433-0.0000018653D1-0.0000186534m0404-0.00001865341-0.000025551811.2161Axial-1.7771Axial0652.11195357851630.27988394630-652.11195357851630.279883946350100000100000652.11195357851630.27988394630-652.11195357851630.27988394630652.11195357851630.27988394630-652.11195357851630.27988394635-070210.7203352878-1630.27988394630-652.1119535785-1630.27988394630-69558.608381709302KLL-070210.7203352878-1630.2798839463Fuezas actuantesF20.000TnKLL-1-0.00000004330.00001430220.0000025552DesplazamientosD20.0000255518mU105u105U20.00002555182u2-0.00001865342f11.7772Cortantef21.2162Cortante01630.27988394635434.2662798210-1630.27988394632717.13313991056T1001000T1T001000T1 k101630.27988394635434.2662798210-1630.27988394632717.1331399105K1 =T1 k1 T1T01630.27988394635434.2662798210-1630.27988394632717.133139910561112.9377341074-1630.27988394639144.058726845501630.27988394632717.1331399105-1112.9377341074-01854.896223512231112.9377341074-1630.27988394639144.0587268455F310.000Tn-m-0.00000186530.00000255520.0001100432D30.0011004322rad06060.001100432230.001100432232.9483Momento4.0623Momentok1-65211.19535785250065211.1953578525001000100000100-65211.19535785250065211.195357852500-65211.19535785250065211.1953578525001-65211.19535785250065211.1953578525000004-65211.195357852500F41.216Tn-0.00001865341-0.000018653410707-1.2164Axial1.7777Axial0-652.1119535785-1630.27988394630652.1119535785-1630.279883946320000100000100-652.1119535785-1630.27988394630652.1119535785-1630.27988394630-652.1119535785-1630.27988394630652.1119535785-1630.27988394632K0-652.11195357851630.27988394630652.11195357851630.279883946300050-652.11195357851630.2798839463F51.777Tn0.000025551820.000025551820808-1.7775Cortante-1.2168Cortante01630.27988394632717.13313991050-1630.27988394635434.266279821300000100000101630.27988394632717.13313991050-1630.27988394635434.26627982101630.27988394632717.13313991050-1630.27988394635434.26627982130-1630.27988394632717.133139910501630.27988394635434.2662798210006KRL0-1630.27988394632717.1331399105ReaccionesF62.948Tn-m0.001100432230.0011004322309095.9386Momento2.0209Momento-445.17509364290-1112.9377341074000445.1750936429-0-1112.93773410747-445.17509364290-1112.9377341074F7-1.216Tn0-69558.6083817093-0000-069558.6083817093-080-69558.6083817093-0F8-1.777Tn1112.937734107401854.8962235122000-1112.9377341074-03709.792447024591112.937734107401854.8962235122F92.020Tn-m12378912378969558.608381709300-69558.60838170930010100000-100000445.17509364291112.9377341074-0-445.17509364291112.9377341074445.1750936429-01112.9377341074-445.175093642901112.937734107410445.17509364291112.93773410740-445.17509364291112.93773410742-100000100000-69558.60838170930069558.6083817093-00-069558.608381709300-69558.60838170930201112.93773410743709.79244702450-1112.93773410741854.89622351223T2001000T2T001000T2 k201112.93773410743709.79244702450-1112.93773410741854.8962235122K2 =T2 k2 T2T1112.937734107403709.7924470245-1112.9377341074-01854.89622351223k2-69558.60838170930069558.60838170930070000100000-10-0-445.1750936429-1112.93773410740445.1750936429-1112.9377341074-445.17509364290-1112.9377341074445.1750936429-0-1112.937734107470-445.1750936429-1112.93773410740445.1750936429-1112.93773410748000-10000010069558.6083817093-0-0-69558.60838170930-00-69558.6083817093-0-069558.6083817093-0801112.93773410741854.89622351220-1112.93773410743709.7924470245900000100000101112.93773410741854.89622351220-1112.93773410743709.79244702451112.937734107401854.8962235122-1112.9377341074-03709.79244702459
Elemplo 2ENSAMBLADO DE MATRIZ DE RIGIDEZPrtico de una crujia con cargas puntuales1.-Ingreso de datosDatos del perfil AISC - LRFD
BarraDimensiones de la seccinAreaM. de inerciaMod. ElasticidadLongitudAngulo entre x y XbhAI = bh3/12FyELPerfilAreaAreaInerciaInerciammm2m4kg/cm2Tn/m2mradin2m2in4m410.01935480.00150675782530200000004-90-1.5707963268W27x102300.019354836200.001506757820.0104515920.0005619124253020000000800W24x5516.20.01045159213500.000561912430.01935480.00150675782530200000004901.5707963268W27x102300.019354836200.0015067578
2.-Matriz de rigidez de barra en coordenadas locales3.-Matriz de transformacin4.-Matriz de rigidez de barra en coordenadas globales5.-Ensamblaje de Matriz de rigidez en coordenadas globales6.-Obteniendo los desplazamientos y recciones en coordenadas globales7.-Obteniendo los desplazamientos en coordenadas locales8.-Obteniendo las fuerzas en coordenadas localesEA/L00(-1) EA/L00cossin0000{u} = [T]T {U]{f} = [k] {u]012EI/L36 EI/L20(-1) 12EI/L36 EI/L2(-1) sincos000006EI/L24EI/L0(-1) 6EI/L22EI/L001000k(-1) EA/L00 EA/L00T000cossin00(-1) 12EI/L3(-1) 6 EI/L2012EI/L3(-1) 6 EI/L2000(-1) sincos006EI/L22EI/L0(-1) 6EI/L24EI/L000001
Barra 1Barra 2Barra 1Barra 21011121231011121231234567891011121234569677400-967740040-100000100000-5650.34160252-11300.68320504-05650.34160252-11300.683205045650.341602520-11300.68320504-5650.34160252-0-11300.683205041031779.32160252011300.68320504-26128.9800000-5650.34160252-011300.68320504131779.32160252011300.68320504-26128.98001F120.000Tn0.00022339710.0000013606-0.00006600080.0002048895-0.0000013606-0.0000596523D10.0045m01010.004510.00448154741-2.6211Axial9.6721Axial05650.3416025211300.683205040-5650.3416025211300.683205045100000-1000009677400-96774-000967740-0-96774011097037.39644901251053.585796050-263.39644901251053.58579605000-0-96774-02KLL097037.39644901251053.585796050-263.39644901251053.585796052Fuezas actuantesFLF20.000TnKLL-10.00000136060.0000103201-0.00000068030.00000136060.0000000132-0.0000006803D20.0000mU102u102U20.00002u20.00002707942f110.3282Cortantef2-2.6212Cortante011300.6832050430135.155213440-11300.6832050415067.577606726T1001000T1T001000T1 k1011300.6832050430135.155213440-11300.6832050415067.57760672K1 =T1 k1 