e-portico 2do examen
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porticosTRANSCRIPT
PORTICO 05UNIVERSIDAD ALAS PERUANASCARRERA: INGENIERIA CIVILCURSO: ANALISIS ESTRUCTURAL IIALUMNO: GARCIA CONDORCALLO, ALANEJERCICIO PRACTICO DE PORTICO POR EL METODO DE RIGIDEZRELACION S - R - CSRC180PI200
Paso 01Numeramos las barras Numeramos los Grados de Libertad ( DOF ) libres y restringidos de la estructura
Barra123A (m)0.1700.1500.150Inercia (m4)0.00197843140.0031250.003125FC (Kg/cm2)280280280E (Tn/m)2509980.079602232509980.079602232509980.07960223L (m)6.005.006.32Angulo (grados)090108.43Grados (Rad)0.000000001.570796331.89254688Paso 02Esta es la matriz de RIGIDEZ en coordenadas globales para la barra de un portico
Paso 03Podemos encontrar esta matriz para todas las barras del portico de la sgte manera:Coordenadas Globales ( Barra del Portico )
TIPO DE FIGURA4
L1F`c3Rectangulo1Circulo2S. Tubular3Seccion 4Seccion 5ITEMAYAYIdAd2Seccion 6ITEMAYAYIdAd21140b(m)0.40r(m)0.3r(m)0.4a(m)0.6a(m)0.3a(m)0.32175h(m)0.60A(m2)0.2827433388r(m)0.2b(m)0.25b(m)0.410.30.50.150.0250.10.003b(m)0.410.450.750.33750.084375-0.1260.0073210A(m2)0.24I(m4)0.0063617251A(m2)0.3769911184c(m)0.25c(m)0.3c(m)0.34280I0.0072As0.2544690049I(m4)0.0188495559d(m)0.25d(m)120.120.850.1020.0009-0.250.0075d(m)1.520.120.150.0180.00090.4740.0275315As 0.2As0.1884955592A(m2)0.2125A(m2)0.49A(m2)0.696420I(m4)0.0038641238I(m4)0.03640.420.2520.02590.0105I(m4)0.11938026320.570.35550.0852750.034As0.1770833333As0.25As0.375YC=0.6MYC=0.624MMx0.0640625Yg0.3014705882INERCIA TOTAL0.0364m4INERCIA TOTAL0.1193802632m4
VIGA1CO,CA05A (m)0.213123456Inercia (m4)0.00386192382.530.00-0.00-92382.53-0.00-0.00FC (Kg/cm2)21020.00806.352015.87-0.00-806.352015.87E (Tn/m)2173706.513-0.002015.876719.580.00-2015.873359.79L (m)5.004-92382.53-0.000.0092382.530.000.00Angulo05-0.00-806.35-2015.870.00806.35-2015.87Radianes06-0.002015.873359.790.00-2015.876719.58COS1SEN0
TIPO DE FIGURA4
L1F`c3Rectangulo1Circulo2S. Tubular3Seccion 4Seccion 5ITEMAYAYIdAd2Seccion 6ITEMAYAYIdAd21140b(m)0.40r(m)1r(m)4a(m)0.6a(m)0.3a(m)0.32175h(m)0.60A(m2)3.1415926536r(m)2b(m)0.25b(m)0.410.30.50.150.0250.10.003b(m)0.410.450.750.33750.084375-0.1260.0073210A(m2)0.24I(m4)0.7853981634A(m2)37.6991118431c(m)0.25c(m)0.3c(m)0.34280I0.0072As2.8274333882I(m4)188.4955592154d(m)0.25d(m)120.120.850.1020.0009-0.250.0075d(m)1.520.120.150.0180.00090.4740.0275315As 0.2As18.8495559215A(m2)0.2125A(m2)0.49A(m2)0.696420I(m4)0.0038641238I(m4)0.03640.420.2520.02590.0105I(m4)0.11938026320.570.35550.0852750.034As0.1770833333As0.25As0.375YC=0.600M YC=0.624MMx0.0640625Yg0.3014705882INERCIA TOTAL0.0364m4INERCIA TOTAL0.1193802632m4
VIGA2CO,CA05A (m)0.213789101112Inercia (m4)0.004792382.530.00-0.00-92382.53-0.00-0.00FC (Kg/cm2)210.00080.00806.352015.87-0.00-806.352015.87E (Tn/m)2173706.5129-0.002015.876719.580.00-2015.873359.79L (m)5.0010-92382.53-0.000.0092382.530.000.00Angulo011-0.00-806.35-2015.870.00806.35-2015.87Radianes0.0012-0.002015.873359.790.00-2015.876719.58COS1SEN0
TIPO DE FIGURA4
L1F`c3Rectangulo1Circulo2S. Tubular3Seccion 4Seccion 5ITEMAYAYIdAd2Seccion 6ITEMAYAYIdAd21140b(m)0.40r(m)1r(m)4a(m)0.6a(m)0.3a(m)0.32175h(m)0.60A(m2)3.1415926536r(m)2b(m)0.25b(m)0.410.30.50.150.0250.10.003b(m)0.410.450.750.33750.084375-0.1260.0073210A(m2)0.24I(m4)0.7853981634A(m2)37.6991118431c(m)0.25c(m)0.3c(m)0.34280I0.0072As2.8274333882I(m4)188.4955592154d(m)0.25d(m)120.120.850.1020.0009-0.250.0075d(m)1.520.120.150.0180.00090.4740.0275315As 0.2As18.8495559215A(m2)0.2125A(m2)0.49A(m2)0.696420I(m4)0.0038641238I(m4)0.03640.420.2520.02590.0105I(m4)0.11938026320.570.35550.0852750.034As0.1770833333As0.25As0.375YC=0.600M YC=0.624MMx0.0640625Yg0.3014705882INERCIA TOTAL0.0364m4INERCIA TOTAL0.1193802632m4
VIGA3CO,CA05A (m)0.213131415161718Inercia (m4)0.0041392382.530.00-0.00-92382.53-0.00-0.00FC (Kg/cm2)210.000140.00806.352015.87-0.00-806.352015.87E (Tn/m)2173706.51215-0.002015.876719.580.00-2015.873359.79L (m)5.0016-92382.53-0.000.0092382.530.000.00Angulo017-0.00-806.35-2015.870.00806.35-2015.87Radianes0.0018-0.002015.873359.790.00-2015.876719.58COS1SEN0
TIPO DE FIGURA6
L1F`c3Rectangulo1Circulo2S. Tubular3Seccion 4Seccion 5ITEMAYAYIdAd2Seccion 6ITEMAYAYIdAd21140b(m)0.40r(m)1r(m)4a(m)0.6a(m)0.3a(m)0.252175h(m)0.60A(m2)3.1415926536r(m)2b(m)0.2b(m)0.410.30.50.150.0250.10.003b(m)0.7510.250.50.1250.0208333333-0.1610.0063210A(m2)0.24I(m4)0.7853981634A(m2)37.6991118431c(m)0.2c(m)0.3c(m)0.254280I0.0072As2.8274333882I(m4)188.4955592154d(m)0.25d(m)120.120.850.1020.0009-0.250.0075d(m)120.18750.1250.02343750.00097656250.2140.0095315As 0.2As18.8495559215A(m2)0.17A(m2)0.49A(m2)0.81256420I(m4)0.0019784314I(m4)0.03640.420.2520.02590.0105I(m4)0.03687686010.43750.14843750.02180989580.015As0.1416666667As0.25As0.2083333333YC=0.600MYC=0.339MMx0.041Yg0.2411764706INERCIA TOTAL0.0364m4INERCIA TOTAL0.0368768601m4
COLUMNA4CO,CA30A (m)0.813789123Inercia (m4)0.037735626.430.00-53439.65-35626.43-0.00-53439.65FC (Kg/cm2)21080.00588712.180.00-0.00-588712.180.00E (Tn/m)2173706.519-53439.650.00106879.2953439.65-0.0053439.65L (m)3.001-35626.43-0.0053439.6535626.430.0053439.65Angulo902-0.00-588712.18-0.000.00588712.18-0.00Radianes1.573-53439.650.0053439.6553439.65-0.00106879.29RADIANES(180)-ATAN(B175/C175)COS0SEN1
TIPO DE FIGURA6
L1F`c3Rectangulo1Circulo2S. Tubular3Seccion 4Seccion 5ITEMAYAYIdAd2Seccion 6ITEMAYAYIdAd21140b(m)0.40r(m)1r(m)4a(m)0.6a(m)0.3a(m)0.252175h(m)0.60A(m2)3.1415926536r(m)2b(m)0.2b(m)0.410.30.50.150.0250.10.003b(m)0.7510.250.50.1250.0208333333-0.1610.0063210A(m2)0.24I(m4)0.7853981634A(m2)37.6991118431c(m)0.2c(m)0.3c(m)0.254280I0.0072As2.8274333882I(m4)188.4955592154d(m)0.25d(m)120.120.850.1020.0009-0.250.0075d(m)120.18750.1250.02343750.00097656250.2140.0095315As 0.2As18.8495559215A(m2)0.17A(m2)0.49A(m2)0.81256420I(m4)0.0019784314I(m4)0.03640.420.2520.02590.0105I(m4)0.03687686010.43750.14843750.02180989580.015As0.1416666667As0.25As0.2083333333YC=0.600MYC=0.339MMx0.041Yg0.2411764706INERCIA TOTAL0.0364m4INERCIA TOTAL0.0368768601m4
COLUMNA5CO,CA30A (m)0.813131415789Inercia (m4)0.0371335626.430.00-53439.65-35626.43-0.00-53439.65FC (Kg/cm2)210140.00588712.180.00-0.00-588712.180.00E (Tn/m)2173706.5115-53439.650.00106879.2953439.65-0.0053439.65L (m)3.007-35626.43-0.0053439.6535626.430.0053439.65Angulo908-0.00-588712.18-0.000.00588712.18-0.00Radianes1.579-53439.650.0053439.6553439.65-0.00106879.29RADIANES(180)-ATAN(B175/C175)COS0SEN1
TIPO DE FIGURA6
L1F`c3Rectangulo1Circulo2S. Tubular3Seccion 4Seccion 5ITEMAYAYIdAd2Seccion 6ITEMAYAYIdAd21140b(m)0.40r(m)1r(m)4a(m)0.6a(m)0.3a(m)0.252175h(m)0.60A(m2)3.1415926536r(m)2b(m)0.2b(m)0.410.30.50.150.0250.10.003b(m)0.7510.250.50.1250.0208333333-0.1610.0063210A(m2)0.24I(m4)0.7853981634A(m2)37.6991118431c(m)0.2c(m)0.3c(m)0.254280I0.0072As2.8274333882I(m4)188.4955592154d(m)0.25d(m)120.120.850.1020.0009-0.250.0075d(m)120.18750.1250.02343750.00097656250.2140.0095315As 0.2As18.8495559215A(m2)0.17A(m2)0.49A(m2)0.81256420I(m4)0.0019784314I(m4)0.03640.420.2520.02590.0105I(m4)0.03687686010.43750.14843750.02180989580.015As0.1416666667As0.25As0.2083333333YC=0.600MYC=0.339MMx0.041Yg0.2411764706INERCIA TOTAL0.0364m4INERCIA TOTAL0.0368768601m4
COLUMNA6CO,CA3.50A (m)0.813192021131415Inercia (m4)0.0371922435.300.00-39261.78-22435.30-0.00-39261.78FC (Kg/cm2)210200.00504610.440.00-0.00-504610.440.00E (Tn/m)2173706.5121-39261.780.0091610.8239261.78-0.0045805.41L (m)3.5013-22435.30-0.0039261.7822435.300.0039261.78Angulo9014-0.00-504610.44-0.000.00504610.44-0.00Radianes1.5715-39261.780.0045805.4139261.78-0.0091610.82RADIANES(180)-ATAN(B175/C175)COS0SEN1
TIPO DE FIGURA2
