portico plano comprobacion con sap

8/17/2019 Portico Plano Comprobacion Con SAP

1/155

METODO MATRICIAL DE RIGIDEZ POR SISTEMATIZA

ANALIZAR EL PORTICO PLANO MOSTRADO

E = 2.00E+06 Tn/m2

ELEM B H AX AY L

m m m m m

1 0.4 0.4 5 4 6.403124242 0.4 0.4 -4 4 5.65685425

NUDOS Y ELEMENTOS sis!m" #$%&"$

MATRIZ DE TRANSFORMACION [A]


2/155

1 2 3 4 5

1 0 0 0 0

0 1 0 0 0

[A]1 = 0 0 1 0 0

0 0 0 1 0

0 0 0 0 1

0 0 0 0 0

1 2 3 4 5

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

MATRIZ DE RIGIDEZ DEL ELEMENTO [k]i sis!m" $%'"$

[A]2 =


3/155

()*i

(,* !$ !$!m!n% !n '%%!n""s $%'"$!s

45.60 0 0 -45.60

0 15.03 624.3 0

()*1 0 624.3 2665.3 0

-45.60 0 0 45.60

0 -15.03 -624.3 0

0 624.3 1332.68 0

56568.54 0 0 -56568.54

0 282.84 800.00 0

()*2 0 800.00 3016. 0

-56568.54 0 0 56568.54

0 -282.84 -800.00 0

0 800.00 1508.4 0

MATRIZ DE TRANSFORMACION [R]i !s $" m"i ! "ns%m"

0 0

0 0

(R*i 0 0 1 0

0 0 0

0 0 0

0 0 0 0

0.8086881 0.6246505 0 0

-0.6246505 0.8086881 0 0

COS α SEN α

-SEN α COS α

COS α

-SEN α


4/155

0 0 0 0.8086881

0 0 0 -0.6246505

0 0 0 0

-0.01068 0.01068 0 0

-0.01068 -0.01068 0 0(R*2 0 0 1 0

0 0 0 -0.01068

0 0 0 -0.01068

0 0 0 0

MATRIZ DE RIGIDEZ DEL ELEMENTO [k*]i !n i!''i%n !$ sis!m" #$

1 2 3 4

3054.04 24283.21 -30.05 -3054.04

24283.21 1621.5 48.5 -24283.21

()*1 -30.05 48.5 2665.3 30.05

-3054.04 -24283.21 30.05 3054.04

-24283.21 -1621.5 -48.5 24283.21

-30.05 48.5 1332.68 30.05

8 4

28425.6 -28142.85 -565.6 -28425.6

-28142.85 28425.6 -565.6 28142.85

()*2 -565.6 -565.6 3016. 565.6

-28425.6 28142.85 565.6 28425.6

28142.85 -28425.6 565.6 -28142.85

-565.6 -565.6 1508.4 565.6

ENSAMBLAE DE LA MATRIZ DE RIGIDEZ DE LA ESTRUCTURA [!]

1 2 3 4 5

3054.04 24283.21 -30.05 -3054.04 -24283.21

24283.21 1621.5 48.5 -24283.21 -1621.5

-30.05 48.5 2665.3 30.05 -48.5

-3054.04 -24283.21 30.05 3054.04 24283.21

[!]1 = -24283.21 -1621.5 -48.5 24283.21 1621.5

-30.05 48.5 1332.68 30.05 -48.5

0 0 0 0 0

0 0 0 0 0

0 0 0 0 0

1 2 3 4 5

0 0 0 0 0

*[


5/155

0 0 0 0 0

0 0 0 0 0

0 0 0 28425.6 -28142.85

[!]2 = 0 0 0 -28142.85 28425.6

0 0 0 565.6 565.6

0 0 0 -28425.6 28142.85

0 0 0 28142.85 -28425.60 0 0 565.6 565.6

1 2 3 4 5

3054.04 24283.21 -30.05 -3054.04 -24283.21

24283.21 1621.5 48.5 -24283.21 -1621.5

-30.05 48.5 2665.3 30.05 -48.5

-3054.04 -24283.21 30.05 584.3 -385.64

[!] = -24283.21 -1621.5 -48.5 -385.64 4804.2

-30.05 48.5 1332.68 55.4 8.12

- - - -28425.6 28142.85

- - - 28142.85 -28425.6

- - - 565.6 565.6

FUERZAS DE EMPOTRAMIENTO "#$% &' ($$)&'++, -$(+-&,

ELEM ./ .0 AX AY L

T'm T'm m m m

1 0 0 5 4 6.40312424

2 -6 0 -4 4 5.65685425

- 1

- 2

9:%71 - 3 9:%72

- 4

- 5

- 6

FUERZAS DE EMPOTRAMIENTO "#*$% &' ($$)&'+

- 1

- 2

9:%71 - 3 9:%72

- 4

- 5

- 6

FUERZAS DE FIACION "R%

9:07

! (R* T

! ; 9:

07

!


