espectro RNC 1.5. USANDO EL ESPECTRO DE RESPUESTA TERICA SEGN R.N.C. -2003Se considerar para cada modo una aceleracin del suelo segn la expresin siguiente en la que "C" se obtendr segn el periodo correspondiente a cada modo.Donde:* Z : Factor de ZonaPara nuestro caso, la edificacin estar ubicada en Tarapoto que segn el mapa ssmico le corresponde la zona 2; por lo tanto:Z =0.30* U : Factor de Uso e Importancia:Depende de la categora de la edificacin, para nuestro caso es de categora C (viviendas); por lo tanto:U =1.00* S : Factor de Suelo:Para nuestro caso se considerar suelo tipo S3 (suelos fleccibles);; por lo tanto:S =1.40Tp =0.90seg.* R : Coeficiente de Reduccin de Fuerza Ssmica:Slo prticos de concreto armado (Se tomar 3/4R (8) por ser estructura irregular)R =6.00* C : Factor de Amplificacin:C 2.5Tp = 0.90 seg. para suelo S3T = Periodo de vibracin de la edificacing = 980 cm/seg (Aceleracin de la gravedad)

Sai = ZUSCi x g RC = 2.5 Tp TSdi = Sai WRoberto Carlos:

X1.5.1.- DESPLAZAMIENTOS LATERALES MXIMOS ENTREPISOFORMA DE MODOFDMANLISIS EN LA DIRECCIN "X"10.3867479129*Clculo de C (Factor de Amplificacin):20.35479178T=hn/CThn(m)=12.5CT=3530.202766304840.0567174517T =0.357wn=11.4525365868T=0.55C =2.5 x0.90wn=28.5648385257T=0.220.357wn=44.034531904T=0.14wn=51.1575996309T=0.12C =6.30> 2.5C =2.50Formas de ModoFPMW (rad/seg)T (seg)CiSai (cm/seg)Sdi = Sai/W (cm)Yi = FPM x Sdi (cm)10.38711.4530.5502.50171.501.3080.505720.35528.5650.2202.50171.500.2100.074630.20344.0350.1402.50171.500.0880.017940.05751.1580.1202.50171.500.0660.0037MODOS DE VIBRACIN:Forma de Modo123411.002.0753.0443.479Nivel1.002.003.004.0021.001.090-0.300-1.36011.001.001.001.0031.00-0.510-0.8501.00022.081.09-0.51-1.4941.00-1.4901.810-1.20033.04-0.30-0.851.8143.48-1.361.00-1.20Con los valores de Yi calculamos los desplazamientos:i =forma de modo=nivel-Debido a la primera forma de modo:1.0000.5057X =2.075x0.5057=1.04943.0441.53923.4791.7595-Debido a la segunda forma de modo:1.0000.0746X =1.090x0.0746=0.0813-0.300-0.0224-1.360-0.1014-Debido a la tercera forma de modo:1.0000.0179X =-0.510x0.0179=-0.0091-0.850-0.01521.0000.0179-Debido a la cuarta forma de modo:1.0000.0037X =-1.490x0.0037=-0.00551.8100.0067-1.200-0.0045DESPLAZAMIENTOS TOTALES Y RELATIVOS:NivelX (cm)X real (cm)D (cm)D real (cm)10.53410.53412.4032.40321.07580.54174.8412.43731.55050.47486.9772.13641.79270.24228.0671.090FUERZAS SSMICAS Y CORTANTES MXIMAS:NivelRigidez (K) Ton/cmV = Kx . Xreal (Tn)F (Tn)1218.76116.8422.922173.4093.9232.18KL=218.763130.0561.7430.24KL=173.44130.0531.5031.50KL=130.05KL=130.05CUADRO RESUMEN: EN LA DIRECCIN X-XNivelX (cm)X real (cm)D (cm)D real (cm)F (Tn)V (Tn)10.5340982090.5340982092.4032.40322.92116.8421.07575484810.54165663914.8412.43732.1893.9231.55051227680.47475742876.9772.13630.2461.7441.79270561870.24219334198.0671.09031.5031.50CLCULO DE LA FUERZA CORTANTE EN LA BASE: (Mtodo Esttico)P1 =243.56Tnm1=243.564P2 =216.52Tnm2=216.5207625P3 =169.96Tnm3=169.9643625P4 =121.69Tnm4=121.6932375P =751.74TnVB =131.55TnSEGN RNC 97: es necesario incrementar el cortante para cumplir los mnimos sealados, debido que:116.84B >118.40B =1.013352507!Ser necesario incrementar el cortanteSolicitaciones FinalesNivelF (Tn)V (Tn)123.22118.40232.6195.18330.6562.57431.9231.92

X = x YiX =( 0.25 (l X 1l+ lX 2l+l X 3l+l X 4l ) + 075 ( (lX 1l) + ( LX 2l) + ( lX 3l) + (l X 4l)D = X x (0.75*R)VB = ZUSCP RP = P1+P2+P3+P4V BASE (mtodo dinmico) > 90% V BASE (mtodo esttico)Fn = VnFn-1 = Vn-1 - Vn-2

