PORTICO 05UNIVERSIDAD ALAS PERUANASCARRERA: INGENIERIA CIVILCURSO: ANALISIS ESTRUCTURAL IIALUMNO: GARCIA CONDORCALLO, ALANEJERCICIO PRACTICO DE PORTICO POR EL METODO DE RIGIDEZRELACION S - R - CSRC180PI200Paso 01Numeramos las barras Numeramos los Grados de Libertad ( DOF ) libres y restringidos de la estructuraBarra123A (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 porticoPaso 03Podemos encontrar esta matriz para todas las barras del portico de la sgte manera:Coordenadas Globales ( Barra del Portico )TIPO DE FIGURA4L1F`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 TOTAL0.1193802632m4VIGA1CO,CA1E-455A (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)5.004-92382.53-0.000.0092382.530.000.00Angulo05-0.00-806.35-2015.870.00806.35-2015.87Radianes06-0.002015.873359.790.00-2015.876719.58COS1SEN0TIPO DE FIGURA4L1F`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 TOTAL0.1193802632m4VIGA2CO,CA1E-455A (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)5.0010-92382.53-0.000.0092382.530.000.00Angulo011-0.00-806.35-2015.870.00806.35-2015.87Radianes0.0012-0.002015.873359.790.00-2015.876719.58COS1SEN0TIPO DE FIGURA4L1F`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 TOTAL0.1193802632m4VIGA3CO,CA1E-455A (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)5.0016-92382.53-0.000.0092382.530.000.00Angulo017-0.00-806.35-2015.870.00806.35-2015.87Radianes0.0018-0.002015.873359.790.00-2015.876719.58COS1SEN0TIPO DE FIGURA6L1F`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 TOTAL0.0368768601m4COLUMNA4CO,CA31E-45A (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)COS0SEN1TIPO DE FIGURA6L1F`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 TOTAL0.0368768601m4COLUMNA5CO,CA31E-45A (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)COS0SEN1TIPO DE FIGURA6L1F`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 TOTAL0.0368768601m4COLUMNA6CO,CA3.51E-45A (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)COS0SEN1TIPO DE FIGURA2L1F`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 TOTAL0.0368768601m4COLUMNA7CO,CA31E-45A (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)COS0SEN1TIPO DE FIGURA2L1F`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 TOTAL0.0368768601m4COLUMNA8CO,CA31E-45A (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)COS0SEN1TIPO DE FIGURA2L1F`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 TOTAL0.0368768601m4COLUMNA9CO,CA3.51E-45A (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)COS0SEN11234567891011121314151617181920212223241184765.050.000.00-92382.53-0.00-0.00-92382.53-0.000.000.000.000.0020.001612.700.00-0.00-806.352015.87-0.00-806.35-2015.870.000.000.0030.000.0013439.150.00-2015.873359.79-0.002015.873359.790.000.000.004-92382.53-0.000.00128008.960.0053439.650.000.000.00-35626.43-0.0053439.655-0.00-806.35-2015.870.00589518.53-2015.870.000.000.00-0.00-588712.18-0.006-0.002015.873359.7953439.65-2015.87113598.870.000.000.00-53439.650.0053439.657-92382.53-0.00-0.000.000.000.0092382.530.00-0.000.000.000.008-0.00-806.352015.870.000.000.000.00806.352015.870.000.000.0090.00-2015.873359.790.000.000.00-0.002015.876719.580.000.000.00100.000.000.00-35626.43-0.00-53439.650.000.000.0035626.430.00-53439.65110.000.000.00-0.00-588712.180.000.000.000.000.00588712.180.00120.000.000.0053439.65-0.0053439.650.000.000.00-53439.650.00106879.29131415161718192021222324Paso 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 indica10TN70.000M2-7.5TN80.000M3-6.25TN-M90.000RAD40TN100.000M5-14TN110.000M6-0.125TN-M120.000RADPaso 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 enterCOMPROBACION112345610.00000988360.0000054170.00000108320.0000089426-0.0000000037-0.00000433520.0000054170.000641230.0000042720.00001083390.000000835-0.00001658730.00000108320.0000042720.00007527640.00000216640.0000002519-0.000003316840.00000894260.00001083390.00000216640.0000178852-0.0000000074-0.00000867015-0.00000000370.0000008350.0000002519-0.00000000740.00000169830.00000001146-0.000004335-0.000016587-0.0000033168-0.00000867010.00000001140.00001327427891011121-92382.5267569577-1.83152355079698E-414.0317460855437E-430000.00002-1.83152355079698E-41-806.3492171087-2015.87304277180000.000-7.53-4.0317460855437E-432015.87304277183359.78840461980000.000-6.254000-35626.4315467765-053439.64732016470.00005000-0-588712.180313946-00.000-146000-53439.6473201647053439.64732016470.000-0.125Paso 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 SIGNO1-0.0000468034M74.3238118813TN70TN2-0.0048455413M82.8879126211TN80TN3-0.00050563RAD98.0691863754TN-M90TN-M4-0.0000936067M10-4.3238118813TN100TN5-0.0000316149M1118.6120873789TN110TN60.0001433147RAD122.6563754794TN-M120TN-M74.3238118813TN82.8879126211TN98.0691863754TN-M10-4.3238118813TN1118.6120873789TN122.6563754794TN-M

