Ejercicios de Analisis Estructural II-metodo Matricial

8/17/2019 Ejercicios de Analisis Estructural II-metodo Matricial

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1)CALCULO de [k]

BARRA L(m) EA(cte) k = EA/L

1 3 1 0.33

2 3 1 0.33

3 3 1 0.33

4 3 1 0.33

5 3 1 0.33

6 3 1 0.33

7 3 1 0.33

8 3 1 0.33

3 1 0.33

10 3 1 0.33

11 3 1 0.33

2) !ALORE" U#$%AR$O"


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3) CALCULO &E [']

B C D E Fnudos

[ 1 ]= [ 8 ]= [ 6 ]=[(64*0.50/0.87)]

[ 2 ]= [ 3 ]= [ 11 ]= [ ]= [ 5 ]=[(6

[ 10 ]= [ 7 ]= [ 4 ]=[(64*0.50/(+0.87

〖 1][ 〗 ,0- ,^ 0- ,0- ,0-

[ 2]〗 ^ 〖 2][ 〗 ,0- ,0- ,0-^ ,0- +〖 [ 3]〗 ^ 〖 3][ 〗 ^ ,0- ,0-

,0- ,0- 〖+ [ 4]〗 ^ 〖 4][ 〗 ,0-^ ,0- ,0- ,0-〖 [ 5]〗 ^ 〖+ [ 5]〗 ^ ,0-,0- ,0- 〖 [ 6]〗 ^ ,0-

〖+ 6][ 〗 ,0-^ ,0- +〖 7][ 〗 ^ ,0- ,0- 〖 [ 7]〗 ^

,0- 〖 [ 8]〗 ,0- ,0- ,0-^

,0- ,0- ,0- ,0- 〖 ][ 〗 ^

+ 10][ 〗 ,0- ,0- ,0- ,0-^

,0- ,0- ,0- ,0- ,0- 〖


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0.5

1

0

0

0[a]= 0

0

0

0

0.5

0

0.330

0

0

0

[k]= 00

0

0

0

0

0.5

0.87

0

0

0

0

0

0

0

0

0

0

〖 ][ 〗 ^ =


7/64

0.17

0.2

0

00

0

0

0

0

0

0

barras 01

234 0.55 06 0.337 08 09 010 011 0

G 00

0.08

0.145

.0E15

5.22E15

.0E15

1.57E16

.0E15

2.61E16

6.02E00

3.13E16

4.11E00

〖 ][ 〗 ]^ [ =

]=[

〖 ][ 〗 ^(!" = − − − − − − − − − − −

*1/0)]

)]

