Hoja1PORTICOS

[F]=5[u]=u1z0u1y001x5u2z0u2y002x7.5u3z0u3y003x7.5u4z0u4y004x3.4 Calculando la submatriz de rigidez en coordenadas locales y globalesElementos 1 y 2

E1EA20II3IL4

raz5.0000EIraax0.5625EIrabx1.1250EIrbax1.1250EIr11x3.0000EIr22x3.0000EIr12x1.5000EIr21x1.5000EI3.5-3.6 Submatriz de rigidez en coordenadas locales y globales

125.00000.00000.0000Angulo=901.5708K11=K11=0.00000.56251.1250A=5.0000seno=1.00000.00001.12503.0000B=0.5625coseno=0.0000C=3.0000120.56250.0000-1.1250D=1.1250K11=K11=0.00005.00000.0000E=1.1250-1.12500.00003.0000

12-5.00000.00000.0000Angulo=901.5708K12=K12=0.0000-0.56251.1250A=-5.0000seno=1.00000.0000-1.12501.5000B=-0.5625coseno=0.0000C=1.500012-0.5625-0.0000-1.1250D=1.1250K12=K12=-0.0000-5.00000.0000E=-1.12501.1250-0.00001.5000

12-5.00000.00000.0000Angulo=901.5708K21=K21=0.0000-0.5625-1.1250A=-5.0000seno=1.00000.00001.12501.5000B=-0.5625coseno=0.0000C=1.500012-0.5625-0.00001.1250D=-1.1250K21=K21=-0.0000-5.0000-0.0000E=1.1250-1.12500.00001.5000

125.00000.00000.0000Angulo=901.5708K22=K22=0.00000.5625-1.1250A=5.0000seno=1.00000.0000-1.12503.0000B=0.5625coseno=0.0000C=3.0000120.56250.00001.1250D=-1.1250K22=K22=0.00005.0000-0.0000E=-1.12501.1250-0.00003.0000

3.4 Calculando la submatriz de rigidez en coordenadas locales y globalesElementos 3 y 4

E1EA20II2IL3

raz6.6667EIraax0.8889EIrabx1.3333EIrbax1.3333EIr11x2.6667EIr22x2.6667EIr12x1.3333EIr21x1.3333EI3.5-3.6 Submatriz de rigidez en coordenadas locales y globales

346.66670.00000.0000Angulo=901.5708K11=K11=0.00000.88891.3333A=6.6667seno=1.00000.00001.33332.6667B=0.8889coseno=0.0000C=2.6667340.88890.0000-1.3333D=1.3333K11=K11=0.00006.66670.0000E=1.3333-1.33330.00002.6667

34-6.66670.00000.0000Angulo=901.5708K12=K12=0.0000-0.88891.3333A=-6.6667seno=1.00000.0000-1.33331.3333B=-0.8889coseno=0.0000C=1.333334-0.8889-0.0000-1.3333D=1.3333K12=K12=-0.0000-6.66670.0000E=-1.33331.3333-0.00001.3333

34-6.66670.00000.0000Angulo=901.5708K21=K21=0.0000-0.8889-1.3333A=-6.6667seno=1.00000.00001.33331.3333B=-0.8889coseno=0.0000C=1.333334-0.8889-0.00001.3333D=-1.3333K21=K21=-0.0000-6.6667-0.0000E=1.3333-1.33330.00001.3333

346.66670.00000.0000Angulo=901.5708K22=K22=0.00000.8889-1.3333A=6.6667seno=1.00000.0000-1.33332.6667B=0.8889coseno=0.0000C=2.6667340.88890.00001.3333D=-1.3333K22=K22=0.00006.6667-0.0000E=-1.33331.3333-0.00002.6667

3.4 Calculando la submatriz de rigidez en coordenadas locales y globalesElementos 5 y 6

E1EA20II1IL8

raz2.5000EIraax0.0234EIrabx0.0938EIrbax0.0938EIr11x0.5000EIr22x0.5000EIr12x0.2500EIr21x0.2500EI3.5-3.6 Submatriz de rigidez en coordenadas locales y globales

562.50000.00000.0000Angulo=00.0000K11=K11=0.00000.02340.0938A=2.5000seno=0.00000.00000.09380.5000B=0.0234coseno=1.0000C=0.5000562.50000.00000.0000D=0.0938K11=K11=0.00000.02340.0938E=0.09380.00000.09380.5000

56-2.50000.00000.0000Angulo=00.0000K12=K12=0.0000-0.02340.0938A=-2.5000seno=0.00000.0000-0.09380.2500B=-0.0234coseno=1.0000C=0.250056-2.50000.00000.0000D=0.0938K12=K12=0.0000-0.02340.0938E=-0.09380.0000-0.09380.2500

34-2.50000.00000.0000Angulo=00.0000K21=K21=0.0000-0.0234-0.0938A=-2.5000seno=0.00000.00000.09380.2500B=-0.0234coseno=1.0000C=0.250056-2.50000.00000.0000D=-0.0938K21=K21=0.0000-0.0234-0.0938E=0.09380.00000.09380.2500

342.50000.00000.0000Angulo=00.0000K22=K22=0.00000.0234-0.0938A=2.5000seno=0.00000.0000-0.09380.5000B=0.0234coseno=1.0000C=0.5000562.50000.00000.0000D=-0.0938K22=K22=0.00000.0234-0.0938E=-0.09380.0000-0.09380.5000ENSAMBLE DE LA MATRIZ DE RIGIDEZ GLOBAL

[K]=3.95140.0000-0.2083-2.50000.00000.0000-0.8889-0.0000-1.33330.00000.00000.00000.000011.69010.09380.0000-0.02340.0938-0.0000-6.66670.00000.00000.00000.0000-0.20830.09386.16670.0000-0.09380.25001.3333-0.00001.33330.00000.00000.0000-2.50000.00000.00003.95140.0000-0.20830.00000.00000.0000-0.8889-0.0000-1.33330.0000-0.0234-0.09380.000011.6901-0.09380.00000.00000.0000-0.0000-6.66670.00000.00000.09380.2500-0.2083-0.09386.16670.00000.00000.00001.3333-0.00001.3333-0.8889-0.00001.33330.00000.00000.00003.38890.00001.3333-2.50000.00000.0000-0.0000-6.6667-0.00000.00000.00000.00000.00006.69010.09370.0000-0.02340.0938-1.33330.00001.33330.00000.00000.00001.33330.09373.16670.0000-0.09380.25000.00000.00000.0000-0.8889-0.00001.3333-2.50000.00000.00003.38890.00001.33330.00000.00000.0000-0.0000-6.6667-0.00000.0000-0.0234-0.09380.00006.6901-0.09380.00000.00000.0000-1.33330.00001.33330.00000.09380.25001.3333-0.09383.1667OBTENCION DE LOS DESPLAZAMIENTOS Y GIROS GLOBALES[F]=[K] [u]

[u]=67.5665u1z1.5248u1y-22.672101x67.5665u2z-1.5248u2y-22.672102x138.3331u3z2.0415u3y-18.880603x138.3331u4z-2.0415u4y-18.880604xCALCULO DE DEFORMACINES EN COORDENADAS LOCALES Y ELMENTOS MECANICOSELEMENTO 1ELEMENTO 2

Angulo=901.5708Angulo=901.5708seno=1.0000seno=1.0000coseno=0.0000coseno=0.0000

[T]0.00001.00000000[T]0.00001.00000000-1.00000.00000000-1.00000.000000000010000010000000.00001.000000000.00001.00000000-1.00000.00000000-1.00000.00000000001000001[u] = [T][u1][u] = [T][u1]1 [u]0.0000Empotrado1 [u]0.00002 [u]0.0000Empotrado2 [u]0.00000.00000.00000.00000.00000.00000.00000.00000.000067.5665u1z1.524867.5665u2z-1.52481.5248u1y-67.5665-1.5248u2y-67.5665-22.672101x-22.6721-22.672102x-22.6721

[K]500-500[K]500-50000.56251.1250-0.56251.12500.56251.1250-0.56251.12501.12530-1.1251.501.12530-1.1251.5-500500-5005000-0.5625-1.12500.5625-1.1250-0.5625-1.12500.5625-1.12501.1251.50-1.125301.1251.50-1.1253[F] = [K] [u][F] = [K] [u][F]-7.6240[F]7.624012.500012.500042.004142.00417.6240-7.6240-12.5000-12.50007.99597.9959ELEMENTO 3ELEMENTO 4

