calculo de estructura de tipo cercha por el metodo matricial

7/26/2019 Calculo de Estructura de Tipo Cercha Por El Metodo Matricial

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SIN TOMAR E

DATOS :

E:

A:P.U. =

Barra

1

2

3

4

5

6

7

Barra 1

Dx1 Dy1 Dx2 Dy2

0.20! 0.44!432 "0.20! "0.44!432 Dx1

#1"2= 0.44!432 0.71!10112 "0.44!432 "0.71!10112Dy1

"0.20! "0.44!432 0.20! 0.44!432 Dx2

"0.44!432 "0.71!10112 0.44!432 0.71!10112 Dy2

Barra 2

Dx1 Dy1 Dx3 Dy3

1 0 "1 0 Dx1

#1"3= 0 0 0 0 Dy1

"1 0 1 0 Dx3

0 0 0 0 Dy3

Barra 3

Dx2 Dy2 Dx3 Dy3

0.20! "0.44!432 "0.20! 0.44!432 Dx2#2"3= "0.44!432 0.71!10112 0.44!432 "0.71!10112Dy2

"0.20! 0.44!432 0.20! "0.44!432 Dx3

0.44!432 "0.71!10112 "0.44!432 0.71!10112 Dy3

Barra 4

Dx2 Dy2 Dx4 Dy4

1 0 "1 0 Dx2

1 3

24

5

1

2

3

4

5

6

7


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#2"4= 0 0 0 0 Dy2

"1 0 1 0 Dx4

0 0 0 0 Dy4

Barra 5

Dx3 Dy3 Dx4 Dy40.20! 0.44!432 "0.20! "0.44!432 Dx3

#3"4= 0.44!432 0.71!10112 "0.44!432 "0.71!10112Dy3

"0.20! "0.44!432 0.20! 0.44!432 Dx4

"0.44!432 "0.71!10112 0.44!432 0.71!10112 Dy4

Barra 6

Dx3 Dy3 Dx5 Dy5

1 0 "1 0 Dx3

#3"5= 0 0 0 0 Dy3

"1 0 1 0 Dx50 0 0 0 Dy5

Barra 7

Dx4 Dy4 Dx5 Dy5

0.20! "0.44!432 "0.20! 0.44!432 Dx4

#4"5= "0.44!432 0.71!10112 0.44!432 "0.71!10112Dy4

"0.20! 0.44!432 0.20! "0.44!432 Dx5

0.44!432 "0.71!10112 "0.44!432 0.71!10112 Dy5

MATRI$ ENSAMBLADA

Dx1 Dy1 Dx2 Dy2 Dx3

476534.613 174!35.3 "10!334.613 "174!35.3 "367200

174!35.3 27!!6.60! "174!35.3 "27!!6.60! 0

"10!334.613 "174!35.3 556!.226 0 "10!334.613

"174!35.3 "27!!6.60! 0 55!7!3.217 174!35.3

#= "367200 0 "10!334.613 174!35.3 !5306!.226

0 0 174!35.3 "27!!6.60! 0

0 0 "367200 0 "10!334.613

0 0 0 0 "174!35.30 0 0 0 "367200

0 0 0 0 0

D%&%r'()a)&% 0.00

MATRI$ REDUCIDA

Dx2 Dy2 Dx4 Dy4


3/25

556!.226 0 "367200 0 Dx2

#r%*= 0 55!7!3.217 0 0 Dy2

"367200 0 556!.226 0 Dx4

0 0 0 55!7!3.217 Dy4

MATRI$ REEDUCIDA IN+ERTIDA , DESPLA$AMIENTOS

Dx2 Dy2 Dx4 Dy4

2.1E"06 0.00E-00 1.76E"06 0.00E-00 Dx2

#r%* ()= 0.00E-00 1.7!E"06 0.00E-00 0.00E-00 Dy2

1.76E"06 0.00E-00 2.1E"06 0.00E-00 Dx4

0.00E-00 0.00E-00 0.00E-00 1.7!E"06 Dy4

%/%r/ %) arra/

.0!7E"006

1"2= 3!231.222 0.52!!!!4 0.47!!3 0 =

0

1"3= 367200 1 0 0 =

".10E"006

2"3= 3!231.222 0.52!!!!4 "0.47!!3 0 =

5.2462E"006

2"4= 367200 1 0 0 =

1.4056E"005

3"4= 3!231.222 0.52!!!!4 0.47!!3 0 =

0

3"5= 367200 1 0 0 =

"1.406E"005


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4"5= 3!231.222 0.52!!!!4 "0.47!!3 0 =

