Port. 1ING.LaminaJ.R.T.G.METODO DE CROSSMC-01Calcular los Cortantes y Momentos de la estructura adjunta:Datos:WW=3.00Tn-mVigaa1bL1=8.00m.Tramobhhbh3/12ab30.0066.6770.00857500.00H=4.00m.bc30.000.0070.00857500.0034HI 1=857,500.00cm4=3.764IColumnaI3=I4=227,812.50cm4=1ITramobhbh3/12dead30.0045.00227812.50be30.0045.00227812.50L1cf30.0045.00227812.50MOMENTO DE EMPOTRAMIENTO PERFECTO (M ik)M ik = w L2/12M ab=-16.00Tn-m.M ba=16.00Tn-m.RIGIDECES RELATIVAS (K ik)FACTORES DE DISTRIBUCION (Cik)K ik = I / LC ik = Kik / KiKab = I 1 / L1=0.47ICab = Kab / Kab+Kad=-0.653Cba = Kba / Kba+Kbe=-0.653Kda = I 3 / H=0.25ICad = Kad / Kab+Kad=-0.347Cbe = Kbe / Kba+Kbe=-0.347Keb = I 4 / H=0.25I-1.000-1.0008.243-8.243-0.0020.0050.003-0.008-0.0170.0510.026-0.079-0.1580.4820.241-0.739-1.4784.5252.263-6.930-13.86010.4485.224-16.00016.000-0.653-0.6538.2430.0030.0270.2562.4055.552-0.347ab-0.347-7.364-0.785-0.084-0.009-0.001-8.2434.1210.0010.0140.1281.2022.7760.0000.000-3.682-0.393-0.042-0.004-0.000-4.121deFUERZAS CORTANTESVik = +Vik-(Mik+Mki)/ LikVki = -Vki-(Mki+Mik)/ LkiVIGASCOLUMNASVab = +Vab-(Mab+Mba)/Lab=12.00Tn.Vda = +Vda-(Mda+Mad)/Lda=-3.09Tn.Vba = -Vba-(Mba+Mab)/Lba=-12.00Tn.Vad = -Vad-(Mad+Mda)/Lad=-3.09Tn.Veb = +Veb-(Meb+Mbe)/Leb=3.09Tn.Vbe = -Vbe-(Mbe+Meb)/Lbe=3.09Tn.DIAGRAMA DE FUERZAS CORTANTES (Tn.)Se calcula la distancia al punto de inflexin para conocerla ubicacin de momento mximo positivo en el DMF de12.00la viga.Se considera los cortantes como valores absolutos.V1-12.00-3.093.09V2XXLX = V1. L / (V1+V2)X=4.00m.DIAGRAMA DE MOMENTOS FLECTORES (Tn-m.)-8.24-8.24-8.24-8.2415.76La reaccin vertical en cada apoyo se obtienesumando los cortantes en la vigas de cadap=0.76m.p6.48m.qnivel en su eje de accin vertical..q=0.76m.3.09Tn.4.124.123.09Tn.4.12Tn-m4.12Tn-m12.00Tn.12.00Tn.Obtencin del Momento Mximo PositivoAplicamos un corte en el punto de inflexin del cortanteen el tramo ab.M+VabWxL1VadTaxM+ = W* L12 / 8MabX1M+abL1 = 2 (2 M+ / W )1/2La determinacin de los sentidos de las fuerzas y MomentosLos signos de los momentos que se obtienen directamentede la estructura, se obtiene de los diagramas de Fuerzasde las cargas distribuidas y otras, se determinarn porcortantes y Momentos.anlisis.Para el desarrollo del problema se tomarn los signos, talcomo se indica en los diagramas de fuerzas cortantes yMomentos Flectores.+Por esta razn los dos primeros monomios de la ecuacinque se expresa se ha considerado con signo positivo.-M+ab =Vab. X + Mab - W.X2 /2M+ab=15.76Tn-m.El clculista puede elegir otras opciones para el clculo delmomento mximo positivo.