Angulo=901.5708Angulo=901.5708seno=1.0000seno=1.0000coseno=0.0000coseno=0.0000

[T]0.00001.00000000[T]0.00001.00000000-1.00000.00000000-1.00000.000000000010000010000000.00001.000000000.00001.00000000-1.00000.00000000-1.00000.00000000001000001[u] = [T][u1][u] = [T][u1]3 [u]67.5665u1z3 [u]1.52484 [u]67.5665u2z4 [u]-1.52481.5248u1y-67.5665-1.5248u2y-67.5665-22.672101x-22.6721-22.672102x-22.6721138.3331u3z2.0415138.3331u4z-2.04152.0415u3y-138.3331-2.0415u4y-138.3331-18.880603x-18.8806-18.880604x-18.8806

[K]6.666670.000000.00000-6.666670.000000.00000[K]6.666670.000000.00000-6.666670.000000.000000.000000.888891.333330.00000-0.888891.333330.000000.888891.333330.00000-0.888891.333330.000001.333332.666670.00000-1.333331.333330.000001.333332.666670.00000-1.333331.33333-6.666670.000000.000006.666670.000000.00000-6.666670.000000.000006.666670.000000.000000.00000-0.88889-1.333330.000000.88889-1.333330.00000-0.88889-1.333330.000000.88889-1.333330.000001.333331.333330.00000-1.333332.666670.000001.333331.333330.00000-1.333332.66667[F] = [K] [u][F] = [K] [u][F]-3.4444[F]3.44447.50007.50008.72238.72233.4444-3.4444-7.5000-7.500013.777713.7777ELEMENTO 5ELEMENTO 6

Angulo=00.0000Angulo=00.0000seno=0.0000seno=0.0000coseno=1.0000coseno=1.0000

[T]1.00000.00000000[T]1.00000.000000000.00001.000000000.00001.000000000010000010000001.00000.000000001.00000.000000000.00001.000000000.00001.00000000001000001[u] = [T][u1][u] = [T][u1]5 [u]67.5665u1z5 [u]67.56656 [u]138.3331u3z6 [u]138.33311.5248u1y1.52482.0415u3y2.0415-22.672101x-22.6721-18.880603x-18.880667.5665u2z67.5665138.3331u4z138.3331-1.5248u2y-1.5248-2.0415u4y-2.0415-22.672102x-22.6721-18.880604x-18.8806

[K]2.500000.000000.00000-2.500000.000000.00000[K]2.500000.000000.00000-2.500000.000000.000000.000000.023440.093750.00000-0.023440.093750.000000.023440.093750.00000-0.023440.093750.000000.093750.500000.00000-0.093750.250000.000000.093750.500000.00000-0.093750.25000-2.500000.000000.000002.500000.000000.00000-2.500000.000000.000002.500000.000000.000000.00000-0.02344-0.093750.000000.02344-0.093750.00000-0.02344-0.093750.000000.02344-0.093750.000000.093750.250000.00000-0.093750.500000.000000.093750.250000.00000-0.093750.50000[F] = [K] [u][F] = [K] [u][F]0.0000[F]-0.0000-4.1796-3.4444-16.7182-13.77770.00000.00004.17963.4444-16.7182-13.7777

Hoja2PORTICOS

[F]=10[u]=u1z0u1y001x0u2z0u2y002x15u3z0u3y003x0u4z0u4y004x3.4 Calculando la submatriz de rigidez en coordenadas locales y globalesElementos 1 y 2

E1EA20II3IL4

raz5.0000EIraax0.5625EIrabx1.1250EIrbax1.1250EIr11x3.0000EIr22x3.0000EIr12x1.5000EIr21x1.5000EI3.5-3.6 Submatriz de rigidez en coordenadas locales y globales

125.00000.00000.0000Angulo=901.5708K11=K11=0.00000.56251.1250A=5.0000seno=1.00000.00001.12503.0000B=0.5625coseno=0.0000C=3.0000120.56250.0000-1.1250D=1.1250K11=K11=0.00005.00000.0000E=1.1250-1.12500.00003.0000

12-5.00000.00000.0000Angulo=901.5708K12=K12=0.0000-0.56251.1250A=-5.0000seno=1.00000.0000-1.12501.5000B=-0.5625coseno=0.0000C=1.500012-0.5625-0.0000-1.1250D=1.1250K12=K12=-0.0000-5.00000.0000E=-1.12501.1250-0.00001.5000

12-5.00000.00000.0000Angulo=901.5708K21=K21=0.0000-0.5625-1.1250A=-5.0000seno=1.00000.00001.12501.5000B=-0.5625coseno=0.0000C=1.500012-0.5625-0.00001.1250D=-1.1250K21=K21=-0.0000-5.0000-0.0000E=1.1250-1.12500.00001.5000

125.00000.00000.0000Angulo=901.5708K22=K22=0.00000.5625-1.1250A=5.0000seno=1.00000.0000-1.12503.0000B=0.5625coseno=0.0000C=3.0000120.56250.00001.1250D=-1.1250K22=K22=0.00005.0000-0.0000E=-1.12501.1250-0.00003.0000

3.4 Calculando la submatriz de rigidez en coordenadas locales y globalesElementos 3 y 4

E1EA20II2IL3

raz6.6667EIraax0.8889EIrabx1.3333EIrbax1.3333EIr11x2.6667EIr22x2.6667EIr12x1.3333EIr21x1.3333EI3.5-3.6 Submatriz de rigidez en coordenadas locales y globales

346.66670.00000.0000Angulo=901.5708K11=K11=0.00000.88891.3333A=6.6667seno=1.00000.00001.33332.6667B=0.8889coseno=0.0000C=2.6667340.88890.0000-1.3333D=1.3333K11=K11=0.00006.66670.0000E=1.3333-1.33330.00002.6667

34-6.66670.00000.0000Angulo=901.5708K12=K12=0.0000-0.88891.3333A=-6.6667seno=1.00000.0000-1.33331.3333B=-0.8889coseno=0.0000C=1.333334-0.8889-0.0000-1.3333D=1.3333K12=K12=-0.0000-6.66670.0000E=-1.33331.3333-0.00001.3333

34-6.66670.00000.0000Angulo=901.5708K21=K21=0.0000-0.8889-1.3333A=-6.6667seno=1.00000.00001.33331.3333B=-0.8889coseno=0.0000C=1.333334-0.8889-0.00001.3333D=-1.3333K21=K21=-0.0000-6.6667-0.0000E=1.3333-1.33330.00001.3333

346.66670.00000.0000Angulo=901.5708K22=K22=0.00000.8889-1.3333A=6.6667seno=1.00000.0000-1.33332.6667B=0.8889coseno=0.0000C=2.6667340.88890.00001.3333D=-1.3333K22=K22=0.00006.6667-0.0000E=-1.33331.3333-0.00002.6667

3.4 Calculando la submatriz de rigidez en coordenadas locales y globalesElementos 5 y 6

E1EA20II1IL8

raz2.5000EIraax0.0234EIrabx0.0938EIrbax0.0938EIr11x0.5000EIr22x0.5000EIr12x0.2500EIr21x0.2500EI3.5-3.6 Submatriz de rigidez en coordenadas locales y globales

562.50000.00000.0000Angulo=00.0000K11=K11=0.00000.02340.0938A=2.5000seno=0.00000.00000.09380.5000B=0.0234coseno=1.0000C=0.5000562.50000.00000.0000D=0.0938K11=K11=0.00000.02340.0938E=0.09380.00000.09380.5000

56-2.50000.00000.0000Angulo=00.0000K12=K12=0.0000-0.02340.0938A=-2.5000seno=0.00000.0000-0.09380.2500B=-0.0234coseno=1.0000C=0.250056-2.50000.00000.0000D=0.0938K12=K12=0.0000-0.02340.0938E=-0.09380.0000-0.09380.2500

34-2.50000.00000.0000Angulo=00.0000K21=K21=0.0000-0.0234-0.0938A=-2.5000seno=0.00000.00000.09380.2500B=-0.0234coseno=1.0000C=0.250056-2.50000.00000.0000D=-0.0938K21=K21=0.0000-0.0234-0.0938E=0.09380.00000.09380.2500