L1F`c3Rectangulo1Circulo2S. Tubular3Seccion 4Seccion 5ITEMAYAYIdAd2Seccion 6ITEMAYAYIdAd21140b(m)0.40r(m)0.4r(m)4a(m)0.6a(m)0.3a(m)0.252175h(m)0.60A(m2)0.5026548246r(m)2b(m)0.2b(m)0.410.30.50.150.0250.10.003b(m)0.7510.250.50.1250.0208333333-0.1610.0063210A(m2)0.24I(m4)0.020106193A(m2)37.6991118431c(m)0.2c(m)0.3c(m)0.254280I0.0072As0.4523893421I(m4)188.4955592154d(m)0.25d(m)120.120.850.1020.0009-0.250.0075d(m)120.18750.1250.02343750.00097656250.2140.0095315As 0.2As18.8495559215A(m2)0.17A(m2)0.49A(m2)0.81256420I(m4)0.0019784314I(m4)0.03640.420.2520.02590.0105I(m4)0.03687686010.43750.14843750.02180989580.015As0.1416666667As0.25As0.2083333333YC=0.600MYC=0.339MMx0.041Yg0.2411764706INERCIA TOTAL0.0364m4INERCIA TOTAL0.0368768601m4
COLUMNA7CO,CA30A (m)0.503101112456Inercia (m4)0.0201019424.430.00-29136.64-19424.43-0.00-29136.64FC (Kg/cm2)210110.00364208.020.00-0.00-364208.020.00E (Tn/m)2173706.5112-29136.640.0058273.2829136.64-0.0029136.64L (m)3.004-19424.43-0.0029136.6419424.430.0029136.64Angulo905-0.00-364208.02-0.000.00364208.02-0.00Radianes1.576-29136.640.0029136.6429136.64-0.0058273.28RADIANES(180)-ATAN(B175/C175)COS0SEN1
TIPO DE FIGURA2
L1F`c3Rectangulo1Circulo2S. Tubular3Seccion 4Seccion 5ITEMAYAYIdAd2Seccion 6ITEMAYAYIdAd21140b(m)0.40r(m)0.4r(m)4a(m)0.6a(m)0.3a(m)0.252175h(m)0.60A(m2)0.5026548246r(m)2b(m)0.2b(m)0.410.30.50.150.0250.10.003b(m)0.7510.250.50.1250.0208333333-0.1610.0063210A(m2)0.24I(m4)0.020106193A(m2)37.6991118431c(m)0.2c(m)0.3c(m)0.254280I0.0072As0.4523893421I(m4)188.4955592154d(m)0.25d(m)120.120.850.1020.0009-0.250.0075d(m)120.18750.1250.02343750.00097656250.2140.0095315As 0.2As18.8495559215A(m2)0.17A(m2)0.49A(m2)0.81256420I(m4)0.0019784314I(m4)0.03640.420.2520.02590.0105I(m4)0.03687686010.43750.14843750.02180989580.015As0.1416666667As0.25As0.2083333333YC=0.600MYC=0.339MMx0.041Yg0.2411764706INERCIA TOTAL0.0364m4INERCIA TOTAL0.0368768601m4
COLUMNA8CO,CA30A (m)0.503161718222324Inercia (m4)0.0201619424.430.00-29136.64-19424.43-0.00-29136.64FC (Kg/cm2)210170.00364208.020.00-0.00-364208.020.00E (Tn/m)2173706.5118-29136.640.0058273.2829136.64-0.0029136.64L (m)3.0022-19424.43-0.0029136.6419424.430.0029136.64Angulo9023-0.00-364208.02-0.000.00364208.02-0.00Radianes1.5724-29136.640.0029136.6429136.64-0.0058273.28RADIANES(180)-ATAN(B175/C175)COS0SEN1
TIPO DE FIGURA2
L1F`c3Rectangulo1Circulo2S. Tubular3Seccion 4Seccion 5ITEMAYAYIdAd2Seccion 6ITEMAYAYIdAd21140b(m)0.40r(m)0.4r(m)4a(m)0.6a(m)0.3a(m)0.252175h(m)0.60A(m2)0.5026548246r(m)2b(m)0.2b(m)0.410.30.50.150.0250.10.003b(m)0.7510.250.50.1250.0208333333-0.1610.0063210A(m2)0.24I(m4)0.020106193A(m2)37.6991118431c(m)0.2c(m)0.3c(m)0.254280I0.0072As0.4523893421I(m4)188.4955592154d(m)0.25d(m)120.120.850.1020.0009-0.250.0075d(m)120.18750.1250.02343750.00097656250.2140.0095315As 0.2As18.8495559215A(m2)0.17A(m2)0.49A(m2)0.81256420I(m4)0.0019784314I(m4)0.03640.420.2520.02590.0105I(m4)0.03687686010.43750.14843750.02180989580.015As0.1416666667As0.25As0.2083333333YC=0.600MYC=0.339MMx0.041Yg0.2411764706INERCIA TOTAL0.0364m4INERCIA TOTAL0.0368768601m4
COLUMNA9CO,CA3.50A (m)0.503222324161718Inercia (m4)0.0202212232.290.00-21406.51-12232.29-0.00-21406.51FC (Kg/cm2)210230.00312178.300.00-0.00-312178.300.00E (Tn/m)2173706.5124-21406.510.0049948.5321406.51-0.0024974.26L (m)3.5016-12232.29-0.0021406.5112232.290.0021406.51Angulo9017-0.00-312178.30-0.000.00312178.30-0.00Radianes1.5718-21406.510.0024974.2621406.51-0.0049948.53RADIANES(180)-ATAN(B175/C175)COS0SEN1
1234567891011121314151617181920212223241184765.050.000.00-92382.53-0.00-0.00-92382.53-0.000.000.000.000.0020.001612.700.00-0.00-806.352015.87-0.00-806.35-2015.870.000.000.0030.000.0013439.150.00-2015.873359.79-0.002015.873359.790.000.000.004-92382.53-0.000.00128008.960.0053439.650.000.000.00-35626.43-0.0053439.655-0.00-806.35-2015.870.00589518.53-2015.870.000.000.00-0.00-588712.18-0.006-0.002015.873359.7953439.65-2015.87113598.870.000.000.00-53439.650.0053439.657-92382.53-0.00-0.000.000.000.0092382.530.00-0.000.000.000.008-0.00-806.352015.870.000.000.000.00806.352015.870.000.000.0090.00-2015.873359.790.000.000.00-0.002015.876719.580.000.000.00100.000.000.00-35626.43-0.00-53439.650.000.000.0035626.430.00-53439.65110.000.000.00-0.00-588712.180.000.000.000.000.00588712.180.00120.000.000.0053439.65-0.0053439.650.000.000.00-53439.650.00106879.29131415161718192021222324
Paso 04A partir de las matrices de todas las barras se obtiene esta matriz de toda la estructura sumando las componentes de cada matriz en funcin de sus grados de libertad con lo cual tenemos una matriz de 8x8 que luego particionamos como se indica
10TN70.000M2-7.5TN80.000M3-6.25TN-M90.000RAD40TN100.000M5-14TN110.000M6-0.125TN-M120.000RAD
Paso 05Para invertir la matriz (kff) seleccionamos las celdas (E170:H173) la funcion es =MINVERSA(E161:H164) y sin soltar presionamos "CTROL" + "SHIFT", sin soltar damos enterCOMPROBACION1
12345610.00000988360.0000054170.00000108320.0000089426-0.0000000037-0.00000433520.0000054170.000641230.0000042720.00001083390.000000835-0.00001658730.00000108320.0000042720.00007527640.00000216640.0000002519-0.000003316840.00000894260.00001083390.00000216640.0000178852-0.0000000074-0.00000867015-0.00000000370.0000008350.0000002519-0.00000000740.00000169830.00000001146-0.000004335-0.000016587-0.0000033168-0.00000867010.00000001140.0000132742
7891011121-92382.5267569577-000000.00002-0-806.3492171087-2015.87304277180000.000-7.53-02015.87304277183359.78840461980000.000-6.254000-35626.4315467765-053439.64732016470.00005000-0-588712.180313946-00.000-146000-53439.6473201647053439.64732016470.000-0.125
Paso 06Para Multiplicar una matriz con el vector de cargas nodales seleccionamos las celdas (E187:E190) la funcion es =MMULT(E170:H173,E149:E152) y sin soltar presionamos "CTROL" + "SHIFT", sin soltar damos enterDatos del MEP CON SU SIGNO
1-0.0000468034M74.3238118813TN70TN2-0.0048455413M82.8879126211TN80TN3-0.00050563RAD98.0691863754TN-M90TN-M4-0.0000936067M10-4.3238118813TN100TN5-0.0000316149M1118.6120873789TN110TN60.0001433147RAD122.6563754794TN-M120TN-M
74.3238118813TN82.8879126211TN98.0691863754TN-M10-4.3238118813TN1118.6120873789TN122.6563754794TN-M
1m6m2m0.50m5m1320.30mb
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PORTICO 04UNIVERSIDAD ALAS PERUANASCARRERA: INGENIERIA CIVILCURSO: ANALISIS ESTRUCTURAL IIALUMNO: GARCIA CONDORCALLO, ALANEJERCICIO PRACTICO DE PORTICO POR EL METODO DE RIGIDEZRELACION S - R - CSRC180PI200
Paso 01Numeramos las barras Numeramos los Grados de Libertad ( DOF ) libres y restringidos de la estructura
Barra123A (m)0.1700.1500.150Inercia (m4)0.00197843140.0031250.003125FC (Kg/cm2)280280280E (Tn/m)2509980.079602232509980.079602232509980.07960223L (m)6.005.006.32Angulo (grados)090108.43Grados (Rad)0.000000001.570796331.89254688Paso 02Esta es la matriz de RIGIDEZ en coordenadas globales para la barra de un portico
Paso 03Podemos encontrar esta matriz para todas las barras del portico de la sgte manera:Coordenadas Globales ( Barra del Portico )
TIPO DE FIGURA1
L1F`c4Rectangulo1Circulo2S. Tubular3Seccion 4Seccion 5ITEMAYAYIdAd2Seccion 6ITEMAYAYIdAd21140b(m)0.20r(m)0.3r(m)0.4a(m)0.6a(m)0.3a(m)0.32175h(m)0.30A(m2)0.2827433388r(m)0.2b(m)0.2b(m)0.410.30.50.150.0250.10.003b(m)0.410.450.750.33750.084375-0.1260.0073210A(m2)0.06I(m4)0.0063617251A(m2)0.3769911184c(m)0.2c(m)0.3c(m)0.34280I0.00045As0.2544690049I(m4)0.0188495559d(m)0.25d(m)120.120.850.1020.0009-0.250.0075d(m)1.520.120.150.0180.00090.4740.0275315As 0.05As0.1884955592A(m2)0.17A(m2)0.49A(m2)0.696420I(m4)0.0019784314I(m4)0.03640.420.2520.02590.0105I(m4)0.11938026320.570.35550.0852750.034As0.1416666667As0.25As0.375YC=0.6MYC=0.624MMx0.041Yg0.2411764706INERCIA TOTAL0.0364m4INERCIA TOTAL0.1193802632m4
VIGA1CO,CA04A (m)0.060456123Inercia (m4)0.00045445000.000.00-0.00-45000.00-0.00-0.00FC (Kg/cm2)28050.00253.13506.25-0.00-253.13506.25E (Tn/m)3000000.006-0.00506.251350.000.00-506.25675.00L (m)4.001-45000.00-0.000.0045000.000.000.00Angulo02-0.00-253.13-506.250.00253.13-506.25Radianes03-0.00506.25675.000.00-506.251350.00COS1SEN0