T1T-11300.68320504030135.1552134411300.68320504-015067.577606721211300.683205041053.5857960535754.279459040-1053.585796052809.5621228000-11300.68320504015067.57760672311300.683205041053.5857960535754.279459040-1053.585796052809.56212283F30.000Tn-m-0.0000660008-0.00000068030.000047679-0.00005965230.00000068030.0000151475DesplazamientosD3-0.0013rad0303-0.00133-0.0013268182330.6533Momento-10.6613Momentok1-9677400967740010000-10000010-05650.3416025211300.683205040-5650.3416025211300.68320504-5650.34160252-011300.683205045650.34160252011300.683205041-26128.980031779.32160252-011300.68320504-5650.34160252011300.683205040004-26128.980031779.32160252-011300.683205045F40.000Tn0.00020488950.0000013606-0.00005965230.0002233971-0.0000013606-0.0000660008D40.0041m0.004540.000027079440.004170.004111396172.6214Axial-9.6727Axial0-5650.34160252-11300.6832050405650.34160252-11300.683205042000100000-100-96774-0-0967740-0-0-96774-0096774-02K0-263.3964490125-1053.58579605-097037.3964490125-1053.585796050-96774000050-263.3964490125-1053.58579605-097037.3964490125-1053.585796056F5-10.000Tn-0.00000136060.00000001320.0000006803-0.00000136060.00001032010.0000006803D5-0.0001m0.00005-0.00448154745-0.00018-0.00013041298-10.3285Cortante2.6218Cortante011300.6832050415067.577606720-11300.6832050430135.155213443000001000001011300.6832050415067.577606720-11300.6832050430135.15521344-11300.68320504015067.5776067211300.68320504-030135.15521344301053.585796052809.562122811300.68320504-1053.5857960535754.27945904-11300.68320504-015067.57760672000601053.585796052809.562122811300.68320504-1053.5857960535754.279459046F60.000Tn-m-0.0000596523-0.00000068030.0000151475-0.00006600080.00000068030.000047679D6-0.0012rad-0.00136-0.00132681826-0.00129-0.001199849910.6616Momento-10.3049Momento000-5650.341602520-11300.683205045650.34160252-0-11300.683205040007000-5650.341602520-11300.683205047F7-9.67Tn0000-96774-0-096774-000080000-96774-08F812.62Tn00011300.68320504015067.57760672-11300.68320504-030135.155213440009KRL00011300.68320504015067.577606729ReaccionesFRF928.38Tn-m123456123456-5650.34160252-0-11300.683205040000005650.341602520-11300.6832050410-5650.34160252-0-11300.6832050400010F10-10.33Tn26128.9800-26128.9800110000010000026128.9800-26128.980026128.9800-26128.98001-0-967740000000096774011-0-96774000011F11-2.62Tn0263.39644901251053.585796050-263.39644901251053.5857960520100000100000263.39644901251053.585796050-263.39644901251053.585796050263.39644901251053.585796050-263.39644901251053.58579605211300.68320504-015067.57760672000000-11300.68320504030135.155213441211300.68320504-015067.5776067200012F1230.65Tn-m01053.585796055619.12424560-1053.585796052809.56212283T2001000T2T001000T2 k201053.585796055619.12424560-1053.585796052809.5621228K2 =T2 k2 T2T01053.585796055619.12424560-1053.585796052809.56212283k2-26128.980026128.98004000100000100-26128.980026128.9800-26128.980026128.980040-263.3964490125-1053.585796050263.3964490125-1053.5857960550000100000100-263.3964490125-1053.585796050263.3964490125-1053.585796050-263.3964490125-1053.585796050263.3964490125-1053.58579605501053.585796052809.56212280-1053.585796055619.1242456600000100000101053.585796052809.56212280-1053.585796055619.124245601053.585796052809.56212280-1053.585796055619.124245664567894567899677400-967740040100000-1000005650.3416025211300.68320504-0-5650.3416025211300.683205045650.34160252-011300.68320504-5650.34160252011300.68320504405650.3416025211300.683205040-5650.3416025211300.683205045-100000100000-967740096774-00-09677400-9677405011300.6832050430135.155213440-11300.6832050415067.577606726T3001000T2T001000T3 k3011300.6832050430135.155213440-11300.6832050415067.57760672K3 =T3 k3 T3T11300.68320504030135.15521344-11300.68320504-015067.577606726k3-9677400967740070000100000-10-0-5650.34160252-11300.6832050405650.34160252-11300.68320504-5650.341602520-11300.683205045650.34160252-0-11300.6832050470-5650.34160252-11300.6832050405650.34160252-11300.683205048000-10000010096774-0-0-967740-00-96774-0-096774-08011300.6832050415067.577606720-11300.6832050430135.155213449000001000001011300.6832050415067.577606720-11300.6832050430135.1552134411300.68320504015067.57760672-11300.68320504-030135.155213449
Ejemplo 3ENSAMBLADO DE MATRIZ DE RIGIDEZ PARA ESTRUCTURAS CON CARGAS EN LAS BARRASPrtico con carga puntual y carga uniformemente repartida w=1 Tn/m1.-Ingreso de datos
BarraDimensiones de la seccinAreaM. de inerciaMod. ElasticidadLongitudAngulo entre x y XbhAI = bh3/12f'cELmmm2m4kg/cm2Tn/m2mradEII/A10.250.910.22750.015699395864500012901.570796326810126.11031250.06900833330.069444444420.250.910.22750.01569939586450001200
2.-Matriz de rigidez de barra en coordenadas locales3.-Matriz de transformacin4.-Matriz de rigidez de barra en coordenadas globales5.-Ensamblaje de Matriz de rigidez en coordenadas globales6.-Identificando la matriz de rigidez KLL y KRL7.-Determinando las fuerzas en los nudos8.-Obteniendo los desplazamientos en coordenadas globales9.-Obteniendo los desplazamientos en coordenadas locales10.-Obteniendo las fuerzas en coordenadas locales11.-Fuerzas internas en las barras en coordenadas locales12.-Determinacin de las recciones13.-Recciones totalesEA/L00(-1) EA/L00cossin0000{UL} = [KLL]-1{FL}{u} = [T]T {U]{fL} = [k] {u]{f} ={fL} + {fE}{RL} = [KRL] {UL]{R} = {RL} +{RE}012EI/L36 EI/L20(-1) 12EI/L36 EI/L2(-1) sincos000006EI/L24EI/L0(-1) 6EI/L22EI/L001000k(-1) EA/L00 EA/L00T000cossin00(-1) 12EI/L3(-1) 6 EI/L2012EI/L3(-1) 6 EI/L2000(-1) sincos006EI/L22EI/L0(-1) 6EI/L24EI/L000001Fuerzas de empotramiento en coordenadasBarra 1Barra 2Barra 1Barra 2Barra 1Barra 2 globales para cada gdl restringido1234561234561234567894691.-Momentos de empotramiento para carga puntualFuerzas de empotramiento en cada barra en coord. LocalFuerzas de empotramiento en cada barra en coord. GlobalFuerzas de empotramiento en nudos en coord. GlobalFuerzas en nudos en coord. GlobalFuerzas L en nudos en coord. Global12228.12500-12228.1250010100000-10000070.3202105035421.9212630208-0-70.3202105035421.921263020870.3202105035-0421.9212630208-70.32021050350421.9212630208170.3202105035-0421.9212630208-70.32021050350421.9212630208000112298.4452105035-421.9212630208040.00008151080.0000058222-0.0000029111Carga actuanteP8Tn{FE}= [T]{f}{FL}= {F}-{FE}F44.000TnD40.0001804883m01010.000180488340.00018048834-0.0001Axial2.2074Axial-0.0001Axial2.2074AxialF1-1.793Tn-4.0001-5.793Tn1070.3202105035421.92126302080-70.3202105035421.92126302082-100000100000-12228.1250012228.125-00-012228.12500-12228.12502-012228.12500-12228.12500002KLL-421.92126302086750.74020833331687.68505208336KLL-10.00000582220.0001697095-0.0000848547a6m0Tn1-4Tn1-4Tn10Tn14Tn1Fuezas actuantesF6-24.000TnDesplazamientosD6-0.0042194481m{U1}02{u1}02{U2}05{u2}05{fL1}-1.7932Cortante{fL2}-0.6405Cortante{f1}-5.7932Cortante{f2}5.3605CortanteF20.000Tn-0.0002-0.000Tn20421.92126302083375.37010416670-421.92126302081687.68505208333T1001000T1T001000T1 k10421.92126302083375.37010416670-421.92126302081687.6850520833K1 =T1 k1 