TOMANDO EN CUENTA EL PESO PROPIO CARA LIN. 0.7074!

BARRA 1 D1 D,1 D2 D,2

0.20! 0.44!432 "0.20! "0.44!432 D1

#1"2= 0.44!432 0.71!10112 "0.44!432 "0.71!10112D,1

"0.20! "0.44!432 0.20! 0.44!432 D2

"0.44!432 "0.71!10112 0.44!432 0.71!10112 D,2

BARRA 2

D1 D,1 D3 D,3

1 0 "1 0 D1

#1"3= 0 0 0 0 D,1

"1 0 1 0 D30 0 0 0 D,3

BARRA 3

D2 D,2 D3 D,3

0.20! "0.44!432 "0.20! 0.44!432 D2

#2"3= "0.44!432 0.71!10112 0.44!432 "0.71!10112D,2

"0.20! 0.44!432 0.20! "0.44!432 D3

0.44!432 "0.71!10112 "0.44!432 0.71!10112D,3

BARRA 4

D2 D,2 D4 D,4

1 0 "1 0 D2

#2"4= 0 0 0 0 D,2

"1 0 1 0 D4

0 0 0 0 D,4

BARRA 5

D3 D,3 D4 D,4

0.20! 0.44!432 "0.20! "0.44!432 D3

#3"4= 0.44!432 0.71!10112 "0.44!432 "0.71!10112D,3

"0.20! "0.44!432 0.20! 0.44!432 D4"0.44!432 "0.71!10112 0.44!432 0.71!10112 D,4

BARRA 6

D3 D,3 D5 D,5

1 0 "1 0 D3

#3"5= 0 0 0 0 D,3

"1 0 1 0 D5

0 0 0 0 D,5


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BARRA 7

D4 D,4 D5 D,5

0.20! "0.44!432 "0.20! 0.44!432 D4

#4"5= "0.44!432 0.71!10112 0.44!432 "0.71!10112D,4

"0.20! 0.44!432 0.20! "0.44!432 D5

0.44!432 "0.71!10112 "0.44!432 0.71!10112D,5MATRI$ ENSAMBLADA

D1 D,1 D2 D,2 D3

476534.613 174!35.3 "10!334.613 "174!35.3 "367200

174!35.3 27!!6.60! "174!35.3 "27!!6.60! 0

"10!334.613 "174!35.3 556!.226 0 "10!334.613

"174!35.3 "27!!6.60! 0 55!7!3.217 174!35.3

"367200 0 "10!334.613 174!35.3 !5306!.226

#= 0 0 174!35.3 "27!!6.60! 0

0 0 "367200 0 "10!334.613

0 0 0 0 "174!35.30 0 0 0 "367200

0 0 0 0 0

DETERM. 0.00

MATRI$ REDUCIDA

Dx2 Dy2 Dx4 Dy4

556!.226 0 "367200 0 Dx2

0 55!7!3.217 0 0 Dy2

# r%*8 "367200 0 556!.226 0 Dx4

0 0 0 55!7!3.217 Dy4

MATRI$ IN+ERTIDA

Dx2 Dy2 Dx4 Dy4

2.112E"006 0 1.761!E"006 0 Dx2

# () 0 1.764E"006 0 0 Dy2

1.761!E"006 0 2.112E"006 0 Dx4

0 0 0 1.764E"006 Dy4


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N CUENTA EL PESO PROPIO

20400000 T9M2

0.0! M27.61 T9'3

Nudos Nudo (i) Nudo (j)

Xi Yi Xj Yj L1"2 0 0 2.5 4 4.716!!057

1"3 0 0 5 0 5

2"3 2.5 4 5 0 4.716!!057

2"4 2.5 4 7.5 4 5

3"4 5 0 7.5 4 4.716!!057

3"5 5 0 10 0 5

4"5 7.5 4 10 0 4.716!!057

Dx1 Dy1 Dx2 Dy2

10!334.612 174!35.3 "10!334.612 "174!35.3

#1"2= 174!35.305 27!!6.60! "174!35.305 "27!!6.60!

