Examen Directo

Direccion X-XDISENO DE LOSAS ARMADAS EN DOS DIRECCIONE METODO DIRECTO (DIRECCION X-X)Datos:Espesor de Losa0.14m.Seccion Viga (X-X)Seccion Columna(X-X)Carga Viva900Kg/m2.b=0.25m.b=0.25m.Piso Terminado115Kg/m2.h=0.6m.h=0.25m.F'c=210Kg/cm2Longitudes entre ejes XLongitudes entre ejes YFy=4200Kg/cm2L1x=4.00m.L1y=4.00m.L2x=4.00m.L2y=4.00m.L3x=4.00m.L3y=4.00m.SOLUCION1.- Verificacion del Espesor de losah=0.09m.h=0.0833333333m.h=0.14m.2.- Metrado de CargasCarga MuertaCarga VivaPeso Propio336Kg/m2.Carga Viva900Kg/m2.Piso Terminado115Kg/m2.WL=900Kg/m2.Wd=451Kg/m2.Carga AmplificadaWu=1.40Wd+1.70WLWu=2161.4Kg/m2.3.- Calculo del Mo en los Paos.Pao Al2=4.00ln=3.75Mo=121578.75Kg-m.Pao Bl2=4.00ln=3.75Mo=121578.75Kg-m.Pao Cl2=2.00ln=3.75Mo=60789.38Kg-m.Pao Dl2=2.00ln=3.75Mo=60789.38Kg-m.4.- Momentos Negativos y Positivos AmplificadosFranja 1Pao CMinterior(-)0.7060789.38= 42552.56 Kg-mMo=60789.38Kg-m.M(+)0.5760789.38= 34649.94 Kg-mPao ExteriorMexterior(-)0.1660789.38= 9726.30 Kg-mPao DM(-)0.6560789.38= 39513.09 Kg-mMo=60789.38Kg-m.M(+)0.3560789.38= 21276.28 Kg-mPao InteriorFranja 2Pao AMinterior(-)0.70121578.75= 85105.13 Kg-mMo=121578.75Kg-m.M(+)0.57121578.75= 69299.89 Kg-mPao ExteriorMexterior(-)0.16121578.75= 19452.60 Kg-mPao BM(-)0.65121578.75= 79026.19 Kg-mMo=121578.75Kg-m.M(+)0.35121578.75= 42552.56 Kg-mPao Interior5.- Momentos Amplificados en la Franja de Columna1.Calculo del Momento de Inercia ya) Franja 10.710.1410.230.1150.36908582090.4620.530.09940.25Inercia de la VigaIv=0.007 m4Inercia de la LosaIL=0.000 m415.2812991711b) Franja 20.510.250.510.1410.3231250.16156250.44142038430.5120.576250.07087520.576250.0708750.25Inercia de la VigaIv=0.011 m4Inercia de la LosaIL=0.001 m411.68969650046.- Momentos en cada Franjaa) Franja 1Calculo del "C"0.710.710.460.140.140.140.460.460.600.250.250.25X1=0.25X1=0.25Y1=0.46Y1=0.60X2=0.14X2=0.14Y2=0.71Y2=0.46C=0.0021442606C=0.0026447606Se Eligira el C maxC=0.0026447606Calculo del2.8915020773Ahora Hallaremos los Porcentajes para la Franja Columnaa)Momento Negativo Interior E-060 13.6.4.12.00= 0.507.64064958554.0090%b)Momento Negativo Exterior E-060 13.6.4.12.00= 0.507.64064958552.89150207734.0088%c)Momento Positivo2.00= 0.507.64064958554.0090%FRANJA COLUMNAFRANJA CENTRALPaoMomentos (Kg-m)Momento Vigas (85%)Momento Losa(15%)Momento LosaCMexterior(-)= 9726.307275.27241283.87161167.156M(+)= 34649.9426507.206968754677.742406253464.994375Minterior(-)=42552.5632552.71031255744.59593754255.25625DMinterior(-)=39513.0930227.516718755334.267656253951.309375M(+)= 21276.2816276.355156252872.297968752127.628125Calculo del Refuerzo de la Losa en la Franja Columnad=11.00cm.b=100cm.VARILLADIAMETROAREAPaoMomento Losa(15%)AsAs minAs UsarS(cm)S maxSusarRefuerzoNpulg.cmcm2C1283.87 Kg-m0.581 