e-portico 2do examen alan
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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
1m
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5m
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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
1m
6m
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5m
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b
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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
1m
6m
2m
0.50m
5m
1
3
2
0.30m
b
c
a
d
b
c
a
d
b
c
a
d
b
c
a
d
b
c
a
d
b
c
a
d
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
1m
6m
2m
0.50m
5m
1
3
2
0.30m
b
c
a
d
b
c
a
d
b
c
a
d
b
c
a
d
b
c
a
d
b
c
a
d
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
4 Tn
3 Tn/m
2m
2m
3m
6m
2m
2m
4m
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
1m
6m
2m
0.50m
5m
1
3
2
0.30m
b
c
a
d
b
c
a
d
b
c
a
d
b
c
a
d
b
c
a
d
b
c
a
d
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
c
a
d
b
c
a
d
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
1m
6m
2m
0.50m
5m
1
3
2
0.30m