YANLISIS EN LA DIRECCIN "Y"DESPLAZAMIENTOS LATERALES MXIMOS ENTREPISO*Clculo de C (Factor de Amplificacin):T=hn/CThn(m)=12.5CT=35T =0.357C =2.5 x0.90FORMA DE MODOF.P.M.0.35710.347085501120.3343393206C =6.30> 2.5C =2.5030.22196533540.0963191975Formas de ModoFPMW (rad/seg)T (seg)CiSai (cm/seg)Sdi = Sai/W (cm)Yi = FPM x Sdi (cm)10.34710.530.6002.50171.501.5480.5372wn=10.526859828T=0.620.33426.040.2402.50171.500.2530.0846wn=26.0411213276T=0.2430.22239.200.1602.50171.500.1120.0248wn=39.2026976113T=0.1640.09645.780.1402.50171.500.0820.0079wn=45.7838399438T=0.14MODOS DE VIBRACIN:Forma de Modo1234Nivel112.2483.3523.92411111211.230-0.180-1.55022.24819624821.23-0.3-1.331-0.300-1.0401.04033.3520923521-0.18-1.041.3241-1.3001.320-0.76043.9235209235-1.551.04-0.76Con los valores de Yi calculamos los desplazamientos:i =forma de modo=nivel-Debido a la primera forma de modo:1.0000.5372X =2.248x0.5372=1.20763.3521.80063.9242.1076-Debido a la segunda forma de modo:1.0000.0846X =1.230x0.0846=0.1040-0.180-0.0152-1.550-0.1311-Debido a la tercera forma de modo:1.0000.0248X =-0.300x0.0248=-0.0074-1.040-0.02581.0400.0258-Debido a la cuarta forma de modo:1.0000.0079X =-1.300x0.0079=-0.01021.3200.0104-0.760-0.0060DESPLAZAMIENTOS TOTALES Y RELATIVOS:NivelX (cm)X real (cm)D (cm)D real (cm)10.57190.57192.5732.57321.24150.66965.5873.01331.81370.57228.1612.57542.15140.33789.6811.520FUERZAS SSMICAS Y CORTANTES MXIMAS:NivelRigidez (K) Ton/cmV = Kx . Xreal (Tn)F (Tn)1200.88114.8822.022138.6892.8631.38KL=200.883107.4461.4829.36KL=138.68495.0832.1232.12KL=107.44KL=95.08CUADRO RESUMEN: EN LA DIRECCIN Y-YNivelX (cm)X real (cm)D (cm)D real (cm)F (Tn)V (Tn)10.57190.57188616282.5732.57322.02114.8821.24146015040.66957398765.5873.01331.3892.8631.81366132880.57220117858.1612.57529.3661.4842.15143420880.337772889.6811.52032.1232.12CLCULO DE LA FUERZA CORTANTE EN LA BASE: (Mtodo Esttico)P1 =243.56TnP2 =216.52Tnm1=243.564P3 =169.96Tnm2=216.5207625P4 =121.69Tnm3=169.9643625m4=121.6932375P =751.74TnVB =131.55TnSEGN RNC 2003: es necesario incrementar el cortante para cumplir los mnimos sealados, debido que:114.88B >118.40B =1.0306312206!Ser necesario incrementar el cortanteSolicitaciones FinalesNivelF (Tn)V (Tn)122.70118.40232.3495.70330.2663.36433.1033.10

X = x YiX = 0.25 (l X 1l+ lX 2l+l X 3l+l X 4l ) + 075 ( (lX 1l) + ( LX 2l) + ( lX 3l) + (l X 4l)D = X * 0.75*RVB = ZUSCP RP = P1+P2+P3+P4V BASE (mtodo dinmico) > 90% V BASE (mtodo esttico)Fn = VnFn-1 = Vn-1 - Vn-2D1 Max. = 0.007*he = 2.45 cm

respuesta-Lima1.6. USANDO EL ESPECTRO DE RESPUESTA DE VELOCIDAD DEL SISMO OCURRIDO EN LIMA - PER (N-82-W), 17-10-66, CUYA ACELERACIN MXIMA REGISTRADA HA SIDO 263.32 GAL. (RNC 2003)Este mtodo se aplicar consisderando el espectro de velocidad del sismo ocurrido en Lima, producido el 17 de Octubre de 1966 registrada en la estacin N-82-W, se cree convniente tomar este indicador puesto que sismicamente Tarapoto se ubica en la misma zona que Lima, adems ha sido la fecha de sismo de mayor intensidad de todos los tiempos, alcanzando una aceleracin mxima de 263.321gal, adems se tendr en cuenta un amortiguamiento del 10% y una aceleracin mxima probable de 300 gals.Donde:Sai =Aceleracin del sueloW =FrecuenciaRd =Factor de Ductilidad(8.00)Sdi =Desplazamiento del pisoSv =Velocidad normalizada por 300 galsSv' =Velocidad leida directamente del espectro

Sv = 300 x Sv' 263.321Sdi = Sai WSai = Sv x W Rd

X-Lima1ANLISIS EN LA DIRECCIN "X"DESPLAZAMIENTOS LATERALES MXIMOS ENTREPISOFormas de ModoFPMW (rad/seg)T (seg)Sv' (cm/seg)Sv (cm/seg)Sai (cm/seg)Sdi = Sai/W (cm)Yi = FPM x Sdi (cm)10.38711.45253658680.55070.580.320114.9840.8770.33920.35528.56483852570.22050.857.876206.6530.2530.09030.20344.0345319040.1403944.432244.5700.1260.02640.05751.15759963090.1203843.293276.8470.1060.006MODOS DE VIBRACIN:Forma de Modo123411.0002.0753.0443.47921.0001.090-0.300-1.36031.000-0.510-0.8501.00041.000-1.4901.810-1.200Con los valores de Yi calculamos los desplazamientos:i =forma de modo=nivel-Debido a la primera forma de modo:1.0000.339X =2.075x0.339=0.7043.0441.0323.4791.180-Debido a la segunda forma de modo:1.0000.090X =1.090x0.090=0.098-0.300-0.027-1.360-0.122-Debido a la tercera forma de modo:1.0000.026X =-0.510x0.026=-0.013-0.850-0.0221.0000.026-Debido a la cuarta forma de modo:1.0000.006X =-1.490x0.006=-0.0091.8100.011-1.200-0.007DESPLAZAMIENTOS TOTALES Y RELATIVOS:NivelX (cm)X real (cm)D (cm)D real (cm)10.37890.37891.7052.27420.73880.35983.3242.15931.04740.30864.7131.85241.22340.17605.5051.056