cm21.980 cm21.980 cm23/8352828.003/8@2821/40.630.320.714677.74 Kg-m2.183 cm21.980 cm22.183 cm21/2552828.001/2@2833/80.950.711.275539.43 Kg-m2.601 cm21.980 cm22.601 cm21/2452828.001/2@2841/21.271.271.27D55/81.591.992872.30 Kg-m1.321 cm21.980 cm21.980 cm21/2602828.001/2@2863/41.912.871.27812.545.07Calculo del Refuerzo de la Losa en la Franja Centrald=11.00cm.b=100cm.VARILLADIAMETROAREAPaoMomento Losa(15%)AsAs minAs UsarS(cm)S maxSusarRefuerzoNpulg.cmcm2C1167.16 Kg-m0.527 cm21.980 cm21.980 cm23/8352828.003/8@2821/40.630.320.713464.99 Kg-m1.602 cm21.980 cm21.980 cm23/8352828.003/8@2833/80.950.710.714103.28 Kg-m1.907 cm21.980 cm21.980 cm23/8352828.003/8@2841/21.271.270.71D55/81.591.992127.63 Kg-m0.972 cm21.980 cm21.980 cm23/8352828.003/8@2863/41.912.870.71812.545.076.- Momentos en cada Franjab) Franja 2Calculo del "C"1.261.260.510.250.510.140.140.140.140.510.510.510.250.250.25X1=0.25X1=0.25Y1=0.51Y1=0.65X2=0.14X2=0.14Y2=1.26Y2=0.51C=0.0029X2=0.14Y2=0.51C=0.0033Se Eligira el C maxC=0.0033103257Calculo del1.8095803845Ahora Hallaremos los Porcentajes para la Franja Columnaa)Momento Negativo Interior E-060 13.6.4.14.00= 1.0011.68969650044.0090%b)Momento Negativo Exterior E-060 13.6.4.14.00= 1.0011.68969650041.80958038454.0090%c)Momento Positivo4.00= 1.0011.68969650044.0090%FRANJA COLUMNAFRANJA CENTRALPaoMomentos (Kg-m)Momento Vigas (85%)Momento Losa(15%)Momento LosaAMexterior(-)= 19452.6014881.2392626.1011945.26M(+)= 69299.8953014.41393759355.48481256929.98875Minterior(-)=85105.1365105.42062511489.1918758510.5125BMinterior(-)=79026.1960455.033437510668.53531257902.61875M(+)=42552.5632552.71031255744.59593754255.25625Calculo del Refuerzo de la Losa en la Franja Columnad=11.00cm.b=100cm.VARILLADIAMETROAREAPaoMomento Losa(15%)AsAs minAs UsarS(cm)S maxSusarRefuerzoNpulg.cmcm2A2626.10 Kg-m1.205 cm21.980 cm21.980 cm23/8352828.003/8@2821/40.630.320.719355.48 Kg-m4.492 cm21.980 cm24.492 cm21/2252825.001/2@2533/80.950.711.2711078.86 Kg-m5.365 cm21.980 cm25.365 cm21/2202820.001/2@2041/21.271.271.27B55/81.591.995744.60 Kg-m2.701 cm21.980 cm22.701 cm21/2452828.001/2@2863/41.912.871.27812.545.07Calculo del Refuerzo de la Losa en la Franja Centrald=11.00cm.b=100cm.VARILLADIAMETROAREAPaoMomento LosaAsAs minAs UsarS(cm)S maxSusarRefuerzoNpulg.cmcm2A1945.26 Kg-m0.887 cm21.980 cm21.980 cm23/8352828.003/8@2821/40.630.320.716929.99 Kg-m3.282 cm21.980 cm23.282 cm21/2352828.001/2@2833/80.950.711.278206.57 Kg-m3.916 cm21.980 cm23.916 cm21/2302828.001/2@2841/21.271.271.27B55/81.591.994255.26 Kg-m1.980 cm21.980 cm21.980 cm21/2602828.001/2@2863/41.912.871.27812.545.07

12Y_iA_OY_1=12Y_iA_OY_1=21122_t_t=_t=12_t_t=_t=122