T1T421.921263020803375.3701041667-421.9212630208-01687.68505208333421.921263020803375.3701041667-421.9212630208-01687.6850520833000301687.68505208333375.37010416679-0.0000029111-0.00008485470.0003386912b6m-4Tn2-0Tn2-0Tn20Tn20Tn2F92.000Tn-mD90.0027022517rad0303-0.00421944816-0.00421944816-7.1973Momento-9.6826Momento-19.1973Momento2.3186Momento{RL}F3-7.197Tn-m{RE}-12.0003{R}-19.197Tn-m3k1-12228.1250012228.1250040000100000-10-0-70.3202105035-421.9212630208070.3202105035-421.9212630208-70.32021050350-421.921263020870.3202105035-0-421.92126302084-70.32021050350-421.921263020812298.4452105035-0-421.9212630208-12228.125004-70.3202105035421.921263020801LongitudL12m{fE1}-12Tn-m3{FE1}-12Tn-m3{FE}-12Tn-m3{F}0Tn-m3{FL}12Tn-m30.000180488340407070.0004Axial-2.2077Axial0.0004Axial-2.2077AxialF5-0.640Tn6.00055.360Tn50-70.3202105035-421.9212630208070.3202105035-421.92126302085000-10000010012228.125-0-0-12228.1250-00-12228.125-0-012228.125-05K0-12228.125-0-012298.4452105035421.92126302080-70.3202105035421.921263020850002CorteV4Tn0Tn4-4Tn4-4Tn40Tn44Tn4050.0001804883508081.7935Cortante0.6408Cortante-2.2075Cortante6.6408CortanteF7-2.207Tn0.0007-2.207Tn70421.92126302081687.68505208330-421.92126302083375.370104166760000010000010421.92126302081687.68505208330-421.92126302083375.3701041667421.921263020801687.6850520833-421.9212630208-03375.37010416676421.921263020801687.6850520833-421.9212630208421.92126302086750.74020833330-421.92126302081687.68505208336KRL-421.92126302081687.685052083303MomentoM12Tn-m-4Tn5-0Tn56Tn50Tn5-6Tn5-0.00421944816-0.004219448160.002702251790.00270225179-14.3186Momento2.0009Momento-2.3186Momento-10.0009MomentoF80.640Tn6.00086.640Tn8000-12228.1250012228.125007-0421.9212630208421.9212630208512Tn-m612Tn-m624Tn-m60Tn-m6-24Tn-m60000-70.3202105035-421.9212630208070.3202105035-421.92126302088-12228.1250070Tn70Tn70Tn70000421.92126302081687.68505208330-421.92126302083375.370104166790-421.9212630208-421.921263020882.-Momentos de empotramiento para carga distribuida6Tn80Tn8-6Tn8456789456789Carga actuanteq1Tn/m0Tn40Tn4-12Tn-m9-10Tn-m92Tn-m912228.12500-12228.12500410000010000012228.12500-12228.1250012228.12500-12228.1250046Tn56Tn5070.3202105035421.92126302080-70.3202105035421.92126302085010000010000070.3202105035421.92126302080-70.3202105035421.9212630208070.3202105035421.92126302080-70.3202105035421.92126302085{fE2}12Tn-m6{FE2}12Tn-m60421.92126302083375.37010416670-421.92126302081687.68505208336T2001000T2T001000T2 k20421.92126302083375.37010416670-421.92126302081687.6850520833K2 =T2 k2 T2T0421.92126302083375.37010416670-421.92126302081687.68505208336LongitudL12m0Tn70Tn7k2-12228.1250012228.125007000100000100-12228.1250012228.12500-12228.1250012228.125007CorteV6Tn6Tn86Tn80-70.3202105035-421.9212630208070.3202105035-421.921263020880000100000100-70.3202105035-421.9212630208070.3202105035-421.92126302080-70.3202105035-421.9212630208070.3202105035-421.92126302088MomentoM12Tn-m-12Tn-m9-12Tn-m90421.92126302081687.68505208330-421.92126302083375.370104166790000010000010421.92126302081687.68505208330-421.92126302083375.37010416670421.92126302081687.68505208330-421.92126302083375.37010416679
Elemplo 4ENSAMBLADO DE MATRIZ DE RIGIDEZPrtico de una crujia con carga uniformemente repartida w=1 Tn/m1.-Ingreso de datosDatos del perfil AISC - LRFD
BarraDimensiones de la seccinAreaM. de inerciaMod. ElasticidadLongitudAngulo entre x y XbhAI = bh3/12FyELPerfilAreaAreaInerciaInerciammm2m4kg/cm2Tn/m2mradin2m2in4m410.06250.00011194662802000000014.14213562-45-0.7853981634W27x102300.019354836200.001506757820.30.021118752807937253.9331000W24x5516.20.01045159213500.000561912430.30.021118752807937253.9331000W27x102300.019354836200.0015067578
2.-Matriz de rigidez de barra en coordenadas locales3.-Matriz de transformacin4.-Matriz de rigidez de barra en coordenadas globales5.-Ensamblaje de Matriz de rigidez en coordenadas globales6.-Obteniendo los desplazamientos en coordenadas globales7.-Determinando las fuerzas en los nudos8.-Obteniendo los desplazamientos en coordenadas globales9.-Obteniendo los desplazamientos en coordenadas locales10.-Obteniendo las fuerzas en coordenadas locales11.-Fuerzas internas en las barras en coordenadas locales12.-Determinacin de las recciones13.-Recciones totalesEA/L00(-1) EA/L00cossin0000{UL} = [KLL]-1{FL}{u} = [T]T {U]{fL} = [k] {u]{f} ={fL} + {fE}{RL} = [KRL] {UL]{R} = {RL} +{RE}012EI/L36 EI/L20(-1) 12EI/L36 EI/L2(-1) sincos000006EI/L24EI/L0(-1) 6EI/L22EI/L001000k(-1) EA/L00 EA/L00T000cossin00(-1) 12EI/L3(-1) 6 EI/L2012EI/L3(-1) 6 EI/L2000(-1) sincos006EI/L22EI/L0(-1) 6EI/L24EI/L000001Fuerzas de empotramiento en coordenadasBarra 1Barra 2Barra 3Barra 1Barra 2Barra 3Barra 1Barra 2Barra 3 globales para cada gdl restringido101112123101112123123456789101112123456121.-Momentos de empotramiento para carga puntualFuerzas de empotramiento en cada barra en coord. LocalFuerzas de empotramiento en cada barra en coord. GlobalFuerzas de empotramiento en nudos en coord. GlobalFuerzas en nudos en coord. GlobalFuerzas L en nudos en coord. Global88388.347671636900-88388.34767163690040.7071067812-0.707106781200000.70710678120.7071067812000062500.0000164886-6.7167968813-47.4949262138-62500.00001648866.7167968813-47.494926213844198.923328441144189.4243431958-47.4949262138-44198.9233284411-44189.4243431958-47.494926213810-44236.9192694096-44151.4284022273585.7707564696-6000000047.49492621381Carga actuanteP0Tn{FE}= [T]{f}{FL}= {F}-{FE}F10.000TnD1ERROR:#VALUE!m010ERROR:#VALUE!10ERROR:#VALUE!1ERROR:#VALUE!4ERROR:#VALUE!4ERROR:#VALUE!4ERROR:#VALUE!10AxialERROR:#VALUE!1AxialERROR:#VALUE!4AxialERROR:#VALUE!10AxialERROR:#VALUE!1AxialERROR:#VALUE!1AxialF7ERROR:#VALUE!Tn0.0007ERROR:#VALUE!Tn109.498985245367.16796879540-9.498985245367.167968795450.70710678120.70710678120000-0.70710678120.7071067812000062500.00001648866.716796881347.4949262138-62500.0000164886-6.716796881347.494926213844189.424343195844198.923328441147.4949262138-44189.4243431958-44198.923328441147.494926213811520434.15930844144189.424343195847.4949262138-60000000-60000000-44198.9233284411-44189.424343195847.49492621381KLL-47.494926213847.4949262138316.63284134170-5068.5-25342.5-47.49492621382a0m0Tn100Tn100Tn10Tn10Tn1Fuezas actuantesF2-4.000TnDesplazamientosD2ERROR:#VALUE!m{U1}011{u1}ERROR:#VALUE!11{U2}ERROR:#VALUE!2{u2}ERROR:#VALUE!5{U3}ERROR:#VALUE!5{u3}ERROR:#VALUE!5{fL1}ERROR:#VALUE!11Cortante{fL2}ERROR:#VALUE!2Cortante{fL3}ERROR:#VALUE!5Cortante{f1}ERROR:#VALUE!11Cortante{f2}ERROR:#VALUE!2Cortante{f3}ERROR:#VALUE!2CortanteF8ERROR:#VALUE!Tn0.0008ERROR:#VALUE!Tn2067.1679687954633.26568268340-67.1679687954316.63284134176T1001000T1T001000T1 k1067.1679687954633.26568268340-67.1679687954316.6328413417K1 =T1 k1 