DIRECTO COLUMNA50x50Wu =1.71234L 21L 22L 2330700307503070030A30L 11800B30L 12850C30L 13800D3075702251453045YAA*YIdA*d2122.51350.030375.0227812.520.3559001.5257.51875.0107812.597656.314.7402481.1SUM3225.00138187.5325468.75961,483Ycen42.81,286,95112070225145453045YAA*YIdA*d2122.51350.030375.0227812.524.1786563.6257.53000.0172500.0156250.010.9353953.6SUM4350.00202875384062.51,140,517Ycen46.61,524,580EJETRAMOINERCIA DE VIGA (FCol)INERCIA DE LOSA (FCol)alfaLn/2h losaLn 1(i-1)Ln 1(i+1)Ln 2(i-1)Ln 2(i+1)bwA1-2; 2-3; 3-4Iv1 =1,286,951.31I1xx =540,364.582.3841525080030D1-2; 2-3; 3-4Iv1 =1,286,951.31I1xx =540,364.582.38415258000301A-B; B-C ; C-DIv1 =1,286,951.31I1yy =475,260.422.71365250700304A-B; B-C ; C-DIv1 =1,286,951.31I1yy =475,260.422.7136525700030EJETRAMOINERCIA DE VIGA (FCen)INERCIA DE LOSA (FCen)alfaLn/2h losaLn 1(i-1)Ln 1(i+1)Ln 2(i-1)Ln 2(i+1)bwbwB1-2; 2-3; 3-4Iv2 =1,524,579.74I2xx =1,074,218.751.4282525800850030C1-2; 2-3; 3-4Iv2 =1,524,579.74I2xx =1,074,218.751.42825258508000302A-B; B-C ; C-DIv2 =1,524,579.74I2yy =944,010.421.62725257007500303A-B; B-C ; C-DIv2 =1,524,579.74I2yy =944,010.421.6272525750700030PAOUPDOWNLEFTRIGHPAOalfaBAbetahI2.381.422.711.62I2.037706701.1518.28II2.381.421.621.62II1.767707201.0719.11III2.381.421.622.71III2.037706701.1518.28IV1.421.422.711.62IV1.798206701.2219.72V1.421.421.621.62V1.528207201.1420.74VI1.421.421.622.71VI1.798206701.2219.72VII1.422.382.711.62VII2.037706701.1518.28VIII1.422.381.621.62VIII1.767707201.0719.11IX1.422.381.622.71IX2.037706701.1518.281234L 21L 22L 2330700307503070030A302.382.382.38L 118002.7111.6221.6232.71B301.421.421.42L 128502.7141.6251.6262.71C301.421.421.42L 138002.7171.6281.6292.71D302.382.382.38VERIFICACION DE LAS CONDICIONES PARA USAR EL METODO DIRECTO1.-TRES PAOS EN AMBAS DIRECCIONES2.-PAOS RECTANGULARES DONDE SE CUMPLA: B/A7001.75L2 =>8003.50FcolumnaB850PAO INFERIORL1 =>7001.75L2 =>8502.50Fcentral3.50Fcolumnac) MOMENTO TOTAL ISOSTATICO4.75Fcentralalfa1.421.421.428.25L'2Ln650.00700.00650.00Ln0.65*L1455OK455OK455OK1.7Mo74.0785.9074.07d) MOMENTO DE LOSATRAMO EXTERIORTRAMO INTERIORTRAMO EXTERIORCASO20.16M(-)M(-)0.70M(-)M(-)0.70M(-)M(-)0.1611.8551.8555.8455.8451.8511.850.57M(+)M(+)0.57M(+)42.2230.0742.22e) MOMENTOS EN FRANJA DE COLUMNA123450700507505070050B8.25alfa1.421.421.42Ln7.007.507.00TRAMOS EXTERIORESTRAMOS INTERIORESTRAMOS EXTERIORESL2/L1 =1.18L2/L1 =1.10L2/L1 =1.18a*L2/L1 =1.67a*L2/L1 =1.56a*L2/L1 =1.67e.1 ) % DE MOMENTOS NEGATIVOS75%CASO75%CASO75%CASO1.671.561.6769.6%72.0%69.6%45%45%45%2.001.181.0022.001.101.0022.001.181.002TRAMOS EXTERIORESTRAMOS INTERIORESTRAMOS EXTERIORESe.2 ) % DE MOMENTOS POSITIVOS75%CASO75%CASO75%CASO1.671.101.6769.6%72.0%69.6%45%45%45%2.001.181.0022.001.101.0022.001.181.002TRAMOS EXTERIORESTRAMOS INTERIORESTRAMOS EXTERIORESe.2 ) % DE MOMENTO NEGATIVO EXTERIORCASO 