Port. 2ING.LaminaJ.R.T.G.METODO DE CROSSMC-02Calcular los Cortantes y Momentos de la estructura adjunta:Datos:WW=2.00Tn-mVigaa1b2cL1=6.00m.Tramobhhbh3/12L2=6.00m.ab30.0060.0060.00540000.00H=4.00m.bc30.0060.0060.00540000.00345HI 1=540,000.00cm4=2.00II 2=540,000.00cm4=2.00IColumnaI 3=227,812.50cm4=1.00ITramobhbh3/12defI 4=227,812.50cm4=1.00Iad30.0045.00227812.50I 5=227,812.50cm4=1.00Ibe30.0045.00227812.50L1L2cf30.0045.00227812.50MOMENTO DE EMPOTRAMIENTO PERFECTOM ij = w L2/12Mab=-6.00Tn-m.Mba=6.00Tn-m.Mbc=-6.00Tn-m.Mcb=6.00Tn-m.RIGIDECES RELATIVAS K ik = I / LFACTORES DE DISTRIBUCIONC ik = Kik / S KiKab = I 1 / L1=0.3333ICab = Kab / Kab+Kad=-0.571Cba = Kba / Kba+Kbc+Kbe=-0.364Kbc = I 2 / L2=0.3333ICad = Kad / Kab+Kad=-0.429Cbc = Kbc / Kba+Kbc+Kbe=-0.364Kda = I 3 / H=0.25I-1.000Cbe = Kbe / Kba+Kbc+Kbe=-0.273Keb = I 4 / H=0.25I-1.000Kfc = I 5 / H=0.25ICcb = Kcb / Kcb+Kcf=-0.571Ccf = Kcf / Kcb+Kcf=-0.429-1.0007.7142.571-2.5710.000-7.714-0.000-0.000-0.0000.0000.0000.0000.001-0.000-0.000-0.002-0.0010.0010.0000.0030.006-0.001-0.002-0.017-0.0080.0060.0030.0290.058-0.008-0.017-0.160-0.0800.0580.0290.2790.559-0.080-0.1600.1780.0890.5590.279-0.312-0.623-1.625-3.2503.4291.714-0.623-0.312-6.0006.000-6.0006.000-0.571-0.364-0.364-0.5712.571-0.000-0.001-0.012-0.1200.1342.571-0.429ab-0.273-0.4680.4190.0440.0050.0000.000-0.000c-0.429-2.438-0.120-0.012-0.001-0.000-0.000-2.5710.01.286-0.000-0.001-0.006-0.0600.0671.2860.0000.000-0.2340.2090.0220.0020.0000.000-0.0000.000-1.219-0.060-0.006-0.001-0.000-0.000-1.286defFUERZAS CORTANTESVik = +Vik-(Mik+Mki)/ LikVki = -Vki-(Mki+Mik)/ LkiVIGASCOLUMNASVab = +Vab-(Mab+Mba)/Lab=5.14Tn.Vda = +Vda-(Mda+Mad)/Lda=-0.96Tn.Vba = -Vba-(Mba+Mab)/Lba=-6.86Tn.Vad = -Vad-(Mad+Mda)/Lad=-0.96Tn.Vbc = +Vbc-(Mbc+Mcb)/Lbc=6.86Tn.Veb = +Veb-(Meb+Mbe)/Leb=0.00Tn.Vcb = -Vcb-(Mcb+Mbc)/Lcb=-5.14Tn.Vbe = -Vbe-(Mbe+Meb)/Lbe=-0.00Tn.Vfc = +Vfc-(Mfc+Mcf)/Lfc=0.96Tn.Vcf = -Vcf-(Mcf+Mfc)/Lcf=0.96Tn.DIAGRAMA DE FUERZAS CORTANTES (Tn.)6.865.14V1-5.14-6.86X1=2.57m.V2-0.960.000.96X2=3.43m.XLX1X2X = V1. L / (V1+V2)DIAGRAMA DE MOMENTOS FLECTORES (Tn-m.)-7.71-7.71-2.57-2.57-2.57-2.574.044.04p=0.56m.p4.02m.qr4.02sr=1.42m..q=1.42m.s=0.56m.1.291.290.96Tn.0.96Tn.1.29Tn-m1.29Tn-m5.14Tn.13.71Tn.5.14Tn.Momentos Mximos PositivosAplicamos un corte en el punto de inflexin del cortanteen el tramo ab y bcM+1VabWxL1VadTaxM+1 = W* L12 / 8MabX1M+abL1 = 2 (2 M1 / W )1/2La determinacin de los sentidos de las fuerzas y Momentosde la estructura, se obtiene de los diagramas de FuerzasLos signos de los momentos que se obtienen directamentecortantes y Momentos.de las cargas distribuidas y otras, se determinarn porPara el desarrollo del problema se tomarn los signos, talanlisis.como se indica en los diagramas de fuerzas cortantes yMomentos Flectores.Por esta razn los dos primeros monomios de la ecuacinque se expresa se ha considerado con signo positivo.M+ab =Vab. X1+Mab-W.X12 /2+M+bc =Vbc. X2+Mbc-W.X22 /2El clculista puede elegir otras opciones para el clculo del-momento mximo positivo.M+ab=4.04Tn-m.M+bc=4.04Tn-m.Espero que lo disfruten