X = x YiX = 0.25 (l X 1l+ lX 2l+l X 3l+l X 4l ) + 075 ( (lX 1l) + ( LX 2l) + ( lX 3l) + (l X 4l)D = X x 0.75R

X-Lima2FUERZAS SSMICAS Y CORTANTES MXIMAS:CUADRO RESUMEN: EN LA DIRECCIN X-X* FUERZAS SSMICAS:NivelX (cm)X real (cm)D (cm)D real (cm)F (Tn)V (Tn)10.37890.37891.7052.27430.04119.9620.73880.35983.3242.15933.1889.9131.04740.30864.7131.85228.8856.7341.22340.17605.5051.05627.8527.85m1=0.24830.2483x1.00011.0418355605m2=0.2207F1 =114.984x0.387x0.2207x2.075=20.3659482398CLCULO DE LA FUERZA CORTANTE EN LA BASE: (Mtodo Esttico)m3=0.17330.1733x3.04423.4574019458m4=0.12410.1241x3.47919.2014645003P1 =243.56TnP2 =216.52TnP3 =169.96TnP4 =121.69Tn0.2483x1.00018.2050353465Segn RNC, por ser Zona 1 H = 0.12 PP =751.74TnF2 =206.653x0.355x0.2207x1.090=17.637768498H =90.2090835Tn0.1733x-0.300-3.81H80% =72.17Tn0.1241x-1.360-12.3744383634VB =98.67TnSEGN RNC 2003: es necesario incrementar el cortante para cumplir los mnimos sealados, debido a que:0.2483x1.00012.313F3 =244.570x0.203x0.2207x-0.510=-5.580.1733x-0.850-7.300.1241x1.0006.154119.96B >88.80B =0.7403!No ser necesario incrementar el cortante0.2483x1.0003.899F4 =276.847x0.057x0.2207x-1.490=-5.16Solicitaciones Finales0.1733x1.8104.925NivelF (Tn)V (Tn)0.1241x-1.200-2.34130.04119.96* FUERZAS SSMICAS MXIMAS Y CORTANTES233.1889.91328.8856.73427.8527.85NivelF (Tn)V (Tn)130.04119.96233.1889.91328.8856.73427.8527.85

VB = ZUSCP = H RP = P1+P2+P3+P4V BASE (mtodo dinmico) > 90% V BASE (mtodo esttico)Fi = Sai x FPM x ma x iF = 0.25 (l F 1l+ l F 2l+l F 3l+l F 4l ) + 075 ( (l F 1l) + ( l F 2l) + ( l F 3l) + (l F 4l)

Y-Lima1ANLISIS EN LA DIRECCIN "Y"DESPLAZAMIENTOS LATERALES MXIMOS ENTREPISOFormas de ModoFPMW (rad/seg)T (seg)Sv' (cm/seg)Sv (cm/seg)Sai (cm/seg)Sdi = Sai/W (cm)Yi = FPM x Sdi (cm)10.34710.5268598280.6007484.308110.9371.0010.347520.33426.04112132760.24051.859.015192.1030.2830.094730.22239.20269761130.1604146.711228.9000.1490.033140.09645.78383994380.1403944.432254.2860.1210.0117MODOS DE VIBRACIN:Forma de Modo123411.0002.2483.3523.92421.0001.230-0.180-1.55031.000-0.300-1.0401.04041.000-1.3001.320-0.760Con los valores de Yi calculamos los desplazamientos:i =forma de modo=nivel-Debido a la primera forma de modo:1.0000.3475X =2.248x0.3475=0.78123.3521.16473.9241.3633-Debido a la segunda forma de modo:1.0000.0947X =1.230x0.0947=0.1165-0.180-0.0170-1.550-0.1468-Debido a la tercera forma de modo:1.0000.0331X =-0.300x0.0331=-0.0099-1.040-0.03441.0400.0344-Debido a la cuarta forma de modo:1.0000.0117X =-1.300x0.0117=-0.01521.3200.0154-0.760-0.0089DESPLAZAMIENTOS TOTALES Y RELATIVOS:NivelX (cm)X real (cm)D (cm)D real (cm)10.3930.39311.7692.35920.8230.43013.7042.58131.1820.35885.3192.15341.4170.23516.3771.410

X = x YiX = 0.25 (l X 1l+ lX 2l+l X 3l+l X 4l ) + 075 ( (lX 1l) + ( LX 2l) + ( lX 3l) + (l X 4l)D = X * 0.75*R