TIPO DE FIGURA1
L1F`c4Rectangulo1Circulo2S. Tubular3Seccion 4Seccion 5ITEMAYAYIdAd2Seccion 6ITEMAYAYIdAd21140b(m)0.20r(m)1r(m)4a(m)0.6a(m)0.3a(m)0.32175h(m)0.30A(m2)3.1415926536r(m)2b(m)0.2b(m)0.410.30.50.150.0250.10.003b(m)0.410.450.750.33750.084375-0.1260.0073210A(m2)0.06I(m4)0.7853981634A(m2)37.6991118431c(m)0.2c(m)0.3c(m)0.34280I0.00045As2.8274333882I(m4)188.4955592154d(m)0.25d(m)120.120.850.1020.0009-0.250.0075d(m)1.520.120.150.0180.00090.4740.0275315As 0.05As18.8495559215A(m2)0.17A(m2)0.49A(m2)0.696420I(m4)0.0019784314I(m4)0.03640.420.2520.02590.0105I(m4)0.11938026320.570.35550.0852750.034As0.1416666667As0.25As0.375YC=0.600M YC=0.624MMx0.041Yg0.2411764706INERCIA TOTAL0.0364m4INERCIA TOTAL0.1193802632m4
COLUMNA2CO,CA40A (m)0.060789123Inercia (m4)0.000457253.130.00-506.25-253.13-0.00-506.25FC (Kg/cm2)280.00080.0045000.000.00-0.00-45000.000.00E (Tn/m)3000000.0009-506.250.001350.00506.25-0.00675.00L (m)4.001-253.13-0.00506.25253.130.00506.25Angulo902-0.00-45000.00-0.000.0045000.00-0.00Radianes1.573-506.250.00675.00506.25-0.001350.00COS0SEN1
123456789145253.130.00506.25-45000.00-0.000.00-253.13-0.00506.2520.0045253.13-506.25-0.00-253.13-506.25-0.00-45000.00-0.003506.25-506.252700.00-0.00506.25675.00-506.250.00675.004-45000.00-0.00-0.0045000.000.00-0.000.000.000.005-0.00-253.13506.250.00253.13506.250.000.000.0060.00-506.25675.00-0.00506.251350.000.000.000.007-253.13-0.00-506.250.000.000.00253.130.00-506.258-0.00-45000.000.000.000.000.000.0045000.000.009506.25-0.00675.000.000.000.00-506.250.001350.00
Paso 04A partir de las matrices de todas las barras se obtiene esta matriz de toda la estructura sumando las componentes de cada matriz en funcin de sus grados de libertad con lo cual tenemos una matriz de 8x8 que luego particionamos como se indica
10TN40.000M2-6TN50.000M31.667TN-M60.000RAD70.000M80.000M90.000RAD
Paso 05Para invertir la matriz (kff) seleccionamos las celdas (E170:H173) la funcion es =MINVERSA(E161:H164) y sin soltar presionamos "CTROL" + "SHIFT", sin soltar damos enterCOMPROBACION1
12300010.0000221445-0.0000000465-0.00000416082-0.00000004650.00002214450.00000416083-0.00000416080.00000416080.0003719307
4567891-45000.00-0.000.00-253.13-0.00506.252-0.00-253.13-506.25-0.00-45000.00-0.003-0.00506.25675.00-506.250.00675.000.0000.0000.000-6.0000.0001.667
Paso 06Para Multiplicar una matriz con el vector de cargas nodales seleccionamos las celdas (E187:E190) la funcion es =MMULT(E170:H173,E149:E152) y sin soltar presionamos "CTROL" + "SHIFT", sin soltar damos enterDatos del MEP CON SU SIGNO
1-0.0000066568M40.2995557929TN40TN2-0.0001259307M50.333117011TN54TN30.0005950435RAD60.4654068259TN-M62.667TN-M7-0.2995557929TN7-2TN85.666882989TN80TN90.3982843896TN-M92TN-M
40.2995557929TN54.333117011TN63.1324068259TN-M7-2.2995557929TN85.666882989TN92.3982843896TN-M
-2530-506.2-20-4500000506.206752
1m6m2m0.50m5m1320.30mb
cadb
cadb
cadb
cadaa
PORTICO 03UNIVERSIDAD ALAS PERUANASCARRERA: INGENIERIA CIVILCURSO: ANALISIS ESTRUCTURAL IIALUMNO: GARCIA CONDORCALLO, ALANEJERCICIO PRACTICO DE PORTICO POR EL METODO DE RIGIDEZRELACION S - R - CSRC180PI200
Paso 01Numeramos las barras Numeramos los Grados de Libertad ( DOF ) libres y restringidos de la estructura
Barra123A (m)0.1700.1500.150Inercia (m4)0.00197843140.0031250.003125FC (Kg/cm2)280280280E (Tn/m)2509980.079602232509980.079602232509980.07960223L (m)6.005.006.32Angulo (grados)090108.43Grados (Rad)0.000000001.570796331.89254688Paso 02Esta es la matriz de RIGIDEZ en coordenadas globales para la barra de un portico
Paso 03Podemos encontrar esta matriz para todas las barras del portico de la sgte manera:Coordenadas Globales ( Barra del Portico )
TIPO DE FIGURA1
L1F`c4Rectangulo1Circulo2S. Tubular3Seccion 4Seccion 5ITEMAYAYIdAd2Seccion 6ITEMAYAYIdAd21140b(m)0.40r(m)0.3r(m)0.4a(m)0.6a(m)0.3a(m)0.32175h(m)0.60A(m2)0.2827433388r(m)0.2b(m)0.2b(m)0.410.30.50.150.0250.10.003b(m)0.410.450.750.33750.084375-0.1260.0073210A(m2)0.24I(m4)0.0063617251A(m2)0.3769911184c(m)0.2c(m)0.3c(m)0.34280I0.0072As0.2544690049I(m4)0.0188495559d(m)0.25d(m)120.120.850.1020.0009-0.250.0075d(m)1.520.120.150.0180.00090.4740.0275315As 0.2As0.1884955592A(m2)0.17A(m2)0.49A(m2)0.696420I(m4)0.0019784314I(m4)0.03640.420.2520.02590.0105I(m4)0.11938026320.570.35550.0852750.034As0.1416666667As0.25As0.375YC=0.6MYC=0.624MMx0.041Yg0.2411764706INERCIA TOTAL0.0364m4INERCIA TOTAL0.1193802632m4
VIGA1CO,CA05A (m)0.240123456Inercia (m4)0.007201120479.040.00-0.00-120479.04-0.00-0.00FC (Kg/cm2)28020.001734.904337.25-0.00-1734.904337.25E (Tn/m)2509980.083-0.004337.2514457.490.00-4337.257228.74L (m)5.004-120479.04-0.000.00120479.040.000.00Angulo05-0.00-1734.90-4337.250.001734.90-4337.25Radianes06-0.004337.257228.740.00-4337.2514457.49COS1SEN0
TIPO DE FIGURA1
L1F`c4Rectangulo1Circulo2S. Tubular3Seccion 4Seccion 5ITEMAYAYIdAd2Seccion 6ITEMAYAYIdAd21140b(m)0.40r(m)1r(m)4a(m)0.6a(m)0.3a(m)0.32175h(m)0.60A(m2)3.1415926536r(m)2b(m)0.2b(m)0.410.30.50.150.0250.10.003b(m)0.410.450.750.33750.084375-0.1260.0073210A(m2)0.24I(m4)0.7853981634A(m2)37.6991118431c(m)0.2c(m)0.3c(m)0.34280I0.0072As2.8274333882I(m4)188.4955592154d(m)0.25d(m)120.120.850.1020.0009-0.250.0075d(m)1.520.120.150.0180.00090.4740.0275315As 0.2As18.8495559215A(m2)0.17A(m2)0.49A(m2)0.696420I(m4)0.0019784314I(m4)0.03640.420.2520.02590.0105I(m4)0.11938026320.570.35550.0852750.034As0.1416666667As0.25As0.375YC=0.600M YC=0.624MMx0.041Yg0.2411764706INERCIA TOTAL0.0364m4INERCIA TOTAL0.1193802632m4
COLUMNA2CO,CA30A (m)0.240789123Inercia (m4)0.00778031.940.00-12047.90-8031.94-0.00-12047.90FC (Kg/cm2)280.00080.00200798.410.00-0.00-200798.410.00E (Tn/m)2509980.0809-12047.900.0024095.8112047.90-0.0012047.90L (m)3.001-8031.94-0.0012047.908031.940.0012047.90Angulo902-0.00-200798.41-0.000.00200798.41-0.00Radianes1.573-12047.900.0012047.9012047.90-0.0024095.81COS0SEN1
TIPO DE FIGURA1
L1F`c4Rectangulo1Circulo2S. Tubular3Seccion 4Seccion 5ITEMAYAYIdAd2Seccion 6ITEMAYAYIdAd21140b(m)0.40r(m)1r(m)4a(m)0.6a(m)0.3a(m)0.32175h(m)0.60A(m2)3.1415926536r(m)2b(m)0.2b(m)0.410.30.50.150.0250.10.003b(m)0.410.450.750.33750.084375-0.1260.0073210A(m2)0.24I(m4)0.7853981634A(m2)37.6991118431c(m)0.2c(m)0.3c(m)0.34280I0.0072As2.8274333882I(m4)188.4955592154d(m)0.25d(m)120.120.850.1020.0009-0.250.0075d(m)1.520.120.150.0180.00090.4740.0275315As 0.2As18.8495559215A(m2)0.17A(m2)0.49A(m2)0.696420I(m4)0.0019784314I(m4)0.03640.420.2520.02590.0105I(m4)0.11938026320.570.35550.0852750.034As0.1416666667As0.25As0.375YC=0.600MYC=0.624MMx0.041Yg0.2411764706INERCIA TOTAL0.0364m4INERCIA TOTAL0.1193802632m4
COLUMNA3CO,CA30A (m)0.240101112456Inercia (m4)0.007108031.940.00-12047.90-8031.94-0.00-12047.90FC (Kg/cm2)280110.00200798.410.00-0.00-200798.410.00E (Tn/m)2509980.0812-12047.900.0024095.8112047.90-0.0012047.90L (m)3.004-8031.94-0.0012047.908031.940.0012047.90Angulo905-0.00-200798.41-0.000.00200798.41-0.00Radianes1.576-12047.900.0012047.9012047.90-0.0024095.81COS0SEN1
1234567891011121128510.980.0012047.90-120479.04-0.00-0.00-8031.94-0.0012047.900.000.000.0020.00202533.304337.25-0.00-1734.904337.25-0.00-200798.41-0.000.000.000.00312047.904337.2538553.290.00-4337.257228.74-12047.900.0012047.900.000.000.004-120479.04-0.000.00128510.980.0012047.900.000.000.00-8031.94-0.0012047.905-0.00-1734.90-4337.250.00202533.30-4337.250.000.000.00-0.00-200798.41-0.006-0.004337.257228.7412047.90-4337.2538553.290.000.000.00-12047.900.0012047.907-8031.94-0.00-12047.900.000.000.008031.940.00-12047.900.000.000.008-0.00-200798.410.000.000.000.000.00200798.410.000.000.000.00912047.90-0.0012047.900.000.000.00-12047.900.0024095.810.000.000.00100.000.000.00-8031.94-0.00-12047.900.000.000.008031.940.00-12047.90110.000.000.00-0.00-200798.410.000.000.000.000.00200798.410.00120.000.000.0012047.90-0.0012047.900.000.000.00-12047.900.0024095.81