Direccion Y-YDISENO DE LOSAS ARMADAS EN DOS DIRECCIONE METODO DIRECTO (DIRECCION Y-Y)Datos:Espesor de Losa0.14m.Seccion Viga (Y-Y)Seccion Columna(Y-Y)Carga Viva900Kg/m2.b=0.25m.b=0.25m.Piso Terminado115Kg/m2.h=0.5m.h=0.25m.F'c=210Kg/cm2Longitudes entre ejes XLongitudes entre ejes YFy=4200Kg/cm2L1x=5.00m.L1y=6.00m.L2x=4.00m.L2y=6.00m.L3x=3.00m.L3y=6.00m.SOLUCION1.- Verificacion del Espesor de losah=0.12m.h=0.1166666667m.h=0.14m.2.- Metrado de CargasCarga MuertaCarga VivaPeso Propio336Kg/m2.Carga Viva900Kg/m2.Piso Terminado115Kg/m2.WL=900Kg/m2.Wd=451Kg/m2.Carga AmplificadaWu=1.40Wd+1.70WLWu=2161.4Kg/m2.3.- Calculo del Mo en los Paos.Pao Al2=6.00ln=4.75Mo=292599.53Kg-m.Pao Bl2=6.00ln=3.75Mo=182368.13Kg-m.Pao Cl2=3.00ln=2.75Mo=49036.76Kg-m.Pao Dl2=3.00ln=3.75Mo=91184.06Kg-m.4.- Momentos Negativos y Positivos AmplificadosFranja 1Pao CMinterior(-)0.7049036.76= 34325.73 Kg-mMo=49036.76Kg-m.M(+)0.5749036.76= 27950.95 Kg-mPao ExteriorMexterior(-)0.1649036.76= 7845.88 Kg-mPao DM(-)0.6591184.06= 59269.64 Kg-mMo=91184.06Kg-m.M(+)0.3591184.06= 31914.42 Kg-mPao InteriorFranja 2Pao AMinterior(-)0.70292599.53= 204819.67 Kg-mMo=292599.53Kg-m.M(+)0.57292599.53= 166781.73 Kg-mPao ExteriorMexterior(-)0.16292599.53= 46815.92 Kg-mPao BM(-)0.65182368.13= 118539.28 Kg-mMo=182368.13Kg-m.M(+)0.35182368.13= 63828.84 Kg-mPao Interior5.- Momentos Amplificados en la Franja de Columna1.Calculo del Momento de Inercia ya) Franja 10.610.1410.180.090.30172177880.3620.430.08540.25Inercia de la VigaIv=0.004 m4Inercia de la LosaIL=0.001 m45.6125753491b) Franja 20.360.250.360.1410.250.1250.33035429580.3620.430.050420.430.05040.25Inercia de la VigaIv=0.005 m4Inercia de la LosaIL=0.001 m43.33584425876.- Momentos en cada Franjaa) Franja 1Calculo del "C"0.610.610.360.140.140.140.360.360.500.250.250.25X1=0.25X1=0.25Y1=0.36Y1=0.50X2=0.14X2=0.14Y2=0.61Y2=0.36C=0.0015319606C=0.0020324606Se Eligira el C maxC=0.0020324606Calculo del1.4813852527Ahora Hallaremos los Porcentajes para la Franja Columnaa)Momento Negativo Interior E-060 13.6.4.13.00= 0.603.36754520955.0085%b)Momento Negativo Exterior E-060 13.6.4.13.00= 0.603.36754520951.48138525275.0085%c)Momento Positivo3.00= 0.603.36754520955.0085%FRANJA COLUMNAFRANJA CENTRALPaoMomentos (Kg-m)Momento Vigas (85%)Momento Losa(15%)Momento LosaCMexterior(-)= 7845.885668.6497451000.3499551176.8823M(+)= 27950.9520194.56471656253563.74671468754192.64319375Minterior(-)=34325.7324800.3426343754376.5310531255148.8600625DMinterior(-)=59269.6442822.31535156257556.87917968758890.44609375M(+)= 31914.4223058.16980468754069.08878906254787.16328125Calculo del Refuerzo de la Losa en Franja Columnad=11.00cm.b=100cm.VARILLADIAMETROAREAPaoMomento Losa(15%)AsAs minAs UsarS(cm)S maxSusarRefuerzoNpulg.cmcm2C1000.35 Kg-m0.451 cm21.980 cm21.980 cm21/4152815.001/4@1521/40.630.320.323563.75 Kg-m1.649 cm21.980 cm21.980 cm23/8352828.003/8@2833/80.950.710.715966.71 