Ejercicios de Celocia Por El Metodo Matricial

7/26/2019 Ejercicios de Celocia Por El 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 Dx2 Dy2

0 0 0 0 Dx1

K12= 0 1 0 1 Dy1

0 0 0 0 Dx2

0 1 0 1 Dy2

Barra 2

Dx2 Dy2 Dx3 Dy3

1 0 1 0 Dx2

K23= 0 0 0 0 Dy2

1 0 1 0 Dx3

0 0 0 0 Dy3

Barra 3

Dx1 Dy1 Dx3 Dy3

0.64 0.4! 0.64 0.4! Dx1K13= 0.4! 0.36 0.4! 0.36 Dy1

0.64 0.4! 0.64 0.4! Dx3

0.4! 0.36 0.4! 0.36 Dy3

Barra 4

Dx3 Dy3 Dx4 Dy4

1 0 1 0 Dx3

6T"M

!T

3.0

4.0

3.0

4.0

1

2 3 4

5

1

2

3

4

56


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K34= 0 0 0 0 Dy3

1 0 1 0 Dx4

0 0 0 0 Dy4

Barra 5

Dx3 Dy3 Dx5 Dy50.36 0.4! 0.36 0.4! Dx3

K35= 0.4! 0.64 0.4! 0.64 Dy3

0.36 0.4! 0.36 0.4! Dx5

0.4! 0.64 0.4! 0.64 Dy5

Barra 6

Dx4 Dy4 Dx5 Dy5

0 0 0 0 Dx4

K45= 0 1 0 1 Dy4

0 0 0 0 Dx50 1 0 1 Dy5

MATRI# ENSAMBLADA

Dx1 Dy1 Dx2 Dy2 Dx3

23500! 1$6256 0 0 23500!

1$6256 $441%2 0 612000 1$6256

0 0 45%000 0 45%000

0 612000 0 612000 0

K= 23500! 1$6256 45%000 0 143!200

1$6256 1321%2 0 0 0

0 0 0 0 612000

0 0 0 0 0

0 0 0 0 1321%2

0 0 0 0 1$6256

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

MATRI# REDUCIDA

Dx1 Dy1 Dx3 Dy3

23500! 1$6256 23500! 1$6256 Dx1

Kr&+= 1$6256 $441%2 1$6256 1321%2 Dy1

23500! 1$6256 143!200 0 Dx3

1$6256 1321%2 0 36$200 Dy3

MATRI# REEDUCIDA IN,ERTIDA - DESPLA#AMIENTOS


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Dx1 Dy1 Dx3 Dy3

%.!5E06 1.23E06 1.46E06 4.2%E06 Dx1

Kr&+ )*= 1.23E06 1.63E06 3.33E23 2.2$E22 Dy1

1.46E06 3.33E23 %.34E0$ $.00E0$ Dx3

4.2%E06 2.2$E22 $.00E0$ 4.$!E06 Dy3

&/&r/ &* arra/

$.!$!E005

12= 612000 0 1 %.!03%E006 =

1.16$1E005

23= 45%000 1 0 3.42!5E005 =

6.$11E005

13= 36$200 0.! 0.6 4.40!!E005 =

1.16$E005

34= 612000 1 0 3.42!E005 =

0

45= 45%000 0 1 0 =

1.16$E005

35= 36$200 0.6 0.! 3.42!E005 =

TOMANDO EN CUENTA EL PESO PROPIO CARA LIN. 0.$0$4%

BARRA 1

D71 D-1 D72 D-2

0 0 0 0 D71

K 12 = 0 1 0 1 D-1

0 0 0 0 D72

0 1 0 1 D-2


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BARRA 2

D72 D-2 D73 D-3

1 0 1 0 D72

K 23 = 0 0 0 0 D-2

1 0 1 0 D73

0 0 0 0 D-3

BARRA 3

D71 D-1 D73 D-3

0.64 0.4! 0.64 0.4! D71

K 13 = 0.4! 0.36 0.4! 0.36 D-1

0.64 0.4! 0.64 0.4! D73

0.4! 0.36 0.4! 0.36 D-3

BARRA 4

D73 D-3 D74 D-4

1 0 1 0 D73K 34 = 0 0 0 0 D-3

1 0 1 0 D74

0 0 0 0 D-4

BARRA 5

D74 D-4 D75 D-5

0 0 0 0 D74

K 45 = 0 1 0 1 D-4

0 0 0 0 D75

0 1 0 1 D-5

BARRA 6

D73 D-3 D75 D-5

0.36 0.4! 0.36 0.4! D73

K 35 = 0.4! 0.64 0.4! 0.64 D-3

0.36 0.4! 0.36 0.4! D75

0.4! 0.64 0.4! 0.64 D-5

MATRI# ENSAMBLADA

D71 D-1 D72 D-2 D7323500! 1$6256 0 0 23500!