Paso 04A partir de las matrices de todas las barras se obtiene esta matriz de toda la estructura sumando las componentes de cada matriz en funcin de sus grados de libertad con lo cual tenemos una matriz de 8x8 que luego particionamos como se indica
10TN70.000M2-7.5TN80.000M3-6.25TN-M90.000RAD40TN100.000M5-14TN110.000M6-0.125TN-M120.000RAD
Paso 05Para invertir la matriz (kff) seleccionamos las celdas (E170:H173) la funcion es =MINVERSA(E161:H164) y sin soltar presionamos "CTROL" + "SHIFT", sin soltar damos enterCOMPROBACION1
12345610.00010544350.0000011649-0.00002821750.0001013511-0.0000011649-0.000026643520.00000116490.0000049708-0.00000077660.00000116490.0000000093-0.00000077663-0.0000282175-0.00000077660.0000345516-0.00002664350.00000077660.000002022440.00010135110.0000011649-0.00002664350.0001054435-0.0000011649-0.00002821755-0.00000116490.00000000930.0000007766-0.00000116490.00000497080.00000077666-0.0000266435-0.00000077660.0000020224-0.00002821750.00000077660.0000345516
7891011121-8031.9362547271-012047.90438209070000.00002-0-200798.406368178-00000.000-7.53-12047.9043820907012047.90438209070000.000-6.254000-8031.9362547271-012047.90438209070.00005000-0-200798.406368178-00.000-146000-12047.9043820907012047.90438209070.000-0.125
Paso 06Para Multiplicar una matriz con el vector de cargas nodales seleccionamos las celdas (E187:E190) la funcion es =MMULT(E170:H173,E149:E152) y sin soltar presionamos "CTROL" + "SHIFT", sin soltar damos enterDatos del MEP CON SU SIGNO
10.0001872616M71.1615044248TN70TN2-0.0000324608M86.5180712454TN80TN3-0.0002212482RAD9-0.4094679042TN-M90TN-M40.0001776209M10-1.1615044248TN100TN5-0.0000746118M1114.9819287546TN110TN6-0.0000220067RAD121.8748241312TN-M120TN-M
71.1615044248TN86.5180712454TN9-0.4094679042TN-M10-1.1615044248TN1114.9819287546TN121.8748241312TN-M
1m6m2m0.50m5m1320.30mb
cadb
cadb
cadb
cadb
cadb
cad
PORTICO 02UNIVERSIDAD ALAS PERUANASCARRERA: INGENIERIA CIVILCURSO: ANALISIS ESTRUCTURAL IIALUMNO: GARCIA CONDORCALLO, ALANEJERCICIO PRACTICO DE PORTICO POR EL METODO DE RIGIDEZRELACION S - R - CSRC180PI200
Paso 01Numeramos las barras Numeramos los Grados de Libertad ( DOF ) libres y restringidos de la estructura
Barra123A (m)0.1700.1500.150Inercia (m4)0.00197843140.0031250.003125FC (Kg/cm2)280280280E (Tn/m)2509980.079602232509980.079602232509980.07960223L (m)6.005.006.32Angulo (grados)090108.43Grados (Rad)0.000000001.570796331.89254688Paso 02Esta es la matriz de RIGIDEZ en coordenadas globales para la barra de un portico
Paso 03Podemos encontrar esta matriz para todas las barras del portico de la sgte manera:Coordenadas Globales ( Barra del Portico )
TIPO DE FIGURA4
L1F`c4Rectangulo1Circulo2S. Tubular3Seccion 4Seccion 5ITEMAYAYIdAd2Seccion 6ITEMAYAYIdAd21140b(m)0.30r(m)0.3r(m)0.4a(m)0.6a(m)0.3a(m)0.32175h(m)0.15A(m2)0.2827433388r(m)0.2b(m)0.2b(m)0.410.30.50.150.0250.10.003b(m)0.410.450.750.33750.084375-0.1260.0073210A(m2)0.045I(m4)0.0063617251A(m2)0.3769911184c(m)0.2c(m)0.3c(m)0.34280I0.000084375As0.2544690049I(m4)0.0188495559d(m)0.25d(m)120.120.850.1020.0009-0.250.0075d(m)1.520.120.150.0180.00090.4740.0275315As 0.0375As0.1884955592A(m2)0.17A(m2)0.49A(m2)0.696420I(m4)0.0019784314I(m4)0.03640.420.2520.02590.0105I(m4)0.11938026320.570.35550.0852750.034As0.1416666667As0.25As0.375YC=0.6MYC=0.624MMx0.041Yg0.2411764706INERCIA TOTAL0.0364m4INERCIA TOTAL0.1193802632m4
BARRA1CO,CA06A (m)0.170123456Inercia (m4)0.00198171116.100.00-0.00-71116.10-0.00-0.00FC (Kg/cm2)28020.00275.88827.64-0.00-275.88827.64E (Tn/m)2509980.083-0.00827.643310.550.00-827.641655.27L (m)6.004-71116.10-0.000.0071116.100.000.00Angulo05-0.00-275.88-827.640.00275.88-827.64Radianes06-0.00827.641655.270.00-827.643310.55COS1SEN0
TIPO DE FIGURA1
L1F`c4Rectangulo1Circulo2S. Tubular3Seccion 4Seccion 5ITEMAYAYIdAd2Seccion 6ITEMAYAYIdAd21140b(m)0.30r(m)1r(m)4a(m)0.6a(m)0.3a(m)0.32175h(m)0.50A(m2)3.1415926536r(m)2b(m)0.2b(m)0.410.30.50.150.0250.10.003b(m)0.410.450.750.33750.084375-0.1260.0073210A(m2)0.15I(m4)0.7853981634A(m2)37.6991118431c(m)0.2c(m)0.3c(m)0.34280I0.003125As2.8274333882I(m4)188.4955592154d(m)0.25d(m)120.120.850.1020.0009-0.250.0075d(m)1.520.120.150.0180.00090.4740.0275315As 0.125As18.8495559215A(m2)0.17A(m2)0.49A(m2)0.696420I(m4)0.0019784314I(m4)0.03640.420.2520.02590.0105I(m4)0.11938026320.570.35550.0852750.034As0.1416666667As0.25As0.375YC=0.600M YC=0.624MMx0.041Yg0.2411764706INERCIA TOTAL0.0364m4INERCIA TOTAL0.1193802632m4
BARRA2CO,CA50A (m)0.150789123Inercia (m4)0.0037752.990.00-1882.49-752.99-0.00-1882.49FC (Kg/cm2)280.00080.0075299.400.00-0.00-75299.400.00E (Tn/m)2509980.0809-1882.490.006274.951882.49-0.003137.48L (m)5.001-752.99-0.001882.49752.990.001882.49Angulo902-0.00-75299.40-0.000.0075299.40-0.00Radianes1.573-1882.490.003137.481882.49-0.006274.95COS0SEN1
TIPO DE FIGURA1
L1F`c4Rectangulo1Circulo2S. Tubular3Seccion 4Seccion 5ITEMAYAYIdAd2Seccion 6ITEMAYAYIdAd21140b(m)0.30r(m)1r(m)4a(m)0.6a(m)0.3a(m)0.32175h(m)0.50A(m2)3.1415926536r(m)2b(m)0.2b(m)0.410.30.50.150.0250.10.003b(m)0.410.450.750.33750.084375-0.1260.0073210A(m2)0.15I(m4)0.7853981634A(m2)37.6991118431c(m)0.2c(m)0.3c(m)0.34280I0.003125As2.8274333882I(m4)188.4955592154d(m)0.25d(m)120.120.850.1020.0009-0.250.0075d(m)1.520.120.150.0180.00090.4740.0275315As 0.125As18.8495559215A(m2)0.17A(m2)0.49A(m2)0.696420I(m4)0.0019784314I(m4)0.03640.420.2520.02590.0105I(m4)0.11938026320.570.35550.0852750.034As0.1416666667As0.25As0.375YC=0.600MYC=0.624MMx0.041Yg0.2411764706INERCIA TOTAL0.0364m4INERCIA TOTAL0.1193802632m4
BARRA3CO,CA62A (m)0.150101112456Inercia (m4)0.003106287.79-17747.20-1116.18-6287.7917747.20-1116.18FC (Kg/cm2)28011-17747.2053613.67-372.0617747.20-53613.67-372.06E (Tn/m)2509980.0812-1116.18-372.064960.781116.18372.062480.39L (m)6.324-6287.7917747.201116.186287.79-17747.201116.18Angulo108517747.20-53613.67372.06-17747.2053613.67372.06Radianes1.896-1116.18-372.062480.391116.18372.064960.78COS-0SEN1
123456789101112171869.100.001882.49-71116.10-0.00-0.00-752.99-0.001882.490.000.000.0020.0075575.28827.64-0.00-275.88827.64-0.00-75299.40-0.000.000.000.0031882.49827.649585.500.00-827.641655.27-1882.490.003137.480.000.000.004-71116.10-0.000.0077403.90-17747.201116.180.000.000.00-6287.7917747.201116.185-0.00-275.88-827.64-17747.2053889.55-455.580.000.000.0017747.20-53613.67372.066-0.00827.641655.271116.18-455.588271.330.000.000.00-1116.18-372.062480.397-752.99-0.00-1882.490.000.000.00752.990.00-1882.490.000.000.008-0.00-75299.400.000.000.000.000.0075299.400.000.000.000.0091882.49-0.003137.480.000.000.00-1882.490.006274.950.000.000.00100.000.000.00-6287.7917747.20-1116.180.000.000.006287.79-17747.20-1116.18110.000.000.0017747.20-53613.67-372.060.000.000.00-17747.2053613.67-372.06120.000.000.001116.18372.062480.390.000.000.00-1116.18-372.064960.78
Paso 04A partir de las matrices de todas las barras se obtiene esta matriz de toda la estructura sumando las componentes de cada matriz en funcin de sus grados de libertad con lo cual tenemos una matriz de 8x8 que luego particionamos como se indica
10.000TN70.000M20.000TN80.000M30.000TN-M90.000RAD40.000TN100.000M50.000TN110.000M60.000TN-M120.000RAD
Paso 05Para invertir la matriz (kff) seleccionamos las celdas (E170:H173) la funcion es =MINVERSA(E161:H164) y sin soltar presionamos "CTROL" + "SHIFT", sin soltar damos enterCOMPROBACION1
12345610.0011592540.0000044169-0.00017837760.00115274520.0003760696-0.000099588520.00000441690.0000132717-0.00000162290.00000442070.000001486-0.00000151793-0.0001783776-0.00000162290.0001357263-0.0001766736-0.0000561598-0.000006251440.00115274520.0000044207-0.00017667360.00116027410.0003785649-0.000100808450.00037606960.000001486-0.00005615980.00037856490.0001421007-0.00003216866-0.0000995885-0.0000015179-0.0000062514-0.0001008084-0.00003216860.0001341342