T1T-47.494926213847.4949262138633.265682683447.4949262138-47.4949262138316.63284134171244189.424343195848221.9204843821-47.49492621380-5068.5-25342.50-5068.5-25342.5-44189.4243431958-44198.9233284411-47.49492621382000025342.584475316.63284134173b0m0Tn110Tn114Tn20Tn2-4Tn2F3-5.333Tn-mD3ERROR:#VALUE!rad012ERROR:#VALUE!12ERROR:#VALUE!3ERROR:#VALUE!6ERROR:#VALUE!6ERROR:#VALUE!6ERROR:#VALUE!12MomentoERROR:#VALUE!3MomentoERROR:#VALUE!6MomentoERROR:#VALUE!12MomentoERROR:#VALUE!3MomentoERROR:#VALUE!3Momento{RL}F9ERROR:#VALUE!Tn-m{RE}0.0009{R}ERROR:#VALUE!Tn-m3k1-88388.34767163690088388.34767163690010000.7071067812-0.707106781200000.70710678120.70710678120-62500.00001648866.716796881347.494926213862500.0000164886-6.716796881347.4949262138-44198.9233284411-44189.424343195847.494926213844198.923328441144189.424343195847.4949262138147.4949262138-47.4949262138134733.170880718025342.584475025342.584475-47.494926213847.4949262138316.63284134173-600000006000000005LongitudL8m{fE1}0Tn-m12{FE1}0Tn-m12{FE}5.3333333333Tn-m3{F}0Tn-m3{FL}-5.3333333333Tn-m3F40.000TnD4ERROR:#VALUE!mERROR:#VALUE!1ERROR:#VALUE!1ERROR:#VALUE!4ERROR:#VALUE!70.000007ERROR:#VALUE!7ERROR:#VALUE!1AxialERROR:#VALUE!4AxialERROR:#VALUE!7AxialERROR:#VALUE!1AxialERROR:#VALUE!4AxialERROR:#VALUE!4AxialF10ERROR:#VALUE!Tn0.00010ERROR:#VALUE!Tn50-9.4989852453-67.167968795409.4989852453-67.167968795420000.70710678120.70710678120000-0.70710678120.70710678120-62500.0000164886-6.7167968813-47.494926213862500.00001648866.7167968813-47.4949262138-44189.4243431958-44198.9233284411-47.494926213844189.424343195844198.9233284411-47.49492621382K-6000000060000000-476235.235980000040-5068.5-25342.505068.5-25342.506CorteV0Tn0Tn10Tn10Tn40Tn40Tn4F5-4.000TnD5ERROR:#VALUE!mERROR:#VALUE!2ERROR:#VALUE!2ERROR:#VALUE!5ERROR:#VALUE!80.000008ERROR:#VALUE!8ERROR:#VALUE!2CortanteERROR:#VALUE!5CortanteERROR:#VALUE!8CortanteERROR:#VALUE!2CortanteERROR:#VALUE!5CortanteERROR:#VALUE!5CortanteF11ERROR:#VALUE!Tn0.00011ERROR:#VALUE!Tn7067.1679687954316.63284134170-67.1679687954633.26568268343000001000001067.1679687954316.63284134170-67.1679687954633.2656826834-47.494926213847.4949262138316.632841341747.4949262138-47.4949262138633.265682683430-5068.5-25342.505068.5-25342.50-4022.997155941-20114.98577970530005-47.494926213847.4949262138316.6328413417000633.265682683412MomentoM0Tn-m0Tn20Tn24Tn50Tn5-4Tn5F65.333Tn-mD6ERROR:#VALUE!radERROR:#VALUE!3ERROR:#VALUE!3ERROR:#VALUE!6ERROR:#VALUE!90.000009ERROR:#VALUE!9ERROR:#VALUE!3MomentoERROR:#VALUE!6MomentoERROR:#VALUE!9MomentoERROR:#VALUE!3MomentoERROR:#VALUE!6MomentoERROR:#VALUE!6MomentoF12ERROR:#VALUE!Tn0.00012ERROR:#VALUE!Tn8025342.5844750-25342.5168950020114.985779705367049.95259901750006-60000000-476235.2359800070Tn-m30Tn-m3-5.3333333333Tn-m60Tn-m65.3333333333Tn-m6-60000000-476235.23598006000000000070-5068.5-25342.50-4022.997155941-20114.985779705308ERROR:#VALUE!ERROR:#VALUE!ERROR:#VALUE!ERROR:#VALUE!ERROR:#VALUE!ERROR:#VALUE!ERROR:#VALUE!0Tn70Tn70Tn70-5068.5-25342.50-4022.997155941-20114.985779705305068.525342.500080KRL025342.584475020114.985779705367049.952599017509ERROR:#VALUE!ERROR:#VALUE!ERROR:#VALUE!ERROR:#VALUE!ERROR:#VALUE!ERROR:#VALUE!ERROR:#VALUE!2.-Momentos de empotramiento para carga distribuida0Tn80Tn80Tn8123456789123025342.584475020114.985779705367049.9525990175025342.51689500009-44198.9233284411-44189.424343195847.4949262138000-47.4949262138ERROR:#VALUE!ERROR:#VALUE!ERROR:#VALUE!ERROR:#VALUE!ERROR:#VALUE!ERROR:#VALUE!ERROR:#VALUE!Carga actuanteq1Tn/m0Tn10Tn10Tn-m90Tn-m90Tn-m9238117.6179900-238117.61799001100000100000238117.6179900-238117.6179900238117.6179900-238117.61799007-44198.9233284411-44189.424343195847.494926213800000044198.923328441144189.4243431958-47.494926213810-44189.4243431958-44198.9233284411-47.494926213800047.4949262138ERROR:#VALUE!ERROR:#VALUE!ERROR:#VALUE!ERROR:#VALUE!ERROR:#VALUE!ERROR:#VALUE!ERROR:#VALUE!4Tn24Tn20Tn100Tn100Tn1002011.498577970510057.49288985260-2011.498577970510057.4928898526201000001000002011.498577970510057.49288985260-2011.498577970510057.492889852602011.498577970510057.49288985260-2011.498577970510057.49288985268-44189.4243431958-44198.9233284411-47.494926213800000044189.424343195844198.923328441147.494926213811ERROR:#VALUE!ERROR:#VALUE!ERROR:#VALUE!ERROR:#VALUE!ERROR:#VALUE!ERROR:#VALUE!ERROR:#VALUE!{fE2}5.3333333333Tn-m3{FE2}5.3333333333Tn-m30Tn110Tn110Tn11010057.492889852667049.95259901750-10057.492889852633524.97629950883T2001000T2T001000T2 k2010057.492889852667049.95259901750-10057.492889852633524.9762995088K2 =T2 k2 T2T010057.492889852667049.95259901750-10057.492889852633524.97629950889-47.494926213847.4949262138316.6328413417000000-47.494926213847.4949262138633.265682683412ERROR:#VALUE!ERROR:#VALUE!ERROR:#VALUE!ERROR:#VALUE!ERROR:#VALUE!ERROR:#VALUE!ERROR:#VALUE!LongitudL8m0Tn40Tn40Tn-m120Tn-m120Tn-m12k2-238117.6179900238117.61799004000100000100-238117.6179900238117.6179900-238117.6179900238117.61799001ERROR:#VALUE!ERROR:#VALUE!ERROR:#VALUE!ERROR:#VALUE!ERROR:#VALUE!ERROR:#VALUE!ERROR:#VALUE!CorteV4Tn4Tn54Tn50-2011.4985779705-10057.492889852602011.4985779705-10057.492889852650000100000100-2011.4985779705-10057.492889852602011.4985779705-10057.49288985260-2011.4985779705-10057.492889852602011.4985779705-10057.49288985262MomentoM5.3333333333Tn-m-5.3333333333Tn-m6-5.3333333333Tn-m6010057.492889852633524.97629950880-10057.492889852667049.95259901756000001000001010057.492889852633524.97629950880-10057.492889852667049.9525990175010057.492889852633524.97629950880-10057.492889852667049.952599017530Tn40Tn40Tn50Tn5{fE3}0Tn-m6{FE3}0Tn-m64567891234560Tn70Tn7238117.6179900-238117.61799004100000100000238117.6179900-238117.6179900238117.6179900-238117.617990010Tn80Tn802011.498577970510057.49288985260-2011.498577970510057.4928898526501000001000002011.498577970510057.49288985260-2011.498577970510057.492889852602011.498577970510057.49288985260-2011.498577970510057.492889852620Tn-m90Tn-m9010057.492889852667049.95259901750-10057.492889852633524.97629950886T3001000T2T001000T3 k3010057.492889852667049.95259901750-10057.492889852633524.9762995088K3 =T3 k3 T3T010057.492889852667049.95259901750-10057.492889852633524.97629950883k3-238117.6179900238117.61799007000100000100-238117.6179900238117.6179900-238117.6179900238117.617990040-2011.4985779705-10057.492889852602011.4985779705-10057.492889852680000100000100-2011.4985779705-10057.492889852602011.4985779705-10057.49288985260-2011.4985779705-10057.492889852602011.4985779705-10057.49288985265010057.492889852633524.97629950880-10057.492889852667049.95259901759000001000001010057.492889852633524.97629950880-10057.492889852667049.9525990175010057.492889852633524.97629950880-10057.492889852667049.95259901756
Elemplo 5ENSAMBLADO DE MATRIZ DE RIGIDEZPrtico de una crujia a dos aguas empotrado1.-Ingreso de datosDatos del perfil AISC - LRFD