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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 - CSRC180PI200Paso 01Numeramos las barras Numeramos los Grados de Libertad ( DOF ) libres y restringidos de la estructuraBarra123A (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 porticoPaso 03Podemos encontrar esta matriz para todas las barras del portico de la sgte manera:Coordenadas Globales ( Barra del Portico )TIPO DE FIGURA1L1F`c4Rectangulo1Circulo2S. Tubular3Seccion 4Seccion 5ITEMAYAYIdAd2Seccion 6ITEMAYAYIdAd21140b(m)0.20r(m)0.4r(m)0.4a(m)0.6a(m)0.3a(m)0.32175h(m)0.30A(m2)0.5026548246r(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)0.020106193A(m2)0.3769911184c(m)0.2c(m)0.3c(m)0.34280I0.00045As0.4523893421I(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 TOTAL0.1193802632m4VIGA1CO,CA1E-454A (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)4.001-45000.00-0.000.0045000.000.000.00Angulo02-0.00-253.13-506.250.00253.13-506.25Radianes03-0.00506.25675.000.00-506.251350.00COS1SEN0TIPO DE FIGURA1L1F`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 TOTAL0.1193802632m4COLUMNA2CO,CA41E-45A (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)4.001-253.13-0.00506.25253.130.00506.25Angulo902-0.00-45000.00-0.000.0045000.00-0.00Radianes1.573-506.250.00675.00506.25-0.001350.00COS0SEN1123456789145253.130.00506.25-45000.00-0.000.00-253.13-0.00506.2520.0045253.13-506.25-0.00-253.13-506.25-0.00-45000.00-0.003506.25-506.252700.00-0.00506.25675.00-506.250.00675.004-45000.00-0.00-0.0045000.000.00-0.000.000.000.005-0.00-253.13506.250.00253.13506.250.000.000.0060.00-506.25675.00-0.00506.251350.000.000.000.007-253.13-0.00-506.250.000.000.00253.130.00-506.258-0.00-45000.000.000.000.000.000.0045000.000.009506.25-0.00675.000.000.000.00-506.250.001350.00Paso 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 indica10TN40.000M2-6TN50.000M31.667TN-M60.000RAD70.000M80.000M90.000RADPaso 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 enterCOMPROBACION112300010.0000221445-0.0000000465-0.00000416082-0.00000004650.00002214450.00000416083-0.00000416080.00000416080.00037193074567891-45000.00-0.000.00-253.13-0.00506.252-0.00-253.13-506.25-0.00-45000.00-0.003-0.00506.25675.00-506.250.00675.000.0000.0000.000-6.0000.0001.667Paso 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 SIGNO1-0.0000066568M40.2995557929TN40TN2-0.0001259307M50.333117011TN54TN30.0005950435RAD60.4654068259TN-M62.667TN-M7-0.2995557929TN7-2TN85.666882989TN80TN90.3982843896TN-M92TN-M40.2995557929TN54.333117011TN63.1324068259TN-M7-2.2995557929TN85.666882989TN92.3982843896TN-M-2530-506.2-20-4500000506.206752

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PORTICO 03UNIVERSIDAD ALAS PERUANASCARRERA: INGENIERIA CIVILCURSO: ANALISIS ESTRUCTURAL IIALUMNO: GARCIA CONDORCALLO, ALANEJERCICIO PRACTICO DE PORTICO POR EL METODO DE RIGIDEZRELACION S - R - CSRC180PI200Paso 01Numeramos las barras Numeramos los Grados de Libertad ( DOF ) libres y restringidos de la estructuraBarra123A (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 porticoPaso 03Podemos encontrar esta matriz para todas las barras del portico de la sgte manera:Coordenadas Globales ( Barra del Portico )TIPO DE FIGURA1L1F`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 TOTAL0.1193802632m4VIGA1CO,CA1E-455A (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)5.004-120479.04-0.000.00120479.040.000.00Angulo05-0.00-1734.90-4337.250.001734.90-4337.25Radianes06-0.004337.257228.740.00-4337.2514457.49COS1SEN0TIPO DE FIGURA1L1F`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 TOTAL0.1193802632m4COLUMNA2CO,CA31E-45A (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)3.001-8031.94-0.0012047.908031.940.0012047.90Angulo902-0.00-200798.41-0.000.00200798.41-0.00Radianes1.573-12047.900.0012047.9012047.90-0.0024095.81COS0SEN1TIPO DE FIGURA1L1F`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 TOTAL0.1193802632m4COLUMNA3CO,CA31E-45A (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)3.004-8031.94-0.0012047.908031.940.0012047.90Angulo905-0.00-200798.41-0.000.00200798.41-0.00Radianes1.576-12047.900.0012047.9012047.90-0.0024095.81COS0SEN11234567891011121128510.980.0012047.90-120479.04-0.00-0.00-8031.94-0.0012047.900.000.000.0020.00202533.304337.25-0.00-1734.904337.25-0.00-200798.41-0.000.000.000.00312047.904337.2538553.290.00-4337.257228.74-12047.900.0012047.900.000.000.004-120479.04-0.000.00128510.980.0012047.900.000.000.00-8031.94-0.0012047.905-0.00-1734.90-4337.250.00202533.30-4337.250.000.000.00-0.00-200798.41-0.006-0.004337.257228.7412047.90-4337.2538553.290.000.000.00-12047.900.0012047.907-8031.94-0.00-12047.900.000.000.008031.940.00-12047.900.000.000.008-0.00-200798.410.000.000.000.000.00200798.410.000.000.000.00912047.90-0.0012047.900.000.000.00-12047.900.0024095.810.000.000.00100.000.000.00-8031.94-0.00-12047.900.000.000.008031.940.00-12047.90110.000.000.00-0.00-200798.410.000.000.000.000.00200798.410.00120.000.000.0012047.90-0.0012047.900.000.000.00-12047.900.0024095.81Paso 