,0-

,0-,0-

,0-

,0-

+〖 8][ 〗 ^

+〖 [ ]〗 ^

〖 [ 10]〗 ^

1[ 1]〗 ^


8/64

2.0E16

2.50E00

1.04E16

2.30E171.32E17

2.30E17

3.6E17

2.30E17

6.61E17

6.60E01

7.3E17

1.65E01

5.28E17

1.15E012.64E17

0

32

64

128

4.55

0

64

64

4.6

0

11.4

0

10.67

][ =

]=[


9/64

21.33

42.67

16.52

0

21.33

21.33

1.650

3.83

10.67

010.67

0

0

37.12

4.82

37.12

4.20

18.56

12.84

18.56

]=[

]=[


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11/64

0.87 0 0 0

0 1 0 0

0 1 0 1

0 0 0 0.5

0 0 0 00 0 0 0.5

0 0.5 0.87 0

0 0.5 0.87 0

0 0 0 0

0.87 0 0 0

0 0 0 0

0 0 0 00.33 0 0 0

0 0.33 0 0

0 0 0.33 0

0 0 0 0.33

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

1 0 0 0

0 0 0 0

1 1 0 0

0 0 0 0

0 1 0.5 0

0 0 0.87 0

0 0 0.5 1

0 0 0.87 0

0 0 0 1

0 0 0 0

0 0 0 0

0 0 0 0

]=[ 〖 ][ 〗 ^ ] ][ [


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0.33 0 0 0

0 0 0 0

0.33 0.33 0 0

0 0 0 00 0.33 0.17 0

0 0 0.2 0

0 0 0.17 0.33

0 0 0.2 0

0 0 0 0.33

0 0 0 0

0 0 0 0

0 0 0 0

0 0.33 0 0

0.50 0 0 0

0 0.83 0 0.33

0 0 0.50 0

0 0.33 0 0.5

0 0 0 0

0 0 0 0.08

0 0 0 0.145

0 0.08 0.15 0.08

0 0.145 0.25 0.15

0.145 0.08 0.15 0

0.2523 0.145 0.25 0

5.22E15 .0E15 1.57E16 .0E15

3.00E15 5.22E15 .01E15 5.22E15

5.22E15 .0E15 1.57E16 .0E15

.01E15 1.57E16 2.70E16 1.57E16

5.22E15 .0E15 1.57E16 .0E15

1.50E16 2.61E16 4.50E16 2.61E16

3.05E00 4.1E00 6.46E00 4.6E00

1.80E16 3.13E16 5.40E16 3.13E16

2.40E00 2.74E00 3.43E00 3.43E00

]=[ 〖 ][ 〗(+1)


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1.20E16 2.0E16 3.60E16 2.0E16

1.44E00 2.50E00 8.62E01 2.50E00

6.00E15 1.04E16 1.80E16 1.04E16

]= ] ][ [ [

[]=[ ] []


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#E$F%C&C%')