Port. 3ING.LaminaJ.R.T.G.METODO DE CROSSMC-03Calcular los Cortantes y Momentos de la estructura adjunta:W1W2Datos:W1=2.60Tn/mVigaa1b2cW2=2.00Tn/mTramobhhbh3/12L1=6.00m.ab30.0060.0060.00540000.00L2=5.00m.bc30.0050.0050.00312500.00345HH=4.50m.I 1=540,000.00cm4=2.370IColumnaI 2=312,500.00cm4=1.372ITramobhbh3/12defI 3=227,812.50cm4=1.000Iad30.0045.00227812.50I 4=312,500.00cm4=1.372Ibe30.0050.00312500.00L1L2I 5=227,812.50cm4=1.000Icf30.0045.00227812.50MOMENTO DE EMPOTRAMIENTO PERFECTOM ij = w L2/12Mab=-7.80Tn-m.Mba=7.80Tn-m.Mbc=-4.17Tn-m.Mcb=4.17Tn-m.RIGIDECES RELATIVAS K ik = I / LFACTORES DE DISTRIBUCIONC ik = Kik / S KiKab = I 1 / L1=0.3950617284ICab = Kab / Kab+Kad=-0.640Cba = Kba / Kba+Kbc+Kbe=-0.406Kbc = I 2 / L2=0.2743484225ICad = Kad / Kab+Kad=-0.360Cbc = Kbc / Kba+Kbc+Kbe=-0.282Kda = I 3 / H=0.2222222222I-1.000Cbe = Kbe / Kba+Kbc+Kbe=-0.313Keb = I 4 / H=0.3048315806I-1.000Kfc = I 5 / H=0.2222222222ICcb = Kcb / Kcb+Kcf=-0.552Ccf = Kcf / Kcb+Kcf=-0.448-1.0008.4041.515-3.2130.000-6.666-0.000-0.000-0.0000.0000.0000.0000.000-0.000-0.000-0.001-0.0000.0000.0000.0010.002-0.000-0.000-0.007-0.0030.0020.0010.0110.022-0.002-0.004-0.067-0.0330.0150.0080.1040.209-0.020-0.0400.7950.3980.1450.073-1.243-2.485-0.913-1.8254.9922.496-1.726-0.863-7.8007.800-4.1674.167-0.640-0.406-0.282-0.5523.213-0.000-0.000-0.004-0.0380.4472.808-0.360ab-0.313-1.9180.1610.0170.0020.0000.000-1.738c-0.448-1.478-0.032-0.003-0.000-0.000-0.000-1.5151.607-0.000-0.000-0.002-0.0190.2241.4040.0000.000-0.9590.0810.0080.0010.0000.000-0.8690.000-0.739-0.016-0.002-0.000-0.000-0.000-0.757defFUERZAS CORTANTESVik = +Vik-(Mik+Mki)/ LikVki = -Vki-(Mki+Mik)/ LkiVIGASCOLUMNASVab = +Vab-(Mab+Mba)/Lab=6.93Tn.Vda = +Vda-(Mda+Mad)/Lda=-1.07Tn.Vba = -Vba-(Mba+Mab)/Lba=-8.67Tn.Vad = -Vad-(Mad+Mda)/Lad=-1.07Tn.Vbc = +Vbc-(Mbc+Mcb)/Lbc=6.03Tn.Veb = +Veb-(Meb+Mbe)/Leb=0.58Tn.Vcb = -Vcb-(Mcb+Mbc)/Lcb=-3.97Tn.Vbe = -Vbe-(Mbe+Meb)/Lbe=0.58Tn.Vfc = +Vfc-(Mfc+Mcf)/Lfc=0.50Tn.Vcf = -Vcf-(Mcf+Mfc)/Lcf=0.50Tn.DIAGRAMA DE FUERZAS CORTANTES (Tn.)6.036.93V1-3.97-8.67X1=2.67m.V2-1.070.580.50X2=3.02m.XLX1X2X = V1. L / (V1+V2)DIAGRAMA DE MOMENTOS FLECTORES (Tn-m.)-8.40-6.67-3.21-1.51-3.21-1.74-1.516.042.43p=0.21m.p4.91m.qr3.11sr=1.46m..q=0.88m.s=0.43m.1.610.761.07Tn.0.870.58Tn.0.50Tn.1.61Tn-m0.87Tn-m0.76Tn-m6.93Tn.14.70Tn.3.97Tn.Momentos Mximos PositivosAplicamos un corte en el punto de inflexin del cortanteen el tramo ab y bcM+1VabW1xL1VadTaxM+1 = W1* L12 / 8MabX1M+abL1 = 2 (2 M1 / W1 )1/2La determinacin de los sentidos de las fuerzas y Momentosde la estructura, se obtiene de los diagramas de FuerzasLos signos de los momentos que se obtienen directamentecortantes y Momentos.de las cargas distribuidas y otras, se determinarn porPara el desarrollo del problema se tomarn los signos, talanlisis.como se indica en los diagramas de fuerzas cortantes yMomentos Flectores.Por esta razn los dos primeros monomios de la ecuacinque se expresa se ha considerado con signo positivo.M+ab =Vab. X1+Mab-W1.X12 /2+M+bc =Vbc. X2+Mbc-W2.X22 /2El clculista puede elegir otras opciones para el clculo del-momento mximo positivo.M+ab=6.04Tn-m.M+bc=2.43Tn-m.