342.50000.00000.0000Angulo=00.0000K22=K22=0.00000.0234-0.0938A=2.5000seno=0.00000.0000-0.09380.5000B=0.0234coseno=1.0000C=0.5000562.50000.00000.0000D=-0.0938K22=K22=0.00000.0234-0.0938E=-0.09380.0000-0.09380.5000ENSAMBLE DE LA MATRIZ DE RIGIDEZ GLOBAL

[K]=3.95140.0000-0.2083-2.50000.00000.0000-0.8889-0.0000-1.33330.00000.00000.00000.000011.69010.09380.0000-0.02340.0938-0.0000-6.66670.00000.00000.00000.0000-0.20830.09386.16670.0000-0.09380.25001.3333-0.00001.33330.00000.00000.0000-2.50000.00000.00003.95140.0000-0.20830.00000.00000.0000-0.8889-0.0000-1.33330.0000-0.0234-0.09380.000011.6901-0.09380.00000.00000.0000-0.0000-6.66670.00000.00000.09380.2500-0.2083-0.09386.16670.00000.00000.00001.3333-0.00001.3333-0.8889-0.00001.33330.00000.00000.00003.38890.00001.3333-2.50000.00000.0000-0.0000-6.6667-0.00000.00000.00000.00000.00006.69010.09370.0000-0.02340.0938-1.33330.00001.33330.00000.00000.00001.33330.09373.16670.0000-0.09380.25000.00000.00000.0000-0.8889-0.00001.3333-2.50000.00000.00003.38890.00001.33330.00000.00000.0000-0.0000-6.6667-0.00000.0000-0.0234-0.09380.00006.6901-0.09380.00000.00000.0000-1.33330.00001.33330.00000.09380.25001.3333-0.09383.1667OBTENCION DE LOS DESPLAZAMIENTOS Y GIROS GLOBALES[F]=[K] [u]

[u]=68.5136u1z1.5248u1y-22.949501x66.6194u2z-1.5248u2y-22.394802x139.8419u3z2.0415u3y-19.010603x136.8244u4z-2.0415u4y-18.750604xCALCULO DE DEFORMACINES EN COORDENADAS LOCALES Y ELMENTOS MECANICOSELEMENTO 1ELEMENTO 2

Angulo=901.5708Angulo=901.5708seno=1.0000seno=1.0000coseno=0.0000coseno=0.0000

[T]0.00001.00000000[T]0.00001.00000000-1.00000.00000000-1.00000.000000000010000010000000.00001.000000000.00001.00000000-1.00000.00000000-1.00000.00000000001000001[u] = [T][u1][u] = [T][u1]1 [u]0.0000Empotrado1 [u]0.00002 [u]0.0000Empotrado2 [u]0.00000.00000.00000.00000.00000.00000.00000.00000.000068.5136u1z1.524866.6194u2z-1.52481.5248u1y-68.5136-1.5248u2y-66.6194-22.949501x-22.9495-22.394802x-22.3948

[K]500-500[K]500-50000.56251.1250-0.56251.12500.56251.1250-0.56251.12501.12530-1.1251.501.12530-1.1251.5-500500-5005000-0.5625-1.12500.5625-1.1250-0.5625-1.12500.5625-1.12501.1251.50-1.125301.1251.50-1.1253[F] = [K] [u][F] = [K] [u][F]-7.6240[F]7.624012.720712.279342.653541.35477.6240-7.6240-12.7207-12.27938.22937.7625ELEMENTO 3ELEMENTO 4

Angulo=901.5708Angulo=901.5708seno=1.0000seno=1.0000coseno=0.0000coseno=0.0000

[T]0.00001.00000000[T]0.00001.00000000-1.00000.00000000-1.00000.000000000010000010000000.00001.000000000.00001.00000000-1.00000.00000000-1.00000.00000000001000001[u] = [T][u1][u] = [T][u1]3 [u]68.5136u1z3 [u]1.52484 [u]66.6194u2z4 [u]-1.52481.5248u1y-68.5136-1.5248u2y-66.6194-22.949501x-22.9495-22.394802x-22.3948139.8419u3z2.0415136.8244u4z-2.04152.0415u3y-139.8419-2.0415u4y-136.8244-19.010603x-19.0106-18.750604x-18.7506

[K]6.666670.000000.00000-6.666670.000000.00000[K]6.666670.000000.00000-6.666670.000000.000000.000000.888891.333330.00000-0.888891.333330.000000.888891.333330.00000-0.888891.333330.000001.333332.666670.00000-1.333331.333330.000001.333332.666670.00000-1.333331.33333-6.666670.000000.000006.666670.000000.00000-6.666670.000000.000006.666670.000000.000000.00000-0.88889-1.333330.000000.88889-1.333330.00000-0.88889-1.333330.000000.88889-1.333330.000001.333331.333330.00000-1.333332.666670.000001.333331.333330.00000-1.333332.66667[F] = [K] [u][F] = [K] [u][F]-3.4444[F]3.44447.45627.54388.55838.88633.4444-3.4444-7.4562-7.543813.810213.7452ELEMENTO 5ELEMENTO 6

Angulo=00.0000Angulo=00.0000seno=0.0000seno=0.0000coseno=1.0000coseno=1.0000

[T]1.00000.00000000[T]1.00000.000000000.00001.000000000.00001.000000000010000010000001.00000.000000001.00000.000000000.00001.000000000.00001.00000000001000001[u] = [T][u1][u] = [T][u1]5 [u]68.5136u1z5 [u]68.51366 [u]139.8419u3z6 [u]139.84191.5248u1y1.52482.0415u3y2.0415-22.949501x-22.9495-19.010603x-19.010666.6194u2z66.6194136.8244u4z136.8244-1.5248u2y-1.5248-2.0415u4y-2.0415-22.394802x-22.3948-18.750604x-18.7506

[K]2.500000.000000.00000-2.500000.000000.00000[K]2.500000.000000.00000-2.500000.000000.000000.000000.023440.093750.00000-0.023440.093750.000000.023440.093750.00000-0.023440.093750.000000.093750.500000.00000-0.093750.250000.000000.093750.500000.00000-0.093750.25000-2.500000.000000.000002.500000.000000.00000-2.500000.000000.000002.500000.000000.000000.00000-0.02344-0.093750.000000.02344-0.093750.00000-0.02344-0.093750.000000.02344-0.093750.000000.093750.250000.00000-0.093750.500000.000000.093750.250000.00000-0.093750.50000[F] = [K] [u][F] = [K] [u][F]4.7355[F]7.5438-4.1796-3.4444-16.7875-13.8102-4.7355-7.54384.17963.4444-16.6489-13.7452

Hoja3PORTICOS

Momentos de empotramiento perfecto

R18.96R58.4375R21.04R61.5625M16.4M55.625M2-1.6M6-1.875

R47.5R57.5M46.25M5-6.25

[F]=0F1Z[u]=u1Z-8.96F1Yu1Y-6.4M1Xo1X0F2Zu2Z-1.04F2Yu2Y1.6M2Xo2X0F3Zu3Z0F3Yu3Y0M3Xo3X10F4Zu4Z-7.5F4Yu4Y-6.25M4Xo4X0F5Zu5Z-15.9375F5Yu5Y0.625M5Xo5X0F6Zu6Z-1.5625F6Yu6Y1.875M6Xo6X

3.4 Calculando la submatriz de rigidez en coordenadas locales y globalesElementos 1, 2, 3, 4 y 5

E1EA10II3IL3

raz3.3333EIraax1.3333EIrabx2.0000EIrbax2.0000EIr11x4.0000EIr22x4.0000EIr12x2.0000EIr21x2.0000EI3.5-3.6 Submatriz de rigidez en coordenadas locales y globales

1, 2, 3, 4 y 53.33330.00000.0000Angulo=901.5708K11=0.00001.33332.0000A=3.3333seno=1.00000.00002.00004.0000B=1.3333coseno=0.0000C=4.00001, 2, 3, 4 y 51.33330.0000-2.0000D=2.0000K11=0.00003.33330.0000E=2.0000-2.00000.00004.0000

1, 2, 3, 4 y 5-3.33330.00000.0000Angulo=901.5708K12=0.0000-1.33332.0000A=-3.3333seno=1.00000.0000-2.00002.0000B=-1.3333coseno=0.0000C=2.00001, 2, 3, 4 y 5-1.3333-0.0000-2.0000D=2.0000K12=-0.0000-3.33330.0000E=-2.00002.0000-0.00002.0000

