Calculo de Celocias Metodo Matricial

7/26/2019 Calculo de Celocias Metodo Matricial

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SIN TOMAR E

DATOS :

E:

A:P.U. =

Barra

1

2

3

4

5

6

Barra 1

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 2

Dx1 Dy1 Dx4 Dy4

0.64 0.4! -0.64 -0.4! Dx1

1-4= 0.4! 0.36 -0.4! -0.36 Dy1

-0.64 -0.4! 0.64 0.4! Dx4

-0.4! -0.36 0.4! 0.36 Dy4

Barra 3

Dx2 Dy2 Dx4 Dy4

1 0 -1 0 Dx22-4= 0 0 0 0 Dy2

-1 0 1 0 Dx4

0 0 0 0 Dy4

Barra 4

Dx3 Dy3 Dx4 Dy4

0 0 0 0 Dx3

1 3

2 4

51

2

3

45

6


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3-4= 0 1 0 -1 Dy3

0 0 0 0 Dx4

0 -1 0 1 Dy4

Barra 5

Dx4 Dy4 Dx5 Dy50.64 -0.4! -0.64 0.4! Dx4

4-5= -0.4! 0.36 0.4! -0.36 Dy4

-0.64 0.4! 0.64 -0.4! Dx5

0.4! -0.36 -0.4! 0.36 Dy5

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

MATRI" ENSAMBLADA

Dx1 Dy1 Dx2 Dy2 Dx3

6201#1.501 15#503.!#3 0 0 -410166.33#

15#503.!#3 11!12#.$05 0 0 0

0 0 410166.33# 0 0

0 0 0 0 0

= -410166.33# 0 0 0 !20332.6#4

0 0 0 0 0

-210005.164 -15#503.!#3 -410166.33# 0 0

-15#503.!#3 -11!12#.$05 0 0 0

0 0 0 0 -410166.33#

0 0 0 0 0

D%&%r'()a)&% 0

MATRI" REDUCIDA

Dx4 Dy4 Dx5 Dy5!301#6.666 0 -210005.164 15#503.!#3 Dx4

r%*= 0 #!3144.25$ 15#503.!#3 -11!12#.$05Dy4

-210005.164 15#503.!#3 6201#1.501 -15#503.!#3 Dx5

15#503.!#3 -11!12#.$05 -15#503.!#3 11!12#.$05 Dy5

MATRI" REEDUCIDA IN+ERTIDA , DESPLA"AMIENTOS

Dx4 Dy4 Dx5 Dy5


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1.#2E-06 -4.06E-0# 1.34E-22 -2.6$E-06 Dx4