1701225#xyx/yx^3*y/3Ci130700.43630,000459,90045225450.56234,375152,344612,2443045CASO 275252#xyx/yx^3*y/3Ci130450.67405,000234,900451225750.33390,625308,594543,49430EL MENOR VALOR DE C =612,244INERCIA DE LOSA (FCen) (IL) =1,074,219Bt =0.28100%100%97%97.2%93.7%96.5%75%45%94%2.500.280.002.500.280.002.001.181.00L2 / L1 =1.00L2 / L1 =2.00L2 / L1 =1.18Bt =0.28f) MOMENTOS DE FRANJA DE COLUMNA EN VIGAS Y LOSAEn todos los tramos se cumple: "a*L2/L1 > 1" => 85% M()Fcol directo a la viga85%M()Fcol directo a la vigaLos MOMENTOS DE FRANJA DE LOSA se calculan por diferencia de momentos123450700507505070050B8.25MOMENTOS DE LOSA-11.85-51.85-55.84-55.84-51.85-11.8542.2230.0742.22PORCENTAJE PARA FRANJA DE COLUMNA96.5%96.5%72.0%72.0%96.5%96.5%69.6%72.0%69.6%MOMENTOS EN FRANJA DE COLUMNA-11.44-50.05-40.20-40.20-50.05-11.4429.4021.6529.40MOMENTOS EN FRANJA DE CENTRAL-0.41-1.79-15.63-15.63-1.79-0.4112.828.4212.82MOMENTOS DE FRANJA DE COLUMNA EN VIGAS-9.72-42.55-34.17-34.17-42.55-9.7224.9918.4024.99MOMENTOS DE FRANJA DE COLUMNA EN LOSA-1.72-7.51-6.03-6.03-7.51-1.724.413.254.41a) , b) FRANJA DE COLUMNA Y FRANJA CENTRAL12343070030750307003030800PAO INFERIOR1.04FcolumnaL1 =>7001.0375L2 =>4153.11Fcentral1.04Fcolumnac) MOMENTO TOTAL ISOSTATICO3.11Fcentralalfa2.382.382.384.15L'2Ln670.00720.00670.001.7Mo39.5945.7239.59d) MOMENTO DE LOSATRAMO EXTERIORTRAMO INTERIORTRAMO EXTERIORCASO20.16M(-)M(-)0.70M(-)M(-)0.70M(-)M(-)0.166.3327.7129.7229.7227.716.330.57M(+)M(+)0.57M(+)22.5616.0022.56e) MOMENTOS EN FRANJA DE COLUMNA123430700307503070030A304.15alfa2.382.382.38Ln7.007.507.00TRAMOS EXTERIORESTRAMOS INTERIORESTRAMOS EXTERIORESL2/L1 =0.59L2/L1 =0.55L2/L1 =0.59a*L2/L1 =1.41a*L2/L1 =1.32a*L2/L1 =1.41e.1 ) % DE MOMENTOS NEGATIVOS90%CASO90%CASO90%CASO1.411.321.4187.2%88.4%87.2%75%75%75%1.000.590.5011.000.550.5011.000.590.501TRAMOS EXTERIORESTRAMOS INTERIORESTRAMOS EXTERIORESe.2 ) % DE MOMENTOS POSITIVOS90%CASO90%CASO90%CASO1.410.551.4187.2%88.4%87.2%75%75%75%1.000.590.5011.000.550.5011.000.590.501TRAMOS EXTERIORESTRAMOS INTERIORESTRAMOS EXTERIORESe.2 ) % DE MOMENTO NEGATIVO EXTERIORCASO 1701225#xyx/yx^3*y/3Ci130700.43630,000459,90045225450.56234,375152,344612,2443045CASO 275252#xyx/yx^3*y/3Ci130450.67405,000234,900451225750.33390,625308,594543,49430EL MENOR VALOR DE C =612,244INERCIA DE LOSA (FCen) (IL) =540,365Bt =0.57100%100%97.73%97.73%94.3%97.1%90%75%94%2.500.570.002.500.570.001.000.590.50L2 / L1 =0.50L2 / L1 =1.00L2 / L1 =0.59Bt =0.57f) MOMENTOS DE FRANJA DE COLUMNA EN VIGAS Y LOSAEn todos los tramos se cumple: "a*L2/L1 > 1" => 85% M()Fcol directo a la viga85%M()Fcol directo a la vigaLos MOMENTOS DE FRANJA DE LOSA se calculan por diferencia de momentos123450700507505070050A304.15MOMENTOS DE LOSA-6.33-27.71-29.72-29.72-27.71-6.3322.5616.0022.56PORCENTAJE PARA FRANJA DE COLUMNA97.1%97.1%88.4%88.4%97.1%97.1%87.2%88.4%87.2%MOMENTOS EN FRANJA DE COLUMNA-6.15-26.91-26.27-26.27-26.91-6.1519.6814.1419.68MOMENTOS EN FRANJA DE CENTRAL-0.18-0.80-3.45-3.45-0.80-0.182.891.862.89MOMENTOS DE FRANJA DE COLUMNA EN VIGAS-5.23-22.87-22.33-22.33-22.87-5.2316.7312.0216.73MOMENTOS DE FRANJA DE COLUMNA EN LOSA-0.92-4.04-3.94-3.94-4.04-0.922.952.122.95