Port. 4ING.LaminaJ.R.T.G.METODO DE CROSSMC-05Calcular los Cortantes y Momentos de la estructura adjunta:Datos:W1W2W1=4.50Tn/mI 1=540,000.00cm4Vigaa1b2cW2=4.50Tn/mI 2=540,000.00cm4Tramobhbh3/12W3=5.00Tn/mI 3=540,000.00cm4130.0060.00540000.00567h2W4=5.00Tn/mI 4=540,000.00cm4230.0060.00540000.00W3W4L1=5.00m.I 5=227,812.50cm4330.0060.00540000.00L2=5.00m.I 6=227,812.50cm4430.0060.00540000.00d3e4fh1=4.50m.I 7=227,812.50cm4h2=4.00m.I 8=227,812.50cm4Columna8910h1I 9=227,812.50cm4Tramobhbh3/12I 10=227,812.50cm4530.0045.00227812.50ghi630.0045.00227812.50L1L2730.0045.00227812.50830.0045.00227812.50930.0045.00227812.50MOMENTO DE EMPOTRAMIENTO PERFECTORIGIDECES RELATIVAS (Kij)1030.0045.00227812.50TramoWLMijMjiIKijTramoWhMijMjiIKijTn/mm.Tn-mTn-mcm4cm2Tn/mm.Tn-mTn-mcm4cm2ab4.505.00-9.389.38540,000.001080da0.004.000.000.00227,812.50569.53bc4.505.00-9.389.38540,000.001080eb0.004.000.000.00227,812.50569.53de5.005.00-10.4210.42540,000.001080fc0.004.000.000.00227,812.50569.53ef5.005.00-10.4210.42540,000.001080gd0.004.500.000.00227,812.50506.25he0.004.500.000.00227,812.50506.25if0.004.500.000.00227,812.50506.25FACTORES DE DISTRIBUCIONNudoTramoKijCijiijcm2cm3aab1080.001649.53-0.655-1.00ad569.531,649.53-0.345bba1080.002729.53-0.396-1.000bc1080.002729.53-0.396be569.532729.53-0.209ccb1080.001649.53-0.655-1.00cf569.531,649.53-0.345dde1080.002155.78-0.501-1.000da569.532155.78-0.264dg506.252155.78-0.235eed1080.003235.78-0.334-1.000ef1080.003235.78-0.334eb569.533235.78-0.176eh506.253235.78-0.156ffe1080.002155.78-0.501-1.000fc569.532155.78-0.264fi506.252155.78-0.235DIAGRAMA DE ITERACIONES-1.8171.8170.00113.154-13.154-0.001-0.000-0.000-0.000-0.0000.0320.016-0.016-0.032-0.000-0.000-0.000-0.0001.3880.694-0.694-1.388-0.000-0.000-0.000-0.0006.1383.069-3.069-6.1380.0000.0000.0000.000-9.3759.375-9.3759.375-0.655-0.396-0.396-0.655abc1.8170.000-0.0010.017-0.0480.732-2.1193.237-0.3450.000-0.0000.0000.0000.000-0.0000.0000.000-0.209-0.345-3.2372.119-0.7320.048-0.0170.001-0.000-1.817-12.5270.0006.1970.0000.0000.0000.0000.0020.0040.0000.0000.0000.000-0.0000.0000.0000.000-0.0000.0000.000-0.1760.0920.1834.218-0.0000.000-0.0020.008-0.0970.3662.3241.618-0.2640.0000.000-0.264-1.618-2.324-0.3660.097-0.0080.002-0.0000.000-4.218-2.204-4.408-10.41710.417-0.501-0.334-0.334-0.501-10.41710.4171.978-0.000-0.002-0.0862.066-0.235d4.4082.204e-0.156-0.0000.0000.0000.000-0.000f-0.235-2.0660.0860.0020.000-1.9780.0000.000-0.183-0.0920.0000.000-0.004-0.0020.0000.0000.989-0.000-0.001-0.0431.0330.000-0.000-0.0000.000-0.0000.0000.0000.000-0.0000.000-1.0330.0430.0010.000-0.989-6.1970.000g12.527hiFUERZAS CORTANTESVik = +Vik-(Mik+Mki)/ LikVki = -Vki-(Mki+Mik)/ LkiVIGASTramoWLVijVjiMijMjiVijVjiab4.505.0011.25-11.25-1.81713.1548.98(13.52)bc4.505.0011.25-11.25-13.1541.81713.52(8.98)de5.005.0012.5-12.5-6.19712.52711.23(13.77)ef5.005.0012.5-12.5-12.5276.19713.77(11.23)COLUMNASTramoWLVijVjiMijMjiVijVjida04.00004.2181.817(1.51)(1.51)eb04.00000.0000.000(0.00)(0.00)fc04.0000-4.218-1.8171.511.51gd04.50000.9891.978(0.66)(0.66)he04.5000-0.000-0.0000.000.00if04.5000-0.989-1.9780.660.66DIAGRAMA DE FUERZAS CORTANTESDIAGRAMA DE FUERZAS CORTANTES EN VIGAS (Tn.)8.9813.52abc-8.98-13.52X1=2.00m.X2=3.00m.11.2313.77V1def-11.23-13.77X1=2.25m.V2X2=2.75m.XLX1X2X = V1. L / (V1+V2)ghiDIAGRAMA DE FUERZAS CORTANTES EN COLUMNAS (Tn.)abc-1.51-0.001.51def-0.660.000.66ghiDIAGRAMA DE MOMENTOS FLECTORESDIAGRAMA DE MOMENTOS FLECTORES EN VIGAS (Tn-m.)-13.15-13.15-1.82-1.82M+ab=7.15Tn-m.M+bc=7.15Tn-m.abc7.157.15p=0.21m.r=1.22m.q=1.22m.p3.56m.qr3.56ss=0.21m.-12.53-12.53-6.20-6.20M+de=6.42Tn-m.M+ef=6.42Tn-m.def6.426.42p=0.56m.p3.38m.qr3.38sr=1.06m..q=1.06m.s=0.56m.ghiDIAGRAMA DE MOMENTOS FLECTORES EN COLUMNAS (Tn-m.)-1.82-1.824.224.22-1.98-1.980.990.99DIAGRAMA DE REACCIONES4.50Ton/mabc4.50Ton/mdef10ghi2.17Tn.2.17Tn.0.99Tn-m54.57Tn.0.99Tn-m20.22Tn.20.22Tn.