Y-Lima2FUERZAS SSMICAS Y CORTANTES MXIMAS:CUADRO RESUMEN: EN LA DIRECCIN Y-Y* FUERZAS SSMICAS:NivelX (cm)X real (cm)D (cm)D real (cm)F (Tn)V (Tn)10.37890.37891.7052.27428.51116.5820.73880.35983.3242.15931.9988.0731.04740.30864.7131.85228.4556.0741.22340.17605.5051.05627.6227.620.2483x1.0009.561F1 =110.937x0.347x0.2207x2.248=19.1051017863CLCULO DE LA FUERZA CORTANTE EN LA BASE: (Mtodo Esttico)0.1733x3.35222.36800967110.1241x3.92418.7482423327P1 =243.56TnP2 =216.52TnP3 =169.96TnP4 =121.69Tn0.2483x1.00015.9477488576Segn RNC, por ser Zona 1 H = 0.12 PP =751.74TnF2 =192.103x0.334x0.2207x1.230=17.4353276384H =90.2090835Tn0.1733x-0.180-2.004H80% =72.17Tn0.1241x-1.550-12.3545277144VB =98.67TnSEGN RNC 97: es necesario incrementar el cortante para cumplir los mnimos sealados, debido a que:0.2483x1.00012.616F3 =228.900x0.222x0.2207x-0.300=-3.3640.1733x-1.040-9.1570.1241x1.0406.557116.58B >88.80B =0.7617!No ser necesario incrementar el cortante0.2483x1.0006.082F4 =254.286x0.096x0.2207x-1.300=-7.027Solicitaciones Finales0.1733x1.3205.603NivelF (Tn)V (Tn)0.1241x-0.760-2.310128.51116.58* FUERZAS SSMICAS MXIMAS Y CORTANTES231.9988.07328.4556.07427.6227.62NivelF (Tn)V (Tn)128.51116.58231.9988.07328.4556.07427.6227.62

VB = ZUSCP = H RP = P1+P2+P3+P4V BASE (mtodo dinmico) > 90% V BASE (mtodo esttico)Fi = Sai x FPM x ma x iF =1/7.5*( 0.25 (l F 1l+ l F 2l+l F 3l+l F 4l ) + 075 ( (l F 1l) + ( l F 2l) + ( l F 3l) + (l F 4l)))

esttico-equiv.2. ANLISIS ESTTICO EQUIVALENTE2.1 UTILIZANDO EL MTODO ESTTICO EQUIVALENTE SEGN RNC - 2003DETERMINACIN DE LA FUERZA CORTANTE EN LA BASE:Donde:* Z : Factor de ZonaPara nuestro caso, la edificacin estar ubicada en Tarapoto que segn el mapa ssmico le corresponde la zona 2; por lo tanto:Z =0.30* U : Factor de Uso e Importancia:Depende de la categora de la edificacin, para nuestro caso es de categora C (viviendas); por lo tanto:U =1.00* S : Factor de Suelo:Para nuestro caso se considerar suelo tipo S3 (suelos fleccibles);S =1.40Tp =0.90seg.* R : Coeficiente de Reduccin de Fuerza Ssmica:Slo prticos de concreto armado (Se tomar 3/4R (8) por ser estructura irregular)R =6.00* C : Factor de Amplificacin:C 2.5Tp = 0.90 seg. para suelo S3T = Periodo de vibracin de la edificacing = 980 cm/seg (Aceleracin de la gravedad)* T : Periodo Fundamental:Hn =12.50m (altura total)CT =35(slo prticos)T =0.357seg1C =2.5 x0.900.357C =6.30> 2.5C =2.50* P : Peso de la Estructura:P1 =243.56P2 =216.52P3 =169.96P4 =121.69P =751.74TnV =131.55Tn

V = ZUSC x P RC = 2.5 Tp T1Sdi = Sai WT = Hn CT

esttico 1DISTRIBUCIN DE LA FUERZA SSMICA EN ALTURA:Si el periodo fundamental T es mayor que 0.70 seg, una parte de la fuerza cortante V, denominada Fa, deber aplicarse como fuerza concentrada en la parte superior de la estructura. Esta fuerza se deber determinar segn la siguiente expresin:Se tiene que T =0.357< 0.70 seg Fa = 0DISTRIBUCIN DE LOS CORTANTES EN LOS NIVELES:Donde:* Pi = Peso equivalente del nivel i* Hi = Altura desde el nivel 0 al nivel i* Fa = 0NivelPi (Tn)hi (m)Pi x HiV (Tn)Fi (m)Vi (m)1243.563.50852.46131.5520.78520.7852216.526.501407.38131.5534.31555.0993169.969.501614.62131.5539.36894.4674121.6912.501521.13131.5537.088131.555751.735395.59131.555

Fa = 0.07 Tv < 0.15 V0Fi = Pi x Hi x (Vi - Fa) S Pi x Hi

resumen2.2DETERMINACIN DE LOS ESFUERZOS DE DISEO CONSIDERANDO TORSIN EN PLANTA:MTODO A UTILIZAR PARA EL DISEOPara el diseo se ha elegido el espectro de respuesta terica segn el RNC 2003.Eje X - XEje Y - YNivelF (Tn)V (Tn)F (Tn)V (Tn)123.22118.4022.70118.40232.6195.1832.3495.70330.6562.5730.2663.36431.9231.9233.1033.10