1$6256 $441%2 0 612000 1$6256

0 0 45%000 0 45%000

0 612000 0 612000 0

23500! 1$6256 45%000 0 143!200

K= 1$6256 1321%2 0 0 0

0 0 0 0 612000

0 0 0 0 0


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0 0 0 0 1321%2

0 0 0 0 1$6256

DETERM. 0.00

MATRI# REDUCIDA

D71 D-1 D73 D-3

23500! 1$6256 23500! 1$6256 D71

1$6256 $441%2 1$6256 1321%2 D-1

K r&+8 23500! 1$6256 143!200 0 D73

1$6256 1321%2 0 36$200 D-3

MATRI# IN,ERTIDA

D71 D-1 D73 D-3

%.!4$4E006 1.225E006 1.45!%E006 4.2!56E006 D71

K )* 1.225E006 1.6340E006 3.3302E023 2.2$33E022D-11.45!%E006 3.3302E023 %.33$1E00$ $.002!E00$ D73

4.2!56E006 2.2$33E022 $.002!E00$ 4.$!04E006 D-3


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N CUENTA EL PESO PROPIO

20400000 T"M92

0.0% M92$.!61 T"(3

Nudos Nudo (i) Nudo (j)

Xi Yi Xj Yj L12 0 1 0 4 3

23 0 4 4 4 4

13 0 1 4 4 5

34 4 4 $ 4 3

35 4 4 $ 0 5

45 $ 4 $ 0 4

Dx1 Dy1 Dx2 Dy2

0 0 0 0

K12= 0 612000 0 612000

0 0 0 0

0 612000 0 612000

Dx2 Dy2 Dx3 Dy3

45%000 0 45%000 0

K23= 0 0 0 0

45%000 0 45%000 0

0 0 0 0

Dx1 Dy1 Dx3 Dy3

23500! 1$6256 23500! 1$6256K13= 1$6256 1321%2 1$6256 1321%2

23500! 1$6256 23500! 1$6256

1$6256 1321%2 1$6256 1321%2

Dx3 Dy3 Dx4 Dy4

612000 0 612000 0


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K34= 0 0 0 0

612000 0 612000 0

0 0 0 0

Dx3 Dy3 Dx5 Dy51321%2 1$6256 1321%2 1$6256

K35= 1$6256 23500! 1$6256 23500!

1321%2 1$6256 1321%2 1$6256

1$6256 23500! 1$6256 23500!

Dx4 Dy4 Dx5 Dy5

0 0 0 0

K45= 0 45%000 0 45%000

0 0 0 00 45%000 0 45%000

Dy3 Dx4 Dy4 Dx5 Dy5

1$6256 0 0 0 0 Dx1

1321%2 0 0 0 0 Dy1

0 0 0 0 0 Dx2

0 0 0 0 0 Dy2

0 612000 0 1321%2 1$6256 Dx3

36$200 0 0 1$6256 23500! Dy3

0 612000 0 0 0 Dx4

0 0 45%000 0 45%000 Dy4

1$6256 0 0 1321%2 1$6256 Dx5

23500! 0 45%000 1$6256 6%400! Dy5

&ra/ D&/;aa()&*'/


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D

! Dx1 $.!$$%E005 Dx1

0 Dy1 %.!03%E006 Dy1

0 Dx3 1.16$1E005 Dx3

0 Dy3 3.42!5E005 Dy3

%.!03%E006 = 6.00 T TRACCIN

1.16$1E005 = 5.36 T TRACCIN

2.$23E005 = 10.00 T COMPRESION

1.16$E005 = $.14 T COMPRESION

0 = 0.00 T

2.0425E005 = $.50 T TRACCIN

T"(

D71 D-1 D72 D-2

0 0 0 0

K 12 = 0 612000 0 612000

0 0 0 0

0 612000 0 612000


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D72 D-2 D73 D-3

45%000 0 45%000 0

K 23 = 0 0 0 0

45%000 0 45%000 0

0 0 0 0

D71 D-1 D73 D-3

23500! 1$6256 23500! 1$6256

K 13 = 1$6256 1321%2 1$6256 1321%2

23500! 1$6256 23500! 1$6256

1$6256 1321%2 1$6256 1321%2

D73 D-3 D74 D-4

612000 0 612000 0K 34 = 0 0 0 0

612000 0 612000 0

0 0 0 0

D74 D-4 D75 D-5

0 0 0 0

K 45 = 0 45%000 0 45%000

0 0 0 0

0 45%000 0 45%000

D73 D-3 D75 D-5

1321%2 1$6256 1321%2 1$6256

K 35 = 1$6256 23500! 1$6256 23500!