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 indica10TN70.000M2-7.5TN80.000M3-6.25TN-M90.000RAD40TN100.000M5-14TN110.000M6-0.125TN-M120.000RADPaso 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 enterCOMPROBACION112345610.00010544350.0000011649-0.00002821750.0001013511-0.0000011649-0.000026643520.00000116490.0000049708-0.00000077660.00000116490.0000000093-0.00000077663-0.0000282175-0.00000077660.0000345516-0.00002664350.00000077660.000002022440.00010135110.0000011649-0.00002664350.0001054435-0.0000011649-0.00002821755-0.00000116490.00000000930.0000007766-0.00000116490.00000497080.00000077666-0.0000266435-0.00000077660.0000020224-0.00002821750.00000077660.00003455167891011121-8031.9362547271-012047.90438209070000.00002-0-200798.406368178-00000.000-7.53-12047.9043820907012047.90438209070000.000-6.254000-8031.9362547271-012047.90438209070.00005000-0-200798.406368178-00.000-146000-12047.9043820907012047.90438209070.000-0.125Paso 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 SIGNO10.0001872616M71.1615044248TN70TN2-0.0000324608M86.5180712454TN80TN3-0.0002212482RAD9-0.4094679042TN-M90TN-M40.0001776209M10-1.1615044248TN100TN5-0.0000746118M1114.9819287546TN110TN6-0.0000220067RAD121.8748241312TN-M120TN-M71.1615044248TN86.5180712454TN9-0.4094679042TN-M10-1.1615044248TN1114.9819287546TN121.8748241312TN-M

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PORTICO 02UNIVERSIDAD ALAS PERUANASCARRERA: INGENIERIA CIVILCURSO: ANALISIS ESTRUCTURAL IIALUMNO: GARCIA CONDORCALLO, ALANEJERCICIO PRACTICO DE PORTICO POR EL METODO DE RIGIDEZRELACION S - R - CSRC180PI200Paso 01Numeramos las barras Numeramos los Grados de Libertad ( DOF ) libres y restringidos de la estructuraBarra123A (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 porticoPaso 03Podemos encontrar esta matriz para todas las barras del portico de la sgte manera:Coordenadas Globales ( Barra del Portico )TIPO DE FIGURA4L1F`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 TOTAL0.1193802632m4BARRA1CO,CA1E-456A (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)6.004-71116.10-0.000.0071116.100.000.00Angulo05-0.00-275.88-827.640.00275.88-827.64Radianes06-0.00827.641655.270.00-827.643310.55COS1SEN0TIPO DE FIGURA1L1F`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 TOTAL0.1193802632m4BARRA2CO,CA51E-45A (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)5.001-752.99-0.001882.49752.990.001882.49Angulo902-0.00-75299.40-0.000.0075299.40-0.00Radianes1.573-1882.490.003137.481882.49-0.006274.95COS0SEN1TIPO DE FIGURA1L1F`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 TOTAL0.1193802632m4BARRA3CO,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-0SEN1123456789101112171869.100.001882.49-71116.10-0.00-0.00-752.99-0.001882.490.000.000.0020.0075575.28827.64-0.00-275.88827.64-0.00-75299.40-0.000.000.000.0031882.49827.649585.500.00-827.641655.27-1882.490.003137.480.000.000.004-71116.10-0.000.0077403.90-17747.201116.180.000.000.00-6287.7917747.201116.185-0.00-275.88-827.64-17747.2053889.55-455.580.000.000.0017747.20-53613.67372.066-0.00827.641655.271116.18-455.588271.330.000.000.00-1116.18-372.062480.397-752.99-0.00-1882.490.000.000.00752.990.00-1882.490.000.000.008-0.00-75299.400.000.000.000.000.0075299.400.000.000.000.0091882.49-0.003137.480.000.000.00-1882.490.006274.950.000.000.00100.000.000.00-6287.7917747.20-1116.180.000.000.006287.79-17747.20-1116.18110.000.000.0017747.20-53613.67-372.060.000.000.00-17747.2053613.67-372.06120.000.000.001116.18372.062480.390.000.000.00-1116.18-372.064960.78Paso 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 indica10.000TN70.000M20.000TN80.000M30.000TN-M90.000RAD40.000TN100.000M50.000TN110.000M60.000TN-M120.000RADPaso 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 enterCOMPROBACION112345610.0011592540.0000044169-0.00017837760.00115274520.0003760696-0.000099588520.00000441690.0000132717-0.00000162290.00000442070.000001486-0.00000151793-0.0001783776-0.00000162290.0001357263-0.0001766736-0.0000561598-0.000006251440.00115274520.0000044207-0.00017667360.00116027410.0003785649-0.000100808450.00037606960.000001486-0.00005615980.00037856490.0001421007-0.00003216866-0.0000995885-0.0000015179-0.0000062514-0.0001008084-0.00003216860.00013413427891011121-752.9940238807-01882.48505970170000.0000.0002-0-75299.4023880668-00000.0000.0003-1882.485059701703137.47509950280000.0000.0004000-6287.793350201917747.20371625041116.17633435540.0000.000500017747.2037162504-53613.6699268698372.05877811850.0000.0006000-1116.1763343554-372.05877811852480.39185412310.0000.000Paso 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 CAMBIADO10M70TN70TN20M80TN80TN30RAD90TN-M90TN-M40M100TN100TN50M110TN110TN60RAD120TN-M120TN-M70TN80TN90TN-M100TN110TN120TN-M