1, 2, 3, 4 y 5-3.33330.00000.0000Angulo=901.5708K21=0.0000-1.3333-2.0000A=-3.3333seno=1.00000.00002.00002.0000B=-1.3333coseno=0.0000C=2.00001, 2, 3, 4 y 5-1.3333-0.00002.0000D=-2.0000K21=-0.0000-3.3333-0.0000E=2.0000-2.00000.00002.0000

1, 2, 3, 4 y 53.33330.00000.0000Angulo=901.5708K22=0.00001.3333-2.0000A=3.3333seno=1.00000.0000-2.00004.0000B=1.3333coseno=0.0000C=4.00001, 2, 3, 4 y 51.33330.00002.0000D=-2.0000K22=0.00003.3333-0.0000E=-2.00002.0000-0.00004.0000

3.4 Calculando la submatriz de rigidez en coordenadas locales y globalesElementos 6 y 8

E1EA5II1IL5

raz1.0000EIraax0.0960EIrabx0.2400EIrbax0.2400EIr11x0.8000EIr22x0.8000EIr12x0.4000EIr21x0.4000EI3.5-3.6 Submatriz de rigidez en coordenadas locales y globales

681.00000.00000.0000Angulo=00.0000K11=K11=0.00000.09600.2400A=1.0000seno=0.00000.00000.24000.8000B=0.0960coseno=1.0000C=0.8000681.00000.00000.0000D=0.2400K11=K11=0.00000.09600.2400E=0.24000.00000.24000.8000

68-1.00000.00000.0000Angulo=00.0000K12=K12=0.0000-0.09600.2400A=-1.0000seno=0.00000.0000-0.24000.4000B=-0.0960coseno=1.0000C=0.400068-1.00000.00000.0000D=0.2400K12=K12=0.0000-0.09600.2400E=-0.24000.0000-0.24000.4000

68-1.00000.00000.0000Angulo=00.0000K21=K21=0.0000-0.0960-0.2400A=-1.0000seno=0.00000.00000.24000.4000B=-0.0960coseno=1.0000C=0.400068-1.00000.00000.0000D=-0.2400K21=K21=0.0000-0.0960-0.2400E=0.24000.00000.24000.4000

681.00000.00000.0000Angulo=00.0000K22=K22=0.00000.0960-0.2400A=1.0000seno=0.00000.0000-0.24000.8000B=0.0960coseno=1.0000C=0.8000681.00000.00000.0000D=-0.2400K22=K22=0.00000.0960-0.2400E=-0.24000.0000-0.24000.8000

3.4 Calculando la submatriz de rigidez en coordenadas locales y globalesElementos 7 y 9

E1EA5II1IL4

raz1.2500EIraax0.1875EIrabx0.3750EIrbax0.3750EIr11x1.0000EIr22x1.0000EIr12x0.5000EIr21x0.5000EI3.5-3.6 Submatriz de rigidez en coordenadas locales y globales

791.25000.00000.0000Angulo=00.0000K11=K11=0.00000.18750.3750A=1.2500seno=0.00000.00000.37501.0000B=0.1875coseno=1.0000C=1.0000791.25000.00000.0000D=0.3750K11=K11=0.00000.18750.3750E=0.37500.00000.37501.0000

79-1.25000.00000.0000Angulo=00.0000K12=K12=0.0000-0.18750.3750A=-1.2500seno=0.00000.0000-0.37500.5000B=-0.1875coseno=1.0000C=0.500079-1.25000.00000.0000D=0.3750K12=K12=0.0000-0.18750.3750E=-0.37500.0000-0.37500.5000

79-1.25000.00000.0000Angulo=00.0000K21=K21=0.0000-0.1875-0.3750A=-1.2500seno=0.00000.00000.37500.5000B=-0.1875coseno=1.0000C=0.500079-1.25000.00000.0000D=-0.3750K21=K21=0.0000-0.1875-0.3750E=0.37500.00000.37500.5000

791.25000.00000.0000Angulo=00.0000K22=K22=0.00000.1875-0.3750A=1.2500seno=0.00000.0000-0.37501.0000B=0.1875coseno=1.0000C=1.0000791.25000.00000.0000D=-0.3750K22=K22=0.00000.1875-0.3750E=-0.37500.0000-0.37501.0000ENSAMBLE DE LA MATRIZ DE RIGIDEZ GLOBAL

[K]=3.66670.00000.0000-1.00000.00000.00000.00000.00000.0000-1.3333-0.0000-2.00000.00000.00000.00000.00000.00000.00000.00006.76270.24000.0000-0.09600.24000.00000.00000.0000-0.0000-3.33330.00000.00000.00000.00000.00000.00000.00000.00000.24008.80000.0000-0.24000.40000.00000.00000.00002.0000-0.00002.00000.00000.00000.00000.00000.00000.0000-1.00000.00000.00003.58330.0000-2.0000-1.25000.00000.00000.00000.00000.0000-1.3333-0.0000-2.00000.00000.00000.00000.0000-0.0960-0.24000.00003.61680.13500.0000-0.18750.37500.00000.00000.0000-0.0000-3.33330.00000.00000.00000.00000.00000.24000.4000-2.00000.13505.80000.0000-0.37500.50000.00000.00000.00002.0000-0.00002.00000.00000.00000.00000.00000.00000.0000-1.25000.00000.00003.91670.00000.00000.00000.00000.00000.00000.00000.0000-1.3333-0.0000-2.00000.00000.00000.00000.0000-0.1875-0.37500.00006.8542-0.37500.00000.00000.00000.00000.00000.0000-0.0000-3.33330.00000.00000.00000.00000.00000.37500.50000.0000-0.37509.00000.00000.00000.00000.00000.00000.00002.0000-0.00002.0000-1.3333-0.00002.00000.00000.00000.00000.00000.00000.00002.33330.00002.0000-1.00000.00000.00000.00000.00000.0000-0.0000-3.3333-0.00000.00000.00000.00000.00000.00000.00000.00003.42930.24000.0000-0.09600.24000.00000.00000.0000-2.00000.00002.00000.00000.00000.00000.00000.00000.00002.00000.24004.80000.0000-0.24000.40000.00000.00000.00000.00000.00000.0000-1.3333-0.00002.00000.00000.00000.0000-1.00000.00000.00003.58330.00002.0000-1.25000.00000.00000.00000.00000.0000-0.0000-3.3333-0.00000.00000.00000.00000.0000-0.0960-0.24000.00003.61680.13500.0000-0.18750.37500.00000.00000.0000-2.00000.00002.00000.00000.00000.00000.00000.24000.40002.00000.13505.80000.0000-0.37500.50000.00000.00000.00000.00000.00000.0000-1.3333-0.00002.00000.00000.00000.0000-1.25000.00000.00002.58330.00002.00000.00000.00000.00000.00000.00000.0000-0.0000-3.3333-0.00000.00000.00000.00000.0000-0.1875-0.37500.00003.5208-0.37500.00000.00000.00000.00000.00000.0000-2.00000.00002.00000.00000.00000.00000.00000.37500.50002.0000-0.37505.0000OBTENCION DE LOS DESPLAZAMIENTOS Y GIROS GLOBALES[F]=[K] [u]

[u]=10.9552u1Z-5.7411u1Y-7.2192o1X14.1881u2Z-41.7367u2Y-0.1202o2X11.1425u3Z-4.7589u3Y-2.5126o3X33.8351u4Z-8.2859u4Y-9.5662o4X20.7709u5Z-44.3092u5Y-0.7485o5X15.9514u6Z-7.1417u6Y2.3189o6X

CALCULO DE DEFORMACINES EN COORDENADAS LOCALES Y ELMENTOS MECANICOSELEMENTO 1ELEMENTO 2ELEMENTO 3ELEMENTO 4ELEMENTO 5

Angulo=901.5708Angulo=901.5708Angulo=901.5708Angulo=901.5708Angulo=901.5708seno=1.0000seno=1.0000seno=1.0000seno=1.0000seno=1.0000coseno=0.0000coseno=0.0000coseno=0.0000coseno=0.0000coseno=0.0000