rigidezRESUMEN DE LA RIGIDEZ LATERAL EN CADA PISOEJE X-X (T/CM)KL 1=218.76EJE "X"KL2=173.40KL3=130.05KL4=130.05PrticoEntrepiso1234A54.6943.35--B54.6943.3543.3543.35C54.6943.3543.3543.35D54.6943.3543.3543.35TOTAL218.76173.40130.05130.05POR T A-AKL 1 NIVEL=54.69TN/CMKL 2 NIVEL=43.35POT B,C YDKL 1 NIVEL=54.69KL 2 NIVEL=43.35EJE "Y"KL 3 NIVEL=43.35KL 4 NIVEL=43.35PrticoEntrepisoEJE Y-Y (TN/CM)1234KL 1=200.88150.2234.6726.8623.77KL2=138.68250.2234.6726.8623.77KL3=107.44350.2234.6726.8623.77KL4=95.08450.2234.6726.8623.77POR T 1,2 3 Y4TOTAL200.88138.68107.4495.08KL 1 NIVEL=50.22KL 2 NIVEL=34.67KL 3 NIVEL=26.86KL 4 NIVEL=23.77

torsion* CLCULO DEL CENTRO DE MASA EN CADA NIVEL:NivelXY19.66.9529.66.9539.64.649.64.6* CLCULO DEL CENTRO DE FUERZA CORTANTE EN CADA PISOEJE X - XNivelFiSum. Fi (Vx)YFi x YSum. Fi x YYv431.9231.926.95221.83221.836.950330.6562.576.95213.01434.846.950232.6195.184.6150.01584.856.145EJE "X"123.22118.404.6106.82691.675.842PrticoEntrepiso1234EJE Y - YA54.69043.350--B54.69043.35043.35043.350C54.69043.35043.35043.350D54.69043.35043.350043.3500TOTAL218.76173.400130.050130.050NivelFiSum. Fi (Vy)XFi x XSum. Fi x XXvXiYiXiYi433.1033.109.6317.75317.759.6000.250.250.250.25330.2663.369.6290.51608.269.6006.84.76.84.7232.3495.709.6310.47918.739.60013.29.213.29.2122.70118.409.6217.911136.639.60018.9513.6518.95* CLCULO DEL CENTRO DE RIGIDEZ DE CADA PISO EN AMBAS DIRECCIONES39.227.839.214.15PARA EL PRIMER PISOEJE "Y"EJE X - XPrticoEntrepiso1234XR =9.751150.22034.67026.86023.770250.22034.67026.86023.770350.22034.67026.86023.770450.22034.67026.86023.770EJE Y - YTOTAL201.88140.68110.4499.08YR =6.950XR =9.751mYR =6.950mPARA EL SEGUNDO PISOEJE X - XXR =9.661EJE Y - YYR =6.950XR =9.661mYR =6.950mPARA EL TERCER PISOEJE X - XXR =9.534EJE Y - YYR =4.717XR =9.534mYR =4.717mPARA EL CUARTO PISOEJE X - XXR =9.534EJE Y - YYR =4.717XR =9.534mYR =4.717mCUADRO RESUMEN:NivelXRYR49.5344.71739.5344.71729.6616.95019.7516.950* CLCULO DE LAS EXCENTRICIDADES EN CADA PISO EN AMBAS DIRECCIONESNivelXvYvXRYRexey46.9509.6009.5344.717-2.5844.88336.9509.6009.5344.717-2.5844.88326.1459.6009.6616.950-3.5162.65015.8429.6009.7516.950-3.9102.650* CLCULO DEL MOMENTO DE INERCIA POLAR DE CADA PISO:Aplicaremos la siguiente frmula:Donde:B =Codificacin o denominacin de la columnaKBX =Rigidez lateral de la columna en la direccin XKBY =Rigidez lateral de la columna en la direccin YX =Coordenada de la columna en la direccin XY =Coordenada de la columna en la direccin YXR =Abscisa del centro de rigidezYR =Ordenada del centro de rigidezJ =Momento de inercia polar del piso

Yv = Sum Fi Y Sum FiXv = Sum Fi X Sum FiXR = Sum Kyi (Xi) Sum KyYR = Sum Kxi (Yi) Sum KxXR = Sum Kyi (Xi) Sum KyYR = Sum Kxi (Yi) Sum KxXR = Sum Kyi (Xi) Sum KyYR = Sum Kxi (Yi) Sum Kxex = Xv - XRey = Yv - YRJ = (KXB . YB) + (KBY . XB)XB = X - XRYB = Y - YRXR = Sum Kyi (Xi) Sum KyYR = Sum Kxi (Yi) Sum Kx

I4ANLISIS DEL CUARTO PISOXR =9.534YR =4.717XCOLUMNAKBXKBYXYXBYBKBX * YBKBY * XB7536.341-D7.546.160.250.25-9.28-4.47150.36531.2413409.712-D13.416.166.80.25-2.73-4.47267.5446.0714034.843-D14.036.1613.20.253.67-4.47280.0182.858373.994-D8.376.1618.950.259.42-4.47167.07546.501-C7.5411.170.254.7-9.28-0.020.00962.902-C13.4111.176.84.7-2.73-0.020.0083.493-C14.0311.1713.24.73.67-0.020.00150.164-C8.3711.1718.954.79.42-0.020.00990.561-B7.546.440.259.2-9.284.48151.48554.852-B13.416.446.89.2-2.734.48269.5448.113-B14.036.4413.29.23.674.48282.1086.534-B8.376.4418.959.29.424.48168.32570.791736.444654.05J =6390.49