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EXAMEN PORTICOUNIVERSIDAD ALAS PERUANASCARRERA: INGENIERIA CIVILCURSO: ANALISIS ESTRUCTURAL IIALUMNO: GARCIA CONDORCALLO, ALANEJERCICIO PRACTICO DE PORTICO POR EL METODO DE RIGIDEZRELACION S - R - CSRC180PI200Paso 01Numeramos las barras Numeramos los Grados de Libertad ( DOF ) libres y restringidos de la estructuraBarra123A (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 porticoPaso 03Podemos encontrar esta matriz para todas las barras del portico de la sgte manera:Coordenadas Globales ( Barra del Portico )TIPO DE FIGURA4L100F`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 TOTAL11938026.3157895cm4BARRA1CO,CA1E-456A (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)6.004-71116.10-0.000.0071116.10-275.880.00Angulo05-0.00-275.88-827.64-275.88275.88-827.64Radianes06-0.00827.641655.270.00-827.643310.55COS1SEN0TIPO DE FIGURA1L100F`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 TOTAL11938026.3157895cm4BARRA2CO,CA51E-45A (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)5.007-752.994-0.0001882.485752.9940.0001882.485Angulo908-0.000-75299.402-0.0000.00075299.402-0.000Radianes1.579-1882.4850.0003137.4751882.485-0.0006274.950COS0SEN1TIPO DE FIGURA1L100F`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 TOTAL11938026.3157895cm4BARRA3CO,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-0SEN1123456789101112171116.1020.000-2710.122-71116.102-0.000-0.000-752.994-0.000-1882.4850.0000.0000.00020.00075575.281827.637-0.000-275.879827.637-0.000-75299.4020.0000.0000.0000.0003-2710.122827.6379585.4990.000-827.6371655.2741882.485-0.0003137.4750.0000.0000.0004-71116.102-0.0000.00077069.043-18134.700-1176.5530.0000.0000.000-6287.79317747.204-1116.1765-0.000-275.879-827.637-18134.70053889.549-1199.6960.0000.0000.00017747.204-53613.670-372.0596-0.000827.6371655.274-1176.553-1199.6968271.3330.0000.0000.0001116.176372.0592480.3927-752.994-0.0000.0000.0000.0000.000752.9940.0001882.4850.0000.0000.0008-0.000-75299.4020.0000.0000.0000.0000.00075299.402-0.0000.0000.0000.0009-1882.4850.0000.0000.0000.0000.0001882.485-0.0006274.9500.0000.0000.000100.0000.000-6287.793-6287.79317747.2041116.1760.0000.0000.0006287.793-17741.1661116.176110.0000.00017747.20417747.204-53613.670372.0590.0000.0000.000-17741.16653613.670372.059120.0000.0000.000-1116.176-372.0592480.3920.0000.0000.0001116.176372.0594960.784Paso 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 indica12345697810111212345697810111212.000Tn72.000Tn2-4.020Tn80.000Tn3-1.560Tn100.000Tn40.000Tn110.000Tn5-10.980Tn120.000Tn6-0.020Tn9-2.000Tn1234569171116.1020.000-2710.122-71116.102-0.000-0.000-1882.48520.00075575.281827.637-0.000-275.879827.6370.0003-2710.122827.6379585.4990.000-827.6371655.2743137.4754-71116.102-0.0000.00077069.043-18134.700-1176.5530.0005-0.000-275.879-827.637-18134.70053889.549-1199.6960.0006-0.000827.6371655.274-1176.553-1199.6968271.3330.0009-1882.4850.0000.0000.0000.0000.0006274.950Paso 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 enter12345691-0.00065694230.0000022291-0.0001901616-0.000661057-0.0002273506-0.0000891749-0.000102001920.0000016440.0000132491-0.00000047050.00000164260.0000005931-0.00000091190.00000072843-0.0001232561-0.00000052810.0000725231-0.0001240812-0.000041493-0.0000381288-0.00007323844-0.00066108980.0000022316-0.0001914152-0.0006510789-0.000223964-0.0000870138-0.00010261935-0.00022663170.0000007931-0.0000644392-0.0002232292-0.0000581587-0.0000273723-0.00003576996-0.000102406-0.0000007876-0.0000510406-0.0001003233-0.00003204890.0001122737-0.00000520159-0.00019708270.0000006687-0.0000570485-0.0001983171-0.0000682052-0.00002675250.0001287632781011121-752.994-0.0000.0000.0000.000-1505.9882-0.000-75299.4020.0000.0000.000-0.00031882.485-0.0000.0000.0000.0003764.97040.0000.000-6287.79317747.204-1116.1760.00050.0000.00017747.204-53613.670-372.0590.00060.0000.0001116.176372.0592480.3920.00091882.485-0.0000.0000.0000.0003764.9701507.988-4.020-3766.5300.000-10.980-0.020-3766.970Paso 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 enter10.1123154357m20.0014474431m3-0.1826839525m40.113071512m50.0363343643m60.0577656564m9-0.5666240969m7ERROR:#VALUE!Tn8ERROR:#VALUE!Tn10ERROR:#VALUE!Tn11ERROR:#VALUE!Tn12ERROR:#VALUE!Tn7ERROR:#VALUE!Tn8ERROR:#VALUE!Tn10ERROR:#VALUE!Tn11ERROR:#VALUE!Tn12ERROR:#VALUE!Tn