r%* ()= -4.06E-0# 1.60E-06 -#.0$E-23 2.14E-06 Dy4

2.0#E-22 -5.1!E-23 2.44E-06 3.25E-06 Dx5

-2.6$E-06 2.14E-06 3.25E-06 1.!5E-05 Dy5

%/%r %) arra

0

1-3= 410166.33# 1 0 0 =

0

1-4= 32!133.06$ 0.! 0.6 0 =

0

2-4= 410166.33# 1 0 0 =

-1.500E-006

3-4= 546!!!.44$ 0 1 1.41!#E-006 =

-1.500E-006

4-5= 32!133.06$ 0.! -0.6 1.41!#E-006 =

$.#521E-006

3-5= 410166.33# 1 0 1.6422E-005 =

TOMANDO EN CUENTA EL PESO PROPIO CARA LIN. 0.63221$13

BARRA 1

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


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BARRA 2

Dx1 Dy1 Dx4 Dy4

0.64 0.4! -0.64 -0.4! Dx1

1-4= 0.4! 0.36 -0.4! -0.36 Dy1

-0.64 -0.4! 0.64 0.4! Dx4

-0.4! -0.36 0.4! 0.36 Dy4

BARRA 3

Dx2 Dy2 Dx4 Dy4

1 0 -1 0 Dx2

2-4= 0 0 0 0 Dy2

-1 0 1 0 Dx4

0 0 0 0 Dy4

BARRA 4

Dx3 Dy3 Dx4 Dy4

0 0 0 0 Dx3

3-4= 0 1 0 -1 Dy30 0 0 0 Dx4

0 -1 0 1 Dy4

BARRA 5

Dx4 Dy4 Dx5 Dy5

0.64 -0.4! -0.64 0.4! Dx4

4-5= -0.4! 0.36 0.4! -0.36 Dy4

-0.64 0.4! 0.64 -0.4! Dx5

0.4! -0.36 -0.4! 0.36 Dy5

BARRA 6

Dx3 Dy3 Dx5 Dy5

1 0 -1 0 Dx3

3-5= 0 0 0 0 Dy3

-1 0 1 0 Dx5

0 0 0 0 Dy5

MATRI" ENSAMBLADA

D1 D,1 D2 D,2 D3

6201#1.501 15#503.!#3 0 0 -410166.33#15#503.!#3 11!12#.$05 0 0 0

0 0 410166.33# 0 0

0 0 0 0 0

-410166.33# 0 0 0 !20332.6#4

= 0 0 0 0 0

-210005.164 -15#503.!#3 -410166.33# 0 0

-15#503.!#3 -11!12#.$05 0 0 0

0 0 0 0 -410166.33#


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0 0 0 0 0

DETERM. 0.00

MATRI" REDUCIDA

Dx4 Dy4 Dx5 Dy5!301#6.666 0 -210005.164 15#503.!#3 Dx4

0 #!3144.25$ 15#503.!#3 -11!12#.$05 Dy4

r%*7 -210005.164 15#503.!#3 6201#1.501 -15#503.!#3 Dx5

15#503.!#3 -11!12#.$05 -15#503.!#3 11!12#.$05 Dy5

MATRI" IN+ERTIDA

Dx4 Dy4 Dx5 Dy5

1.#15#E-006 -4.063E-00# 1.33#3E-022 -2.6$4E-006 Dx4

() -4.063E-00# 0.0000016 -#.0!!E-023 2.141#E-006Dy4

2.0#3#E-022 -5.1!4E-023 2.43!0E-006 3.250#E-006 Dx5-2.6$4E-006 2.141#E-006 3.250#E-006 1.!533E-005 Dy5


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N CUENTA EL PESO PROPIO

20400000 T8M92

0.0!0424## M92#.!61 T8'3

NudosNudo (i) Nudo (j)

Xi Yi Xj Yj L1-3 0 0 4 0 4

1-4 0 0 4 3 5

2-4 0 3 4 3 4

3-4 4 0 4 3 3

4-5 4 3 ! 0 5

3-5 4 0 ! 0 4

Dx1 Dy1 Dx3 Dy3

410166.336$ 0 -410166.336$ 0

1-3= 0 0 0 0

-410166.33# 0 410166.336!5 0

0 0 0 0

Dx1 Dy1 Dx4 Dy4

210005.1645 15#503.!#3 -210005.1645 -15#503.!#3

1-4= 15#503.!#34 11!12#.$05 -15#503.!#34 -11!12#.$05

-210005.164 -15#503.!#3 210005.1644# 15#503.!#3

-15#503.!#3 -11!12#.$05 15#503.!#335 11!12#.$05

Dx2 Dy2 Dx4 Dy4

410166.336$ 0 -410166.336$ 02-4= 0 0 0 0

-410166.33# 0 410166.336!5 0

0 0 0 0

Dx3 Dy3 Dx4 Dy4

0 0 0 0


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3-4= 0 546!!!.44$ 0 -546!!!.44$