I3ANLISIS DEL TERCER PISOXR =9.534YR =4.717COLUMNAKBXKBYXYXBYBKBX * YBKBY * XB1-D7.546.160.250.25-9.28-4.47150.36531.242-D13.416.166.80.25-2.73-4.47267.5446.073-D14.036.1613.20.253.67-4.47280.0182.854-D8.376.1618.950.259.42-4.47167.07546.501-C7.5411.170.254.7-9.28-0.020.00962.902-C13.4111.176.84.7-2.73-0.020.0083.499519.443-C14.0311.1713.24.73.67-0.020.00150.1611171.954-C8.3711.1718.954.79.42-0.020.00990.566163.691-B7.549.520.259.2-9.284.48151.48820.472-B13.419.526.89.2-2.734.48269.5471.143-B14.039.5213.29.23.674.48282.10127.954-B8.379.5218.959.29.424.48168.32844.041736.445257.38J =6993.81

I2ANLISIS DEL SEGUNDO PISOXR =9.661YR =6.950COLUMNAKBXKBYXYXBYBKBX * YBKBY * XB1-D7.546.160.250.25-9.41-6.70338.31545.862-D13.416.166.80.25-2.86-6.70601.9650.443-D14.036.1613.20.253.54-6.70630.0277.214-D8.376.1618.950.259.29-6.70375.91531.876163.691-C7.5411.170.254.7-9.41-2.2538.15989.4011171.952-C13.4111.176.84.7-2.86-2.2567.8991.4311171.953-C14.0311.1713.24.73.54-2.2571.05139.956163.694-C8.3711.1718.954.79.29-2.2542.39964.041-B7.5411.170.259.2-9.412.2538.15989.402-B13.4111.176.89.2-2.862.2567.8991.437536.343-B14.0311.1713.29.23.542.2571.05139.9513409.714-B8.3711.1718.959.29.292.2542.39964.0414034.841-A7.546.160.2513.65-9.416.70338.31545.868373.992-A13.416.166.813.65-2.866.70601.9650.443-A14.036.1613.213.653.546.70630.0277.214-A8.376.1618.9513.659.296.70375.91531.874331.376780.41J =11111.78

I1ANLISIS DEL PRIMER PISOXR =9.75YR =6.95COLUMNAKBXKBYXYXBYBKBX * YBKBY * XB1-D11.9711.250.250.25-9.50-6.70537.481015.632-D15.0011.256.80.25-2.95-6.70673.1998.003-D15.3111.2513.20.253.45-6.70687.34133.794-D12.4111.2518.950.259.20-6.70557.15951.901-C11.9713.860.254.7-9.50-2.2560.611251.0611250.032-C15.0013.866.84.7-2.95-2.2575.92120.7213857.953-C15.3113.8613.24.73.45-2.2577.51164.8113857.954-C12.4113.8618.954.79.20-2.2562.831172.5711250.031-B11.9713.860.259.2-9.502.2560.611251.062-B15.0013.866.89.2-2.952.2575.92120.723-B15.3113.8613.29.23.452.2577.51164.814-B12.4113.8618.959.29.202.2562.831172.571-A11.9711.250.2513.65-9.506.70537.481015.6311973.1911973.192-A15.0011.256.813.65-2.956.70673.1998.0014996.4314996.433-A15.3111.2513.213.653.456.70687.34133.7915311.5915311.594-A12.4111.2518.9513.659.206.70557.15951.9012411.3612411.365464.069816.94J =15281.00

mto torsional* CLCULO DEL MOMENTO TORSIONAL TOTAL:EN LA DIRECCIN X - X:NIVELVxeyDyMT1xMT2x431.924.889.20170.55141.18362.574.889.20334.31276.75295.182.6513.90318.37186.071118.402.6513.90396.05231.47EN LA DIRECCIN Y - Y:NIVELVyexDxMT1yMT2y433.10-2.5819.20-53.75-117.30363.36-2.5819.20-102.88-224.54295.70-3.5219.20-244.60-428.341118.40-3.9119.20-349.23-576.56* CLCULO DEL CORTANTE TOTAL:El clculo se realizar por cada nivel y en cada direccinLas frmulas que aplicaremos en cada direccin son:EN LA DIRECCIN X - X:Vt1XB = KXB * YB * MT1xJVt2XB = KXB * YB * MT2xJVDX = KXB * VxSum. KxBVTXB = VDX + VTXB + 0.30 VTYBEN LA DIRECCIN Y - Y:Vt1YB = KYB * XB * MT1yJVt2YB = KYB * XB * MT2yJVDY = KYB * VySum. KyBVTYB = VDY + VTYB + 0.30 VTXB

MT1x = Vx (ey + 0.05*Dy)MT2x = Vx (ey - 0.05*Dy)MT1y = Vy (ex + 0.05*Dx)MT2y = Vy (ex - 0.05*Dx)

V4-XCUARTO PISO - DIRECCIN XVx =31.92J =6390.49MT1x =170.55MT2x =141.18COLUMNAKBXYBVt1XBVt2XBVTXBVDX0.30*VTYBVTXB (total)Vt1XBVt2XB1-D7.54-4.47-0.898-0.7440.0001.8490.3152.1650.0000.0002-D13.41-4.47-1.599-1.3230.0003.2910.0933.3840.0000.0003-D14.03-4.47-1.673-1.3850.0003.4440.0003.4440.0000.0004-D8.37-4.47-0.998-0.8260.0002.0550.0002.0550.0000.0001-C7.54-0.02-0.003-0.0030.0001.8490.5712.4210.0000.0002-C13.41-0.02-0.006-0.0050.0003.2910.1683.4590.0000.0003-C14.03-0.02-0.006-0.0050.0003.4440.0003.4440.0000.0004-C8.37-0.02-0.004-0.0030.0002.0550.0002.0550.0000.0001-B7.544.480.9020.7460.9021.8490.3293.0800.9020.7462-B13.414.481.6041.3281.6043.2910.0974.9921.6041.3283-B14.034.481.6791.3901.6793.4440.0005.1231.6791.3904-B8.374.481.0020.8291.0022.0550.0003.0571.0020.829130.065.18731.9181.57338.678