[T]0.00001.00000000[T]0.00001.00000000[T]0.00001.00000000[T]0.00001.00000000[T]0.00001.00000000-1.00000.00000000-1.00000.00000000-1.00000.00000000-1.00000.00000000-1.00000.000000000010000010000010000010000010000000.00001.000000000.00001.000000000.00001.000000000.00001.000000000.00001.00000000-1.00000.00000000-1.00000.00000000-1.00000.00000000-1.00000.00000000-1.00000.00000000001000001000001000001000001[u] = [T][u1][u] = [T][u1][u] = [T][u1][u] = [T][u1][u] = [T][u1]1 [u]0.0000A1 [u]0.00002 [u]0.0000B2 [u]0.00003 [u]10.955213 [u]-5.74114 [u]14.188124 [u]-41.73675 [u]11.142535 [u]-4.75890.00000.00000.00000.0000-5.7411-10.9552-41.7367-14.1881-4.7589-11.14250.00000.00000.00000.0000-7.2192-7.2192-0.1202-0.1202-2.5126-2.512610.95521-5.741111.14253-4.758933.83514-8.285920.77095-44.309215.95146-7.1417-5.7411-10.9552-4.7589-11.1425-8.2859-33.8351-44.3092-20.7709-7.1417-15.9514-7.2192-7.2192-2.5126-2.5126-9.5662-9.5662-0.7485-0.74852.31892.3189

[K]3.33330.00000.0000-3.33330.00000.0000[K]3.33330.00000.0000-3.33330.00000.0000[K]3.33330.00000.0000-3.33330.00000.0000[K]3.33330.00000.0000-3.33330.00000.0000[K]3.33330.00000.0000-3.33330.00000.00000.00001.33332.00000.0000-1.33332.00000.00001.33332.00000.0000-1.33332.00000.00001.33332.00000.0000-1.33332.00000.00001.33332.00000.0000-1.33332.00000.00001.33332.00000.0000-1.33332.00000.00002.00004.00000.0000-2.00002.00000.00002.00004.00000.0000-2.00002.00000.00002.00004.00000.0000-2.00002.00000.00002.00004.00000.0000-2.00002.00000.00002.00004.00000.0000-2.00002.0000-3.33330.00000.00003.33330.00000.0000-3.33330.00000.00003.33330.00000.0000-3.33330.00000.00003.33330.00000.0000-3.33330.00000.00003.33330.00000.0000-3.33330.00000.00003.33330.00000.00000.0000-1.3333-2.00000.00001.3333-2.00000.0000-1.3333-2.00000.00001.3333-2.00000.0000-1.3333-2.00000.00001.3333-2.00000.0000-1.3333-2.00000.00001.3333-2.00000.0000-1.3333-2.00000.00001.3333-2.00000.00002.00002.00000.0000-2.00004.00000.00002.00002.00000.0000-2.00004.00000.00002.00002.00000.0000-2.00004.00000.00002.00002.00000.0000-2.00004.00000.00002.00002.00000.0000-2.00004.0000[F] = [K] [u][F] = [K] [u][F] = [K] [u][F] = [K] [u][F] = [K] [u][F]19.1369[F]15.8631[F]8.4827[F]8.5748[F]7.94250.16869.8314-3.06427.03986.02447.472117.2597-2.249311.18804.2050-19.1369-15.8631-8.4827-8.5748-7.9425-0.1686-9.83143.0642-7.0398-6.0244-6.966212.2344-6.94339.931413.8681ELEMENTO 6ELEMENTO 8

Angulo=00.0000Angulo=00.0000seno=0.0000seno=0.0000coseno=1.0000coseno=1.0000

[T]1.00000.00000000[T]1.00000.000000000.00001.000000000.00001.000000000010000010000001.00000.000000001.00000.000000000.00001.000000000.00001.00000000001000001[u] = [T][u1][u] = [T][u1]6 [u]10.955216 [u]10.95528 [u]33.835148 [u]33.8351-5.7411-5.7411-8.2859-8.2859-7.2192-7.2192-9.5662-9.566214.1881214.188120.7709520.7709-41.7367-41.7367-44.3092-44.3092-0.1202-0.1202-0.7485-0.7485

[K]1.000000.000000.00000-1.000000.000000.00000[K]1.000000.000000.00000-1.000000.000000.000000.000000.096000.240000.00000-0.096000.240000.000000.096000.240000.00000-0.096000.240000.000000.240000.800000.00000-0.240000.400000.000000.240000.800000.00000-0.240000.40000-1.000000.000000.000001.000000.000000.00000-1.000000.000000.000001.000000.000000.000000.00000-0.09600-0.240000.000000.09600-0.240000.00000-0.09600-0.240000.000000.09600-0.240000.000000.240000.400000.00000-0.240000.800000.000000.240000.400000.00000-0.240000.80000[F] = [K] [u][F] = [K] [u][F]-3.2328[F]13.06421.69410.98272.81560.69333.2328-13.0642-1.6941-0.98275.65524.2204ELEMENTO 7ELEMENTO 9

Angulo=00.0000Angulo=00.0000seno=0.0000seno=0.0000coseno=1.0000coseno=1.0000

[T]1.00000.00000000[T]1.00000.000000000.00001.000000000.00001.000000000010000010000001.00000.000000001.00000.000000000.00001.000000000.00001.00000000001000001[u] = [T][u1][u] = [T][u1]7 [u]14.188127 [u]14.18819 [u]20.770959 [u]20.7709-41.7367-41.7367-44.3092-44.3092-0.1202-0.1202-0.7485-0.748511.1425311.142515.9514615.9514-4.7589-4.7589-7.1417-7.1417-2.5126-2.51262.31892.3189

[K]1.250000.000000.00000-1.250000.000000.00000[K]1.250000.000000.00000-1.250000.000000.000000.000000.187500.375000.00000-0.187500.375000.000000.187500.375000.00000-0.187500.375000.000000.375001.000000.00000-0.375000.500000.000000.375001.000000.00000-0.375000.50000-1.250000.000000.000001.250000.000000.00000-1.250000.000000.000001.250000.000000.000000.00000-0.18750-0.375000.000000.18750-0.375000.00000-0.18750-0.375000.000000.18750-0.375000.000000.375000.500000.00000-0.375001.000000.000000.375000.500000.00000-0.375001.00000[F] = [K] [u][F] = [K] [u][F]3.8070[F]6.0244-7.9206-6.3800-15.2432-13.5268-3.8070-6.02447.92066.3800-16.4394-11.9931VERIFICACION DEL EQUILIBRIO

ELEMENTOSFASE 1FASE 2EFECTIVA

60-3.2328-3.23281zMomentos de empotramiento perfecto8.961.694110.65411y6.42.81569.21561xR18.96R58.437503.23283.23282zR21.04R61.56251.04-1.6941-0.65412yM16.4M55.625-1.65.65524.05522xM2-1.6M6-1.875

R47.5703.80703.8070R57.51.04-7.9206-6.8806M46.25-1.6-15.2432-16.8432M5-6.250-3.8070-3.807007.92067.92060-16.4394-16.4394

8013.064213.06427.50.98278.48276.250.69336.94330-13.0642-13.06427.5-0.98276.5173-6.254.2204-2.0296

906.02446.02448.4375-6.38002.05755.625-13.5268-7.90180-6.0244-6.02441.56256.38007.9425-1.875-11.9931-13.8681

Hoja5PORTICOS

[F]=0[u]=u1z-16.5u1y3.781301x5.5u2z-8.25u2y7.562502x0u3z-7.7988u3y-23.359403x3u4z-17.0156u4y23.396504x3.4 Calculando la submatriz de rigidez en coordenadas locales y globalesElemento 1

E1EA1II1IL6.05032

raz0.1653EIraax0.0542EIrabx0.1639EIrbax0.1639EIr11x0.6611EIr22x0.6611EIr12x0.3306EIr21x0.3306EI3.5-3.6 Submatriz de rigidez en coordenadas locales y globales

10.16530.00000.0000Angulo=65.37643521391.1410K11=0.00000.05420.1639A=0.1653seno=0.90910.00000.16390.6611B=0.0542coseno=0.4167C=0.661110.07350.0421-0.1490D=0.1639K11=0.04210.14600.0683E=0.1639-0.14900.06830.6611

1-0.16530.00000.0000Angulo=65.37643521391.1410K12=0.0000-0.05420.1639A=-0.1653seno=0.90910.0000-0.16390.3306B=-0.0542coseno=0.4167C=0.33061-0.0735-0.0421-0.1490D=0.1639K12=-0.0421-0.14600.0683E=-0.16390.1490-0.06830.3306

