Metodo de Rigides( en Vigas y Poricos)[1]

VIGAS 1MATRIZ RIGIDES (solo por flexion)

I.

1. Sistemas Adoptados.

I1 = I.I2 = 2I.

2. Matriz Rigides de los Elementos [ S ][ S1 ] =S11S12S21S22[ S ] =[S1]00[S2][ S2 ] =S11S12S21S22

0000[ S ] =360000840048(4*4)

3. Matriz de Compatibilidad [ B ] (ncl * ncg )

-0.210[ B ] =-0.2010.2010.200(4*3)

4. Matriz { f. } (M.E.P)

0{ f. } =8.438-5.6255.625(4*1)

5. Matriz { P }

{ P } = { P1 } + { P2 } + { P3 }

013.5P1 =0P2 =000

{ P3 } = [ B ]T { -f. }

-0.2-0.20.20.2[ B ] T =10000110(3*4)

15.18761.6876{ P } =0{ P3 } =0-2.813(3*1)-2.813

6. Matriz [ K ][ K ] = [ B ]T [ S ] [ B ]-0.6-1.22.42.4[ B ]T[S] =00003684(3*4)1.32-0.61.2[ K ] =0000.6314(3*3)7. Matriz { X }(Desplazamiento de coordenadas Globales){ X } = [ K ]-1 { P } 1.3200.6[ K ]-1 = -0.6031.2014(3*3)

18.359832{ X } =-17.55156-21.15688(3*1)

8. Matriz { Fx } { Fx } = [ S ] [ B ] { X } 000[ S][B ] =-1.8362.4082.404(4*3)0{ Fx } =-212.6436576-125.1914432-40.5639232(4*1)

9. Matriz { F } { F } = { f. } + { Fx }0{ F } =-204.2056576-130.8164432-34.9389232

VIGAS 2MATRIZ RIGIDES (solo por flexion)2. Matriz Rigides de los Elementos [ S ]2100012000[ S ] =002100012000000.5(5*5)3. Matriz de Compatibilidad [ B ] (ncl * ncg )-10-11[ B ] =11[B]T=-1-11111001100105*2(2*5)4. Matriz { f. } (M.E.P)0{ f. } =000(4*1)5. Matriz { P } { P } =20(2*1)6. Matriz [ K ][B]T[S] =-3-3330.512210(2*5)[ K ] = [ B ]T [ S ] [ B ][ K ] =12.5004(2*2)7. Matriz { X }(Desplazamiento de coordenadas Globales){ X } = [ K ]-1 { P } [ K ]-1 =0.08000.25(2*2)

[ K ] =0.160(2*1)

8. Matriz { Fx } { Fx } = [ S ] [ B ] { X } -31-32[S][B] =32310.50(5*2)

-0.48{ Fx } =-0.480.480.480.08(5*1)

9. Matriz { F } { F } = { f. } + { Fx }-0.48-0.48{ F } =0.480.480.08(5*1)esfuerzo en el tirante0.1810831489(tn/cm2)

PORTICOS 1MATRIZ RIGIDES EN PORTICOS

2. Matriz Rigides de los Elementos [ S ]

10.500000.510000[ S] = 000.80.400000.40.80000000.5710.28600000.2860.571(6*6)


00-0.2510-0.25[ B ] =10001001-0.14300-0.143(6*3)

4. Matriz { f. } (M.E.P)011000[ B ]T =0001100-0.25-0.2500-0.143-0.143{ f. } =0-4.174.17006*1

5. Matriz { P } 004.17{P1} =5{P2} =0{ P } =0.8310616

{ P3 } = [ B ]T { -f. }4.17{ P3 }=-4.170

6. Matriz [ K ]

[ K ] = [ B ]T [ S ] [ B ]

0.510.80.400000.40.80.5710.286-0.375-0.37500-0.122551-0.122551(3*6)

1.80.4-0.375[ K ] =0.41.371-0.122551(EI)0.8776591698-0.13028350921.4071282718-0.375-0.1225510.222549586(3*3)-0.13028350920.7864963120.21356855541.40712827180.21356855546.98202216367. Matriz { X }(Desplazamiento de coordenadas Globales){ X } = [ K ]-1 { P }

26.0657557735{ X } =3.52660659221/EI117.7573414114(3*1)

8. Matriz { Fx } { Fx } = [ S ] [ B ] { X }

0.50-0.37510-0.375[S][B] =0.80.400.40.8000.571-0.12255100.286-0.122551(6*3)

-31.1261251425-18.0932472557{ Fx } =22.263247255713.2475875832-12.4175875832-13.42267046196*1

9. Matriz { F } { F } = { f. } + { Fx }-31.1261251425-18.0932472557{ F } =18.093247255717.4175875832-12.4175875832-13.4226704619

S

PORTICO 2

MATRIZ RIGIDES EN PORTICOS


0.6660.33300000.3330.6660000[ S] = 002100(tn/m)001200(EI)000024000000(6*6)


0.167000.16710[ B ] =010(tn/m)(EI)0010.33301000(6*3)