V4-YCUARTO PISO - DIRECCIN YVy =33.10J =6390.49MT1y =-53.75MT2y =-117.30COLUMNAKBYXBVt1YBVt2YBVTYBVDY0.30*VTXBVTYB (total)Vt1YBVt2YB1-D6.16-9.280.4811.0501.0502.1450.0003.1960.4811.0502-D6.16-2.730.1420.3090.3092.1450.0002.4550.1420.3093-D6.163.67-0.190-0.4150.0002.1450.0002.1450.0000.0004-D6.169.42-0.488-1.0650.0002.1450.0002.1450.0000.0001-C11.17-9.280.8721.9041.9043.8890.0005.7920.8721.9042-C11.17-2.730.2570.5610.5613.8890.0004.4490.2570.5613-C11.173.67-0.344-0.7520.0003.8890.0003.8890.0000.0004-C11.179.42-0.885-1.9310.0003.8890.0003.8890.0000.0001-B6.44-9.280.5031.0971.0972.2410.2713.6080.5031.0972-B6.44-2.730.1480.3230.3232.2410.4813.0450.1480.3233-B6.443.67-0.198-0.4330.0002.2410.5042.7450.0000.0004-B6.449.42-0.510-1.1130.0002.2410.3012.5410.0000.00095.095.24433.0991.55639.899

V3-XTERCER PISO - DIRECCIN XVx =62.57J =6993.81MT1x =334.31MT2x =276.75COLUMNAKBXYBVt1XBVt2XBVTXBVDX0.30*VTYBVTXB (total)Vt1XBVt2XB1-D7.54-4.47-1.609-1.3320.0003.6250.5514.1760.0000.0002-D13.41-4.47-2.863-2.3700.0006.4510.1626.6130.0000.0003-D14.03-4.47-2.997-2.4810.0006.7510.0006.7510.0000.0004-D8.37-4.47-1.788-1.4800.0004.0280.0004.0280.0000.0001-C7.54-0.02-0.006-0.0050.0003.6250.9994.6240.0000.0002-C13.41-0.02-0.011-0.0090.0006.4510.2946.7450.0000.0003-C14.03-0.02-0.011-0.0090.0006.7510.0006.7510.0000.0004-C8.37-0.02-0.007-0.0060.0004.0280.0004.0280.0000.0001-B7.544.481.6151.3371.6153.6250.8516.0921.6151.3372-B13.414.482.8742.3792.8746.4510.2519.5752.8742.3793-B14.034.483.0082.4903.0086.7510.0009.7593.0082.4904-B8.374.481.7951.4861.7954.0280.0005.8231.7951.486130.069.29162.5673.10874.966

V3-YTERCER PISO - DIRECCIN YVy =63.36J =6993.81MT1y =-102.88MT2y =-224.54COLUMNAKBYXBVt1YBVt2YBVTYBVDY0.30*VTXBVTYB (total)Vt1YBVt2YB1-D6.16-9.280.8421.8371.8373.6360.0005.4730.8421.8372-D6.16-2.730.2480.5410.5413.6360.0004.1770.2480.5413-D6.163.67-0.332-0.7250.0003.6360.0003.6360.0000.0004-D6.169.42-0.854-1.8630.0003.6360.0003.6360.0000.0001-C11.17-9.281.5263.3303.3306.5900.0009.9191.5263.3302-C11.17-2.730.4490.9810.9816.5900.0007.5700.4490.9813-C11.173.67-0.603-1.3150.0006.5900.0006.5900.0000.0004-C11.179.42-1.548-3.3770.0006.5900.0006.5900.0000.0001-B9.52-9.281.3002.8372.8375.6150.4858.9371.3002.8372-B9.52-2.730.3830.8360.8365.6150.8627.3130.3830.8363-B9.523.67-0.513-1.1200.0005.6150.9026.5170.0000.0004-B9.529.42-1.319-2.8780.0005.6150.5386.1530.0000.000107.4210.36163.3602.78776.509

V2-XSEGUNDO PISO - DIRECCIN XVx =95.18J =11111.78MT1x =318.37MT2x =186.07COLUMNAKBXYBVt1XBVt2XBVTXBVDX0.30*VTYBVTXB (total)Vt1XBVt2XB1-D7.54-6.70-1.447-0.8460.0004.1360.6714.8070.0000.0002-D13.41-6.70-2.574-1.5040.0007.3600.2047.5640.0000.0003-D14.03-6.70-2.694-1.5750.0007.7030.0007.7030.0000.0004-D8.37-6.70-1.608-0.9400.0004.5960.0004.5960.0000.0001-C7.54-2.25-0.486-0.2840.0004.1361.2165.3520.0000.0002-C13.41-2.25-0.864-0.5050.0007.3600.3707.7290.0000.0003-C14.03-2.25-0.905-0.5290.0007.7030.0007.7030.0000.0004-C8.37-2.25-0.540-0.3160.0004.5960.0004.5960.0000.0001-B7.542.250.4860.2840.4864.1361.2165.8380.4860.2842-B13.412.250.8640.5050.8647.3600.3708.5940.8640.5053-B14.032.250.9050.5290.9057.7030.0008.6070.9050.5294-B8.372.250.5400.3160.5404.5960.0005.1360.5400.3161-A7.546.701.4470.8461.4474.1360.6716.2541.4470.8462-A13.416.702.5741.5042.5747.3600.20410.1382.5741.5043-A14.036.702.6941.5752.6947.7030.00010.3972.6941.5754-A8.376.701.6080.9401.6084.5960.0006.2031.6080.940173.4211.1295.184.92111.22