1-0.16530.00000.0000Angulo=65.37643521391.1410K21=0.0000-0.0542-0.1639A=-0.1653seno=0.90910.00000.16390.3306B=-0.0542coseno=0.4167C=0.33061-0.0735-0.04210.1490D=-0.1639K21=-0.0421-0.1460-0.0683E=0.1639-0.14900.06830.3306

10.16530.00000.0000Angulo=65.37643521391.1410K22=0.00000.0542-0.1639A=0.1653seno=0.90910.0000-0.16390.6611B=0.0542coseno=0.4167C=0.661110.07350.04210.1490D=-0.1639K22=0.04210.1460-0.0683E=-0.16390.1490-0.06830.6611

Elemento 2

E1EA1II1IL6.05032

raz0.1653EIraax0.0542EIrabx0.1639EIrbax0.1639EIr11x0.6611EIr22x0.6611EIr12x0.3306EIr21x0.3306EI3.5-3.6 Submatriz de rigidez en coordenadas locales y globales

20.16530.00000.0000Angulo=114.62356478612.0006K11=0.00000.05420.1639A=0.1653seno=0.90910.00000.16390.6611B=0.0542coseno=-0.4167C=0.661120.0735-0.0421-0.1490D=0.1639K11=-0.04210.1460-0.0683E=0.1639-0.1490-0.06830.6611

2-0.16530.00000.0000Angulo=114.62356478612.0006K12=0.0000-0.05420.1639A=-0.1653seno=0.90910.0000-0.16390.3306B=-0.0542coseno=-0.4167C=0.33062-0.07350.0421-0.1490D=0.1639K12=0.0421-0.1460-0.0683E=-0.16390.14900.06830.3306

2-0.16530.00000.0000Angulo=114.62356478612.0006K21=0.0000-0.0542-0.1639A=-0.1653seno=0.90910.00000.16390.3306B=-0.0542coseno=-0.4167C=0.33062-0.07350.04210.1490D=-0.1639K21=0.0421-0.14600.0683E=0.1639-0.1490-0.06830.3306

20.16530.00000.0000Angulo=114.62356478612.0006K22=0.00000.0542-0.1639A=0.1653seno=0.90910.0000-0.16390.6611B=0.0542coseno=-0.4167C=0.661120.0735-0.04210.1490D=-0.1639K22=-0.04210.14600.0683E=-0.16390.14900.06830.66113.4 Calculando la submatriz de rigidez en coordenadas locales y globalesElemento 3

E1EA1II1IL3.3001

raz0.3030EIraax0.3339EIrabx0.5509EIrbax0.5509EIr11x1.2121EIr22x1.2121EIr12x0.6060EIr21x0.6060EI3.5-3.6 Submatriz de rigidez en coordenadas locales y globales

30.30300.00000.0000Angulo=65.37643521391.1410K11=0.00000.33390.5509A=0.3030seno=0.90910.00000.55091.2121B=0.3339coseno=0.4167C=1.212130.3285-0.0117-0.5008D=0.5509K11=-0.01170.30840.2295E=0.5509-0.50080.22951.2121

3-0.30300.00000.0000Angulo=65.37643521391.1410K12=0.0000-0.33390.5509A=-0.3030seno=0.90910.0000-0.55090.6060B=-0.3339coseno=0.4167C=0.60603-0.32850.0117-0.5008D=0.5509K12=0.0117-0.30840.2295E=-0.55090.5008-0.22950.6060

3-0.30300.00000.0000Angulo=65.37643521391.1410K21=0.0000-0.3339-0.5509A=-0.3030seno=0.90910.00000.55090.6060B=-0.3339coseno=0.4167C=0.60603-0.32850.01170.5008D=-0.5509K21=0.0117-0.3084-0.2295E=0.5509-0.50080.22950.6060

30.30300.00000.0000Angulo=65.37643521391.1410K22=0.00000.3339-0.5509A=0.3030seno=0.90910.0000-0.55091.2121B=0.3339coseno=0.4167C=1.212130.3285-0.01170.5008D=-0.5509K22=-0.01170.3084-0.2295E=-0.55090.5008-0.22951.2121

3.4 Calculando la submatriz de rigidez en coordenadas locales y globalesElemento 4

E1EA1II1IL3.3001

raz0.3030EIraax0.3339EIrabx0.5509EIrbax0.5509EIr11x1.2121EIr22x1.2121EIr12x0.6060EIr21x0.6060EI3.5-3.6 Submatriz de rigidez en coordenadas locales y globales

40.30300.00000.0000Angulo=114.62356478612.0006K11=0.00000.33390.5509A=0.3030seno=0.90910.00000.55091.2121B=0.3339coseno=-0.4167C=1.212140.32850.0117-0.5008D=0.5509K11=0.01170.3084-0.2295E=0.5509-0.5008-0.22951.2121

44-0.30300.00000.0000Angulo=114.62356478612.0006K12=0.0000-0.33390.5509A=-0.3030seno=0.90910.0000-0.55090.6060B=-0.3339coseno=-0.4167C=0.60604-0.3285-0.0117-0.5008D=0.5509K12=-0.0117-0.3084-0.2295E=-0.55090.50080.22950.6060

4-0.30300.00000.0000Angulo=114.62356478612.0006K21=0.0000-0.3339-0.5509A=-0.3030seno=0.90910.00000.55090.6060B=-0.3339coseno=-0.4167C=0.60604-0.3285-0.01170.5008D=-0.5509K21=-0.0117-0.30840.2295E=0.5509-0.5008-0.22950.6060

40.30300.00000.0000Angulo=114.62356478612.0006K22=0.00000.3339-0.5509A=0.3030seno=0.90910.0000-0.55091.2121B=0.3339coseno=-0.4167C=1.212140.32850.01170.5008D=-0.5509K22=0.01170.30840.2295E=-0.55090.50080.22951.2121

3.4 Calculando la submatriz de rigidez en coordenadas locales y globalesElemento 5

E1EA1II1IL8.25

raz0.1212EIraax0.0214EIrabx0.0882EIrbax0.0882EIr11x0.4848EIr22x0.4848EIr12x0.2424EIr21x0.2424EI3.5-3.6 Submatriz de rigidez en coordenadas locales y globales

50.12120.00000.0000Angulo=00.0000K11=0.00000.02140.0882A=0.1212seno=0.00000.00000.08820.4848B=0.0214coseno=1.0000C=0.484850.12120.00000.0000D=0.0882K11=0.00000.02140.0882E=0.08820.00000.08820.4848

5-0.12120.00000.0000Angulo=00.0000K12=0.0000-0.02140.0882A=-0.1212seno=0.00000.0000-0.08820.2424B=-0.0214coseno=1.0000C=0.24245-0.12120.00000.0000D=0.0882K12=0.0000-0.02140.0882E=-0.08820.0000-0.08820.2424

5-0.12120.00000.0000Angulo=00.0000K21=0.0000-0.0214-0.0882A=-0.1212seno=0.00000.00000.08820.2424B=-0.0214coseno=1.0000C=0.24245-0.12120.00000.0000D=-0.0882K21=0.0000-0.0214-0.0882E=0.08820.00000.08820.2424

50.12120.00000.0000Angulo=00.0000K22=0.00000.0214-0.0882A=0.1212seno=0.00000.0000-0.08820.4848B=0.0214coseno=1.0000C=0.484850.12120.00000.0000D=-0.0882K22=0.00000.0214-0.0882E=-0.08820.0000-0.08820.48483.4 Calculando la submatriz de rigidez en coordenadas locales y globalesElemento 6

E1EA1II1IL5.5

raz0.1818EIraax0.0721EIrabx0.1983EIrbax0.1983EIr11x0.7273EIr22x0.7273EIr12x0.3636EIr21x0.3636EI3.5-3.6 Submatriz de rigidez en coordenadas locales y globales

60.18180.00000.0000Angulo=00.0000K11=0.00000.07210.1983A=0.1818seno=0.00000.00000.19830.7273B=0.0721coseno=1.0000C=0.727360.18180.00000.0000D=0.1983K11=0.00000.07210.1983E=0.19830.00000.19830.7273

6-0.18180.00000.0000Angulo=00.0000K12=0.0000-0.07210.1983A=-0.1818seno=0.00000.0000-0.19830.3636B=-0.0721coseno=1.0000C=0.36366-0.18180.00000.0000D=0.1983K12=0.0000-0.07210.1983E=-0.19830.0000-0.19830.3636