Port. 5ING.LaminaJ.R.T.G.METODO DE CROSSMC-05Calcular los Cortantes y Momentos de la estructura adjunta:W1Datos:W2W1=4.50Tn/mL1=5.00m.Vigaa1b2cW2=2.50Tn/mL2=5.00m.Tramobhbh3/12W3=3.00Tn/mh1=4.50m.130.0060.00540000.00567W4=5.00Tn/mh2=4.00m.230.0060.00540000.00W4h2330.0060.00540000.00W3430.0060.00540000.00d3e4fI 1=540,000.00cm4I 5=227,812.50cm4ColumnaI 2=540,000.00cm4I 6=227,812.50cm4Tramobhbh3/128910I 3=540,000.00cm4I 7=227,812.50cm4530.0045.00227812.50h1I 4=540,000.00cm4I 8=227,812.50cm4630.0045.00227812.50I 9=227,812.50cm4730.0045.00227812.50ghiI 10=227,812.50cm4830.0045.00227812.50L1L2930.0045.00227812.501030.0045.00227812.50MOMENTO DE EMPOTRAMIENTO PERFECTORIGIDECES RELATIVAS (Kij)TramoWLMijMjiIKijTramoWhMijMjiIKijTn/mm.Tn-mTn-mcm4cm2Tn/mm.Tn-mTn-mcm4cm2ab4.505.00-9.389.38540,000.001080da0.004.000.000.00227,812.50569.53bc2.505.00-5.215.21540,000.001080eb0.004.000.000.00227,812.50569.53de3.005.00-6.256.25540,000.001080fc0.004.000.000.00227,812.50569.53ef5.005.00-10.4210.42540,000.001080gd0.004.500.000.00227,812.50506.25he0.004.500.000.00227,812.50506.25if0.004.500.000.00227,812.50506.25FACTORES DE DISTRIBUCIONNudoTramoKijCijiijcm2cm3aab1080.001649.53-0.655-1.00ad569.531,649.53-0.345bba1080.002729.53-0.396-1.000bc1080.002729.53-0.396be569.532729.53-0.209ccb1080.001649.53-0.655-1.00cf569.531,649.53-0.345dde1080.002155.78-0.501-1.000da569.532155.78-0.264dg506.252155.78-0.235eed1080.003235.78-0.334-1.000ef1080.003235.78-0.334eb569.533235.78-0.176eh506.253235.78-0.156ffe1080.002155.78-0.501-1.000fc569.532155.78-0.264fi506.252155.78-0.235DIAGRAMA DE ITERACIONES-2.1080.7190.04510.738-9.7240.044-0.043-0.086-0.086-0.0430.2250.1130.0880.176-0.160-0.320-0.320-0.1601.8180.909-0.170-0.340-0.472-0.943-0.943-0.4726.6783.339-1.435-2.870-0.824-1.649-1.649-0.824-9.3759.375-5.2085.208-0.655-0.396-0.396-0.655abc2.1080.024-0.0260.119-0.1840.959-2.3063.522-0.345-1.014-0.0450.016-0.1690.071-0.4980.481-0.869-0.209-0.345-1.5140.991-0.179-0.1090.093-0.0240.023-0.719-10.9330.0146.130-0.010-0.0210.0590.030-0.045-0.0900.2680.1340.7860.008-0.0230.031-0.0840.141-0.2490.9610.000-0.176-0.206-0.4123.079-0.0110.012-0.0510.059-0.3670.4791.1861.761-0.2641.8230.911-0.264-0.757-2.552-0.090-0.2170.046-0.0480.012-0.011-3.616-2.420-4.839-10.41710.417-0.501-0.334-0.334-0.501-6.2506.2500.672-0.010-0.045-0.3271.054-0.235d2.2491.125e-0.1560.8550.1260.0280.0021.010f-0.235-2.268-0.193-0.042-0.010-2.5130.9111.823-0.697-0.3480.1340.268-0.097-0.0480.0300.0590.336-0.005-0.023-0.1630.5270.000-0.021-0.0100.0000.4270.0630.0140.0010.5050.000-1.134-0.096-0.021-0.005-1.257-3.7400.014g9.132hiFUERZAS CORTANTESVik = +Vik-(Mik+Mki)/ LikVki = -Vki-(Mki+Mik)/ LkiVIGASTramoWLVijVjiMijMjiVijVjiab4.505.0011.25-11.25-2.10810.7389.52(12.98)bc2.505.006.25-6.25-9.7240.7198.05(4.45)de3.005.007.5-7.5-3.7409.1326.42(8.58)ef5.005.0012.5-12.5-10.9336.13013.46(11.54)COLUMNASTramoWLVijVjiMijMjiVijVjida04.00003.0792.108(1.30)(1.30)eb04.00000.786-1.0140.060.06fc04.0000-3.616-0.7191.081.08gd04.50000.3360.672(0.22)(0.22)he04.50000.5051.010(0.34)(0.34)if04.5000-1.257-2.5130.840.84DIAGRAMA DE FUERZAS CORTANTESDIAGRAMA DE FUERZAS CORTANTES EN VIGAS (Tn.)9.528.05abc-4.45-12.98X1=2.12m.X2=3.22m.6.4213.46V1def-11.54-8.58X1=2.14m.V2X2=2.69m.XLX1X2X = V1. L / (V1+V2)ghiDIAGRAMA DE FUERZAS CORTANTES EN COLUMNAS (Tn.)abc-1.300.061.08def-0.22-0.340.84ghiDIAGRAMA DE MOMENTOS FLECTORESDIAGRAMA DE MOMENTOS FLECTORES EN VIGAS (Tn-m.)-10.74-9.72-2.11-0.72M+ab=7.97Tn-m.M+bc=3.24Tn-m.abc7.973.24p=0.23m.r=2.02m.q=1.00m.p3.76m.qr2.40ss=0.58m.-9.13-10.93-3.74-6.13M+de=3.13Tn-m.M+ef=7.19Tn-m.def3.137.19p=0.96m.p2.36m.qr3.57sr=0.91m..q=1.68m.s=0.52m.ghiDIAGRAMA DE MOMENTOS FLECTORES EN COLUMNAS (Tn-m.)-2.11-0.723.083.62-0.67-2.510.341.26DIAGRAMA DE REACCIONES4.50Ton/mabc2.50Ton/mdef10ghi1.52Tn.1.92Tn.0.34Tn-m43.07Tn.1.26Tn-m15.95Tn.15.99Tn.