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PLANTILLA ORIGINALUNIVERSIDAD ALAS PERUANASCARRERA: INGENIERIA CIVILCURSO: ANALISIS ESTRUCTURAL IIALUMNO: GARCIA CONDORCALLO, ALANEJERCICIO PRACTICO DE PORTICO POR EL METODO DE RIGIDEZRELACION S - R - CSRC180PI200Paso 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 porticoPaso 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)6.00m4-86948.2600.0000.00086948.260-44440.2220.000Angulo050.000-44440.222-133320.666-44440.22244440.222-133320.666Radianes060.000133320.666266641.3320.000-133320.666533282.664COS1SEN0BARRA 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-1BARRA 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-1123456978101112186948.2600.000-133644.772-86948.2600.0000.000324.106-162.053-0.0000.0000.0000.00020.00082852.787133320.6660.000-44440.222133320.666-0.000-0.000-38412.5650.0000.0000.0003-133644.772133320.666534146.9470.000-133320.666266641.332432.141-324.1060.0000.0000.0000.0004-86948.2600.0000.00086948.260-44440.222-334.4770.0000.0000.000-95.565-0.000334.47750.000-44440.222-133320.666-44440.22283462.510-133320.6660.0000.0000.000-0.000-39022.288-0.00060.000133320.666266641.332-334.477-133320.666534843.5560.0000.0000.000-334.4770.000780.4469324.106-0.0000.0000.0000.0000.000864.283-324.1060.0000.0000.0000.0007-162.053-0.0000.0000.0000.0000.000-324.106162.0530.0000.0000.0000.0008-0.000-38412.5650.0000.0000.0000.0000.0000.00038412.5650.0000.0000.000100.0000.000-95.565-95.565-0.000-334.4770.0000.0000.00095.5650.000-334.477110.0000.000-0.000-0.000-39022.2880.0000.0000.0000.0000.00039022.2880.000120.0000.000334.477334.477-0.000780.446-334.4770.0000.000-334.4770.0001560.892Paso 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 indica12345697810111212345697810111212.000Tn72.000Tn2-4.020Tn80.000Tn3-1.560Tn100.000Tn40.000Tn110.000Tn5-10.980Tn120.000Tn6-0.020Tn9-2.000Tn1234569186948.2600.000-133644.772-86948.2600.0000.000324.10620.00082852.787133320.6660.000-44440.222133320.666-0.0003-133644.772133320.666534146.9470.000-133320.666266641.332432.1414-86948.2600.0000.00086948.260-44440.222-334.4770.00050.000-44440.222-133320.666-44440.22283462.510-133320.6660.00060.000133320.666266641.332-334.477-133320.666534843.5560.0009324.106-0.0000.0000.0000.0000.000864.283Paso 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 enter12345691-0.00000302660.0000017435-0.0000033566-0.0000093579-0.0000123734-0.00000185140.000002813320.00000174560.0000249822-0.00000238420.00000541220.0000071982-0.0000032410.00000053753-0.000003359-0.00000238510.0000011825-0.0000051741-0.0000035446-0.00000088180.00000066844-0.00000936050.0000054071-0.0000051695-0.000001392-0.0000069079-0.00000049350.00000609495-0.00001237840.0000071924-0.0000035403-0.00000691290.00001067370.00000262840.00000641216-0.000001852-0.000003242-0.0000008809-0.00000049370.00000262910.00000377210.00000113590.000001135-0.00000065380.00000125870.00000350920.000004640.00000069430.0011559738781011121-162.053-0.0000.0000.0000.000-324.1062-0.000-38412.5650.0000.0000.000-0.0003-324.1060.0000.0000.0000.000-648.21240.0000.000-95.565-0.000334.4770.00050.0000.000-0.000-39022.288-0.0000.00060.0000.000-334.4770.000780.4460.0009-324.1060.0000.0000.0000.000-648.212326.106-4.020646.6520.000-10.980-0.020646.212Paso 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 enter1-0.0012106803m2-0.0008045441m30.0001497115m4-0.002402625m5-0.002328633m6-0.0004560875m90.7481399475m781.83Tn830.90Tn100.37Tn1190.87Tn12-251.34Tn783.826Tn830.905Tn100.368Tn1190.869Tn12-251.345Tn

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EXAMEN FINALUNIVERSIDAD ALAS PERUANASCARRERA: INGENIERIA CIVILCURSO: ANALISIS ESTRUCTURAL IIALUMNO: GARCIA CONDORCALLO, ALANEJERCICIO PRACTICO DE PORTICO POR EL METODO DE RIGIDEZRELACION S - R - CSRC180PI200Paso 01Numeramos las barras Numeramos los Grados de Libertad ( DOF ) libres y restringidos de la estructuraBarra123A (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 porticoPaso 03Podemos encontrar esta matriz para todas las barras del portico de la sgte manera:Coordenadas Globales ( Barra del Portico )TIPO DE FIGURA1L1F`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 TOTAL0.1193802632m4VIGA1CO,CA1E-454A (m)0.240123456Inercia (m4)0.007201120000.000.00-0.00-120000.00-0.00-0.00FC (Kg/cm2)28020.002700.005400.00-0.00-2700.005400.00E (Tn/m)2000000.003-0.005400.0014400.000.00-5400.007200.00L (m)4.004-120000.00-0.000.00120000.000.000.00Angulo05-0.00-2700.00-5400.000.002700.00-5400.00Radianes06-0.005400.007200.000.00-5400.0014400.00COS1SEN0TIPO DE FIGURA2L1F`c4Rectangulo1Circulo2S. Tubular3Seccion 4Seccion 5ITEMAYAYIdAd2Seccion 6ITEMAYAYIdAd21140b(m)0.40r(m)0.15r(m)4a(m)0.6a(m)0.3a(m)0.32175h(m)0.60A(m2)0.0706858347r(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)0.0003976078A(m2)37.6991118431c(m)0.2c(m)0.3c(m)0.34280I0.0072As0.0636172512I(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 TOTAL0.1193802632m4COLUMNA2CO,CA42.3094010768A (m)0.071789123Inercia (m4)0.000397607877724.6013211.66-193.69-7724.60-13211.66-193.69FC (Kg/cm2)280.000813211.6622980.11111.83-13211.66-22980.11111.83E (Tn/m)2000000.0009-193.69111.83688.68193.69-111.83344.34L (m)4.61880215351-7724.60-13211.66193.697724.6013211.66193.69Angulo602-13211.66-22980.11-111.8313211.6622980.11-111.83Radianes1.053-193.69111.83344.34193.69-111.83688.68COS1SEN1TIPO DE FIGURA2L1F`c4Rectangulo1Circulo2S. Tubular3Seccion 4Seccion 5ITEMAYAYIdAd2Seccion 