"10!334.613 "174!35.3 10!334.6127! 174!35.3

"174!35.3 "27!!6.60! 174!35.3047 27!!6.60!

Dx1 Dy1 Dx3 Dy3

367200 0 "367200 0

#1"3= 0 0 0 0

"367200 0 367200 0

0 0 0 0

Dx2 Dy2 Dx3 Dy3

10!334.612 "174!35.3 "10!334.612 174!35.3#2"3= "174!35.3 27!!6.60! 174!35.3047 "27!!6.60!

"10!334.613 174!35.3 10!334.6127! "174!35.3

174!35.305 "27!!6.60! "174!35.305 27!!6.60!

Dx2 Dy2 Dx4 Dy4

367200 0 "367200 0


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#2"4= 0 0 0 0

"367200 0 367200 0

0 0 0 0

Dx3 Dy3 Dx4 Dy410!334.612 174!35.3 "10!334.612 "174!35.3

#3"4= 174!35.305 27!!6.60! "174!35.305 "27!!6.60!

"10!334.613 "174!35.3 10!334.6127! 174!35.3

"174!35.3 "27!!6.60! 174!35.3047 27!!6.60!

Dx3 Dy3 Dx5 Dy5

367200 0 "367200 0

#3"5= 0 0 0 0

"367200 0 367200 00 0 0 0

Dx4 Dy4 Dx5 Dy5

10!334.612 "174!35.3 "10!334.612 174!35.3

#4"5= "174!35.3 27!!6.60! 174!35.3047 "27!!6.60!

"10!334.613 174!35.3 10!334.6127! "174!35.3

174!35.305 "27!!6.60! "174!35.305 27!!6.60!

Dy3 Dx4 Dy4 Dx5 Dy5

0 0 0 0 0 Dx1

0 0 0 0 0 Dy1

174!35.3 "367200 0 0 0 Dx2

"27!!6.60! 0 0 0 0 Dy2

0 "10!334.613 "174!35.3 "367200 0 Dx3

55!7!3.217 "174!35.3 "27!!6.60! 0 0 Dy3

"174!35.3 556!.226 0 "10!334.613 174!35.3047 Dx4

"27!!6.60! 0 55!7!3.2175 174!35.3 "27!!6.607 Dy40 "10!334.613 174!35.305 476534.613 "174!35.305Dx5

0 174!35.3 "27!!6.60! "174!35.3 27!!6.6075 Dy5


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%ra/ D%/;


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"7.450E"006 = "2.!0 T COMPRESION

T9'

D1 D,1 D2 D,2

10!334.612 174!35.3 "10!334.612 "174!35.3

#1"2= 174!35.305 27!!6.60! "174!35.305 "27!!6.60!

"10!334.613 "174!35.3 10!334.6127! 174!35.3

"174!35.3 "27!!6.60! 174!35.3047 27!!6.60!

D1 D,1 D3 D,3

367200 0 "367200 0

#1"3= 0 0 0 0

"367200 0 367200 00 0 0 0

D2 D,2 D3 D,3

10!334.612 "174!35.3 "10!334.612 174!35.3

#2"3= "174!35.3 27!!6.60! 174!35.3047 "27!!6.60!

"10!334.613 174!35.3 10!334.6127! "174!35.3

174!35.305 "27!!6.60! "174!35.305 27!!6.60!