Port. 6ING.LaminaJ.R.T.G.METODO DE CROSSMC-05Calcular los Cortantes y Momentos de la estructura adjunta:W2Datos:W1W1=2.50Tn/mL1=5.00m.Vigaa1b2cW2=4.50Tn/mL2=5.00m.Tramobhbh3/12W3=5.00Tn/mh1=4.50m.130.0060.00540000.00567W4=3.00Tn/mh2=4.00m.230.0060.00540000.00W3h2330.0060.00540000.00W4430.0060.00540000.00d3e4fI 1=540,000.00cm4I 5=227,812.50cm4ColumnaI 2=540,000.00cm4I 6=227,812.50cm4Tramobhbh3/128910I 3=540,000.00cm4I 7=227,812.50cm4530.0045.00227812.50h1I 4=540,000.00cm4I 8=227,812.50cm4630.0045.00227812.50I 9=227,812.50cm4730.0045.00227812.50ghiI 10=227,812.50cm4830.0045.00227812.50L1L2930.0045.00227812.501030.0045.00227812.50MOMENTO DE EMPOTRAMIENTO PERFECTORIGIDECES RELATIVAS (Kij)TramoWLMijMjiIKijTramoWhMijMjiIKijTn/mm.Tn-mTn-mcm4cm2Tn/mm.Tn-mTn-mcm4cm2ab2.505.00-5.215.21540,000.001080da0.004.000.000.00227,812.50569.53bc4.505.00-9.389.38540,000.001080eb0.004.000.000.00227,812.50569.53de5.005.00-10.4210.42540,000.001080fc0.004.000.000.00227,812.50569.53ef3.005.00-6.256.25540,000.001080gd0.004.500.000.00227,812.50506.25he0.004.500.000.00227,812.50506.25if0.004.500.000.00227,812.50506.25FACTORES DE DISTRIBUCIONNudoTramoKijCijiijcm2cm3aab1080.001649.53-0.655-1.00ad569.531,649.53-0.345bba1080.002729.53-0.396-1.000bc1080.002729.53-0.396be569.532729.53-0.209ccb1080.001649.53-0.655-1.00cf569.531,649.53-0.345dde1080.002155.78-0.501-1.000da569.532155.78-0.264dg506.252155.78-0.235eed1080.003235.78-0.334-1.000ef1080.003235.78-0.334eb569.533235.78-0.176eh506.253235.78-0.156ffe1080.002155.78-0.501-1.000fc569.532155.78-0.264fi506.252155.78-0.235DIAGRAMA DE ITERACIONES-0.7192.108-0.0449.724-10.738-0.0450.0430.0860.0860.043-0.176-0.088-0.113-0.2250.1600.3200.3200.1600.3400.170-0.909-1.8180.4720.9430.9430.4722.8701.435-3.339-6.6780.8241.6491.6490.824-5.2085.208-9.3759.375-0.655-0.396-0.396-0.655abc0.719-0.0230.024-0.0930.1090.179-0.9911.514-0.3451.0140.045-0.0160.169-0.0710.498-0.4810.869-0.209-0.345-3.5222.306-0.9590.184-0.1190.026-0.024-2.108-9.132-0.0143.7400.0100.021-0.059-0.0300.0480.097-0.268-0.134-0.786-0.0080.023-0.0310.084-0.1410.249-0.9610.000-0.1760.3480.6973.6050.011-0.0120.048-0.0460.2170.0902.5520.757-0.264-1.823-0.911-0.264-1.761-1.186-0.4790.367-0.0590.051-0.0120.011-3.068-1.125-2.249-6.2506.250-0.501-0.334-0.334-0.501-10.41710.4172.5130.0100.0420.1932.268-0.235d4.8392.420e-0.156-0.855-0.126-0.028-0.002-1.010f-0.235-1.0540.3270.0450.010-0.672-0.911-1.8230.4120.206-0.134-0.2680.0900.045-0.030-0.0591.2570.0050.0210.0961.1340.0000.0210.0100.000-0.427-0.063-0.014-0.001-0.5050.000-0.5270.1630.0230.005-0.336-6.130-0.014g10.933hiFUERZAS CORTANTESVik = +Vik-(Mik+Mki)/ LikVki = -Vki-(Mki+Mik)/ LkiVIGASTramoWLVijVjiMijMjiVijVjiab2.505.006.25-6.25-0.7199.7244.45(8.05)bc4.505.0011.25-11.25-10.7382.10812.98(9.52)de5.005.0012.5-12.5-6.13010.93311.54(13.46)ef3.005.007.5-7.5-9.1323.7408.58(6.42)COLUMNASTramoWLVijVjiMijMjiVijVjida04.00003.6050.719(1.08)(1.08)eb04.0000-0.7861.014(0.06)(0.06)fc04.0000-3.068-2.1081.291.29gd04.50001.2572.513(0.84)(0.84)he04.5000-0.505-1.0100.340.34if04.5000-0.336-0.6720.220.22DIAGRAMA DE FUERZAS CORTANTESDIAGRAMA DE FUERZAS CORTANTES EN VIGAS (Tn.)4.4512.98abc-9.52-8.05X1=1.78m.X2=2.88m.11.548.58V1def-6.42-13.46X1=2.31m.V2X2=2.86m.XLX1X2X = V1. L / (V1+V2)ghiDIAGRAMA DE FUERZAS CORTANTES EN COLUMNAS (Tn.)abc-1.08-0.061.29def-0.840.340.22ghiDIAGRAMA DE MOMENTOS FLECTORESDIAGRAMA DE MOMENTOS FLECTORES EN VIGAS (Tn-m.)-9.72-10.74-0.72-2.11M+ab=3.24Tn-m.M+bc=7.97Tn-m.abc3.247.97p=0.17m.r=0.36m.q=1.61m.p3.22m.qr5.05ss=-0.41m.-10.93-9.13-6.13-3.74M+de=7.19Tn-m.M+ef=3.13Tn-m.def7.193.13p=-0.09m.p4.80m.qr3.17sr=1.28m..q=0.29m.s=0.56m.ghiDIAGRAMA DE MOMENTOS FLECTORES EN COLUMNAS (Tn-m.)-0.72-2.113.613.07-2.51-0.671.260.34DIAGRAMA DE REACCIONES2.50Ton/mabc4.50Ton/mdef10ghi1.92Tn.1.52Tn.1.26Tn-m43.07Tn.0.34Tn-m15.99Tn.15.95Tn.