COEFICIENTESMETODO DE COEFICIENTES1234700750700A800123B850456C800789DH losa =0.20mPPlosa480Kg/cm2PPpt100Kg/cm2PPtab0Kg/cm2s/c400Kg/cm2F.C.1.4F.C.1.7Wcm812Kg/cm2Wcv680Kg/cm2Wct1492Kg/cm2CM Amplificada Mo (+) debido a CMCV Amplificada Mo (+) debido a CVCT Amplificada Mo (-)PAOBAmCASOCbMb (+)CaMa (+)CbMb (+)CaMa (+)CbMb (+)CaMa (+)I8007000.8840.02021.050.03471.380.02441.060.04161.390.03703.530.06304.61II8007500.9420.01530.800.02060.940.02361.030.03081.180.03893.720.05214.37III8007000.8830.02261.180.02811.120.02541.110.03831.280.06636.330.00000.00IV8507000.8280.01600.940.03131.240.02041.000.04301.430.04294.630.05283.86V8507500.8820.01360.800.02271.040.02111.030.03521.350.03433.700.05674.76VI8507000.8280.01600.940.03131.240.02041.000.04301.430.04294.630.05283.86VII8007000.8840.02021.050.03471.380.02441.060.04161.390.03703.530.06304.61VIII8007500.9490.01610.830.02491.140.02391.040.03291.260.02492.380.06645.57IX8007000.8840.02021.050.03471.380.02441.060.04161.390.03703.530.06304.610B0

Hoja1PAO EXTERIORPAO INTERIORPAO EXTERIORMeMiM(-)M(-)MiMeM(+)extM(+)M(+)extSE CALCULA EL "Mo" PARA C/TRAMO"Me" DEPENDE DE LA RIGIDEZ QUE PROVEE EL APOYOa)MOMENTOS DE LOSA - PAO INTERIOR2 M(-) y 1 M(+)- Ambos M(-)M(-) =0.65*Mo- M(+)M(+) =0.35*Mob)MOMENTOS DE LOSA - PAO EXTERIORMoBorde exterior no restringido (1)Losa con vigas en todos sus apoyos (2)Losas s/vigas interioresBorde exterior total mente restringido (5)s/vigas de borde (3)c/vigas de borde (4)Mi(-)0.750.700.700.700.65Me(+)0.630.570.520.500.35Me(-)0.000.160.260.300.65(1) El apoyo (viga) es de poco peralte, poca rigidez o carece de viga, tb cuando se apoya en puro de ladrillo (simplemente apoyado)(2) Losa con vigas en todos los lados (todos los elementos)(3) Losa sin vigas en todos los paos(4) Losa sin interiores pero con vigas en los bordes extremos(5) La viga de apoyo es muy peraltada o muro de concreto de apoyo ((I viga / I losa) > 5)Mo ()Mo ()(Viga)(Franja de columna)Mo ()Mo ()(Momentos de losa)(Losa)Mo ()(Franja de central)Cuando calculamos los M(+) y M(-) de la losa tenemos q calcular el M(+) y M(-) EN LA FRANJA DE LA COLUMNA y por diferencia hallamos el M(+) y M(-) EN LA FRANJA CENTRALLuego distribuimos los Mo DE FRANJA DE COLUMNA en Mo DE VIGA y Mo DE LOSA, aunque no siempre ser as ya que podemos encontrarnos con losas sin vigas.c)MOMENTOS EN FRANJA DE COLUMNAc.1)Momentos Negativos Int. (M(-), Mi.-L2 / L10.501.002.00*(L2/L1)=00.750.750.75*(L2/L1)10.900.750.45c.2)Momentos Positivos Int. (Mext(+), M(+)).