D2 D,2 D4 D,4

367200 0 "367200 0

#2"4= 0 0 0 0

"367200 0 367200 0

0 0 0 0

D3 D,3 D4 D,4

103146.0674 165033.70 "103146.0674 "165033.70

#3"4= 165033.707! 264053.!33 "165033.707! "264053.!33

"103146.067 "165033.70 103146.06742 165033.70"165033.70 "264053.!33 165033.7077 264053.!33

D3 D,3 D5 D,5

3!231.2215 0 "3!231.2215 0

#3"5= 0 0 0 0

"3!231.222 0 3!231.22154 0

0 0 0 0


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D4 D,4 D5 D,5

10!334.612 "174!35.3 "10!334.612 174!35.3

#4"5= "174!35.3 27!!6.60! 174!35.3047 "27!!6.60!

"10!334.613 174!35.3 10!334.6127! "174!35.3

174!35.305 "27!!6.60! "174!35.305 27!!6.60!

+E

D,3 D4 D,4 D5 D,5

0 0 0 0 0 D1

0 0 0 0 0 D,1

174!35.3 "367200 0 0 0 D2

"27!!6.60! 0 0 0 0 D,2

0 "10!334.613 "174!35.3 "367200 0 D3

55!7!3.217 "174!35.3 "27!!6.60! 0 0 D,3

"174!35.3 556!.226 0 "10!334.613 174!35.3047 D4

"27!!6.60! 0 55!7!3.2175 174!35.3 "27!!6.607 D,40 "10!334.613 174!35.305 476534.613 "174!35.305D5

0 174!35.3 "27!!6.60! "174!35.3 27!!6.6075 D,5

DE$PLA$AMIENTOS

"MEP D

0 Dx2 .0!7E"006 Dx2 '

"5.105!4! Dy2 "!.1211E"006 Dy2 '

5 Dx4 1.4056E"005 Dx4 '

"!.22!3! Dy4 "1.7547E"005 Dy4 '


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l mE A E*A/L os s!"