Port. 7ING.LaminaJ.R.T.G.METODO DE CROSSMC-05Calcular los Cortantes y Momentos de la estructura adjunta:Datos:W1W2W1=4.50Tn/mI 1=540,000.00cm4Vigaa1b2cW2=4.50Tn/mI 2=540,000.00cm4Tramobhbh3/12W3=5.00Tn/mI 3=540,000.00cm4130.0060.00540000.00567h2W4=5.00Tn/mI 4=540,000.00cm4230.0060.00540000.00W3W4W5=5.00Tn/mI 5=227,812.50cm4330.0060.00540000.00W6=5.00Tn/mI 6=227,812.50cm4430.0060.00540000.00d3e4fL1=5.00m.I 7=227,812.50cm41430.0060.00540000.00L2=5.00m.I 8=227,812.50cm41530.0060.00540000.008910h1h1=4.50m.I 9=227,812.50cm4W5W6h2=4.00m.I 10=227,812.50cm4giI 11=227,812.50cm4Columna1415I 12=227,812.50cm4Tramobhbh3/12I 13=227,812.50cm4530.0045.00227812.50111213h1I 14=540,000.00cm4630.0045.00227812.50I 15=540,000.00cm4730.0045.00227812.50ghi830.0045.00227812.50L1L2930.0045.00227812.501030.0045.00227812.501130.0045.00227812.501230.0045.00227812.501330.0045.00227812.50MOMENTO DE EMPOTRAMIENTO PERFECTORIGIDECES RELATIVAS (Kij)TramoWLMijMjiIKijTramoWhMijMjiIKijTn/mm.Tn-mTn-mcm4cm2Tn/mm.Tn-mTn-mcm4cm2ab4.505.00-9.389.38540,000.001080da0.004.000.000.00227,812.50569.53bc4.505.00-9.389.38540,000.001080eb0.004.000.000.00227,812.50569.53de5.005.00-10.4210.42540,000.001080fc0.004.000.000.00227,812.50569.53ef5.005.00-10.4210.42540,000.001080gd0.004.500.000.00227,812.50506.25he0.004.500.000.00227,812.50506.25if0.004.500.000.00227,812.50506.25FACTORES DE DISTRIBUCIONNudoTramoKijCijiijcm2cm3aab1080.001649.53-0.655-1.00ad569.531,649.53-0.345bba1080.002729.53-0.396-1.000bc1080.002729.53-0.396be569.532729.53-0.209ccb1080.001649.53-0.655-1.00cf569.531,649.53-0.345dde1080.002155.78-0.501-1.000da569.532155.78-0.264dg506.252155.78-0.235eed1080.003235.78-0.334-1.000ef1080.003235.78-0.334eb569.533235.78-0.176eh506.253235.78-0.156ffe1080.002155.78-0.501-1.000fc569.532155.78-0.264fi506.252155.78-0.235DIAGRAMA DE ITERACIONES-1.8171.8170.00113.154-13.154-0.001-0.000-0.000-0.000-0.0000.0320.016-0.016-0.032-0.000-0.000-0.000-0.0001.3880.694-0.694-1.388-0.000-0.000-0.000-0.0006.1383.069-3.069-6.1380.0000.0000.0000.000-9.3759.375-9.3759.375-0.655-0.396-0.396-0.655abc1.8170.000-0.0010.017-0.0480.732-2.1193.237-0.3450.000-0.0000.0000.0000.000-0.0000.0000.000-0.209-0.345-3.2372.119-0.7320.048-0.0170.001-0.000-1.817-12.5270.0006.1970.0000.0000.0000.0000.0020.0040.0000.0000.0000.000-0.0000.0000.0000.000-0.0000.0000.000-0.1760.0920.1834.218-0.0000.000-0.0020.008-0.0970.3662.3241.618-0.2640.0000.000-0.264-1.618-2.324-0.3660.097-0.0080.002-0.0000.000-4.218-2.204-4.408-10.41710.417-0.501-0.334-0.334-0.501-10.41710.4171.978-0.000-0.002-0.0862.066-0.235d4.4082.204e-0.156-0.0000.0000.0000.000-0.000f-0.235-2.0660.0860.0020.000-1.9780.0000.000-0.183-0.0920.0000.000-0.004-0.0020.0000.0000.989-0.000-0.001-0.0431.0330.000-0.000-0.0000.000-0.0000.0000.0000.000-0.0000.000-1.0330.0430.0010.000-0.989-6.1970.000g12.527hiFUERZAS CORTANTESVik = +Vik-(Mik+Mki)/ LikVki = -Vki-(Mki+Mik)/ LkiVIGASTramoWLVijVjiMijMjiVijVjiab4.505.0011.25-11.25-1.81713.1548.98(13.52)bc4.505.0011.25-11.25-13.1541.81713.52(8.98)de5.005.0012.5-12.5-6.19712.52711.23(13.77)ef5.005.0012.5-12.5-12.5276.19713.77(11.23)COLUMNASTramoWLVijVjiMijMjiVijVjida04.00004.2181.817(1.51)(1.51)eb04.00000.0000.000(0.00)(0.00)fc04.0000-4.218-1.8171.511.51gd04.50000.9891.978(0.66)(0.66)he04.5000-0.000-0.0000.000.00if04.5000-0.989-1.9780.660.66DIAGRAMA DE FUERZAS CORTANTESDIAGRAMA DE FUERZAS CORTANTES EN VIGAS (Tn.)8.9813.52abc-8.98-13.52X1=2.00m.X2=3.00m.11.2313.77V1def-11.23-13.77X1=2.25m.V2X2=2.75m.XLX1X2X = V1. L / (V1+V2)ghiDIAGRAMA DE FUERZAS CORTANTES EN COLUMNAS (Tn.)abc-1.51-0.001.51def-0.660.000.66ghiDIAGRAMA DE MOMENTOS FLECTORESDIAGRAMA DE MOMENTOS FLECTORES EN VIGAS (Tn-m.)-13.15-13.15-1.82-1.82M+ab=7.15Tn-m.M+bc=7.15Tn-m.abc7.157.15p=0.21m.r=1.22m.q=1.22m.p3.56m.qr3.56ss=0.21m.-12.53-12.53-6.20-6.20M+de=6.42Tn-m.M+ef=6.42Tn-m.def6.426.42p=0.56m.p3.38m.qr3.38sr=1.06m..q=1.06m.s=0.56m.ghiDIAGRAMA DE MOMENTOS FLECTORES EN COLUMNAS (Tn-m.)-1.82-1.824.224.22-1.98-1.980.990.99DIAGRAMA DE REACCIONES4.50Ton/mabc4.50Ton/mdef10ghi2.17Tn.2.17Tn.0.99Tn-m54.57Tn.0.99Tn-m20.22Tn.20.22Tn.