6ITEMAYAYIdAd21140b(m)0.40r(m)0.15r(m)4a(m)0.6a(m)0.3a(m)0.32175h(m)0.60A(m2)0.0706858347r(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)0.0003976078A(m2)37.6991118431c(m)0.2c(m)0.3c(m)0.34280I0.0072As0.0636172512I(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 TOTAL0.1193802632m4COLUMNA3CO,CA51E-45A (m)0.071101112456Inercia (m4)0.00039760781076.340.00-190.85-76.34-0.00-190.85FC (Kg/cm2)280110.0028274.330.00-0.00-28274.330.00E (Tn/m)2000000.0012-190.850.00636.17190.85-0.00318.09L (m)5.004-76.34-0.00190.8576.340.00190.85Angulo905-0.00-28274.33-0.000.0028274.33-0.00Radianes1.576-190.850.00318.09190.85-0.00636.17COS0SEN11234567891011121127724.6013211.66193.69-120000.00-0.00-0.00-7724.60-13211.66193.690.000.000.00213211.6625680.115288.17-0.00-2700.005400.00-13211.66-22980.11-111.830.000.000.003193.695288.1715088.680.00-5400.007200.00-193.69111.83344.340.000.000.004-120000.00-0.000.00120076.340.00190.850.000.000.00-76.34-0.00190.855-0.00-2700.00-5400.000.0030974.33-5400.000.000.000.00-0.00-28274.33-0.006-0.005400.007200.00190.85-5400.0015036.170.000.000.00-190.850.00318.097-7724.60-13211.66-193.690.000.000.007724.6013211.66-193.690.000.000.008-13211.66-22980.11111.830.000.000.0013211.6622980.11111.830.000.000.009193.69-111.83344.340.000.000.00-193.69111.83688.680.000.000.00100.000.000.00-76.34-0.00-190.850.000.000.0076.340.00-190.85110.000.000.00-0.00-28274.330.000.000.000.000.0028274.330.00120.000.000.00190.85-0.00318.090.000.000.00-190.850.00636.17Paso 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 indicaMEP TRIANGULARANGULO1.0471975512UaqRaRAHRAV65.42222222229263.7394697185-55.231.86973485931312.8TN70.000MUbqRbRBHRBV2-74.3627146716TN80.000M-65.422222222292148.7254293432128.8-74.3627146716365.4222222222TN-M90.000RAD4-9.568TN100.000MDOF LIBRE 118450TN110.000MDOF LIBRE 306-14.72TN-M120.000RADMEP CARGA PUNTUALPaso 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 enterCOMPROBACIONUaRa1-58.8882.432UbRb123456-14.72-9.56810.0028568407-0.00162164260.00034757730.0028544297-0.00001553390.00037414162-0.00162164260.0009637667-0.0002073012-0.0016202570.0000089814-0.000223064930.0003475773-0.00020730120.00013256620.00034734210.00000659810.000008931140.0028544297-0.0016202570.00034734210.0028603491-0.00001553440.00037368135-0.00001553390.00000898140.0000065981-0.00001553440.00003535270.000006508560.0003741416-0.00022306490.00000893110.00037368130.00000650850.00013993427891011121-7724.5999645229-13211.6588075431193.69039109280000.000312.82-13211.6588075431-22980.1095024759-111.82719943690000.000-74.36271467163-193.6903910928111.8271994369344.33847305380000.00065.42222222224000-76.3407014822-0190.85175370560.000-9.5685000-0-28274.3338823081-00.00006000-190.85175370560318.0862561760.000-14.72Paso 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 SIGNO11.0041302359M7-202.1089303832TN7-55.2TN2-0.5736940757M8-68.2079211344TN831.8697348593TN30.1293555863RAD9303.1870849848TN-M965.4222222222TN-MRESPUESTA0.010032078141.0032078104M10-101.1230696168TN1082.432TN5-0.0050424048M11142.570635806TN110TN60.1285682796RAD12232.3597726746TN-M12-58.88TN-M7-257.3089303832TN8-36.3381862751TN9368.609307207TN-M10-18.6910696168TN11142.570635806TN12173.4797726746TN-M

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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 armadura12345678Paso 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=20000Angulo06-10106-100000100000Radianes05000050000COS1SEN0BARRA 2E2.00E+06KN/M34783478A0.05M310-103100000-100000L10.00Mk1 =10000.0040000=40000Angulo07-10107-100000100000Radianes08000080000COS1SEN0BARRA 3E2.00E+06KN/M12341234A0.05M13.75247184141245E-336.1257422745431E-17-3.75247184141245E-33-6.1257422745431E-1710.000.00-0.00-0.00L10.00Mk1 =10000.0026.1257422745431E-171-6.1257422745431E-17-1=20.0010000.00-0.00-10000.00Angulo90.003-3.75247184141245E-33-6.1257422745431E-173.75247184141245E-336.1257422745431E-173-0.00-0.000.000.00Radianes1.5707963274-6.1257422745431E-17-16.1257422745431E-1714-0.00-10000.000.0010000.00COS0.000000000SEN1.000000000BARRA 4E2.00E+06KN/M65786578A0.05M63.75247184141245E-336.1257422745431E-17-3.75247184141245E-33-6.1257422745431E-1760.000.00-0.00-0.00L10.00Mk1 =10000.0056.1257422745431E-171-6.1257422745431E-17-1=50.0010000.00-0.00-10000.00Angulo90.007-3.75247184141245E-33-6.1257422745431E-173.75247184141245E-336.1257422745431E-177-0.00-0.000.000.00Radianes1.5707963278-6.1257422745431E-17-16.1257422745431E-1718-0.00-10000.000.0010000.00COS0.00000000SEN1.000000000BARRA 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=23535.533535.53-3535.53-3535.53Angulo45.007-0.5-0.50.50.57-3535.53-3535.533535.533535.53Radianes0.7853981638-0.5-0.50.50.58-3535.53-3535.533535.533535.53COS0.70710678SEN0.707106781BARRA 