BarraDimensiones de la seccinAreaM. de inerciaMod. ElasticidadLongitudAngulo entre x y XbhAI = bh3/12FyELPerfilAreaAreaInerciaInerciammm2m4kg/cm2Tn/m2mradin2m2in4m410.03387090.00292194462530200000006-90-1.5707963268W27x17852.50.033870970200.002921944620.0129677160.00076170352530200000006.185-14.036-0.2449744138W24x6820.10.01296771618300.000761703530.0129677160.00076170352530200000006.18514.0360.2449744138W24x6820.10.01296771618300.000761703540.03387090.00292194462530200000006901.5707963268W27x17852.50.033870970200.00292194462.-Matriz de rigidez de barra en coordenadas locales3.-Matriz de transformacin4.-Matriz de rigidez de barra en coordenadas globales5.-Ensamblaje de Matriz de rigidez en coordenadas globales6.-Obteniendo los desplazamientos y recciones en coordenadas globales7.-Obteniendo los desplazamientos en coordenadas locales8.-Obteniendo las fuerzas en coordenadas localesEA/L00(-1) EA/L00cossin0000{u} = [T]T {U]{f} = [k] {u]012EI/L36 EI/L20(-1) 12EI/L36 EI/L2(-1) sincos000006EI/L24EI/L0(-1) 6EI/L22EI/L001000k(-1) EA/L00 EA/L00T000cossin00(-1) 12EI/L3(-1) 6 EI/L2012EI/L3(-1) 6 EI/L2000(-1) sincos006EI/L22EI/L0(-1) 6EI/L24EI/L000001
Barra 1Barra 2Barra 1Barra 213141512313141512312345678910111213141512345678911290300-11290300130-100000100000-3246.60511968-9739.81535904-03246.60511968-9739.815359043246.605119680-9739.81535904-3246.60511968-0-9739.815359041342758.29433351689684.58700135989160.3120078785-39511.6892138368-9684.5870013598-579.5033511615000000-3246.60511968-09739.81535904142758.29433351689684.58700135989160.3120078785-39511.6892138368-9684.5870013598-579.50335116150001F10.000Tn0.00045456630.000000954-0.00008935080.00041783810.00011280910.00004354880.0003793487-0.000000954-0.0000859495D10.00215m01010.002110.00208431791-0.6101Axial-2.3141Axial03246.605119689739.815359040-3246.605119689739.8153590414100000-10000011290300-112903-0001129030-0-1129030149684.5870013598116096.7446230052318.0552677455-9684.5870013598-3193.74462300462318.0552677455000000-0-112903-02KLL9684.5870013598116096.7446230052318.0552677455-9684.5870013598-3193.74462300462318.05526774550002Fuezas actuantesFLF20.000TnKLL-10.0000009540.0000088526-0.0000003180.00000205690.0000044286-0.00000094680.0000009540.0000000046-0.000000318D20.00001mU102u102U20.00002u2-0.00051550422f12.2332Cortantef2-0.0502Cortante09739.8153590438959.261436160-9739.8153590419479.6307180815T1001000T1T001000T1 k109739.8153590438959.261436160-9739.8153590419479.63071808K1 =T1 k1 T1T-9739.81535904038959.261436169739.81535904-019479.63071808159160.31200787852318.055267745548811.5299418738579.5033511615-2318.05526774554926.1342528569000000-9739.81535904019479.6307180839160.31200787852318.055267745548811.5299418738579.5033511615-2318.05526774554926.13425285690003F30.000Tn-m-0.0000893508-0.0000003180.0000399028-0.00008794370.0000025991-0.0000145163-0.00008594950.0000003180.0000185307DesplazamientosD3-0.00049rad0303-0.00053-0.0004864743311.4363Momento-1.9603Momentok1-112903001129030010000-10000010-03246.605119689739.815359040-3246.605119689739.81535904-3246.60511968-09739.815359043246.6051196809739.815359041-39511.6892138368-9684.5870013598579.503351161579023.378427673601159.006702323-39511.68921383689684.5870013598579.50335116150000004-39511.6892138368-9684.5870013598579.503351161579023.378427673601159.006702323-39511.68921383689684.5870013598579.50335116154F40.000Tn0.00041783810.0000020569-0.00008794370.0004316607-00.00004267490.0004178381-0.0000020569-0.0000879437D40.00236m0.002140.000005399740.002470.002139498170.6104Axial2.3147Axial0-3246.60511968-9739.8153590403246.60511968-9739.815359042000100000-100-112903-0-01129030-0-0-112903-00112903-02K-9684.5870013598-3193.7446230046-2318.055267745506387.489246009109684.5870013598-3193.74462300462318.05526774550000005-9684.5870013598-3193.7446230046-2318.055267745506387.489246009109684.5870013598-3193.74462300462318.05526774555F50.000Tn0.00011280910.00000442860.000002599100.0005049491-0-0.00011280910.0000044286-0.0000025991D5-0.00064m0.00005-0.00214711355-0.00068-0.00119301458-2.2335Cortante0.0508Cortante09739.8153590419479.630718080-9739.8153590438959.26143616300000100000109739.8153590419479.630718080-9739.8153590438959.26143616-9739.81535904019479.630718089739.81535904-038959.261436163-579.50335116152318.05526774554926.13425285691159.006702323019704.5370114276-579.5033511615-2318.05526774554926.13425285690000006-579.50335116152318.05526774554926.13425285691159.006702323019704.5370114276-579.5033511615-2318.05526774554926.13425285696F60.000Tn-m0.0000435488-0.0000009468-0.00001451630.0000426749-00.0000582820.00004354880.0000009468-0.0000145163D60.00025rad-0.00056-0.000486474360.000290.000246486391.9606Momento1.6519Momento000-39511.68921383689684.5870013598-579.503351161542758.2943335168-9684.58700135989160.3120078785-3246.6051196809739.815359040007000-39511.68921383689684.5870013598-579.503351161542758.2943335168-9684.58700135989160.31200787857F75.660Tn0.00037934870.000000954-0.00008594950.0004178381-0.00011280910.00004354880.0004545663-0.000000954-0.0000893508D70.00257m0009684.5870013598-3193.7446230046-2318.0552677455-9684.5870013598116096.744623005-2318.05526774550-112903000080009684.5870013598-3193.7446230046-2318.0552677455-9684.5870013598116096.744623005-2318.05526774558F80.000Tn-0.0000009540.00000000460.000000318-0.00000205690.00000442860.0000009468-0.0000009540.00000885260.000000318D8-0.00001m000579.50335116152318.05526774554926.13425285699160.3120078785-2318.055267745548811.5299418738-9739.81535904-019479.630718080009000579.50335116152318.05526774554926.13425285699160.3120078785-2318.055267745548811.52994187389F90.000Tn-m-0.0000859495-0.0000003180.0000185307-0.0000879437-0.0000025991-0.0000145163-0.00008935080.0000003180.0000399028D9-0.00051rad123456123456000000-3246.605119680-9739.815359043246.60511968-0-9739.8153590400010000000-3246.605119680-9739.8153590410F10-3.427Tn41932.792239288600-41932.79223928860010.9701435307-0.242531502600000.97014353070.2425315026000040680.827117117-187.3899276189-579.5033511615-40680.827117117187.3899276189-579.503351161539511.68921383689684.5870013598-579.5033511615-39511.6892138368-9684.5870013598-579.503351161510000000-112903-0-0112903-0000110000000-112903-011F110.610Tn0772.64159755272389.39414043180-772.64159755272389.394140431820.24253150260.97014353070000-0.24253150260.9701435307000010170.0231096386749.5732474522318.0552677455-10170.0231096386-749.5732474522318.05526774559684.58700135983193.74462300462318.0552677455-9684.5870013598-3193.74462300462318.055267745520000009739.81535904019479.63071808-9739.81535904-038959.26143616000120000009739.81535904019479.6307180812ReaccionesFRF1215.208Tn-m02389.39414043189852.26850571380-2389.39414043184926.13425285693T2001000T2T001000T2 k202389.39414043189852.26850571380-2389.39414043184926.1342528569K2 =T2 k2 