-L2 / L10.501.002.00*(L2/L1)=00.600.600.60*(L2/L1)10.900.750.45c.3)Momentos Negativos Ext. (Me).-Bt =Ecb*CBt =Rigidez torsional viga borde transversal2*Ecs*Is2*Rigidez por flexion losaBt =C=Rigidez torsional de la viga extrema transversal2*IL2*Momento de inercia de la losaC =sum(1-0.63*x/y)*(x^3*y/3)12O12iXYx/yx^3*y/3Ci1x1y1x1/y1x1^3*y1/3C12x2y2x2/y2x2^3*y2/3C2x : menor dimensionC=C1+C2y : mayor dimensionDe los dos casos se elige el menor valor de CL2 / L10.501.002.00Puede darse el caso de que no haya vigas exteriores perimetricas*(L2/L1)=0Bt = 01.001.000.60Bt 2.50.750.750.75a = 0B 0y viceversa*(L2/L1)0Bt = 01.001.001.00a 0B = 0Bt 2.50.900.750.45d)MOMENTOS DE FRANJA DE COLUMNA EN VIGAS*(L2/L1)185% M() Fcol directo a la viga*(L2/L1)M()viga + M()ppM()losatLOSA =>+=HLuCvn+m-bwwM(+)ppDebido al peso propio de la viga si es que hubiese un muro encima de la vigaDa.2)EJE EXTERIOR (EJE A)a.2.1. Sin Vigas:M() Fcol eje AhLsa.2.2. Losa Con Vigas:VIGA =>M()viga + M()ppM()losaLOSA =>HLs-bwa)FRANJA CENTRALEJE BM()Fcentral eje B+M()p =p*M()Fcentral eje Bp + qpqM()q =q*M()Fcentral eje Bp + qEJE AM()Fcentral eje AM()r =M()Fcentral eje ArEJE CM()Fcentral eje C+M()t =t*M()Fcentral eje Ct + wtwM()w =w*M()Fcentral eje Ct + wb)FRANJA CENTRAL F1M()r rp M()pHLM()u = M()r + M()pr + pb)FRANJA CENTRAL F2M()q qt M()tHLM()u = M()q + M()tq + t

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Sheet3

Sheet1 (3)85751202553055XY1-0.63*X/YX3*Y/3d120851226,667193,067230551495,000324,900SUM517,96785752120553055XY1-0.63*X/YX3*Y/3d120551146,667113,067230751675,000504,900SUM617,9670.5621,100,000si la via fuwra 3.60 no necwsariamentw el carro influye . sino mas bien solo seria ha 3.14 por ejemplp

COEFICIENTES (2)METODO DE COEFICIENTESH losa =0.20CM Amplificada Mo (+) debido a carga vivaCV Amplificada Mo (+) debido a carga vivaCT Amplificada Mo (-)PAOBAmCASOPPlosaPPptPPtabWcmCbMb (+)CaMa (+)s/cWcvCbMb (+)CaMa (+)WctCbMb (+)CaMa (+)I7706700.87Caso 448010008120.01760.850.03831.404006800.02130.860.04671.4314920.03192.820.06814.56II7707200.94Caso 948010008120.01400.670.02671.124006800.02110.850.03731.3114920.02282.020.06955.38III7706700.87Caso 448010008120.01760.850.03831.404006800.02130.860.04671.4314920.03192.820.06814.56IV8206700.82Caso 848010008120.01780.970.02781.014006800.02281.040.03851.1814920.04794.810.04743.17V8207200.88Caso 248010008120.01901.040.02050.864006800.02381.090.03061.0814920.03913.920.05194.01VI8206700.82Caso 848010008120.01780.970.02781.014006800.02281.040.03851.1814920.04794.810.04743.17VII7706700.87Caso 448010008120.01760.850.03831.404006800.02130.860.04671.4314920.03192.820.06814.56VIII7707200.94Caso 948010008120.01400.670.02671.124006800.02110.850.03731.3114920.02282.020.06955.38IX7706700.87Caso 448010008120.01760.850.03831.404006800.02130.860.04671.4314920.03192.820.06814.56