7891011121-752.9940238807-01882.48505970170000.0000.0002-0-75299.4023880668-00000.0000.0003-1882.485059701703137.47509950280000.0000.0004000-6287.793350201917747.20371625041116.17633435540.0000.000500017747.2037162504-53613.6699268698372.05877811850.0000.0006000-1116.1763343554-372.05877811852480.3918541230.0000.000
Paso 06Para Multiplicar una matriz con el vector de cargas nodales seleccionamos las celdas (E187:E190) la funcion es =MMULT(E170:H173,E149:E152) y sin soltar presionamos "CTROL" + "SHIFT", sin soltar damos enterDatos del MEP CON SIGNO CAMBIADO
10M70TN70TN20M80TN80TN30RAD90TN-M90TN-M40M100TN100TN50M110TN110TN60RAD120TN-M120TN-M
70TN80TN90TN-M100TN110TN120TN-M
1m6m2m0.50m5m1320.30mb
cadb
cadb
cadb
cadb
cadb
cad
EXAMEN PORTICOUNIVERSIDAD ALAS PERUANASCARRERA: INGENIERIA CIVILCURSO: ANALISIS ESTRUCTURAL IIALUMNO: GARCIA CONDORCALLO, ALANEJERCICIO PRACTICO DE PORTICO POR EL METODO DE RIGIDEZRELACION S - R - CSRC180PI200
Paso 01Numeramos las barras Numeramos los Grados de Libertad ( DOF ) libres y restringidos de la estructura
Barra123A (m)0.1700.1500.150Inercia (m4)0.00197843140.0031250.003125FC (Kg/cm2)280280280E (Tn/m)2509980.079602232509980.079602232509980.07960223L (m)6.005.006.32Angulo (grados)090108.43Grados (Rad)0.000000001.570796331.89254688Paso 02Esta es la matriz de RIGIDEZ en coordenadas globales para la barra de un portico
Paso 03Podemos encontrar esta matriz para todas las barras del portico de la sgte manera:Coordenadas Globales ( Barra del Portico )
TIPO DE FIGURA4
L100F`c4Rectangulo1Circulo2S. Tubular3Seccion 4Seccion 5ITEMAYAYIdAd2Seccion 6ITEMAYAYIdAd21140b(cm)0.30r(cm)0.3R(cm)0.4a(cm)0.6a(cm)30a(cm)302175h(cm)0.15A(cm2)0.2827433388r(cm)0.2b(cm)0.2b(cm)401300050150000250000010300000b(cm)4014500753375008437500-12.632718005.5403210A(cm2)0.045I(cm4)0.0063617251A(cm2)0.3769911184c(cm)0.2c(cm)30c(cm)304280I0.000084375As0.2544690049I(cm4)0.0188495559d(cm)0.25d(cm)100212008510200090000-25750000d(cm)1502120015180009000047.3682692520.7765315As 0.0375As0.1884955592A(cm2)0.17A(cm2)4900A(cm2)69006420I(cm4)0.0019784314I(cm4)3640000420025200025900001050000I(cm4)11938026.3157895570035550085275003410526.316As0.1416666667As2500As3750YC=60cmYC=62.3684210526cmMx0.041Yg0.2411764706INERCIA TOTAL3640000cm4INERCIA TOTAL11938026.3157895cm4
BARRA1CO,CA06A (m)0.170123456Inercia (m4)0.00198171116.100.00-827.64-71116.10-0.00-0.00FC (Kg/cm2)28020.00275.88827.64-0.00-275.88827.64E (Tn/m)2509980.083-827.64827.643310.550.00-827.641655.27L (m)6.004-71116.10-0.000.0071116.10-275.880.00Angulo05-0.00-275.88-827.64-275.88275.88-827.64Radianes06-0.00827.641655.270.00-827.643310.55COS1SEN0
TIPO DE FIGURA1
L100F`c4Rectangulo1Circulo2S. Tubular3Seccion 4Seccion 5ITEMAYAYIdAd2Seccion 6ITEMAYAYIdAd21140b(cm)0.30r(cm)1R(cm)4a(cm)0.6a(cm)30a(cm)302175h(cm)0.50A(cm2)3.1415926536r(cm)2b(cm)0.2b(cm)401300050150000250000010300000b(cm)4014500753375008437500-12.632718005.5403210A(cm2)0.15I(cm4)0.7853981634A(cm2)37.6991118431c(cm)0.2c(cm)30c(cm)304280I0.003125As2.8274333882I(cm4)188.4955592154d(cm)0.25d(cm)100212008510200090000-25750000d(cm)1502120015180009000047.3682692520.7765315As 0.125As18.8495559215A(cm2)0.17A(cm2)4900A(cm2)69006420I(cm4)0.0019784314I(cm4)3640000420025200025900001050000I(cm4)11938026.3157895570035550085275003410526.316As0.1416666667As2500As3750YC=60cmYC=62.3684210526cmMx0.041Yg0.2411764706INERCIA TOTAL3640000cm4INERCIA TOTAL11938026.3157895cm4
BARRA2CO,CA50A (m)0.150123789Inercia (m4)0.00310.0000.000-1882.485-752.994-0.000-1882.485FC (Kg/cm2)280.00020.00075299.4020.000-0.000-75299.4020.000E (Tn/m)2509980.0803-1882.4850.0006274.9501882.485-0.0003137.475L (m)5.007-752.994-0.0001882.485752.9940.0001882.485Angulo908-0.000-75299.402-0.0000.00075299.402-0.000Radianes1.579-1882.4850.0003137.4751882.485-0.0006274.950COS0SEN1
TIPO DE FIGURA1
L100F`c4Rectangulo1Circulo2S. Tubular3Seccion 4Seccion 5ITEMAYAYIdAd2Seccion 6ITEMAYAYIdAd21140b(cm)0.30r(cm)1R(cm)4a(cm)0.6a(cm)30a(cm)302175h(cm)0.50A(cm2)3.1415926536r(cm)2b(cm)0.2b(cm)401300050150000250000010300000b(cm)4014500753375008437500-12.632718005.5403210A(cm2)0.15I(cm4)0.7853981634A(cm2)37.6991118431c(cm)0.2c(cm)30c(cm)304280I0.003125As2.8274333882I(cm4)188.4955592154d(cm)0.25d(cm)100212008510200090000-25750000d(cm)1502120015180009000047.3682692520.7765315As 0.125As18.8495559215A(cm2)0.17A(cm2)4900A(cm2)69006420I(cm4)0.0019784314I(cm4)3640000420025200025900001050000I(cm4)11938026.3157895570035550085275003410526.316As0.1416666667As2500As3750YC=60cmYC=62.3684210526cmMx0.041Yg0.2411764706INERCIA TOTAL3640000cm4INERCIA TOTAL11938026.3157895cm4
BARRA3CO,CA62A (m)0.150456101112Inercia (m4)0.00345952.940-17858.821-1176.553-6287.79317747.204-1116.176FC (Kg/cm2)2805-17858.82153613.670-372.05917747.204-53613.670-372.059E (Tn/m)2509980.086-1176.553-372.0594960.7841116.176372.0592480.392L (m)6.3210-6287.79317747.2041116.1766287.793-17741.1661116.176Angulo1081117747.204-53613.670372.059-17741.16653613.670372.059Radianes1.8912-1116.176-372.0592480.3921116.176372.0594960.784COS-0SEN1
123456789101112171116.1020.000-2710.122-71116.102-0.000-0.000-752.994-0.000-1882.4850.0000.0000.00020.00075575.281827.637-0.000-275.879827.637-0.000-75299.4020.0000.0000.0000.0003-2710.122827.6379585.4990.000-827.6371655.2741882.485-0.0003137.4750.0000.0000.0004-71116.102-0.0000.00077069.043-18134.700-1176.5530.0000.0000.000-6287.79317747.204-1116.1765-0.000-275.879-827.637-18134.70053889.549-1199.6960.0000.0000.00017747.204-53613.670-372.0596-0.000827.6371655.274-1176.553-1199.6968271.3330.0000.0000.0001116.176372.0592480.3927-752.994-0.0000.0000.0000.0000.000752.9940.0001882.4850.0000.0000.0008-0.000-75299.4020.0000.0000.0000.0000.00075299.402-0.0000.0000.0000.0009-1882.4850.0000.0000.0000.0000.0001882.485-0.0006274.9500.0000.0000.000100.0000.000-6287.793-6287.79317747.2041116.1760.0000.0000.0006287.793-17741.1661116.176110.0000.00017747.20417747.204-53613.670372.0590.0000.0000.000-17741.16653613.670372.059120.0000.0000.000-1116.176-372.0592480.3920.0000.0000.0001116.176372.0594960.784
Paso 04A partir de las matrices de todas las barras se obtiene esta matriz de toda la estructura sumando las componentes de cada matriz en funcin de sus grados de libertad con lo cual tenemos una matriz de 8x8 que luego particionamos como se indica
123456978101112123456978101112
12.000Tn72.000Tn2-4.020Tn80.000Tn3-1.560Tn100.000Tn40.000Tn110.000Tn5-10.980Tn120.000Tn6-0.020Tn9-2.000Tn
1234569171116.1020.000-2710.122-71116.102-0.000-0.000-1882.48520.00075575.281827.637-0.000-275.879827.6370.0003-2710.122827.6379585.4990.000-827.6371655.2743137.4754-71116.102-0.0000.00077069.043-18134.700-1176.5530.0005-0.000-275.879-827.637-18134.70053889.549-1199.6960.0006-0.000827.6371655.274-1176.553-1199.6968271.3330.0009-1882.4850.0000.0000.0000.0000.0006274.950
Paso 05Para invertir la matriz (kff) seleccionamos las celdas (E170:H173) la funcion es =MINVERSA(E161:H164) y sin soltar presionamos "CTROL" + "SHIFT", sin soltar damos enter
12345691-0.00065694230.0000022291-0.0001901616-0.000661057-0.0002273506-0.0000891749-0.000102001920.0000016440.0000132491-0.00000047050.00000164260.0000005931-0.00000091190.00000072843-0.0001232561-0.00000052810.0000725231-0.0001240812-0.000041493-0.0000381288-0.00007323844-0.00066108980.0000022316-0.0001914152-0.0006510789-0.000223964-0.0000870138-0.00010261935-0.00022663170.0000007931-0.0000644392-0.0002232292-0.0000581587-0.0000273723-0.00003576996-0.000102406-0.0000007876-0.0000510406-0.0001003233-0.00003204890.0001122737-0.00000520159-0.00019708270.0000006687-0.0000570485-0.0001983171-0.0000682052-0.00002675250.0001287632
781011121-752.994-0.0000.0000.0000.000-1505.9882-0.000-75299.4020.0000.0000.000-0.00031882.485-0.0000.0000.0000.0003764.97040.0000.000-6287.79317747.204-1116.1760.00050.0000.00017747.204-53613.670-372.0590.00060.0000.0001116.176372.0592480.3920.00091882.485-0.0000.0000.0000.0003764.970