Kg-m2.809 cm21.980 cm22.809 cm23/8252825.003/8@2541/21.271.270.71D55/81.591.994069.09 Kg-m1.891 cm21.980 cm21.980 cm23/8352828.003/8@2863/41.912.870.71812.545.07Calculo del Refuerzo de la Losa en Franja Centrald=11.00cm.b=100cm.VARILLADIAMETROAREAPaoMomento LosaAsAs minAs UsarS(cm)S maxSusarRefuerzoNpulg.cmcm2C1176.88 Kg-m0.531 cm21.980 cm21.980 cm21/4152815.001/4@1521/40.630.320.324192.64 Kg-m1.950 cm21.980 cm21.980 cm21/4152815.001/4@1533/80.950.710.327019.65 Kg-m3.327 cm21.980 cm23.327 cm21/4102810.001/4@1041/21.271.270.32D55/81.591.994787.16 Kg-m2.236 cm21.980 cm22.236 cm21/4152815.001/4@1563/41.912.870.32812.545.076.- Momentos en cada Franjab) Franja 2Calculo del "C"0.970.970.360.250.360.140.140.140.140.360.360.360.250.250.25X1=0.25X1=0.25Y1=0.36Y1=0.50X2=0.14X2=0.14Y2=0.97Y2=0.36C=0.0019X2=0.14Y2=0.36C=0.0023Se Eligira el C maxC=0.002281067Calculo del0.8312926263Ahora Hallaremos los Porcentajes para la Franja Columnaa)Momento Negativo Interior E-060 13.6.4.16.00= 1.204.00301311055.0072%b)Momento Negativo Exterior E-060 13.6.4.16.00= 1.204.00301311050.83129262635.0072%c)Momento Positivo6.00= 1.204.00301311055.0072%FRANJA COLUMNAFRANJA CENTRALPaoMomentos (Kg-m)Momento Vigas (85%)Momento Losa(15%)Momento LosaAMexterior(-)= 46815.9228651.3454885056.11979213108.45872M(+)= 166781.73102070.41830118012.42675946698.88419Minterior(-)=204819.67125349.6365122120.5240957349.5069BMinterior(-)=118539.2872546.04012512802.24237533190.99875M(+)=63828.8439063.2523756893.51512517872.07625Calculo del Refuerzo de la Losa en la Franja Columnad=11.00cm.b=100cm.d=VARILLADIAMETROAREAPaoMomento Losa(15%)AsAs minAs UsarS(cm)S maxSusarRefuerzoNpulg.cmcm2A5056.12 Kg-m2.366 cm21.980 cm22.366 cm23/8302828.003/8@2821/40.630.320.7118012.43 Kg-m8.989 cm21.980 cm28.989 cm21/2102810.001/2@1033/80.950.711.2717461.38 Kg-m8.695 cm21.980 cm28.695 cm21/2102810.001/2@1041/21.271.271.27B55/81.591.996893.52 Kg-m3.264 cm21.980 cm23.264 cm21/2352828.001/2@2863/41.912.871.27812.545.07Calculo del Refuerzo de la Losa en la Franja Centrald=11.00cm.b=100cm.d=VARILLADIAMETROAREAPaoMomento Losa(15%)AsAs minAs UsarS(cm)S maxSusarRefuerzoNpulg.cmcm2A13108.46 Kg-m6.409 cm21.980 cm26.409 cm23/8102810.003/8@1021/40.630.320.7146698.88 Kg-m25.502 cm21.980 cm225.502 cm25/85285.005/8@533/80.950.711.9945270.25 Kg-m24.627 cm21.980 cm224.627 cm23/4102810.003/4@1041/21.271.272.87B55/81.591.9917872.08 Kg-m8.914 cm21.980 cm28.914 cm25/8202820.005/8@2063/41.912.871.99812.545.07

h=l_n/40h=Perimetro/180M_o=(W_u l_2 l_n^2)/8M_o=(W_u l_2 l_n^2)/8M_o=(W_u l_2 l_n^2)/8M_o=(W_u l_2 l_n^2)/812Y_iA_OY=(Y_i A_oi)/(A_oi )YI_V=1/12 L_x1 L_y1^3+A_o1 (Y-Y_1)" " ^2+1/12 L_x2 L_y2^3+A_o2 (Y-Y_2)" " ^2I_L=1/12 l_2 h_f^3_1=I_V/I_L_1=12Y_iA_OY=(Y_i A_oi)/(A_oi )YI_V=1/12 L_x1 L_y1^3+A_o1 (Y-Y_1)" " ^2+1/12 L_x2 L_y2^3+A_o2 (Y-Y_2)" " ^2I_L=1/12 l_2 h_f^3_1=I_V/I_L_1=2C=(1-0.63 X/Y)(X^3 Y)/31122_t_t=C/(2I_losa )_t=l_2/l_1 =_1 l_2/l_1 =l_2/l_1 =_1 l_2/l_1 =_t=l_2/l_1 =_1 l_2/l_1 =C=(1-0.63 X/Y)(X^3 Y)/312_t_t=C/(2I_losa )_t=l_2/l_1 =_1 l_2/l_1 =l_2/l_1 =_1 l_2/l_1 =_t=l_2/l_1 =_1 l_2/l_1 =122