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-0.70710678SEN0.70710678112345678113535.533535.53-0.00-0.000.00-10000.00-3535.53-3535.5323535.5313535.53-0.00-10000.000.000.00-3535.53-3535.533-0.00-0.0013535.53-3535.533535.53-3535.53-10000.000.004-0.00-10000.00-3535.5313535.53-3535.533535.530.000.0050.00-10000.003535.53-3535.5313535.53-3535.53-0.00-10000.0060.000.00-3535.533535.53-3535.5313535.53-0.00-0.007-3535.53-3535.53-10000.000.00-0.00-10000.0013535.533535.538-3535.53-3535.530.000.00-0.00-0.003535.5313535.53Paso 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 indica123456781234567810.00KN20.00KN32.00KN4-4.00KN50.00KNPaso 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 enter1234510.000100-0.000100-0.000017-0.000083-0.0000172-0.0001000.0003830.0000660.0003170.0000663-0.0000000.0000000.0000830.000017-0.0000174-0.0001000.0003830.0000830.0004000.0000835-0.0001000.0003830.0000490.0003340.00014960.00MPaso 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 enter10.0002970563M2-0.0011372583M30.0000970563M4-0.0014343146M5-0.001240202M6-1.03KN72.00KN82.97KN

MURO DE CORTECURSO: ANALISIS ESTRUCTURAL IIEJERCICIO PRACTICO DE MUROS DE CORTERELACION S - R - CSRC180PI200Paso 01Numeramos las barras Numeramos los Grados de Libertad ( DOF ) libres y restringidos de la estructura100005015042550015015075757575Paso 03Podemos encontrar esta matriz para todas las barras del portico de la sgte manera:TIPO DE FIGURA1F`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)0.0074As0.2Mx0.084PLACA1Yg0.35As (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)4252-44350183.2510896718744350183.2413739860690TIPO DE FIGURA1F`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)0.0074As0.2Mx0.084PLACA2Yg0.35As (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)4254-44350183.2510896718744350183.2413739860690TIPO DE FIGURA1F`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)0.0074As0.2Mx0.084VIGA3Yg0.35As (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)500a75b751234567891011123080932119364-6521211936400-230157200002211936414564510598-211936455293659444350183-44350183051089671870003-6521-21193642308093-211936400000-2301572042119364552936594-21193641456451059844350183000-44350183051089671875044350183044350183417413-208707044350183-20870704435018360-4435018300-2087072087070-443501830007-230157200000230157200008051089671870044350183-443501830137398606900009000-44350183-2087070002087070-443501831000-23015720000002301572011000510896718744350183000-44350183013739860690Paso 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 indica123456978101112345697810111234510.0000004336-0.00000000020.0000000009-0.00000000020.00000003422-0.00000000020.00000000010.00000000020.0000000001-0.000000018730.00000000090.00000000020.00000043360.0000000002-0.00000003424-0.00000000020.00000000010.00000000020.0000000001-0.000000018750.0000000342-0.0000000187-0.0000000342-0.00000001870.000006367FUERZA10000kgDESPLZAMIENTO0.0636704269cm1010.0003422431cm202-0.0001868864cmK LATERAL DEL PORTICO157058.786718254kg/cm303-0.0003422431cm1570587.86718254Tn/m404-0.0001868864cm51000050.0636704269cm67891060.00-44350183.240.000.00-208706.747-2301571.600.000.000.000.0080.005108967187.060.000.0044350183.2490.000.000.00-44350183.24-208706.74100.000.00-2301571.600.000.00110.000.000.005108967187.0644350183.246-5000kg60kg7-787.6970815163kg70kg81868998.44850721kg80kg9-5000kg90kg10787.6970815163kg100kg111868998.44850721kg110kg6-5000kg6-5Tn7-787.6970815163kg7-0.7876970815Tn81868998.44850721kg.cm818.6899844851Tn.m9-5000kg9-5Tn10787.6970815163kg100.7876970815Tn111868998.44850721kg.cm1118.6899844851Tn.m

MC-SECCIONESCURSO: ANALISIS ESTRUCTURAL IIEJERCICIO PRACTICO DE MUROS DE CORTERELACION S - R - CSRC180PI200Paso 01Numeramos las barras Numeramos los Grados de Libertad ( DOF ) libres y restringidos de la estructura100005015042550015015075757575Paso 03Podemos encontrar esta matriz para todas las barras del portico de la sgte manera:TIPO DE FIGURA5L100F`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 TOTAL11938026.3157895cm4PLACA1As (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)4252-22634031.9294801608522634031.916671447475TIPO DE FIGURA3F`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)0.0074As0.2Mx0.084Yg0.35PLACA2As (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)4254-1361.01928141361.04385630TIPO DE FIGURA1F`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)0.0074As0.2Mx0.084Yg0.35VIGA3As (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)500a75b751234567891011125126772119364-6521211936400-25061560000221193647496097383-211936455293659422634032-22634032029480160850003-6521-211936425803-211936400000-19282042119364552936594-21193648250355381361000-13610192814502263403201361106519-106513022634032-60136160-2263403200-1065131065130-226340320007-250615600000250615600008029480160850022634032-22634032066714474750009000-1361-600060-13611000-19282000000192820110001928141361000-13610385630Paso 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 