T2T-579.50335116152318.05526774559852.2685057138579.5033511615-2318.05526774554926.13425285693-3246.60511968-0-9739.815359040000000003246.605119680-9739.8153590413KRL-3246.60511968-0-9739.8153590400000013F13-2.233Tnk2-41932.79223928860041932.79223928860040000.9701435307-0.242531502600000.97014353070.24253150260-40680.827117117187.3899276189579.503351161540680.827117117-187.3899276189579.5033511615-39511.6892138368-9684.5870013598579.503351161539511.68921383689684.5870013598579.50335116154-0-11290300000000000112903014-0-112903000000014F14-0.610Tn0-772.6415975527-2389.39414043180772.6415975527-2389.394140431850000.24253150260.97014353070000-0.24253150260.97014353070-10170.0231096386-749.573247452-2318.055267745510170.0231096386749.573247452-2318.0552677455-9684.5870013598-3193.7446230046-2318.05526774559684.58700135983193.7446230046-2318.055267745559739.81535904-019479.63071808000000000-9739.81535904038959.26143616159739.81535904-019479.6307180800000015F1511.436Tn-m02389.39414043184926.13425285690-2389.39414043189852.2685057138600000100000102389.39414043184926.13425285690-2389.39414043189852.2685057138-579.50335116152318.05526774554926.1342528569579.5033511615-2318.05526774559852.2685057138645678945678941932.792239288600-41932.79223928860040.97014353070.242531502600000.9701435307-0.2425315026000040680.827117117187.3899276189579.5033511615-40680.827117117-187.3899276189579.503351161539511.6892138368-9684.5870013598579.5033511615-39511.68921383689684.5870013598579.503351161540772.64159755272389.39414043180-772.64159755272389.39414043185-0.24253150260.970143530700000.24253150260.97014353070000-10170.0231096386749.5732474522318.055267745510170.0231096386-749.5732474522318.0552677455-9684.58700135983193.74462300462318.05526774559684.5870013598-3193.74462300462318.0552677455502389.39414043189852.26850571380-2389.39414043184926.13425285696T3001000T3T001000T3 k302389.39414043189852.26850571380-2389.39414043184926.1342528569K3 =T3 k3 T3T579.50335116152318.05526774559852.2685057138-579.5033511615-2318.05526774554926.13425285696k3-41932.79223928860041932.79223928860070000.97014353070.242531502600000.9701435307-0.24253150260-40680.827117117-187.3899276189-579.503351161540680.827117117187.3899276189-579.5033511615-39511.68921383689684.5870013598-579.503351161539511.6892138368-9684.5870013598-579.503351161570-772.6415975527-2389.39414043180772.6415975527-2389.39414043188000-0.24253150260.970143530700000.24253150260.9701435307010170.0231096386-749.573247452-2318.0552677455-10170.0231096386749.573247452-2318.05526774559684.5870013598-3193.7446230046-2318.0552677455-9684.58700135983193.7446230046-2318.0552677455802389.39414043184926.13425285690-2389.39414043189852.2685057138900000100000102389.39414043184926.13425285690-2389.39414043189852.2685057138579.50335116152318.05526774554926.1342528569-579.5033511615-2318.05526774559852.2685057138978910111278910111211290300-1129030070100000-1000003246.605119689739.81535904-0-3246.605119689739.815359043246.60511968-09739.81535904-3246.6051196809739.81535904703246.605119689739.815359040-3246.605119689739.815359048-100000100000-11290300112903-00-011290300-1129030809739.8153590438959.261436160-9739.8153590419479.630718089T4001000T4T001000T4 k409739.8153590438959.261436160-9739.8153590419479.63071808K4 =T4 k4 T4T9739.81535904038959.26143616-9739.81535904-019479.630718089k4-1129030011290300100000100000-10-0-3246.60511968-9739.8153590403246.60511968-9739.81535904-3246.605119680-9739.815359043246.60511968-0-9739.81535904100-3246.60511968-9739.8153590403246.60511968-9739.8153590411000-100000100112903-0-0-1129030-00-112903-0-0112903-01109739.8153590419479.630718080-9739.8153590438959.261436161200000100000109739.8153590419479.630718080-9739.8153590438959.261436169739.81535904019479.63071808-9739.81535904-038959.2614361612
Elemplo 6ENSAMBLADO DE MATRIZ DE RIGIDEZPrtico de una crujia a dos aguas apoyado1.-Ingreso de datosDatos del perfil AISC - LRFD
BarraDimensiones de la seccinAreaM. de inerciaMod. ElasticidadLongitudAngulo entre x y XbhAI = bh3/12FyELPerfilAreaAreaInerciaInerciammm2m4kg/cm2Tn/m2mradin2m2in4m410.03387090.00292194462530200000006-90-1.5707963268W27x17852.50.033870970200.002921944620.0129677160.00076170352530200000006.185-14.036-0.2449744138W24x6820.10.01296771618300.000761703530.0129677160.00076170352530200000006.18514.0360.2449744138W24x6820.10.01296771618300.000761703540.03387090.00292194462530200000006901.5707963268W27x17852.50.033870970200.00292194462.-Matriz de rigidez de barra en coordenadas locales3.-Matriz de transformacin4.-Matriz de rigidez de barra en coordenadas globales5.-Ensamblaje de Matriz de rigidez en coordenadas globales6.-Obteniendo los desplazamientos y recciones en coordenadas globales7.-Obteniendo los desplazamientos en coordenadas locales8.-Obteniendo las fuerzas en coordenadas localesEA/L00(-1) EA/L00cossin0000{u} = [T]T {U]{f} = [k] {u]012EI/L36 EI/L20(-1) 12EI/L36 EI/L2(-1) sincos000006EI/L24EI/L0(-1) 6EI/L22EI/L001000k(-1) EA/L00 EA/L00T000cossin00(-1) 12EI/L3(-1) 6 EI/L2012EI/L3(-1) 6 EI/L2000(-1) sincos006EI/L22EI/L0(-1) 6EI/L24EI/L000001
Barra 1Barra 2Barra 1Barra 213141512313141512312345678910111213141512345678911290300-11290300130-100000100000-3246.60511968-9739.81535904-03246.60511968-9739.815359043246.605119680-9739.81535904-3246.60511968-0-9739.815359041342758.29433351689684.58700135989160.3120078785-39511.6892138368-9684.5870013598-579.5033511615000000-3246.60511968-09739.81535904142758.29433351689684.58700135989160.3120078785-39511.6892138368-9684.5870013598-579.50335116150001F10.000Tn0.00310363230.0000044283-0.00040344750.00306123250.00014343870.0002021440.0030106571-0.0000044283-0.000410258-0.0005475353-0.0005741843D10.01704m01010.017010.01653763431-2.8301Axial-3.1341Axial03246.605119689739.815359040-3246.605119689739.8153590414100000-10000011290300-112903-0001129030-0-1129030149684.5870013598116096.7446230052318.0552677455-9684.5870013598-3193.74462300462318.0552677455000000-0-112903-02KLL9684.5870013598116096.7446230052318.0552677455-9684.5870013598-3193.74462300462318.05526774550002Fuezas actuantesFLF20.000TnKLL-10.00000442830.0000088572-0.00000073810.00000553550.0000044286-0.00000073810.00000442830-0.0000007381-0.0000007381-0.0000007381D20.00003mU102u102U20.00002u2-0.00410849822f132.7072Cortantef2-2.1342Cortante09739.8153590438959.261436160-9739.8153590419479.6307180815T1001000T1T001000T1 k109739.8153590438959.261436160-9739.8153590419479.63071808K1 =T1 k1 