$E&CC%*E+

0.5 0.87 0

0 0 0

0 0 0

0 0 0.5

0 0 1

0 0 0

0 0 0

0 0 0

0 0 0

0 0 0

1 0 0

& E

]=[ 〖 ][ 〗 ]^ [

]=[ 〖〖 [ 〗 ]_ 〗 ]^ [

〖 [ 〗 ]=_


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0 0 0 0

0 0 0 0

0 0 0 0

0.87 0.5 0.87 0

0 1 0 10.87 0 0 0.5

0 0 0 0.5

0 0 0 0

0 0 0 1

0 0 0 0

0 0 0 0

0 0 0 00 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0.33 0 0 0

0 0.33 0 0

0 0 0.33 0

0 0 0 0.33

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0.5 0.5 0

0 0.87 0.87 0

0.5 0 0 0

0.87 0 0 0

0 0 0 0

0 0 0 0

0.5 0.5 0 1

0.87 0.87 0 0

0 0 0.5 1

0 0 0.87 0


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18/64

6.00E16 2.70E00 7.21E16 4.20E00

2.87E01 3.00E00 0.00E00 3.00E00

3.00E16 3.75E01 3.60E16 3.75E01


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BARRA

0 10 20 3

0.87 40 50 60 70 80 90 100 11


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0 0 0 0

0 0 0 0

0.5 1 0 0

0.87 0 0 0


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0 0 0

0 0 0

0 0 0

0 0 0

0 0 00.87 0 0

0.87 0 0

0 0.5 0.87

0 1 0

0 0.5 0.87

0 1 0

0 00 0

0 0

0 0

0 0

0 0

0 0

0 0

0 0

0.33 0

0 0.33

0.5 0

0.87 0

0 0

0 0

0 0

0 0

0 0

0 0

0 0

0 0

0.5 1

0.87 0


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0.17 0

0.2 0

0 0

0 00 0

0 0

0 0

0 0

0 0

0 0

0.17 0.33

0.2 0

0 0.08 0.15

0 0.15 0.25

0.15 0.08 0.15

0.25 0.15 0.25

0.15 0 0

0.25 0 0

0 0 0

0 0 0

0 0.33 0

0.50 0 0

0 0.83 0

0 0 0.50

2.0E16 5.21E01 1.04E16

1.20E16 3.00E01 6.00E15

2.0E16 5.21E01 1.04E16

3.60E16 2.55E00 1.80E16

2.0E16 5.21E01 1.04E16

6.00E16 5.40E00 3.00E16

4.87E00 3.00E00 4.51E00

7.21E16 6.82E00 3.60E16

0.00E00 3.00E00 2.74E00

][ =


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4.80E16 3.7E00 2.40E16

5.75E01 3.00E00 1.15E00

2.40E16 1.13E00 1.20E16


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0 0 0 1

0 0 0 0

0 0 0 0

0 0 0 0


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0

0

0

0

0

0

0

0

0


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8

0

6


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C,-C.-* DE [a] / [k]

B&$$& -(s" E (kbs2" & = s21 25 2000 10

2 25 2000 10

3 20 2000 10

4 20 2000 10

5 15 2000 10

#&-*$E+ .%&$%*+

=


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0.8

[a]= 00.6

11600.00

[k]= 00

0.8

0.6

280.00

660

12644.00

132.00

7.5756E005

k = E&- 4.42087E00611600

11600

14500 0.0008841733

14500 0.000847333

1333.3333333333

]=[ 〖 ][

〖 ][ 〗 ^ =

〖 ][ 〗 ]^ [ =

]=[

]=[ 〖 ][ 〗(

〖 ][ 〗 ^(!" = − − − − − − − − − − −

] [ =

]= ] ][ [ [


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0.00122

0.00085

0.00015

14.10

.83

2.14

#E$F%C&C%'

10

20

$E&CC%*E+

0.8 0.6

0 00 0

&

0.8 0

0.6 0

0 0

0 10 0

0 0

1128846000 $E&CC983

]= ] ][ [ [

[ ]= 〖 ][ 〗 ^

]=[

][ =

][ =

]=[

〖 [ 〗 ]_ =

〖〖 [ 〗 ]_ 〗 ^ =

]=[

0

. !!


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128171


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0.6

1

0.8

0 0

11600.00 0

0 14500.00

0 0.6

1 0.8

0 8700.00

11600.00 11600.00

132.00

25056.00

4.42087E006 10

4.01562E005 20

] ]^ [ [

1) ][

]=[


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C

B&$$&+0 0 0 0 1

0 1 0 0 20 0 0.6 0.8 3

B C

$E&CC%*E+

0

0

0

00.6

0.8

%*E+

[]

〖〖 [ 〗 ]_ 〗 ]^ [


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1 C&-C.-* DE [a] / [k]

B&$$& - (" E& (:;" k = E&-1 5 1 0.2

2 5 1 0.23 5 1 0.2

4 5 1 0.2

5 5.83 1 0.17

6 3 1 0.33

7 5.83 1 0.17

8 5.83 1 0.17

3 1 0.33

10 5.83 1 0.17

11 5.36 1 0.1

12 5.36 1 0.1

13 5 1 0.2

11 #EC*$E+ .%&$%*+

2 ]= [ [ 2 ]= [ 3 ]= [ 4 ]=[(64* 1/0) ]


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F.E$


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0

0

0

0

0


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0 0 0

0 0 0

0 0 0

0 0 0

0 0 0

0.2 0.2 0

0 0 0

0 0.2 0.2

0 0 0

0 0 0.2

0 0 0

0 0 0

0 0 0

0 0 00 0 0

0 0 0

0 0 0

0 0 0

0 0 0

0.4 0 0.2

0 0.33 0

0.2 0 0.65

0 0 0

0 0 0.2

0 0 0

0 0 0

0 0 0

0 0 0.13

0 0 0.08

0 0 0

0 0 0

0 0 0.13

0 0.33 0.08

5.00E00 4.63E00 5.00E00

〖 ][ 〗 ]^ [ =

]=[

1)]

1)]

0.37))]

/0.37)]