1321%2 1$6256 1321%2 1$6256

1$6256 23500! 1$6256 23500!

,

D-3 D74 D-4 D75 D-51$6256 0 0 0 0 D71

1321%2 0 0 0 0 D-1

0 0 0 0 0 D72

0 0 0 0 0 D-2

0 612000 0 1321%2 1$6256 D73

36$200 0 0 1$6256 23500! D-3

0 612000 0 0 0 D74

0 0 45%000 0 45%000 D-4


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1$6256 0 0 1321%2 1$6256 D75

23500! 0 45%000 1$6256 6%400! D-5

DE#PLA#AMIENTOS

MEP D

! D71 3.3522E005 D71 (

2.!2%%6 D-1 1.442!E005 D-1 (0 D73 $.245!E006 D73 (

2$.013665 D-3 %.4!51E005 D-3 (


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

20400000 0.0% 612000 0 1

20400000 0.0% 45%000 1 0

20400000 0.0% 36$200 0.! 0.6

20400000 0.0% 612000 1 0

20400000 0.0% 36$200 0.6 0.!

20400000 0.0% 45%000 0 1

Dx1

Dy1

Dx2

Dy2

Dx2

Dy2

Dx3

Dy3

Dx1Dy1

Dx3

Dy3

Dx3


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Dy3

Dx4

Dy4

Dx3

Dy3

Dx5

Dy5

Dx4

Dy4

Dx5Dy5

&ra/ DESPLA#AMIENTOS REACCIONES

D =K


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EP D

D71 !.00 D71 0.00 D71 0.00

D-1 0.00 D-1 1.06 D-1 0.00

D72 0.00 D72 0.00 D72 0.00

D-2 0.00 D-2 1.06 D-2 0.00


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EP D

D72 0.00 D72 0.00 D72 0.00

D-2 0.00 D-2 13.41 D-2 0.00

D73 0.00 D73 0.00 D73 0.00

D-3 0.00 D-3 13.41 D-3 0.00

EP D

D71 0.00 D71 0.00 D71 0.00

D-1 0.00 D-1 1.$$ D-1 0.00

D73 0.00 D73 0.00 D73 0.00

D-3 0.00 D-3 1.$$ D-3 0.00

EP D

D73 0.00 D73 0.00 D73 0.00D-3 0.00 D-3 10.06 D-3 0.00

D74 0.00 D74 0.00 D74 0.00

D-4 0.00 D-4 10.06 D-4 0.00

EP D

D74 0.00 D74 0.00 D74 0.00

D-4 0.00 D-4 1.41 D-4 0.00

D75 0.00 D75 0.00 D75 0.00

D-5 0.00 D-5 1.41 D-5 0.00

EP D

D73 0.00 D73 0.00 D73 0.00

D-3 0.00 D-3 1.$$ D-3 0.00

D75 0.00 D75 0.00 D75 0.00

D-5 0.00 D-5 1.$$ D-5 0.00

CTOR UER#AS EMPOTRAMIENTO PERECTO

MEP MEP! D71 0 D71 ! D71

0 D-1 2.!3 D-1 2.!2%%6 D-1

0 D72 0 D72 0 D72

0 D-2 14.4$6215 D-2 14.4$6215 D-2

0 D73 0 D73 0 D73

0 D-3 2$.013665 D-3 2$.013665 D-3

0 D74 0 D74 0 D74

0 D-4 11.4$6215 D-4 11.4$6215 D-4


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0 D75 0 D75 0 D75

0 D-5 3.1!3$05 D-5 3.1!3$05 D-5


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K


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K


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0 D75 15.$6024!! D75 15.$6024!! D75

0 D-5 21.013665 D-5 24.1%$3$ D-5


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Ejercicios de Celocia Por El Metodo Matricial

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