1507.988-4.020-3766.5300.000-10.980-0.020-3766.970
Paso 06Para Multiplicar una matriz con el vector de cargas nodales seleccionamos las celdas (E187:E190) la funcion es =MMULT(E170:H173,E149:E152) y sin soltar presionamos "CTROL" + "SHIFT", sin soltar damos enter
10.1123154357m20.0014474431m3-0.1826839525m40.113071512m50.0363343643m60.0577656564m9-0.5666240969m
7ERROR:#VALUE!Tn8ERROR:#VALUE!Tn10ERROR:#VALUE!Tn11ERROR:#VALUE!Tn12ERROR:#VALUE!Tn
7ERROR:#VALUE!Tn8ERROR:#VALUE!Tn10ERROR:#VALUE!Tn11ERROR:#VALUE!Tn12ERROR:#VALUE!Tn
1m6m2m0.50m5m1320.30mb
cadb
cadb
cadb
cadb
cadb
cad
PLANTILLA ORIGINALUNIVERSIDAD ALAS PERUANASCARRERA: INGENIERIA CIVILCURSO: ANALISIS ESTRUCTURAL IIALUMNO: GARCIA CONDORCALLO, ALANEJERCICIO PRACTICO DE PORTICO POR EL METODO DE RIGIDEZRELACION S - R - CSRC180PI200
Paso 01Numeramos las barras Numeramos los Grados de Libertad ( DOF ) libres y restringidos de la estructuraBarra123A (m)0.2400.0710.126Inercia (m4)0.3680.0003980.001257FC (Kg/cm2)210210210E (Tn/m)2173706.511928422173706.511928422173706.51192842L (m)6.004.007.00Angulo (grados)0270270Grados (Rad)0.000000004.712388984.71238898Paso 02Esta es la matriz de RIGIDEZ en coordenadas globales para la barra de un portico
Paso 03Podemos encontrar esta matriz para todas las barras del portico de la sgte manera:Coordenadas Globales ( Barra del Portico )BARRA 1A (m)0.240cm123456Inercia (m4)0.368cm4186948.2600.000-133320.666-86948.2600.0000.000FC (Kg/cm2)210.000Kg/cm20.00044440.222133320.6660.000-44440.222133320.666E (Tn/m)2173706.512Tn/m3-133320.666133320.666533282.6640.000-133320.666266641.332L (m)6.00m4-86948.2600.0000.00086948.260-44440.2220.000Angulo050.000-44440.222-133320.666-44440.22244440.222-133320.666Radianes060.000133320.666266641.3320.000-133320.666533282.664COS1SEN0
BARRA 2A (m)0.071cm123789Inercia (m4)0.000cm410.0000.000-324.106-162.053-0.000324.106FC (Kg/cm2)210.000Kg/cm20.00038412.565-0.000-0.000-38412.565-0.000E (Tn/m)2173706.512Tn/m3-324.106-0.000864.283-324.1060.000432.141L (m)4.00m7-162.053-0.000-324.106162.0530.000-324.106Angulo2708-0.000-38412.5650.0000.00038412.5650.000Radianes4.719324.106-0.000432.141-324.1060.000864.283COS-0SEN-1
BARRA 3A (m)0.126cm456101112Inercia (m4)0.001cm440.0000.000-334.477-95.565-0.000334.477FC (Kg/cm2)210.000Kg/cm50.00039022.288-0.000-0.000-39022.288-0.000E (Tn/m)2173706.512Tn/m6-334.477-0.0001560.892-334.4770.000780.446L (m)7.00m10-95.565-0.000-334.47795.5650.000-334.477Angulo27011-0.000-39022.2880.0000.00039022.2880.000Radianes4.7112334.477-0.000780.446-334.4770.0001560.892COS-0SEN-1123456978101112186948.2600.000-133644.772-86948.2600.0000.000324.106-162.053-0.0000.0000.0000.00020.00082852.787133320.6660.000-44440.222133320.666-0.000-0.000-38412.5650.0000.0000.0003-133644.772133320.666534146.9470.000-133320.666266641.332432.141-324.1060.0000.0000.0000.0004-86948.2600.0000.00086948.260-44440.222-334.4770.0000.0000.000-95.565-0.000334.47750.000-44440.222-133320.666-44440.22283462.510-133320.6660.0000.0000.000-0.000-39022.288-0.00060.000133320.666266641.332-334.477-133320.666534843.5560.0000.0000.000-334.4770.000780.4469324.106-0.0000.0000.0000.0000.000864.283-324.1060.0000.0000.0000.0007-162.053-0.0000.0000.0000.0000.000-324.106162.0530.0000.0000.0000.0008-0.000-38412.5650.0000.0000.0000.0000.0000.00038412.5650.0000.0000.000100.0000.000-95.565-95.565-0.000-334.4770.0000.0000.00095.5650.000-334.477110.0000.000-0.000-0.000-39022.2880.0000.0000.0000.0000.00039022.2880.000120.0000.000334.477334.477-0.000780.446-334.4770.0000.000-334.4770.0001560.892
Paso 04A partir de las matrices de todas las barras se obtiene esta matriz de toda la estructura sumando las componentes de cada matriz en funcin de sus grados de libertad con lo cual tenemos una matriz de 8x8 que luego particionamos como se indica
123456978101112123456978101112
12.000Tn72.000Tn2-4.020Tn80.000Tn3-1.560Tn100.000Tn40.000Tn110.000Tn5-10.980Tn120.000Tn6-0.020Tn9-2.000Tn
1234569186948.2600.000-133644.772-86948.2600.0000.000324.10620.00082852.787133320.6660.000-44440.222133320.666-0.0003-133644.772133320.666534146.9470.000-133320.666266641.332432.1414-86948.2600.0000.00086948.260-44440.222-334.4770.00050.000-44440.222-133320.666-44440.22283462.510-133320.6660.00060.000133320.666266641.332-334.477-133320.666534843.5560.0009324.106-0.0000.0000.0000.0000.000864.283
Paso 05Para invertir la matriz (kff) seleccionamos las celdas (E170:H173) la funcion es =MINVERSA(E161:H164) y sin soltar presionamos "CTROL" + "SHIFT", sin soltar damos enter
12345691-0.00000302660.0000017435-0.0000033566-0.0000093579-0.0000123734-0.00000185140.000002813320.00000174560.0000249822-0.00000238420.00000541220.0000071982-0.0000032410.00000053753-0.000003359-0.00000238510.0000011825-0.0000051741-0.0000035446-0.00000088180.00000066844-0.00000936050.0000054071-0.0000051695-0.000001392-0.0000069079-0.00000049350.00000609495-0.00001237840.0000071924-0.0000035403-0.00000691290.00001067370.00000262840.00000641216-0.000001852-0.000003242-0.0000008809-0.00000049370.00000262910.00000377210.00000113590.000001135-0.00000065380.00000125870.00000350920.000004640.00000069430.0011559738
781011121-162.053-0.0000.0000.0000.000-324.1062-0.000-38412.5650.0000.0000.000-0.0003-324.1060.0000.0000.0000.000-648.21240.0000.000-95.565-0.000334.4770.00050.0000.000-0.000-39022.288-0.0000.00060.0000.000-334.4770.000780.4460.0009-324.1060.0000.0000.0000.000-648.212
326.106-4.020646.6520.000-10.980-0.020646.212
Paso 06Para Multiplicar una matriz con el vector de cargas nodales seleccionamos las celdas (E187:E190) la funcion es =MMULT(E170:H173,E149:E152) y sin soltar presionamos "CTROL" + "SHIFT", sin soltar damos enter
1-0.0012106803m2-0.0008045441m30.0001497115m4-0.002402625m5-0.002328633m6-0.0004560875m90.7481399475m
781.83Tn830.90Tn100.37Tn1190.87Tn12-251.34Tn
783.826Tn830.905Tn100.368Tn1190.869Tn12-251.345Tn
4 Tn3 Tn/m2m2m3m6m2m2m4m
EJEMPLO 02RELACION S - R - CSRC180PI200Paso 01Numeramos las barras Numeramos los Grados de Libertad ( DOF ) libres y restringidos de la estructuraBarraUnd.123456E KN/M2.00E+062.00E+062.00E+062.00E+062.00E+062.00E+06A M0.050.050.050.050.050.05LM101010.0010.0014.1414.14Angulo GRADOS0090.0090.0045.00135.00Grados RADIANES0.000000000.000000001.570796331.570796330.785398162.35619449Paso 02Esta es la matriz de RIGIDEZ en coordenadas globales para la barra de una armadura
12345678Paso 03Podemos encontrar esta matriz para todas las barras de la armadura de la sgte manera:Coordenadas Globales ( Barra de Armadura )BARRA 1E2.00E+06KN/M12651265A0.05M110-101100000-100000L10.00Mk1 =10000.0020000=20000Angulo06-10106-100000100000Radianes05000050000COS1SEN0
BARRA 2E2.00E+06KN/M34783478A0.05M310-103100000-100000L10.00Mk1 =10000.0040000=40000Angulo07-10107-100000100000Radianes08000080000COS1SEN0
BARRA 3E2.00E+06KN/M12341234A0.05M100-0-010.000.00-0.00-0.00L10.00Mk1 =10000.00201-0-1=20.0010000.00-0.00-10000.00Angulo90.003-0-0003-0.00-0.000.000.00Radianes1.5707963274-0-1014-0.00-10000.000.0010000.00COS0.000000000SEN1.000000000
BARRA 4E2.00E+06KN/M65786578A0.05M600-0-060.000.00-0.00-0.00L10.00Mk1 =10000.00501-0-1=50.0010000.00-0.00-10000.00Angulo90.007-0-0007-0.00-0.000.000.00Radianes1.5707963278-0-1018-0.00-10000.000.0010000.00COS0.00000000SEN1.000000000
BARRA 5E2.00E+06KN/M12781278A0.05M10.50.5-0.5-0.513535.533535.53-3535.53-3535.53L14.14Mk1 =7071.0720.50.5-0.5-0.5=23535.533535.53-3535.53-3535.53Angulo45.007-0.5-0.50.50.57-3535.53-3535.533535.533535.53Radianes0.7853981638-0.5-0.50.50.58-3535.53-3535.533535.533535.53COS0.70710678SEN0.707106781
BARRA 66E2.00E+06KN/M65346534A0.05M60.5-0.5-0.50.563535.53-3535.53-3535.533535.53L14.14Mk1 =7071.075-0.50.50.5-0.5=5-3535.533535.533535.53-3535.53Angulo135.003-0.50.50.5-0.53-3535.533535.533535.53-3535.53Radianes2.35619449040.5-0.5-0.50.543535.53-3535.53-3535.533535.53COS-0.70710678SEN0.707106781