0 0 0 0

0 -546!!!.44$ 0 546!!!.44$

Dx4 Dy4 Dx5 Dy5210005.1645 -15#503.!#3 -210005.1645 15#503.!#3

4-5= -15#503.!#3 11!12#.$05 15#503.!#335 -11!12#.$05

-210005.164 15#503.!#3 210005.1644# -15#503.!#3

15#503.!#34 -11!12#.$05 -15#503.!#34 11!12#.$05

Dx3 Dy3 Dx5 Dy5

410166.336$ 0 -410166.336$ 0

3-5= 0 0 0 0

-410166.33# 0 410166.336!5 00 0 0 0

Dy3 Dx4 Dy4 Dx5 Dy5

0 -210005.164 -15#503.!#3 0 0 Dx1

0 -15#503.!#3 -11!12#.$05 0 0 Dy1

0 -410166.33# 0 0 0 Dx2

0 0 0 0 0 Dy2

0 0 0 -410166.33# 0 Dx3

546!!!.44$ 0 -546!!!.44$ 0 0 Dy3

0 !301#6.666 0 -210005.164 15#503.!#335 Dx4

-546!!!.44$ 0 #!3144.25$2 15#503.!#3 -11!12#.$05 Dy4

0 -210005.164 15#503.!#34 6201#1.501 -15#503.!#34 Dx5

0 15#503.!#3 -11!12#.$05 -15#503.!#3 11!12#.$0501Dy5

%ra D%;aa'(%)&

D


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-0.#0#106#! Dx4 -1.5005E-006 Dx4

0.#0#106#! Dy4 1.41!#E-006 Dy4

4 Dx5 $.#521E-006 Dx5

0 Dy5 1.6422E-005 Dy5

0 = 0.00 T

0 = 0.00 T

0 = 0.00E


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Dx1 Dy1 Dx4 Dy4

210005.1645 15#503.!#3 -210005.1645 -15#503.!#3

1-4= 15#503.!#34 11!12#.$05 -15#503.!#34 -11!12#.$05

-210005.164 -15#503.!#3 210005.1644# 15#503.!#3

-15#503.!#3 -11!12#.$05 15#503.!#335 11!12#.$05

Dx2 Dy2 Dx4 Dy4

410166.336$ 0 -410166.336$ 0

2-4= 0 0 0 0

-410166.33# 0 410166.336!5 0

0 0 0 0

Dx3 Dy3 Dx4 Dy4

0 0 0 0

3-4= 0 546!!!.44$ 0 -546!!!.44$0 0 0 0

0 -546!!!.44$ 0 546!!!.44$

Dx4 Dy4 Dx5 Dy5

262506.4556 -1$6!#$.!42 -262506.4556 1$6!#$.!42

4-5= -1$6!#$.!42 14#65$.!!1 1$6!#$.!416$ -14#65$.!!1

-262506.456 1$6!#$.!42 262506.4555$ -1$6!#$.!42

1$6!#$.!41# -14#65$.!!1 -1$6!#$.!41# 14#65$.!!1

Dx3 Dy3 Dx5 Dy5

32!133.06$5 0 -32!133.06$5 0

3-5= 0 0 0 0

-32!133.06$ 0 32!133.06$4! 0

0 0 0 0

+E

D,3 D4 D,4 D5 D,5

0 -210005.164 -15#503.!#3 0 0 D10 -15#503.!#3 -11!12#.$05 0 0 D,1

0 -410166.33# 0 0 0 D2

0 0 0 0 0 D,2

0 0 0 -410166.33# 0 D3

546!!!.44$ 0 -546!!!.44$ 0 0 D,3

0 !301#6.666 0 -210005.164 15#503.!#335 D4

-546!!!.44$ 0 #!3144.25$2 15#503.!#3 -11!12#.$05 D,4

0 -210005.164 15#503.!#34 6201#1.501 -15#503.!#34 D5


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0 15#503.!#3 -11!12#.$05 -15#503.!#3 11!12#.$0501 D,5

DE"PLA"AMIENTOS

-MEP D

-0.#0#106#! Dx4 2.4$36E-005 Dx4 '

-10.2$22063 Dy4 -3.3644E-005 Dy4 '