Hoja3AltLetraAltLetraAltLetraAltLetra1513101e1512524102f1523535103g1534546104h1545557105i1556568106j1567579107k157858:108l158959;109m1591060112p1621363?113q1631464@114r1641565A115s1651666B116t1661767C117u1671868D118v1681969E119w1692070F120x1702171G121y1712272H122z1722373I123{1732474J124|1742575K125}1752676L126~1762777M1271772878N1281782979O1291793080P1301803181Q1311813282R13218233!83S13318334"84T13418435#85U13518536$86V13618637%87W13718738&88X1381883989Y13918940(90Z14019041)91[14119142*92\14219243+93]14319344,94^14419445-95_14519546.96`14619647/97a14719748098b14819849199c149199502100d150200

MBD00567A8F.unknown

MBD0059B5E8.unknown

MBD0059B5EA.unknown

MBD0059B5EB.unknown

MBD0059B5E9.unknown

MBD0059B5E6.unknown

MBD0059B5E7.unknown

MBD0059B5E5.unknown

MBD0031C1BD.unknown

MBD00567A8B.unknown

MBD00567A8D.unknown

MBD00567A8E.unknown

MBD00567A8C.unknown

MBD00567A89.unknown

MBD00567A8A.unknown

MBD0032928E.unknown

MBD0003568A.unknown

MBD000BBA1F.unknown

MBD000BBA22.unknown

MBD000BBA23.unknown

MBD000BBA20.unknown

MBD0003568C.unknown

MBD0003568D.unknown

MBD000BBA1E.unknown

MBD0003568B.unknown

MBD00035688.unknown

MBD00035689.unknown

MBD00035687.unknown