47/64

4.56E00 2.67E15 .11E00

5.00E00 .26E00 1.00E01

6.80E01 5.34E15 1.36E00

5.00E00 .3E00 1.00E01

3.20E00 8.01E15 6.3E00

5.00E00 .57E00 1.00E01

7.07E00 1.07E16 1.41E012.70E00 1.58E15 5.40E00

3.20E00 8.01E15 6.3E00

1.16E00 2.64E15 2.32E00

6.80E01 5.34E15 1.36E00

2.70E00 1.58E15 5.40E00

4.56E00 2.67E15 .11E00

.36841738431.040832E017

18.7368347686

2.081664E017

41.03127728

3.12246E017

61.8680028351

4.163328E017

6.172375E016

3.12246E017

1.031332E017

2.081664E017

6.172375E016

1.040832E017

.37

.37

22.36

20.77

72

0

24

0

64

〖 ][ 〗(+1) =

]=[

]=[

c

c


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0

8

0

0

1.87

1.87

4.47

4.15

12.35

04.12

0.00

21.333333333

0

1.4

0.00

0

#E$%F%C&C%')

0.00

0.00

0.4

2.10

0.32

21.33

4.15

0.00

0.00

21.33

1.3

0.55

5.6

7.85

]=[ [

]=[

c

][ =

c

]=[


49/64

$E&CC%*E+ E -*+ &*>*+

1 0 0

0 0 0

0 0 0

0 0 1

0.86 0.51 0

0 0 0

0 0 0

0 0 0

0 0 0

0 0 0.860 0 0

0 0 0

0 0 0

1 0 0

0 0 0

0 0 0

0 0 0

12.4

6.30

4.15

0

[ ]= 〖〖 [〗 ]_ 〗 ^ [

〖 [〗 _

]=

〖〖 [〗 ]_ 〗 ^ =

]=[ c


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0 0 0 0 0

0 0 0 0 0

0 1 0 0 0

0 1 0 1 0

0 0 0 0 00 0 0 0 0

0.51 0 0 0 0

0.51 0 0 0 0

0 0 1 0 0

0 0 0 0.86 0.51

0 0 0 0 0

0 0 0 0 0

1 0 0 0 0

0 0 0 0 0

0 0 0 0 0

0 0 0 0 0

0.2 0 0 0 0

0 0.17 0 0 0

0 0 0.33 0 0

0 0 0 0.17 0

0 0 0 0 0.17

0 0 0 0 00 0 0 0 0

0 0 0 0 0

0 0 0 0 0

0 0 0 0 0

0 0 0 0 0

0 0 1 0 0

0 0 0 0.86 0.86

0 0 0 0.51 0.51

1 0 0 0 0

0 0 0 0 0

1 0 0 0 0

0 0 0 0 0

0 0 0 0 0.86

]=[ 〖 ][ 〗 ] ]^ [ [


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0 0 0 0 0.51

0 0 0 0 0

0 0 0 0 0

0 0.86 0 0.86 0

0 0.51 1 0.51 0

0 0 0 0 0

0 0 0.33 0 0

0 0 0 0.15 0.15

0 0 0 0.0 0.0

0.2 0 0 0 0

0 0 0 0 0

0.2 0 0 0 0

0 0 0 0 0

0 0 0 0 0.150 0 0 0 0.0

0 0 0 0 0

0 0 0 0 0

0 0.15 0 0.15 0

0 0.0 0.33 0.0 0

0 0 0 0 0

0 0 0 0 0

0 0.2 0 0 0

0.2 0 0 0 0

0 0.4 0 0.2 0

0 0 0.33 0 0

0 0.2 0 0.33 0.08

0 0 0 0.08 0.04

0.08 0 0 0.13 0.08

0.04 0 0.33 0.08 0.04

0 0 0 0 0

0.2 0 0 0 0

0.08 0 0 0 0

0.04 0 0 0 0

1.8E00 5.00E00 3.50E00 5.00E00 6.10E00

]=[ 〖 ][ 〗(+1) ][


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][

][ 〗

]^ [


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0

0

0

0

0

0

0

0

0

0.510

0

0

0 0.86 0 0 0

0 0.51 0 0 0

1 0 0 0 0

0 0 0 0 0

]