4 Dx5 -1.6#55E-005 Dx5 '-!.15432# Dy5 -0.00015!26 Dy5 '


11/25

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

20400000 0.0!0424## 410166.336!52# 1 0

20400000 0.0!0424## 32!133.06$4!21 0.! 0.6

20400000 0.0!0424## 410166.336!52# 1 0

20400000 0.0!0424## 546!!!.44$136$ 0 1

20400000 0.0!0424## 32!133.06$4!21 0.! -0.6

20400000 0.0!0424## 410166.336!52# 1 0

Dx1

Dy1

Dx3

Dy3

Dx1

Dy1

Dx4

Dy4

Dx2Dy2

Dx4

Dy4

Dx3


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Dy3

Dx4

Dy4

Dx4

Dy4

Dx5

Dy5

Dx3

Dy3

Dx5Dy5

%ra DESPLA"AMIENTOS REACCIONES

D =D

0 Dx1 0 Dx1 0.0$ T Dx1

0 Dy1 0 Dy1 0.0# T Dy1

0 Dx2 0 Dx2 0.62 T Dx2

0 Dy2 0 Dy2 0.00 T Dy2

0 Dx3 0 Dx3 -4.00 T Dx3

0 Dy3 0 Dy3 -0.#! T Dy3

-0.#0#106#!Dx4 -1.5004#61E-006Dx4 -0.#1 T Dx4

0.#0#106#! Dy4 1.41!66!2E-006 Dy4 0.#1 T Dy4

4 Dx5 $.#521411E-006 Dx5 4.00 T Dx5

0 Dy5 1.642215!E-005 Dy5 0.00 T Dy5


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EP D

Dx1 0.00 Dx1 0 Dx1 0

Dy1 0.00 Dy1 #.26443!26Dy1 0

Dx3 0.00 Dx3 0 Dx3 0

Dy3 0.00 Dy3 #.26443!26Dy3 0


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EP D

Dx1 0.00 Dx1 0 Dx1 0

Dy1 0.00 Dy1 1.5!054#!3Dy1 0

Dx4 -0.#0#106#!Dx4 0 Dx4 0

Dy4 0.#0#106#! Dy4 1.5!054#!3Dy4 0

EP D

Dx2 0.00 Dx2 0 Dx2 0

Dy2 0.00 Dy2 1.26443!26Dy2 0

Dx4 0.00 Dx4 0 Dx4 0

Dy4 0.00 Dy4 1.26443!26Dy4 0

EP D

Dx3 0.00 Dx3 0 Dx3 0

Dy3 0.00 Dy3 1.#6!#25 Dy3 0Dx4 0.00 Dx4 0 Dx4 2.4$36E-005

Dy4 0.00 Dy4 1.#6!#25 Dy4 -3.364E-005

EP D

Dx4 Dx4 0 Dx4 0

Dy4 0.00 Dy4 6.3!5602 Dy4 0

Dx5 4.00 Dx5 0 Dx5 2.4$36E-005

Dy5 0.00 Dy5 6.3!5602 Dy5 -3.364E-005

EP D

Dx3 0.00 Dx3 0 Dx3 0

Dy3 0.00 Dy3 1.#6!#25 Dy3 0

Dx5 0.00 Dx5 0 Dx5 -1.6#6E-005

Dy5 0.00 Dy5 1.#6!#25 Dy5 -0.00015!26

CTOR UER"AS EMPOTRAMIENTO PERECTO

MEP -MEP

0.00 D1 0 D1 0 D10.00 D,1 !.!4 D,1 -!.!44$!60$ D,1

0.00 D2 0 D2 0 D2

0.00 D,2 0 D,2 0 D,2

0.00 D3 0 D3 0 D3

0.00 D,3 10.!01!!!264 D,3 -10.!01!!!3 D,3

-0.#0#106#! D4 0 D4 -0.#0#106#! D4

0.#0#106#!D,4 10.$$$3130$4D,4 -10.2$22063D,4

4.00 D5 0 D5 4 D5


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0 D,5 !.15432# D,5 -!.15432# D,5


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D =D


19/25

D =D


20/25

-0.00015!26 D,5 -!.15432# D,5 0.000 D,5


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22/25


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TT

T

T

T

T

T

T

T


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T

Documents

Calculo de Celocias Metodo Matricial