20400000 0.0! 3!231.221533 0.52!!!!4 0.47!!3

20400000 0.0! 367200 1 0

20400000 0.0! 3!231.221533 0.52!!!!4 "0.47!!3

20400000 0.0! 367200 1 0

20400000 0.0! 3!231.221533 0.52!!!!4 0.47!!3

20400000 0.0! 367200 1 0

20400000 0.0! 3!231.221533 0.52!!!!4 "0.47!!3

Dx1

Dy1

Dx2

Dy2

Dx1

Dy1

Dx3

Dy3

Dx2Dy2

Dx3

Dy3

Dx2


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Dy2

Dx4

Dy4

Dx3

Dy3

Dx4

Dy4

Dx3

Dy3

Dx5Dy5

Dx4

Dy4

Dx5

Dy5

%ra/ DESPLA$AMIENTOS REACCIONES

D =#D

0 Dx1 0 Dx1 "0.!6 T Dx1

0 Dy1 0 Dy1 "1.54 T Dy1

0 Dx2 .0!67E"006 Dx2 0.00 T Dx2

0 Dy2 0 Dy2 0.00 T Dy2

0 Dx3 0 Dx3 "2.50 T Dx3

0 Dy3 0 Dy3 "0.!2 T Dy3

5 Dx4 1.4055!7E"005 Dx4 5.00 T Dx4

0 Dy4 0 Dy4 0.00 T Dy40 Dx5 0 Dx5 "1.54 T Dx5

0 Dy5 0 Dy5 2.46 T Dy5


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EP D

D1 0.00 D1 0 D1 0

D,1 0.00 D,1 1.66612 D,1 0

D2 0.00 D2 0 D2 .0!7E"006

D,2 0.00 D,2 1.66612 D,2 "!.121E"006

EP D

D1 0.00 D1 0 D1 .0!7E"006

D,1 0.00 D,1 6.76725 D,1 "!.121E"006

D3 0.00 D3 0 D3 0D,3 0.00 D,3 6.76725 D,3 0

EP D

D2 0.00 D2 0 D2 .0!7E"006

D,2 0.00 D,2 1.66612 D,2 "!.121E"006

D3 0.00 D3 0 D3 0

D,3 0.00 D,3 1.66612 D,3 0

EP D

D2 0.00 D2 0 D2 .0!7E"006

D,2 0.00 D,2 1.76725 D,2 "!.121E"006

D4 5.00 D4 0 D4 1.4056E"005

D,4 0.00 D,4 1.76725 D,4 "1.755E"005

EP D

D3 5.00 D3 0 D3 0

D,3 0.00 D,3 6.35602 D,3 0

D4 0.00 D4 0 D4 1.4056E"005D,4 0.00 D,4 6.35602 D,4 "1.755E"005

EP D

D3 0.00 D3 0 D3 0

D,3 0.00 D,3 1.76725 D,3 0

D5 0.00 D5 0 D5 0

D,5 0.00 D,5 1.76725 D,5 0


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EP D

D4 0.00 D4 0 D4 1.4056E"005

D,4 0.00 D,4 1.66612 D,4 "1.755E"005

D5 0.00 D5 0 D5 0

D,5 0.00 D,5 1.66612 D,5 0

CTOR UER$AS EMPOTRAMIENTO PERECTO

MEP "MEP

0 D1 0 D1 0 D1

0 D,1 .44 D,1 ".437337 D,1

0 D2 0 D2 0 D2

0 D,2 5.105!4! D,2 "5.105!4! D,2

0 D3 0 D3 0 D3

0 D,3 16.5!1664 D,3 "16.5!1664 D,3

5 D4 0 D4 5 D4

0 D,4 !.22!3! D,4 "!.22!3! D,40 D5 0 D5 0 D5

0 D,5 3.437337 D,5 "3.437337 D,5


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#D =#D-MEP

D1 0.63 D1 0.63 T D1

D,1 1.01 D,1 2.6 T D,1

D2 "0.63 D2 "0.63 T D2

D,2 "1.01 D,2 0.66 T D,2

#D =#D-MEP

D1 3.23 D1 3.23 T D1

D,1 0.00 D,1 6.77 T D,1

D3 "3.23 D3 "3.23 T D3D,3 0.00 D,3 6.77 T D,3

#D =#D-MEP

D2 2.56 D2 2.56 T D2

D,2 "4.0! D,2 "2.43 T D,2

D3 "2.56 D3 "2.56 T D3

D,3 4.0! D,3 5.76 T D,3

#D =#D-MEP

D2 "1.!3 D2 "1.!3 T D2

D,2 0.00 D,2 1.77 T D,2

D4 1.!3 D4 1.!3 T D4

D,4 0.00 D,4 1.77 T D,4

#D =#D-MEP

D3 1.45 D3 1.45 T D3

D,3 2.31 D,3 .70 T D,3

D4 "1.45 D4 "1.45 T D4D,4 "2.31 D,4 4.07 T D,4

#D =#D-MEP

D3 0.00 D3 0.00 T D3

D,3 0.00 D,3 1.77 T D,3

D5 0.00 D5 0.00 T D5

D,5 0.00 D,5 1.77 T D,5


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#D =#D-MEP

D4 4.61 D4 4.61 T D4

D,4 "7.37 D,4 "5.70 T D,4

D5 "4.61 D5 "4.61 T D5

D,5 7.37 D,5 !.04 T D,5

DE$PLA$AMIENTOS REACCIONES

D #D =#D-MEP

0 D1 0.63240516 D1 0.632 D1

0 D,1 1.011425 D,1 !.44! D,1

.0!7E"006 D2 0 D2 0.000 D2

"!.1211E"006 D,2 "5.105!4! D,2 0.000 D,2

0 D3 "1.025!4063 D3 "1.026 D3

0 D,3 6.5466!65 D,3 23.13 D,3

1.4056E"005 D4 5 D4 5.000 D4

"1.7547E"005 D,4 "!.22!3! D,4 0.000 D,40 D5 "4.60646453 D5 "4.606 D5

0 D,5 7.37034325 D,5 10.0 D,5


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calculo de estructura de tipo cercha por el metodo matricial

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