V2-YSEGUNDO PISO - DIRECCIN YVy =95.70J =11111.78MT1y =-244.60MT2y =-428.34COLUMNAKBYXBVt1YBVt2YBVTYBVDY0.30*VTXBVTYB (total)Vt1YBVt2YB1-D6.16-9.411.2772.2362.2364.2530.0006.4891.2772.2362-D6.16-2.860.3880.6800.6804.2530.0004.9330.3880.6803-D6.163.54-0.480-0.8410.0004.2530.0004.2530.0000.0004-D6.169.29-1.260-2.2070.0004.2530.0004.2530.0000.0001-C11.17-9.412.3144.0534.0537.7090.00011.7622.3144.0532-C11.17-2.860.7041.2321.2327.7090.0008.9410.7041.2323-C11.173.54-0.870-1.5240.0007.7090.0007.7090.0000.0004-C11.179.29-2.284-4.0010.0007.7090.0007.7090.0000.0001-B11.17-9.412.3144.0534.0537.7090.14611.9082.3144.0532-B11.17-2.860.7041.2321.2327.7090.2599.2010.7041.2323-B11.173.54-0.870-1.5240.0007.7090.2717.9810.0000.0004-B11.179.29-2.284-4.0010.0007.7090.1627.8710.0000.0001-A6.16-9.411.2772.2362.2364.2530.4346.9231.2772.2362-A6.16-2.860.3880.6800.6804.2530.7725.7050.3880.6803-A6.163.54-0.480-0.8410.0004.2530.8085.0620.0000.0004-A6.169.29-1.260-2.2070.0004.2530.4824.7360.0000.000138.6916.4095.703.34115.44

V1-XPRIMER PISO - DIRECCIN XVx =118.40J =15281.00MT1x =396.05MT2x =231.47COLUMNAKBXYBVt1XBVt2XBVTXBVDX0.30*VTYBVTXB (total)Vt1XBVt2XB1-D11.97-6.70-2.079-1.2150.0006.4801.2107.6900.0000.0002-D15.00-6.70-2.604-1.5220.0008.1160.3768.4920.0000.0003-D15.31-6.70-2.659-1.5540.0008.2870.0008.2870.0000.0004-D12.41-6.70-2.155-1.2600.0006.7170.0006.7170.0000.0001-C11.97-2.25-0.698-0.4080.0006.4801.4907.9700.0000.0002-C15.00-2.25-0.875-0.5110.0008.1160.4638.5790.0000.0003-C15.31-2.25-0.893-0.5220.0008.2870.0008.2870.0000.0004-C12.41-2.25-0.724-0.4230.0006.7170.0006.7170.0000.0001-B11.972.250.6980.4080.6986.4801.4908.6690.6980.4082-B15.002.250.8750.5110.8758.1160.4639.4540.8750.5113-B15.312.250.8930.5220.8938.2870.0009.1800.8930.5224-B12.412.250.7240.4230.7246.7170.0007.4410.7240.4231-A11.976.702.0791.2152.0796.4801.2109.7692.0791.2152-A15.006.702.6041.5222.6048.1160.37611.0962.6041.5223-A15.316.702.6591.5542.6598.2870.00010.9462.6591.5544-A12.416.702.1551.2602.1556.7170.0008.8722.1551.260218.7712.69118.407.08138.16

V1-YPRIMER PISO - DIRECCIN YVy =118.40J =15281.00MT1y =-349.23MT2y =-576.56COLUMNAKBYXBVt1YBVt2YBVTYBVDY0.30*VTXBVTYB (total)Vt1YBVt2YB1-D11.25-9.502.4434.0334.0336.6310.00010.6642.4434.0332-D11.25-2.950.7591.2531.2536.6310.0007.8840.7591.2533-D11.253.45-0.887-1.4640.0006.6310.0006.6310.0000.0004-D11.259.20-2.365-3.9050.0006.6310.0006.6310.0000.0001-C13.86-9.503.0094.9684.9688.1690.00013.1373.0094.9682-C13.86-2.950.9351.5431.5438.1690.0009.7120.9351.5433-C13.863.45-1.092-1.8030.0008.1690.0008.1690.0000.0004-C13.869.20-2.913-4.8100.0008.1690.0008.1690.0000.0001-B13.86-9.503.0094.9684.9688.1690.20913.3463.0094.9682-B13.86-2.950.9351.5431.5438.1690.2629.9740.9351.5433-B13.863.45-1.092-1.8030.0008.1690.2688.4360.0000.0004-B13.869.20-2.913-4.8100.0008.1690.2178.3860.0000.0001-A11.25-9.502.4434.0334.0336.6310.62411.2882.4434.0332-A11.25-2.950.7591.2531.2536.6310.7818.6650.7591.2533-A11.253.45-0.887-1.4640.0006.6310.7987.4290.0000.0004-A11.259.20-2.365-3.9050.0006.6310.6477.2780.0000.000200.8623.59118.403.81145.80

MBD000909A4.unknown

MBD000F1BF3.unknown