6-0.18180.00000.0000Angulo=00.0000K21=0.0000-0.0721-0.1983A=-0.1818seno=0.00000.00000.19830.3636B=-0.0721coseno=1.0000C=0.36366-0.18180.00000.0000D=-0.1983K21=0.0000-0.0721-0.1983E=0.19830.00000.19830.3636

60.18180.00000.0000Angulo=00.0000K22=0.00000.0721-0.1983A=0.1818seno=0.00000.0000-0.19830.7273B=0.0721coseno=1.0000C=0.727360.18180.00000.0000D=-0.1983K22=0.00000.0721-0.1983E=-0.19830.0000-0.19830.7273

ENSAMBLE DE LA MATRIZ DE RIGIDEZ GLOBAL

[K]=0.5103-0.01170.5008-0.18180.00000.0000-0.32850.01170.50080.00000.00000.0000-0.01170.3805-0.03120.0000-0.07210.19830.0117-0.3084-0.22950.00000.00000.00000.5008-0.03121.93940.0000-0.19830.3636-0.50080.22950.60600.00000.00000.0000-0.18180.00000.00000.51030.01170.50080.00000.00000.0000-0.3285-0.01170.50080.0000-0.0721-0.19830.01170.38050.03120.00000.00000.0000-0.0117-0.30840.22950.00000.19830.36360.50080.03121.93940.00000.00000.0000-0.5008-0.22950.6060-0.32850.0117-0.50080.00000.00000.00000.52320.0304-0.3518-0.12120.00000.00000.0117-0.30840.22950.00000.00000.00000.03040.47570.24940.0000-0.02140.08820.5008-0.22950.60600.00000.00000.0000-0.35180.24942.35810.0000-0.08820.24240.00000.00000.0000-0.3285-0.0117-0.5008-0.12120.00000.00000.5232-0.0304-0.35180.00000.00000.0000-0.0117-0.3084-0.22950.0000-0.0214-0.0882-0.03040.4757-0.24940.00000.00000.00000.50080.22950.60600.00000.08820.2424-0.3518-0.24942.3581OBTENCION DE LOS DESPLAZAMIENTOS Y GIROS GLOBALES[F]=[K] [u]

[u]=118.1625u1z-261.6188u1y-3.819301x80.1721u2z-230.3927u2y7.921402x80.5990u3z-184.2504u3y-36.418803x77.7028u4z-180.7846u4y16.390304xCALCULO DE DEFORMACINES EN COORDENADAS LOCALES Y ELMENTOS MECANICOSELEMENTO 1

Angulo=65.37643521391.1410seno=0.9091coseno=0.4167

[T]0.41670.90910000-0.90910.416700000010000000.41670.90910000-0.90910.41670000001[u] = [T][u1]1 [u]80.5990u3z1 [u]-133.9135-184.2504u3y-150.0385-36.418803x-36.4188118.1625u1z-188.5955-261.6188u1y-216.4220-3.819301x-3.8193

[K]0.165280514100-0.16528051410000.05418089950.163905890-0.05418089950.1639058900.163905890.66112205640-0.163905890.3305610282-0.1652805141000.1652805141000-0.0541808995-0.1639058900.0541808995-0.1639058900.163905890.33056102820-0.163905890.6611220564[F] = [K] [u][F]9.0379-2.9985-14.4591-9.03792.9985-3.6830ELEMENTO 2

Angulo=114.62356478612.0006seno=0.9091coseno=-0.4167

[T]-0.41670.90910000-0.9091-0.41670000001000000-0.41670.90910000-0.9091-0.41670000001[u] = [T][u1]2 [u]77.7028u4z2 [u]-196.7201-180.7846u4y4.687816.390304x16.390380.1721u2z-242.8460-230.3927u2y23.11267.921402x7.9214

[K]0.165280514100-0.16528051410000.05418089950.163905890-0.05418089950.1639058900.163905890.66112205640-0.163905890.3305610282-0.1652805141000.1652805141000-0.0541808995-0.1639058900.0541808995-0.1639058900.163905890.33056102820-0.163905890.6611220564[F] = [K] [u][F]7.62372.986610.4346-7.6237-2.98667.6351ELEMENTO 3

Angulo=65.37643521391.1410seno=0.9091coseno=0.4167

[T]0.41670.90910000-0.90910.416700000010000000.41670.90910000-0.90910.41670000001[u] = [T][u1]3 [u]0.000003 [u]0.00000.000000.00000.000000.000080.5990u3z-133.9135-184.2504u3y-150.0385-36.418803x-36.4188

[K]0.303020.000000.00000-0.303020.000000.000000.000000.333890.550930.00000-0.333890.550930.000000.550931.212080.00000-0.550930.60604-0.303020.000000.000000.303020.000000.000000.00000-0.33389-0.550930.000000.33389-0.550930.000000.550930.606040.00000-0.550931.21208[F] = [K] [u][F]40.578630.031760.5895-40.5786-30.031738.5182ELEMENTO 4

Angulo=114.62356478612.0006seno=0.9091coseno=-0.4167

[T]-0.41670.90910000-0.9091-0.41670000001000000-0.41670.90910000-0.9091-0.41670000001[u] = [T][u1]4 [u]0.000004 [u]0.00000.000000.00000.000000.000077.7028u4z-196.7201-180.7846u4y4.687816.390304x16.3903

[K]0.303020.000000.00000-0.303020.000000.000000.000000.333890.550930.00000-0.333890.550930.000000.550931.212080.00000-0.550930.60604-0.303020.000000.000000.303020.000000.000000.00000-0.33389-0.550930.000000.33389-0.550930.000000.550930.606040.00000-0.550931.21208[F] = [K] [u][F]59.61047.46477.3506-59.6104-7.464717.2838ELEMENTO 5

Angulo=00.0000seno=0.0000coseno=1.0000

[T]1.00000.000000000.00001.000000000010000001.00000.000000000.00001.00000000001[u] = [T][u1]5 [u]118.1625u1z5 [u]118.1625-261.6188u1y-261.6188-3.819301x-3.819380.1721u2z80.1721-230.3927u2y-230.39277.921402x7.9214

[K]0.121210.000000.00000-0.121210.000000.000000.000000.021370.088150.00000-0.021370.088150.000000.088150.484850.00000-0.088150.24242-0.121210.000000.000000.121210.000000.000000.00000-0.02137-0.088150.000000.02137-0.088150.000000.088150.242420.00000-0.088150.48485[F] = [K] [u][F]4.6049-0.3057-2.6841-4.60490.30570.1621ELEMENTO 6

Angulo=00.0000seno=0.0000coseno=1.0000

[T]1.00000.000000000.00001.000000000010000001.00000.000000000.00001.00000000001[u] = [T][u1]6 [u]118.1625u1z6 [u]118.1625-261.6188u1y-261.6188-3.819301x-3.819380.1721u2z80.1721-230.3927u2y-230.39277.921402x7.9214

[K]0.121210.000000.00000-0.121210.000000.000000.000000.021370.088150.00000-0.021370.088150.000000.088150.484850.00000-0.088150.24242-0.121210.000000.000000.121210.000000.000000.00000-0.02137-0.088150.000000.02137-0.088150.000000.088150.242420.00000-0.088150.48485[F] = [K] [u][F]4.6049-0.3057-2.6841-4.60490.30570.1621

FormatoEXAMEN PORTICOSALUMNO: RIVERA FERNNDEZ, ALEX ALCARIFORMULASraz00-raz000raaxrabx0-raaxrbax0rabxr11x0-rabxr12x(k')-raz00raz000-raax-rabx0raax-rbax0rbaxr21x0-rbaxr22x

raz00-raz00(k11)'0-raaxrabx(k12)'0-raaxrbax0rabxr11x0-rabxr12x

-raz00raz00(k21)'0-raax-rabx(k22)'0raax-rbax0rbaxr21x0-rbaxr22x

2. Matriz de las fuerzas laterales externas

[F]=10[u]=u1z-18.75u1y-23.437501x0u2z-18.75u2y23.437502x3. Calculando la submatriz de rigidez en coordenadas locales y globalesElemento 1

E1EA0.09II0.000675IL5

raz0.0180EIraax0.0001EIrabx0.0002EIrbax0.0002EIr11x0.0005EIr22x0.0005EIr12x0.0003EIr21x0.0003EICoordenadas localesCoordenadas globales