12345678113535.533535.53-0.00-0.000.00-10000.00-3535.53-3535.5323535.5313535.53-0.00-10000.000.000.00-3535.53-3535.533-0.00-0.0013535.53-3535.533535.53-3535.53-10000.000.004-0.00-10000.00-3535.5313535.53-3535.533535.530.000.0050.00-10000.003535.53-3535.5313535.53-3535.53-0.00-10000.0060.000.00-3535.533535.53-3535.5313535.53-0.00-0.007-3535.53-3535.53-10000.000.00-0.00-10000.0013535.533535.538-3535.53-3535.530.000.00-0.00-0.003535.5313535.53
Paso 04A partir de las matrices de todas las barras se obtiene esta matriz de toda la estructura sumando las componentes de cada matriz en funcin de sus grados de libertad con lo cual tenemos una matriz de 8x8 que luego particionamos como se indica
1234567812345678
10.00KN20.00KN32.00KN4-4.00KN50.00KN
Paso 05Para invertir la matriz (kff) seleccionamos las celdas (E170:H173) la funcion es =MINVERSA(E161:H164) y sin soltar presionamos "CTROL" + "SHIFT", sin soltar damos enter
1234510.000100-0.000100-0.000017-0.000083-0.0000172-0.0001000.0003830.0000660.0003170.0000663-0.0000000.0000000.0000830.000017-0.0000174-0.0001000.0003830.0000830.0004000.0000835-0.0001000.0003830.0000490.0003340.000149
60.00M
Paso 06Para Multiplicar una matriz con el vector de cargas nodales seleccionamos las celdas (E187:E190) la funcion es =MMULT(E170:H173,E149:E152) y sin soltar presionamos "CTROL" + "SHIFT", sin soltar damos enter
10.0002970563M2-0.0011372583M30.0000970563M4-0.0014343146M5-0.001240202M
6-1.03KN72.00KN82.97KN
MURO DE CORTE
CURSO: ANALISIS ESTRUCTURAL II
EJERCICIO PRACTICO DE MUROS DE CORTERELACION S - R - CSRC180PI200
Paso 01Numeramos las barras Numeramos los Grados de Libertad ( DOF ) libres y restringidos de la estructura1000050
150425500
150150
75757575
Paso 03Podemos encontrar esta matriz para todas las barras del portico de la sgte manera:
TIPO DE FIGURA1
F`c3Rectangulo1Circulo2S. Tubular3Seccion 41140b(cm)30.00r(cm)1R(cm)4a(cm)0.62175h(cm)150.00A(cm2)3.1415926536r(cm)2b(cm)0.23210A(cm2)4500I(cm4)0.7853981634A(cm2)37.6991118431c(cm)0.44280I8437500As2.8274333882I(cm4)188.4955592154d(cm)0.35315As 3750As18.8495559215A(cm2)0.246420I(cm4)0.0074As0.2
Mx0.084PLACA1Yg0.35As (cm2)3750G86948.26056785120.3737024226208706.745-44350183.2-208706.745-44350183.2fc (Kg/cm2)21072301571.601-2301571.601E (Kg/cm2)217370.65128-44350183.21373986069044350183.245108967187Area (cm2)45005-208706.74544350183.24208706.744744350183.24Inercia (cm4)84375001-2301571.6012301571.601H de placa (cm)4252-44350183.2510896718744350183.2413739860690
TIPO DE FIGURA1
F`c3Rectangulo1Circulo2S. Tubular3Seccion 41140b(cm)30.00r(cm)1R(cm)4a(cm)0.62175h(cm)150.00A(cm2)3.1415926536r(cm)2b(cm)0.23210A(cm2)4500I(cm4)0.7853981634A(cm2)37.6991118431c(cm)0.44280I8437500As2.8274333882I(cm4)188.4955592154d(cm)0.35315As 3750As18.8495559215A(cm2)0.246420I(cm4)0.0074As0.2
Mx0.084PLACA2Yg0.35As (cm2)3750G86948.2605910115340.3737024229208706.745-44350183.2-208706.745-44350183.2fc (Kg/cm2)210102301571.601-2301571.601E (Kg/cm2)217370.651211-44350183.21373986069044350183.245108967187Area (cm2)45005-208706.74544350183.24208706.744744350183.24Inercia (cm4)84375003-2301571.6012301571.601H de placa (cm)4254-44350183.2510896718744350183.2413739860690
TIPO DE FIGURA1
F`c3Rectangulo1Circulo2S. Tubular3Seccion 41140b(cm)30.00r(cm)1R(cm)4a(cm)0.62175h(cm)50.00A(cm2)3.1415926536r(cm)2b(cm)0.23210A(cm2)1500I(cm4)0.7853981634A(cm2)37.6991118431c(cm)0.44280I312500As2.8274333882I(cm4)188.4955592154d(cm)0.35315As 1250As18.8495559215A(cm2)0.246420I(cm4)0.0074As0.2
Mx0.084VIGA3Yg0.35As (cm2)1250G86948.260512340.03000000016521.122119363.85-6521.122119363.85fc (Kg/cm2)21022119363.85824649907.96-2119363.85552936593.97E (Kg/cm2)217370.65123-6521.12-2119363.856521.12-2119363.85Area (cm2)150042119363.85552936593.97-2119363.85824649907.96Inercia (cm4)312500Long de viga (cm)500a75b75
1234567891011123080932119364-6521211936400-230157200002211936414564510598-211936455293659444350183-44350183051089671870003-6521-21193642308093-211936400000-2301572042119364552936594-21193641456451059844350183000-44350183051089671875044350183044350183417413-208707044350183-20870704435018360-4435018300-2087072087070-443501830007-230157200000230157200008051089671870044350183-443501830137398606900009000-44350183-2087070002087070-443501831000-23015720000002301572011000510896718744350183000-44350183013739860690
Paso 04A partir de las matrices de todas las barras se obtiene esta matriz de toda la estructura sumando las componentes de cada matriz en funcin de sus grados de libertad con lo cual tenemos una matriz de 8x8 que luego particionamos como se indica
12345697810111234569781011
1234510.0000004336-0.00000000020.0000000009-0.00000000020.00000003422-0.00000000020.00000000010.00000000020.0000000001-0.000000018730.00000000090.00000000020.00000043360.0000000002-0.00000003424-0.00000000020.00000000010.00000000020.0000000001-0.000000018750.0000000342-0.0000000187-0.0000000342-0.00000001870.000006367
FUERZA10000kgDESPLZAMIENTO0.0636704269cm1010.0003422431cm202-0.0001868864cmK LATERAL DEL PORTICO157058.786718254kg/cm303-0.0003422431cm1570587.86718254Tn/m404-0.0001868864cm51000050.0636704269cm
67891060.00-44350183.240.000.00-208706.747-2301571.600.000.000.000.0080.005108967187.060.000.0044350183.2490.000.000.00-44350183.24-208706.74100.000.00-2301571.600.000.00110.000.000.005108967187.0644350183.24
6-5000kg60kg7-787.6970815163kg70kg81868998.44850721kg80kg9-5000kg90kg10787.6970815163kg100kg111868998.44850721kg110kg
6-5000kg6-5Tn7-787.6970815163kg7-0.7876970815Tn81868998.44850721kg.cm818.6899844851Tn.m9-5000kg9-5Tn10787.6970815163kg100.7876970815Tn111868998.44850721kg.cm1118.6899844851Tn.m
MC-SECCIONES
CURSO: ANALISIS ESTRUCTURAL II
EJERCICIO PRACTICO DE MUROS DE CORTERELACION S - R - CSRC180PI200
Paso 01Numeramos las barras Numeramos los Grados de Libertad ( DOF ) libres y restringidos de la estructura1000050
150425500
150150
75757575Paso 03Podemos encontrar esta matriz para todas las barras del portico de la sgte manera:
TIPO DE FIGURA5
L100F`c3Rectangulo1Circulo2S. Tubular3Seccion 4Seccion 5ITEMAYAYIdAd2Seccion 6ITEMAYAYIdAd21140b(cm)30.00r(cm)1R(cm)4a(cm)0.6a(cm)30a(cm)302175h(cm)150.00A(cm2)3.1415926536r(cm)2b(cm)0.2b(cm)401300050150000250000010300000b(cm)4014500753375008437500-12.632718005.5403210A(cm2)4500I(cm4)0.7853981634A(cm2)37.6991118431c(cm)0.2c(cm)30c(cm)304280I8437500As2.8274333882I(cm4)188.4955592154d(cm)0.25d(cm)100212008510200090000-25750000d(cm)1502120015180009000047.3682692520.7765315As 3750As18.8495559215A(cm2)0.17A(cm2)4900A(cm2)69006420I(cm4)0.0019784314I(cm4)3640000420025200025900001050000I(cm4)11938026.3157895570035550085275003410526.316As0.1416666667As2500As3750YC=60cmYC=62.3684210526cmMx0.041Yg0.2411764706INERCIA TOTAL3640000cm4INERCIA TOTAL11938026.3157895cm4
PLACA1As (cm2)2500G86948.26056785120.1612179936106513.091-22634031.9-106513.091-22634031.9fc (Kg/cm2)21072506155.743-2506155.743E (Kg/cm2)217370.65128-22634031.9667144747522634031.912948016085Area (cm2)49005-106513.09122634031.91106513.091322634031.91Inercia (cm4)36400001-2506155.7432506155.743H de placa (cm)4252-22634031.9294801608522634031.916671447475
TIPO DE FIGURA3
F`c3Rectangulo1Circulo2S. Tubular3Seccion 41140b(cm)30.00r(cm)1R(cm)4a(cm)0.62175h(cm)150.00A(cm2)3.1415926536r(cm)2b(cm)0.23210A(cm2)4500I(cm4)0.7853981634A(cm2)37.6991118431c(cm)0.44280I8437500As2.8274333882I(cm4)188.4955592154d(cm)0.35315As 3750As18.8495559215A(cm2)0.246420I(cm4)0.0074As0.2
Mx0.084Yg0.35PLACA2As (cm2)18.8495559215G86948.2605910115340.00000834996.405-1361.0-6.405-1361.0fc (Kg/cm2)2101019281.601-19281.601E (Kg/cm2)217370.651211-1361.03856301361.04192814Area (cm2)385-6.4051361.046.40491361.04Inercia (cm4)1883-19281.60119281.601H de placa (cm)4254-1361.01928141361.04385630