Hoja1 (2)DISENO DE LOSAS ARMADAS EN DOS DIRECCIONE METODO DIRECTO (DIRECCION X-X)Datos:Espesor de Losa0.14m.Seccion Viga (X-X)Seccion Columna(X-X)Carga Viva900Kg/m2.b=0.25m.b=0.25m.Piso Terminado115Kg/m2.h=0.6m.h=0.25m.F'c=210Kg/cm2Longitudes entre ejes XLongitudes entre ejes YFy=4200Kg/cm2L1x=6.00m.L1y=5.00m.L2x=6.00m.L2y=4.00m.L3x=6.00m.L3y=5.00m.SOLUCION1.- Verificacion del Espesor de losah=0.14m.h=0.1166666667m.h=0.14m.2.- Metrado de CargasCarga MuertaCarga VivaPeso Propio345Kg/m2.Carga Viva900Kg/m2.Piso Terminado115Kg/m2.WL=900Kg/m2.Wd=460Kg/m2.Carga AmplificadaWu=1.40Wd+1.70WLWu=2174Kg/m2.3.- Calculo del Mo en los Paos.Pao Al2=4.50ln=5.75Mo=323450.44Kg-m.Pao Bl2=4.50ln=5.75Mo=323450.44Kg-m.Pao Cl2=2.50ln=5.75Mo=179694.69Kg-m.Pao Dl2=2.50ln=5.75Mo=179694.69Kg-m.4.- Momentos Negativos y Positivos AmplificadosFranja 1Pao CMinterior(-)0.70179694.69= 125786.28 Kg-mMo=179694.69Kg-m.M(+)0.57179694.69= 102425.97 Kg-mPao ExteriorMexterior(-)0.16179694.69= 28751.15 Kg-mPao DM(-)0.65179694.69= 116801.55 Kg-mMo=179694.69Kg-m.M(+)0.35179694.69= 62893.14 Kg-mPao InteriorFranja 2Pao AMinterior(-)0.70323450.44= 226415.31 Kg-mMo=323450.44Kg-m.M(+)0.57323450.44= 184366.75 Kg-mPao ExteriorMexterior(-)0.16323450.44= 51752.07 Kg-mPao BM(-)0.65323450.44= 210242.78 Kg-mMo=323450.44Kg-m.M(+)0.35323450.44= 113207.65 Kg-mPao Interior5.- Momentos Amplificados en la Franja de Columna1.Calculo del Momento de Inercia ya) Franja 10.710.1410.2281250.11406250.36940059340.4620.5281250.10152343750.25Inercia de la VigaIv=0.007 m4Inercia de la LosaIL=0.001 m411.2915735944b) Franja 20.460.250.460.1410.30.150.40642452760.4620.5281250.065585937520.5281250.06558593750.25Inercia de la VigaIv=0.008 m4Inercia de la LosaIL=0.001 m47.511829436.- Momentos en cada Franjaa) Franja 1Calculo del "C"0.710.710.460.140.140.140.460.460.600.250.250.25X1=0.25X1=0.25Y1=0.46Y1=0.60X2=0.14X2=0.14Y2=0.71Y2=0.46C=0.0021656144C=0.0026667741Se Eligira el C maxC=0.0026667741Calculo del2.1546359702Ahora Hallaremos los Porcentajes para la Franja Columnaa)Momento Negativo Interior E-060 13.6.4.12.50= 0.424.7048223316.0090%b)Momento Negativo Exterior E-060 13.6.4.12.50= 0.424.7048223312.15463597026.0090%c)Momento Positivo2.50= 0.424.7048223316.0090%FRANJA COLUMNAFRANJA CENTRALPaoMomentos (Kg-m)Momento Vigas (85%)Momento Losa(15%)Momento LosaCMexterior(-)= 28751.1521994.629753881.405252875.115M(+)= 