10.01800.00000.0000Angulo=901.5708K11=0.00000.00010.0002A=0.0180seno=1.00000.00000.00020.0005B=0.0001coseno=0.0000C=0.000510.00010.0000-0.0002D=0.0002K11=0.00000.01800.0000E=0.0002-0.00020.00000.0005

1-0.01800.00000.0000Angulo=901.5708K12=0.0000-0.00010.0002A=-0.0180seno=1.00000.0000-0.00020.0003B=-0.0001coseno=0.0000C=0.00031-0.0001-0.0000-0.0002D=0.0002K12=-0.0000-0.01800.0000E=-0.00020.0002-0.00000.0003

1-0.01800.00000.0000Angulo=901.5708K21=0.0000-0.0001-0.0002A=-0.0180seno=1.00000.00000.00020.0003B=-0.0001coseno=0.0000C=0.00031-0.0001-0.00000.0002D=-0.0002K21=-0.0000-0.0180-0.0000E=0.0002-0.00020.00000.0003

10.01800.00000.0000Angulo=901.5708K22=0.00000.0001-0.0002A=0.0180seno=1.00000.0000-0.00020.0005B=0.0001coseno=0.0000C=0.000510.00010.00000.0002D=-0.0002K22=0.00000.0180-0.0000E=-0.00020.0002-0.00000.0005

Elemento 2

E1EA0.18II0.0054IL7.5

raz0.0240EIraax0.0002EIrabx0.0006EIrbax0.0006EIr11x0.0029EIr22x0.0029EIr12x0.0014EIr21x0.0014EICoordenadas localesCoordenadas globales

20.02400.00000.0000Angulo=00.0000K11=0.00000.00020.0006A=0.0240seno=0.00000.00000.00060.0029B=0.0002coseno=1.0000C=0.002920.02400.00000.0000D=0.0006K11=0.00000.00020.0006E=0.00060.00000.00060.0029

2-0.02400.00000.0000Angulo=00.0000K12=0.0000-0.00020.0006A=-0.0240seno=0.00000.0000-0.00060.0014B=-0.0002coseno=1.0000C=0.00142-0.02400.00000.0000D=0.0006K12=0.0000-0.00020.0006E=-0.00060.0000-0.00060.0014

2-0.02400.00000.0000Angulo=00.0000K21=0.0000-0.0002-0.0006A=-0.0240seno=0.00000.00000.00060.0014B=-0.0002coseno=1.0000C=0.00142-0.02400.00000.0000D=-0.0006K21=0.0000-0.0002-0.0006E=0.00060.00000.00060.0014

20.02400.00000.0000Angulo=00.0000K22=0.00000.0002-0.0006A=0.0240seno=0.00000.0000-0.00060.0029B=0.0002coseno=1.0000C=0.002920.02400.00000.0000D=-0.0006K22=0.00000.0002-0.0006E=-0.00060.0000-0.00060.00293.4 Calculando la submatriz de rigidez en coordenadas locales y globalesElemento 3

E1EA0.09II0.000675IL3

raz0.0300EIraax0.0003EIrabx0.0005EIrbax0.0005EIr11x0.0009EIr22x0.0009EIr12x0.0005EIr21x0.0005EICoordenadas localesCoordenadas globales

30.03000.00000.0000Angulo=901.5708K11=0.00000.00030.0005A=0.0300seno=1.00000.00000.00050.0009B=0.0003coseno=0.0000C=0.000930.00030.0000-0.0005D=0.0005K11=0.00000.03000.0000E=0.0005-0.00050.00000.0009

3-0.03000.00000.0000Angulo=901.5708K12=0.0000-0.00030.0005A=-0.0300seno=1.00000.0000-0.00050.0005B=-0.0003coseno=0.0000C=0.00053-0.0003-0.0000-0.0005D=0.0005K12=-0.0000-0.03000.0000E=-0.00050.0005-0.00000.0005

3-0.03000.00000.0000Angulo=901.5708K21=0.0000-0.0003-0.0005A=-0.0300seno=1.00000.00000.00050.0005B=-0.0003coseno=0.0000C=0.00053-0.0003-0.00000.0005D=-0.0005K21=-0.0000-0.0300-0.0000E=0.0005-0.00050.00000.0005

30.03000.00000.0000Angulo=901.5708K22=0.00000.0003-0.0005A=0.0300seno=1.00000.0000-0.00050.0009B=0.0003coseno=0.0000C=0.000930.00030.00000.0005D=-0.0005K22=0.00000.0300-0.0000E=-0.00050.0005-0.00000.0009

4. ENSAMBLE DE LA MATRIZ DE RIGIDEZ GLOBAL

[K]=0.02410.00000.0002-0.02400.00.00.00000.01820.00060.0-0.00020.00060.00020.00060.00340.0-0.00060.0014-0.02400.00.00.02430.00000.00050.0-0.0002-0.00060.00000.0302-0.00060.00.00060.00140.0005-0.00060.0038

5. OBTENCION DE LOS DESPLAZAMIENTOS Y GIROS GLOBALES[F]=[K] [u]

[u]=23,114.12u1z-931.08u1y-11,191.7601x22,684.32u2z-691.35u2y7,799.9402x6. CALCULO DE DEFORMACINES EN COORDENADAS LOCALES Y ELEMENTOS MECANICOSELEMENTO 1

Angulo=901.5708seno=1.0000coseno=0.0000

[T]0.001.000.00.00.00.0-1.000.000.00.00.00.00.00.01.000.00.00.00.00.00.00.001.000.00.00.00.0-1.000.000.00.00.00.00.00.01.00[u] = [T][u1]1 [u]0.001 [u]0.00.000.00.000.023,114.12u1z-931.08-931.08u1y-23,114.12-11,191.7601x-11,191.76

[K]0.020.00.0-0.020.00.00.00.000.000.0-0.000.000.00.000.000.0-0.000.00-0.020.00.00.020.00.00.0-0.00-0.000.00.00-0.000.00.000.000.0-0.000.00[F] = [K] [u]1 [F]16.76-0.320.72-16.760.32-2.30ELEMENTO 2

Angulo=00.0000seno=0.0000coseno=1.0000

[T]1.000.00.00.00.00.00.01.000.00.00.00.00.00.01.000.00.00.00.00.00.01.000.00.00.00.00.00.01.000.00.00.00.00.00.01.00[u] = [T][u1]2 [u]23,114.12u1z2 [u]23114.124823117.08-931.08u1y-931.0827-931.08-11,191.7601x-11191.7592-11188.1422,684.32u2z22684.321922687.31-691.35u2y-691.3504-691.357,799.9402x7799.94037796.22

0.02400-0.02400[K]0.020.00.0-0.020.00.010.315269695500.00015360.0005760-0.00015360.0005760.00.000.000.0-0.000.00-1.990510583500.0005760.002880-0.0005760.001440.00.000.000.0-0.000.00-21.1384382741-0.024000.02400-0.020.00.00.020.00.0-10.31526969550-0.0001536-0.00057600.0001536-0.0005760.0-0.00-0.000.00.00-0.001.990510583500.0005760.001440-0.0005760.002880.00.000.000.0-0.000.006.209608898[F] = [K] [u]2 [F]10.32-1.99-21.14-10.321.996.21

ELEMENTO 3

Angulo=901.5708seno=1.0000coseno=0.0000

[T]0.001.000.00.00.00.0-1.000.000.00.00.00.00.00.01.000.00.00.00.00.00.00.001.000.00.00.00.0-1.000.000.00.00.00.00.00.01.00[u] = [T][u1]3 [u]0.003 [u]0.00.000.00.000.022,684.32u2z-691.35-691.35u2y-22,684.327,799.9402x7,799.94

[K]0.030.00.0-0.030.00.00.00.000.000.0-0.000.000.00.000.000.0-0.000.00-0.030.00.00.030.00.00.0-0.00-0.000.00.00-0.000.00.000.000.0-0.000.00[F] = [K] [u]3 [F]20.7410.3213.72-20.74-10.3217.237. VERIFICACION DEL EQUILIBRIO

ELEMENTOFASE 1FASE 2EFECTIVA

1016.7616.760-0.32-0.3200.720.720-16.76-16.7600.320.320-2.30-2.30

2010.3210.3218.75-1.9916.7623.44-21.142.300-10.32-10.3218.751.9920.74-23.446.21-17.23

3020.7420.74010.3210.32013.7213.720-20.74-20.740-10.32-10.32017.2317.23