T1T-9739.81535904038959.261436169739.81535904-019479.63071808159160.31200787852318.055267745548811.5299418738579.5033511615-2318.05526774554926.1342528569000000-9739.81535904019479.6307180839160.31200787852318.055267745548811.5299418738579.5033511615-2318.05526774554926.13425285690003F30.000Tn-m-0.0004034475-0.00000073810.0000814311-0.00040753410.0000202131-0.0000336907-0.0004102580.00000073810.00005418650.00007547120.0000601464DesplazamientosD3-0.00232rad0303-0.00233-0.00232206033120.7373Momento-15.1353Momentok1-112903001129030010000-10000010-03246.605119689739.815359040-3246.605119689739.81535904-3246.60511968-09739.815359043246.6051196809739.815359041-39511.6892138368-9684.5870013598579.503351161579023.378427673601159.006702323-39511.68921383689684.5870013598579.50335116150000004-39511.6892138368-9684.5870013598579.503351161579023.378427673601159.006702323-39511.68921383689684.5870013598579.50335116154F40.000Tn0.00306123250.0000055355-0.00040753410.0030782661-00.00020146270.0030612325-0.0000055355-0.0004075341-0.0005615411-0.0005615411D40.01733m0.017040.000025064440.017370.016612363172.8304Axial3.1347Axial0-3246.60511968-9739.8153590403246.60511968-9739.815359042000100000-100-112903-0-01129030-0-0-112903-00112903-02K-9684.5870013598-3193.7446230046-2318.055267745506387.489246009109684.5870013598-3193.74462300462318.05526774550000005-9684.5870013598-3193.7446230046-2318.055267745506387.489246009109684.5870013598-3193.74462300462318.05526774555F50.000Tn0.00014343870.00000442860.0000202131-00.0006106135-0-0.00014343870.0000044286-0.00002021310.0000459662-0.0000459662D5-0.00081m0.00005-0.01704031925-0.00088-0.00498986428-32.7075Cortante2.1348Cortante09739.8153590419479.630718080-9739.8153590438959.26143616300000100000109739.8153590419479.630718080-9739.8153590438959.26143616-9739.81535904019479.630718089739.81535904-038959.261436163-579.50335116152318.05526774554926.13425285691159.006702323019704.5370114276-579.5033511615-2318.05526774554926.13425285690000006-579.50335116152318.05526774554926.13425285691159.006702323019704.5370114276-579.5033511615-2318.05526774554926.13425285696F60.000Tn-m0.000202144-0.0000007381-0.00003369070.0002014627-00.00006780880.0002021440.0000007381-0.0000336907-0.0000336907-0.0000336907D60.00114rad-0.00236-0.002322060360.001190.0011441352975.5046Momento1.9399Momento000-39511.68921383689684.5870013598-579.503351161542758.2943335168-9684.58700135989160.3120078785-3246.6051196809739.815359040007000-39511.68921383689684.5870013598-579.503351161542758.2943335168-9684.58700135989160.31200787857F75.660Tn0.00301065710.0000044283-0.0004102580.0030612325-0.00014343870.0002021440.0031036323-0.0000044283-0.0004034475-0.0005741843-0.0005475353D70.01757m0009684.5870013598-3193.7446230046-2318.0552677455-9684.5870013598116096.744623005-2318.05526774550-112903000080009684.5870013598-3193.7446230046-2318.0552677455-9684.5870013598116096.744623005-2318.05526774558F80.000Tn-0.000004428300.0000007381-0.00000553550.00000442860.0000007381-0.00000442830.00000885720.00000073810.00000073810.0000007381D8-0.00003m000579.50335116152318.05526774554926.13425285699160.3120078785-2318.055267745548811.5299418738-9739.81535904-019479.630718080009000579.50335116152318.05526774554926.13425285699160.3120078785-2318.055267745548811.52994187389F90.000Tn-m-0.000410258-0.00000073810.0000541865-0.0004075341-0.0000202131-0.0000336907-0.00040344750.00000073810.00008143110.00006014640.0000754712D9-0.00228rad123456123456000000-3246.605119680-9739.815359043246.60511968-0-9739.8153590400010000000-3246.605119680-9739.8153590410F120.000Tn-0.00-0.00000073810.0000754712-0.00056154110.0000459662-0.0000336907-0.00057418430.00000073810.00006014640.00013914070.0000991482D12-0.00325rad41932.792239288600-41932.79223928860010.9701435307-0.242531502600000.97014353070.2425315026000040680.827117117-187.3899276189-579.5033511615-40680.827117117187.3899276189-579.503351161539511.68921383689684.5870013598-579.5033511615-39511.6892138368-9684.5870013598-579.503351161510000000-112903-0-0112903-0000110000000-112903-011F150.000Tn-0.0005741843-0.00000073810.0000601464-0.0005615411-0.0000459662-0.0000336907-0.00054753530.00000073810.00007547120.00009914820.0001391407D15-0.00310rad0772.64159755272389.39414043180-772.64159755272389.394140431820.24253150260.97014353070000-0.24253150260.9701435307000010170.0231096386749.5732474522318.0552677455-10170.0231096386-749.5732474522318.05526774559684.58700135983193.74462300462318.0552677455-9684.5870013598-3193.74462300462318.055267745520000009739.81535904019479.63071808-9739.81535904-038959.26143616000120000009739.81535904019479.6307180812ReaccionesFRF10-3.14Tn-m02389.39414043189852.26850571380-2389.39414043184926.13425285693T2001000T2T001000T2 k202389.39414043189852.26850571380-2389.39414043184926.1342528569K2 =T2 k2 T2T-579.50335116152318.05526774559852.2685057138579.5033511615-2318.05526774554926.13425285693-3246.60511968-0-9739.815359040000000003246.605119680-9739.8153590413KRL-3246.60511968-0-9739.8153590400000013F112.8298407094Tnk2-41932.79223928860041932.79223928860040000.9701435307-0.242531502600000.97014353070.24253150260-40680.827117117187.3899276189579.503351161540680.827117117-187.3899276189579.5033511615-39511.6892138368-9684.5870013598579.503351161539511.68921383689684.5870013598579.50335116154-0-11290300000000000112903014-0-112903000000014F13-2.5225777624Tn0-772.6415975527-2389.39414043180772.6415975527-2389.394140431850000.24253150260.97014353070000-0.24253150260.97014353070-10170.0231096386-749.573247452-2318.055267745510170.0231096386749.573247452-2318.0552677455-9684.5870013598-3193.7446230046-2318.05526774559684.58700135983193.7446230046-2318.055267745559739.81535904-019479.63071808000000000-9739.81535904038959.26143616159739.81535904-019479.6307180800000015F14-2.8298407094Tn-m02389.39414043184926.13425285690-2389.39414043189852.2685057138600000100000102389.39414043184926.13425285690-2389.39414043189852.2685057138-579.50335116152318.05526774554926.1342528569579.5033511615-2318.05526774559852.26850571386123456789121542758.29433351689684.58700135989160.3120078785-39511.6892138368-9684.5870013598-579.503351161500009739.8153590419684.5870013598116096.7446230052318.0552677455-9684.5870013598-3193.74462300462318.05526774550000-024567894567899160.31200787852318.055267745548811.5299418738579.5033511615-2318.05526774554926.1342528569000019479.63071808341932.792239288600-41932.79223928860040.97014353070.242531502600000.9701435307-0.2425315026000040680.827117117187.3899276189579.5033511615-40680.827117117-187.3899276189579.503351161539511.6892138368-9684.5870013598579.5033511615-39511.68921383689684.5870013598579.50335116154-39511.6892138368-9684.5870013598579.503351161579023.378427673601159.006702323-39511.68921383689684.5870013598579.50335116150040772.64159755272389.39414043180-772.64159755272389.39414043185-0.24253150260.970143530700000.24253150260.97014353070000-10170.0231096386749.5732474522318.055267745510170.0231096386-749.5732474522318.0552677455-9684.58700135983193.74462300462318.05526774559684.5870013598-3193.74462300462318.05526774555KLL-9684.5870013598-3193.7446230046-2318.055267745506387.489246009109684.5870013598-3193.74462300462318.055267745500502389.39414043189852.26850571380-2389.39414043184926.13425285696T3001000T3T001000T3 