c


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0 0 0 0 0

0 0 0 0 0

0 0 0 0 0

0 0 0 0 0

0 0 0 0 0.860 0 0 0 0

0 0 0 0 0.86

0.86 0.51 0 0 0

0 1 0 0 0

0.86 0.51 0 0 0

0 0 0.3 0.37 0.3

0.3 0.37 0.3 0.37 0

0 0 0 1 0

0 0 0 0 0

0 0 0 0 0

0 0 0 0 0

0 0 0 0 0

0 0 0 0 0

0 0 0 0 0

0 0 0 0 0

0 0 0 0 0

0.33 0 0 0 00 0.17 0 0 0

0 0 0.1 0 0

0 0 0 0.1 0

0 0 0 0 0.2

0 0 0 0 0

0 0 0 0 0

0 0 0 0 0

0 0 0 0 1

0 0 0 0 0

1 0 0 0 0

0 0.86 0 0 0

0 0.51 0 0 0

0 0.86 0 0.3 0


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1 0.51 0 0.37 0

0 0 0.3 0.3 0

0 0 0.37 0.37 1

0 0 0.3 0 0

0 0 0.37 0 0

0 0 0 0 0

0 0 0 0 0

0 0 0 0 0

0 0 0 0 0.2

0 0 0 0 0

0.33 0 0 0 0

0 0.15 0 0 0

0 0.0 0 0 0

0 0.15 0 0.17 00.33 0.0 0 0.07 0

0 0 0.17 0.17 0

0 0 0.07 0.07 0.2

0 0 0.17 0 0

0 0 0.07 0 0

0 0 0 0 0

0 0 0 0 0

0.13 0.08 0 0 0.13

0.08 0.04 0 0.2 0.08

0 0 0 0 0

0 0.33 0 0 0

0.13 0.08 0 0 0

0.08 0.04 0 0 0

0.42 0.06 0.16 0.06 0

0.06 0.45 0.06 0.03 0

0.16 0.06 0.32 0 0.16

0.06 0.03 0 0.25 0.06

0 0 0.16 0.06 0.42

0 0 0.06 0.03 0.06

2.8E00 3.50E00 1.27E00 1.8E00 2.53E00

c


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1.58E15 8.01E15 2.64E15 5.34E15 1.58E15

5.5E00 7.00E00 2.54E00 3.5E00 5.05E00

3.17E15 1.60E16 5.2E15 1.07E16 3.17E15

6.3E00 8.87E00 2.72E00 5.82E00 5.01E00

4.75E15 2.40E16 7.3E15 1.60E16 4.75E15

6.0E00 1.03E01 2.4E00 7.78E00 5.07E00

6.33E15 3.20E16 1.06E16 2.14E16 6.33E15.3E14 4.75E15 1.57E15 3.17E15 .3E14

4.75E15 2.40E16 7.3E15 1.60E16 4.75E15

1.57E15 7.3E15 2.62E15 5.2E15 1.57E15

3.17E15 1.60E16 5.2E15 1.07E16 3.17E15

.3E14 4.75E15 1.57E15 3.17E15 .3E14

1.58E15 8.01E15 2.64E15 5.34E15 1.58E15


58/64


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0 0 0 0 0

0 0 0 0 0

0 0.86 0 0 0

0 0.51 0 0 0

c


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0

0

0

0

0.511

0.51

0

0

0

0.37

0

0


61/64

0

0.33

0.08

0.04

0

0

0

0

0

0

0.06

0.03

0.06

0.45

4.63E00

c


62/64

2.67E15

.26E00

5.34E15

.3E00

8.01E15

.57E00

1.07E161.58E15

8.01E15

2.64E15

5.34E15

1.58E15

2.67E15


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Ejercicios de Analisis Estructural II-metodo Matricial

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Transcript of Ejercicios de Analisis Estructural II-metodo Matricial