4. Matriz { f. } (M.E.P)0.1670.167000.3330[ B ]T =0110000000110{ f. } =0-4(tn-m)4006*1

5. Matriz { P } 000{P1} =0{P2} =0{ P } =400-4

{ P3 } = [ B ]T { -f. }0{ P3 }=4-4

6. Matriz [ K ]

[ K ] = [ B ]T [ S ] [ B ]

0.1668330.166833000.6661.3320.3330.6662100001224(3*6)

0.2775002220.1668330.666[ K ] =0.1668332.6661(EI)6.0019983256-0.0008272622-0.99912590570.66614(3*3)-0.00082726220.4139073988-0.1033391105-0.9991259057-0.10333911050.4421892409

7. Matriz { X }(Desplazamiento de coordenadas Globales)

{ X } = [ K ]-1 { P }

3.9931945739{ X } =12.0689860373EI-2.1821134059(3*1)

8. Matriz { Fx }

{ Fx } = [ S ] [ B ] { X }

0.1668330.33300.1668330.6660[S][B] =0210120.66602000(6*3)

1.35516898082.0441413312{ Fx } =1.9558586688(tn/m)-2.2952407745-1.704759225506*1

9. Matriz { F } { F } = { f. } + { Fx }

1.35516898082.0441413312{ F } =-2.0441413312(tn/m)1.7047592255-1.70475922550(6*1)

EXAMEN FINAL



0.890.4400000.440.890000[ S] = 000.7140.64700(tn/m)000.6470.71400(EI)00000.6470.32400000.3240.647(6*6)


00-0.22210-0.222[ B ] =100.179(tn/m)(EI)010.17901-0.16200-0.162(6*3)

4. Matriz { f. } (M.E.P)011000[ B ]T =0001100-0.222-0.2220.1790.179-0.162-0.162{ f. } =0-3.92(tn-m)3.92006*1

5. Matriz { P } 003.92{P1} =5{P2} =0{ P } =1.0882.2510.25

{ P3 } = [ B ]T { -f. }3.92{ P3 }=-3.920

6. Matriz [ K ]

[ K ] = [ B ]T [ S ] [ B ]

0.440.890.7140.64700000.6470.7140.6470.324-0.29526-0.295260.2436190.243619-0.157302-0.157302(3*6)

1.6040.647-0.051641[ K ] =0.6471.3610.086317(EI)0.7912216352-0.39376415220.2779593035-0.0516410.0863170.26927689(3*3)-0.39376415220.9459643706-0.37874464890.2779593035-0.37874464893.8883626376


{ X } = [ K ]-1 { P }

5.5254063865{ X } =1-4.4040466077EI40.5362732845(3*1)

8. Matriz { Fx }

{ Fx } = [ S ] [ B ] { X }

0.440-0.295260.890-0.29526[S][B] =0.7140.6470.2436190.6470.7140.24361900.647-0.15730200.324-0.157302(6*3)

-9.5375612399-7.051128366{ Fx } =10.971128366(tn/m)10.3058550154-9.2258550154-7.80334796116*1

9. Matriz { F } { F } = { f. } + { Fx }

-9.5375612399-7.051128366{ F } =7.051128366(tn/m)14.2258550154-9.2258550154-7.8033479611(6*1)

Hoja1



0.9230.4610000000.4610.923000000[ S] = 000.80.40000(tn/m)000.40.80000(EI)00000.80.40000000.40.800(6*6)0000000.9230.4610000000.4610.923


0000.1541000.154[ B ] =100-0.2(tn/m)(EI)001-0.2001-0.2010-0.2(6*3)0100.1540000.154

4. Matriz { f. } (M.E.P)01100000[ B ]T =00000110000011000{ f. } =00.1540.154-0.2-0.2-0.2-0.20.1540.1544*80(tn-m)0006*1008*1

5. Matriz { P } 000{P1} =0{P2} =0{ P } =000020020{ P3 } = [ B ]T { -f. }0{ P3 }=000

6. Matriz [ K ]

[ K ] = [ B ]T [ S ] [ B ]

0.4610.9230.80.4000000000.40.80.9230.461000.40.80.80.4000.2131360.213136-0.24-0.24-0.24-0.240.2131360.213136

1.72300.4-0.0268640.64076414920.0603810964-0.2845526677-0.3642211877K01.7230.4-0.0268640.06038109640.6407641492-0.2845526677-0.36422118770.40.41.6-0.48-0.2845526677-0.28455266771.35794067281.9688811299-0.026864-0.026864-0.480.323291776-0.3642211877-0.36422118771.96888112995.955901787


{ X } = [ K ]-1 { P }

-7.2844237536-7.2844237536{ X } =139.3776225987EI119.1180357398

8. Matriz { Fx }

{ Fx } = [ S ] [ B ] { X } 0.461000.2131360.923000.2131360.800.4-0.240.400.8-0.2400.40.8-0.24[S][B] =00.80.4-0.2400.92300.21313600.46100.213136

22.030222315118.6648185409-18.6648185409{ Fx } =0(tn/m)0-18.664818540918.66481854096*122.03022231519. Matriz { F } { F } = { f. } + { Fx }

22.030222315118.6648185409{ F } =-18.6648185409(tn/m)00-18.6648185409(6*1)18.664818540922.0302223151

Metodo de Rigides( en Vigas y Poricos)[1]

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