k302389.39414043189852.26850571380-2389.39414043184926.1342528569K3 =T3 k3 T3T579.50335116152318.05526774559852.2685057138-579.5033511615-2318.05526774554926.13425285696-579.50335116152318.05526774554926.13425285691159.006702323019704.5370114276-579.5033511615-2318.05526774554926.1342528569006k3-41932.79223928860041932.79223928860070000.97014353070.242531502600000.9701435307-0.24253150260-40680.827117117-187.3899276189-579.503351161540680.827117117187.3899276189-579.5033511615-39511.68921383689684.5870013598-579.503351161539511.6892138368-9684.5870013598-579.50335116157000-39511.68921383689684.5870013598-579.503351161542758.2943335168-9684.58700135989160.31200787859739.81535904070-772.6415975527-2389.39414043180772.6415975527-2389.39414043188000-0.24253150260.970143530700000.24253150260.9701435307010170.0231096386-749.573247452-2318.0552677455-10170.0231096386749.573247452-2318.05526774559684.5870013598-3193.7446230046-2318.0552677455-9684.58700135983193.7446230046-2318.055267745580009684.5870013598-3193.7446230046-2318.0552677455-9684.5870013598116096.744623005-2318.055267745500802389.39414043184926.13425285690-2389.39414043189852.2685057138900000100000102389.39414043184926.13425285690-2389.39414043189852.2685057138579.50335116152318.05526774554926.1342528569-579.5033511615-2318.05526774559852.26850571389000579.50335116152318.05526774554926.13425285699160.3120078785-2318.055267745548811.529941873819479.63071808090000009739.81535904019479.6307180838959.261436160129739.81535904-019479.63071808000000038959.2614361615000000-3246.605119680-9739.81535904-9739.81535904010KRL0000000-112903-0-0011789101112789101112-3246.60511968-0-9739.815359040000000-9739.815359041311290300-1129030070100000-1000003246.605119689739.81535904-0-3246.605119689739.815359043246.60511968-09739.81535904-3246.6051196809739.815359047-0-1129030000000001403246.605119689739.815359040-3246.605119689739.815359048-100000100000-11290300112903-00-011290300-1129030809739.8153590438959.261436160-9739.8153590419479.630718089T4001000T4T001000T4 k409739.8153590438959.261436160-9739.8153590419479.63071808K4 =T4 k4 T4T9739.81535904038959.26143616-9739.81535904-019479.630718089k4-1129030011290300100000100000-10-0-3246.60511968-9739.8153590403246.60511968-9739.81535904-3246.605119680-9739.815359043246.60511968-0-9739.81535904100-3246.60511968-9739.8153590403246.60511968-9739.8153590411000-100000100112903-0-0-1129030-00-112903-0-0112903-01109739.8153590419479.630718080-9739.8153590438959.261436161200000100000109739.8153590419479.630718080-9739.8153590438959.261436169739.81535904019479.63071808-9739.81535904-038959.2614361612
Elemplo 7ENSAMBLADO DE MATRIZ DE RIGIDEZPrtico de una crujia a dos aguas apoyado con asentamiento1.-Ingreso de datosDatos del perfil AISC - LRFD
BarraDimensiones de la seccinAreaM. de inerciaMod. ElasticidadLongitudAngulo entre x y XbhAI = bh3/12FyELPerfilAreaAreaInerciaInerciammm2m4kg/cm2Tn/m2mradin2m2in4m410.024838660.00167325032530200000006-90-1.5707963268W24x13138.50.0248386640200.001673250320.0104515920.00047450382530200000006.264-16.699-0.2914525318W21x5516.20.01045159211400.000474503830.0104515920.00047450382530200000006.26416.6990.2914525318W21x5516.20.01045159211400.000474503840.024838660.00167325032530200000006901.5707963268W24x13138.50.0248386640200.00167325032.-Matriz de rigidez de barra en coordenadas locales3.-Matriz de transformacin4.-Matriz de rigidez de barra en coordenadas globales5.-Ensamblaje de Matriz de rigidez en coordenadas globales6.-Obteniendo los desplazamientos y recciones en coordenadas globales7.-Obteniendo los desplazamientos en coordenadas locales8.-Obteniendo las fuerzas en coordenadas localesEA/L00(-1) EA/L00cossin0000{u} = [T]T {U]{f} = [k] {u]012EI/L36 EI/L20(-1) 12EI/L36 EI/L2(-1) sincos000006EI/L24EI/L0(-1) 6EI/L22EI/L001000k(-1) EA/L00 EA/L00T000cossin00(-1) 12EI/L3(-1) 6 EI/L2012EI/L3(-1) 6 EI/L2000(-1) sincos006EI/L22EI/L0(-1) 6EI/L24EI/L000001
Barra 1Barra 2Barra 1Barra 213141512313141512312345678910111213141512345678982795.533333333300-82795.533333333300130-100000100000-1859.1670343467-5577.50110304-01859.1670343467-5577.501103041859.16703434670-5577.50110304-1859.1670343467-0-5577.501103041332512.49657423019056.85789597415160.5171899166-30653.3295398834-9056.8578959741-416.9839131234000000-1859.1670343467-05577.50110304132512.49657423019056.85789597415160.5171899166-30653.3295398834-9056.8578959741-416.98391312340001F10.000Tn0.00513928930.0000060391-0.00065441150.00504968130.00027613960.00032881620.0049474597-0.0000060391-0.0006681298-0.0009028-0.0009576166D10.02800m01010.028010.02683150341-2.8301Axial-3.1781Axial01859.16703434675577.501103040-1859.16703434675577.5011030414100000-10000082795.533333333300-82795.5333333333-00082795.53333333330-0-82795.53333333330149056.857895974185975.88426610371389.9679045454-9056.8578959741-3180.35093277041389.9679045454000000-0-82795.5333333333-02KLL9056.857895974185975.88426610371389.9679045454-9056.8578959741-3180.35093277041389.96790454540002Fuezas actuantesFLF20.000TnKLL-10.00000603910.0000120779-0.00000100650.00000785080.000006039-0.00000100650.00000603910-0.0000010065-0.0000010065-0.0000010065D20.00003mU102u102U20.00002u2-0.00801363982f130.9702Cortantef2-2.0012Cortante05577.5011030422310.004412160-5577.5011030411155.0022060815T1001000T1T001000T1 k105577.5011030422310.004412160-5577.5011030411155.00220608K1 =T1 k1 T1T-5577.50110304022310.004412165577.50110304-011155.00220608155160.51718991661389.967904545428370.0788078688416.9839131234-1389.96790454543030.0371978544000000-5577.50110304011155.0022060835160.51718991661389.967904545428370.0788078688416.9839131234-1389.96790454543030.03719785440003F30.000Tn-m-0.0006544115-0.00000100650.0001332399-0.00066232180.0000295976-0.0000548027-0.00066812980.00000100650.00008718360.00012344060.0000969829Desplazamientos 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k405577.5011030422310.004412160-5577.5011030411155.00220608K4 =T4 k4 T4T5577.50110304022310.00441216-5577.50110304-011155.002206089k4-82795.53333333330082795.533333333300100000100000-10-0-1859.1670343467-5577.5011030401859.1670343467-5577.50110304-1859.16703434670-5577.501103041859.1670343467-0-5577.50110304100-1859.1670343467-5577.5011030401859.1670343467-5577.5011030411000-10000010082795.5333333333-0-0-82795.53333333330-00-82795.5333333333-0-082795.5333333333-01105577.5011030411155.002206080-5577.5011030422310.004412161200000100000105577.5011030411155.002206080-5577.5011030422310.004412165577.50110304011155.00220608-5577.50110304-022310.0044121612
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