TIPO DE FIGURA1
F`c3Rectangulo1Circulo2S. Tubular3Seccion 41140b(cm)30.00r(cm)1R(cm)4a(cm)0.62175h(cm)50.00A(cm2)3.1415926536r(cm)2b(cm)0.23210A(cm2)1500I(cm4)0.7853981634A(cm2)37.6991118431c(cm)0.44280I312500As2.8274333882I(cm4)188.4955592154d(cm)0.35315As 1250As18.8495559215A(cm2)0.246420I(cm4)0.0074As0.2
Mx0.084Yg0.35
VIGA3As (cm2)1250G86948.260512340.03000000016521.122119363.85-6521.122119363.85fc (Kg/cm2)21022119363.85824649907.96-2119363.85552936593.97E (Kg/cm2)217370.65123-6521.12-2119363.856521.12-2119363.85Area (cm2)150042119363.85552936593.97-2119363.85824649907.96Inercia (cm4)312500Long de viga (cm)500a75b75
1234567891011125126772119364-6521211936400-25061560000221193647496097383-211936455293659422634032-22634032029480160850003-6521-211936425803-211936400000-19282042119364552936594-21193648250355381361000-13610192814502263403201361106519-106513022634032-60136160-2263403200-1065131065130-226340320007-250615600000250615600008029480160850022634032-22634032066714474750009000-1361-600060-13611000-19282000000192820110001928141361000-13610385630
Paso 04A partir de las matrices de todas las barras se obtiene esta matriz de toda la estructura sumando las componentes de cada matriz en funcin de sus grados de libertad con lo cual tenemos una matriz de 8x8 que luego particionamos como se indica
12345697810111234569781011
1234510.0000003989-0.00000000010.0000000171-0.00000000090.00000002452-0.00000000010.00000000040.000000015-0.0000000003-0.000000092730.00000001710.0000000150.00004963560.0000001174-0.00000318624-0.0000000009-0.00000000030.00000011740.00000000170.000000053850.0000000245-0.0000000927-0.00000318620.00000005380.0000290838
FUERZA10000kgDESPLZAMIENTO0.2908381151cm1010.0002451384cm202-0.000926952cmK LATERAL DEL PORTICO34383.3888350288kg/cm303-0.0318622379cm343833.888350288Tn/m4040.0005382831cm51000050.2908381151cm
67891060.00-22634031.910.000.00-106513.097-2506155.740.000.000.000.0080.002948016085.030.000.0022634031.9190.000.000.00-1361.04-6.40100.000.00-19281.600.000.00110.000.000.00192813.601361.04
6-9997.4045824888kg60kg7-614.3549639935kg70kg83850169.64197901kg80kg9-2.5954175112kg90kg10614.3549639935kg100kg11499.6314252125kg110kg
6-9997.4045824888kg6-9.9974045825Tn7-614.3549639935kg7-0.614354964Tn83850169.64197901kg.cm838.5016964198Tn.m9-2.5954175112kg9-0.0025954175Tn10614.3549639935kg100.614354964Tn11499.6314252125kg.cm110.0049963143Tn.m
b
cadb
cad
PORTICO-PRACTICAUNIVERSIDAD ALAS PERUANASCARRERA: INGENIERIA CIVILCURSO: ANALISIS ESTRUCTURAL IIALUMNO: GARCIA CONDORCALLO, ALANEJERCICIO PRACTICO DE PORTICO POR EL METODO DE RIGIDEZRELACION S - R - CSRC180PI200
Paso 01Numeramos las barras Numeramos los Grados de Libertad ( DOF ) libres y restringidos de la estructura
Barra123A (m)0.1700.1500.150Inercia (m4)0.00197843140.0031250.003125FC (Kg/cm2)280280280E (Tn/m)2509980.079602232509980.079602232509980.07960223L (m)6.005.006.32Angulo (grados)090108.43Grados (Rad)0.000000001.570796331.89254688Paso 02Esta es la matriz de RIGIDEZ en coordenadas globales para la barra de un portico
Paso 03Podemos encontrar esta matriz para todas las barras del portico de la sgte manera:Coordenadas Globales ( Barra del Portico )BARRA 1A (m)0.170cm123456Inercia (m4)0.002cm4171116.1020.000-827.637-71116.1020.0000.000FC (Kg/cm2)280.000Kg/cm20.000275.879827.6370.000-275.879827.637E (Tn/m)2509980.080Tn/m3-827.637827.6373310.5490.000-827.6371655.274L (m)6.00m4-71116.1020.0000.00071116.102-275.8790.000Angulo050.000-275.879-827.637-275.879275.879-827.637Radianes060.000827.6371655.2740.000-827.6373310.549COS1SEN0
BARRA 2A (m)0.150cm123789Inercia (m4)0.003cm410.0000.000-1882.485-752.994-0.000-1882.485FC (Kg/cm2)280.000Kg/cm20.00075299.4020.000-0.000-75299.4020.000E (Tn/m)2509980.080Tn/m3-1882.4850.0006274.9501882.485-0.0003137.475L (m)5.00m7-752.994-0.0001882.485752.9940.0001882.485Angulo908-0.000-75299.402-0.0000.00075299.402-0.000Radianes1.579-1882.4850.0003137.4751882.485-0.0006274.950COS0SEN1
BARRA 3A (m)0.150cm456101112Inercia (m4)0.003cm445952.940-17858.821-1176.553-6287.79317747.204-1116.176FC (Kg/cm2)280.000Kg/cm5-17858.82153613.670-372.05917747.204-53613.670-372.059E (Tn/m)2509980.080Tn/m6-1176.553-372.0594960.7841116.176372.0592480.392L (m)6.32m10-6287.79317747.2041116.1766287.793-17741.1661116.176Angulo1081117747.204-53613.670372.059-17741.16653613.670372.059Radianes1.8912-1116.176-372.0592480.3921116.176372.0594960.784COS-0SEN1123456789101112171116.1020.000-2710.122-71116.1020.0000.000-752.994-0.000-1882.4850.0000.0000.00020.00075575.281827.6370.000-275.879827.637-0.000-75299.4020.0000.0000.0000.0003-2710.122827.6379585.4990.000-827.6371655.2741882.485-0.0003137.4750.0000.0000.0004-71116.1020.0000.00077069.043-18134.700-1176.5530.0000.0000.000-6287.79317747.204-1116.17650.000-275.879-827.637-18134.70053889.549-1199.6960.0000.0000.00017747.204-53613.670-372.05960.000827.6371655.274-1176.553-1199.6968271.3330.0000.0000.0001116.176372.0592480.3927-752.994-0.0000.0000.0000.0000.000752.9940.0001882.4850.0000.0000.0008-0.000-75299.4020.0000.0000.0000.0000.00075299.402-0.0000.0000.0000.0009-1882.4850.0000.0000.0000.0000.0001882.485-0.0006274.9500.0000.0000.000100.0000.000-6287.793-6287.79317747.2041116.1760.0000.0000.0006287.793-17741.1661116.176110.0000.00017747.20417747.204-53613.670372.0590.0000.0000.000-17741.16653613.670372.059
Paso 04A partir de las matrices de todas las barras se obtiene esta matriz de toda la estructura sumando las componentes de cada matriz en funcin de sus grados de libertad con lo cual tenemos una matriz de 8x8 que luego particionamos como se indica
123456978101112123456978101112
12.000Tn72.000Tn2-4.020Tn80.000Tn3-1.560Tn100.000Tn40.000Tn110.000Tn5-10.980Tn120.000Tn6-0.020Tn9-2.000Tn
1234569171116.1020.000-2710.122-71116.1020.0000.000-1882.48520.00075575.281827.6370.000-275.879827.6370.0003-2710.122827.6379585.4990.000-827.6371655.2743137.4754-71116.1020.0000.00077069.043-18134.700-1176.5530.00050.000-275.879-827.637-18134.70053889.549-1199.6960.00060.000827.6371655.274-1176.553-1199.6968271.3330.0009-1882.4850.0000.0000.0000.0000.0006274.950
Paso 05Para invertir la matriz (kff) seleccionamos las celdas (E170:H173) la funcion es =MINVERSA(E161:H164) y sin soltar presionamos "CTROL" + "SHIFT", sin soltar damos enter
12345691-0.00065694230.0000022291-0.0001901616-0.000661057-0.0002273506-0.0000891749-0.000102001920.0000016440.0000132491-0.00000047050.00000164260.0000005931-0.00000091190.00000072843-0.0001232561-0.00000052810.0000725231-0.0001240812-0.000041493-0.0000381288-0.00007323844-0.00066108980.0000022316-0.0001914152-0.0006510789-0.000223964-0.0000870138-0.00010261935-0.00022663170.0000007931-0.0000644392-0.0002232292-0.0000581587-0.0000273723-0.00003576996-0.000102406-0.0000007876-0.0000510406-0.0001003233-0.00003204890.0001122737-0.00000520159-0.00019708270.0000006687-0.0000570485-0.0001983171-0.0000682052-0.00002675250.0001287632
781011121-752.994-0.0000.0000.0000.000-1505.9882-0.000-75299.4020.0000.0000.000-0.00031882.485-0.0000.0000.0000.0003764.97040.0000.000-6287.79317747.204-1116.1760.00050.0000.00017747.204-53613.670-372.0590.00060.0000.0001116.176372.0592480.3920.00091882.485-0.0000.0000.0000.0003764.970
1507.988-4.020-3766.5300.000-10.980-0.020-3766.970
Paso 06Para Multiplicar una matriz con el vector de cargas nodales seleccionamos las celdas (E187:E190) la funcion es =MMULT(E170:H173,E149:E152) y sin soltar presionamos "CTROL" + "SHIFT", sin soltar damos enter
10.1123154357m20.0014474431m3-0.1826839525m40.113071512m50.0363343643m60.0577656564m9-0.5666240969m
7ERROR:#VALUE!Tn8ERROR:#VALUE!Tn10ERROR:#VALUE!Tn11ERROR:#VALUE!Tn12ERROR:#VALUE!Tn
7ERROR:#VALUE!Tn8ERROR:#VALUE!Tn10ERROR:#VALUE!Tn11ERROR:#VALUE!Tn12ERROR:#VALUE!Tn