102425.9778355.86848437513827.50620312510242.5971875Minterior(-)=125786.2896226.5051562516981.1479687512578.628125DMinterior(-)=116801.5589353.18335937515768.20882812511680.1546875M(+)= 62893.1448113.2525781258490.5739843756289.3140625Calculo del Refuerzo de la Losad=11.38cm.b=100cm.VARILLADIAMETROAREAPaoMomento Losa(15%)AsAs minAs UsarS(cm)S maxSusarRefuerzoNpulg.cmcm2C3881.41 Kg-m1.677 cm22.048 cm22.048 cm23/83528.7528.753/[email protected]/40.630.320.7113827.51 Kg-m6.292 cm22.048 cm26.292 cm23/81028.7510.003/8@1033/80.950.710.7116374.68 Kg-m7.526 cm22.048 cm27.526 cm23/81028.7510.003/8@1041/21.271.270.71D55/81.591.9908490.57 Kg-m3.772 cm22.048 cm23.772 cm23/82028.7520.003/8@2063/41.912.870.71812.545.076.- Momentos en cada Franjab) Franja 2Calculo del "C"1.161.160.460.250.460.140.140.140.140.460.460.460.250.250.25X1=0.25X1=0.25Y1=0.46Y1=0.60X2=0.14X2=0.14Y2=1.16Y2=0.46C=0.0026X2=0.14Y2=0.46C=0.0030Se Eligira el C maxC=0.0030288606Calculo del1.3595477612Ahora Hallaremos los Porcentajes para la Franja Columnaa)Momento Negativo Interior E-060 13.6.4.14.50= 0.755.63387207256.0090%b)Momento Negativo Exterior E-060 13.6.4.14.50= 0.755.63387207251.35954776126.0090%c)Momento Positivo4.50= 0.755.63387207256.0090%FRANJA COLUMNAFRANJA CENTRALPaoMomentos (Kg-m)Momento Vigas (85%)Momento Losa(15%)Momento LosaAMexterior(-)= 51752.0739590.333556986.529455175.207M(+)= 184366.75141040.56327187524889.51116562518436.6749375Minterior(-)=226415.31173207.7092812530566.0663437522641.530625BMinterior(-)=210242.78160835.73004687528382.77589062521024.2784375M(+)=113207.6586603.85464062515283.03317187511320.7653125Calculo del Refuerzo de la Losad=11.38cm.b=100cm.VARILLADIAMETROAREAPaoMomento Losa(15%)AsAs minAs UsarS(cm)S maxSusarRefuerzoNpulg.cmcm2A6986.53 Kg-m3.079 cm22.048 cm23.079 cm23/82528.7525.003/8@2521/40.630.320.7124889.51 Kg-m11.780 cm22.048 cm211.780 cm21/21028.7510.001/2@1033/80.950.711.2729474.42 Kg-m14.147 cm22.048 cm214.147 cm21/21028.7510.001/2@1041/21.271.271.27B55/81.591.99015283.03 Kg-m6.995 cm22.048 cm26.995 cm23/81028.7510.003/8@1063/41.912.870.71812.545.07

h=l_n/40h=Perimetro/180M_o=(W_u l_2 l_n^2)/8M_o=(W_u l_2 l_n^2)/8M_o=(W_u l_2 l_n^2)/8M_o=(W_u l_2 l_n^2)/812Y_iA_OY=(Y_i A_oi)/(A_oi )YI_V=1/12 L_x1 L_y1^3+A_o1 (Y-Y_1)" " ^2+1/12 L_x2 L_y2^3+A_o2 (Y-Y_2)" " ^2I_L=1/12 l_2 h_f^3_1=I_V/I_L_1=12Y_iA_OY=(Y_i A_oi)/(A_oi )YI_V=1/12 L_x1 L_y1^3+A_o1 (Y-Y_1)" " ^2+1/12 L_x2 L_y2^3+A_o2 (Y-Y_2)" " ^2I_L=1/12 l_2 h_f^3_1=I_V/I_L_1=2C=(1-0.63 X/Y)(X^3 Y)/31122_t_t=C/(2I_losa )_t=l_2/l_1 =_1 l_2/l_1 =l_2/l_1 =_1 l_2/l_1 =_t=l_2/l_1 =_1 l_2/l_1 =C=(1-0.63 X/Y)(X^3 Y)/312_t_t=C/(2I_losa )_t=l_2/l_1 =_1 l_2/l_1 =l_2/l_1 =_1 l_2/l_1 =_t=l_2/l_1 =_1 l_2/l_1 =122

MBD000BC0B3.unknown

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Examen Directo

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