indica123456978101112345697810111234510.0000003989-0.00000000010.0000000171-0.00000000090.00000002452-0.00000000010.00000000040.000000015-0.0000000003-0.000000092730.00000001710.0000000150.00004963560.0000001174-0.00000318624-0.0000000009-0.00000000030.00000011740.00000000170.000000053850.0000000245-0.0000000927-0.00000318620.00000005380.0000290838FUERZA10000kgDESPLZAMIENTO0.2908381151cm1010.0002451384cm202-0.000926952cmK LATERAL DEL PORTICO34383.3888350288kg/cm303-0.0318622379cm343833.888350288Tn/m4040.0005382831cm51000050.2908381151cm67891060.00-22634031.910.000.00-106513.097-2506155.740.000.000.000.0080.002948016085.030.000.0022634031.9190.000.000.00-1361.04-6.40100.000.00-19281.600.000.00110.000.000.00192813.601361.046-9997.4045824888kg60kg7-614.3549639935kg70kg83850169.64197901kg80kg9-2.5954175112kg90kg10614.3549639935kg100kg11499.6314252125kg110kg6-9997.4045824888kg6-9.9974045825Tn7-614.3549639935kg7-0.614354964Tn83850169.64197901kg.cm838.5016964198Tn.m9-2.5954175112kg9-0.0025954175Tn10614.3549639935kg100.614354964Tn11499.6314252125kg.cm110.0049963143Tn.m

b

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PORTICO-PRACTICAUNIVERSIDAD ALAS PERUANASCARRERA: INGENIERIA CIVILCURSO: ANALISIS ESTRUCTURAL IIALUMNO: GARCIA CONDORCALLO, ALANEJERCICIO PRACTICO DE PORTICO POR EL METODO DE RIGIDEZRELACION S - R - CSRC180PI200Paso 01Numeramos las barras Numeramos los Grados de Libertad ( DOF ) libres y restringidos de la estructuraBarra123A (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 porticoPaso 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)6.00m4-71116.1020.0000.00071116.102-275.8790.000Angulo050.000-275.879-827.637-275.879275.879-827.637Radianes060.000827.6371655.2740.000-827.6373310.549COS1SEN0BARRA 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)5.00m7-752.994-0.0001882.485752.9940.0001882.485Angulo908-0.000-75299.402-0.0000.00075299.402-0.000Radianes1.579-1882.4850.0003137.4751882.485-0.0006274.950COS0SEN1BARRA 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-0SEN1123456789101112171116.1020.000-2710.122-71116.1020.0000.000-752.994-0.000-1882.4850.0000.0000.00020.00075575.281827.6370.000-275.879827.637-0.000-75299.4020.0000.0000.0000.0003-2710.122827.6379585.4990.000-827.6371655.2741882.485-0.0003137.4750.0000.0000.0004-71116.1020.0000.00077069.043-18134.700-1176.5530.0000.0000.000-6287.79317747.204-1116.17650.000-275.879-827.637-18134.70053889.549-1199.6960.0000.0000.00017747.204-53613.670-372.05960.000827.6371655.274-1176.553-1199.6968271.3330.0000.0000.0001116.176372.0592480.3927-752.994-0.0000.0000.0000.0000.000752.9940.0001882.4850.0000.0000.0008-0.000-75299.4020.0000.0000.0000.0000.00075299.402-0.0000.0000.0000.0009-1882.4850.0000.0000.0000.0000.0001882.485-0.0006274.9500.0000.0000.000100.0000.000-6287.793-6287.79317747.2041116.1760.0000.0000.0006287.793-17741.1661116.176110.0000.00017747.20417747.204-53613.670372.0590.0000.0000.000-17741.16653613.670372.059Paso 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 indica12345697810111212345697810111212.000Tn72.000Tn2-4.020Tn80.000Tn3-1.560Tn100.000Tn40.000Tn110.000Tn5-10.980Tn120.000Tn6-0.020Tn9-2.000Tn1234569171116.1020.000-2710.122-71116.1020.0000.000-1882.48520.00075575.281827.6370.000-275.879827.6370.0003-2710.122827.6379585.4990.000-827.6371655.2743137.4754-71116.1020.0000.00077069.043-18134.700-1176.5530.00050.000-275.879-827.637-18134.70053889.549-1199.6960.00060.000827.6371655.274-1176.553-1199.6968271.3330.0009-1882.4850.0000.0000.0000.0000.0006274.950Paso 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 enter12345691-0.00065694230.0000022291-0.0001901616-0.000661057-0.0002273506-0.0000891749-0.000102001920.0000016440.0000132491-0.00000047050.00000164260.0000005931-0.00000091190.00000072843-0.0001232561-0.00000052810.0000725231-0.0001240812-0.000041493-0.0000381288-0.00007323844-0.00066108980.0000022316-0.0001914152-0.0006510789-0.000223964-0.0000870138-0.00010261935-0.00022663170.0000007931-0.0000644392-0.0002232292-0.0000581587-0.0000273723-0.00003576996-0.000102406-0.0000007876-0.0000510406-0.0001003233-0.00003204890.0001122737-0.00000520159-0.00019708270.0000006687-0.0000570485-0.0001983171-0.0000682052-0.00002675250.0001287632781011121-752.994-0.0000.0000.0000.000-1505.9882-0.000-75299.4020.0000.0000.000-0.00031882.485-0.0000.0000.0000.0003764.97040.0000.000-6287.79317747.204-1116.1760.00050.0000.00017747.204-53613.670-372.0590.00060.0000.0001116.176372.0592480.3920.00091882.485-0.0000.0000.0000.0003764.9701507.988-4.020-3766.5300.000-10.980-0.020-3766.970Paso 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 enter10.1123154357m20.0014474431m3-0.1826839525m40.113071512m50.0363343643m60.0577656564m9-0.5666240969m7ERROR:#VALUE!Tn8ERROR:#VALUE!Tn10ERROR:#VALUE!Tn11ERROR:#VALUE!Tn12ERROR:#VALUE!Tn7ERROR:#VALUE!Tn8ERROR:#VALUE!Tn10ERROR:#VALUE!Tn11ERROR:#VALUE!Tn12ERROR:#VALUE!Tn

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