6/155

- 1

- 2

- 3

- 4

9R71 - 5 9R72

- 6

-

- 8

-

9R7 (A* T!

; 9:07!


7/155

9R7 9R71 + 9R72

- 1

- 2

- 3

-0.00 4

9R7 12.00 5 9


8/155

- 2

- 6

9D7 6.62E-06 4

-2.4E-04 5

-1.41E-03 6

- 7

- 8 - 9

CALCULO DE REACCIONES

9

6.34 1 -

4.00 2 -

9


9/155

0.84 5

-3.62 6

?@ERZAS INTERNAS PRIMARIAS 9:%7 !m%"mi!n%

- 1

- 2

9:%71 - 3 9:%72

- 4

- 5

- 6

?@ERZAS INTERNAS TOTALES 9:7

"#4%& = "#:%& ; "#%&

.45 1

-0.84 2

9:71 -1.5 3 9:72

-.45 4

0.84 5

-3.62 6


10/155

ION TOTAL

A I EAL < EIL EIL2 12 EIL6

m2 m< T' T'>m T' T'm

0.16 0.00213333 45.60 2665.3 624.3 15.030.16 0.00213333 56568.54 3016. 800.00 282.84


11/155

6 8

0 0 0 0 1

0 0 0 0 2

0 0 0 0 3

0 0 0 0 4

0 0 0 0 5

1 0 0 0 6

6 8

0 1 0 0

0 0 1 0 8

0 0 0 1

0 0 0 0 4

0 0 0 0 5

1 0 0 0 6


12/155

0 0

-15.03 624.3

-624.3 1332.68

0 0

15.03 -624.3

-624.3 2665.3

0 0

-282.84 800.00

-800.00 1508.4

0 0

282.84 -800.00

-800.00 3016.

i%n!s ! !"s

0 0

0 0

0 0

0

0

0 1

0 0

0 0

SEN α

COS α


13/155

0.6246505 0

0.8086881 0

0 1

0 0

0 00 0

0.01068 0

-0.01068 0

0 1

&"$ ! '%%!n""s

5 6

-24283.21 -30.05 1

-1621.5 48.5 2

-48.5 1332.68 3

24283.21 30.05 4

1621.5 -48.5 5

-48.5 2665.3 6

5 6

28142.85 -565.6

-28425.6 -565.6 8

565.6 1508.4

-28142.85 565.6 4

28425.6 565.6 5

565.6 3016. 6

6 8

-30.05 0 0 0 1

48.5 0 0 0 2

1332.68 0 0 0 3

30.05 0 0 0 4

-48.5 0 0 0 5

2665.3 0 0 0 6

0 0 0 0

0 0 0 0 8

0 0 0 0

6 8

0 0 0 0 1

(B* 7 * 7{ ^ [ {

7{ ^ [ * 7{


14/155

0 0 0 0 2

0 0 0 0 3

565.6 -28425.6 28142.85 565.6 4

565.6 28142.85 -28425.6 565.6 5

3016. -565.6 -565.6 1508.4 6

-565.6 28425.6 -28142.85 -565.6

-565.6 -28142.85 28425.6 -565.6 8 1508.4 -565.6 -565.6 3016.

6 8

-30.05 - - - 1

48.5 - - - 2

1332.68 - - - 3

55.4 -28425.6 28142.85 565.6 4

8.12 28142.85 -28425.6 565.6 5

5682.35 -565.6 -565.6 1508.4 6

-565.6 28425.6 -28142.85 -565.6

-565.6 -28142.85 28425.6 -565.6 8

1508.4 -565.6 -565.6 3016.

. .? @L2 12 @L2 @? L 2

T'm T'm T'>m T' T'

0 0 - - -

-3 3 -8.00 -8.4 8.4

8.4

-8.4 8

-8.00

8.4 4

-8.4 5

8.00 6

+, -$3+-&,

-0.00

12.00 8

-8.00

-0.00 4

12.00 5

8.00 6


15/155

- 1

- 2

- 3

-0.00 4

12.00 5

8.00 6

-0.00

12.00 8

-8.00


16/155

- 1

- 2

- 3

0.00 4

-12.00 5

-8.00 6 0.00

-12.00 8

8.00

6 8 1

-30.05 - - - 1 -

48.5 - - - 2 -

1332.68 - - - 3 -

55.4 -28425.6 28142.85 565.6 4 0.00

8.12 28142.85 -28425.6 565.6 5 -12.00

5682.35 -565.6 -565.6 1508.4 6 -8.00

-565.6 28425.6 -28142.85 -565.6 0.00

-565.6 -28142.85 28425.6 -565.6 8 -12.00

1508.4 -565.6 -565.6 3016. 8.00

$$)&'++, )&,4)i'i+,

6 7 8 9 1

30.05 -28425.6 28142.85 565.6 4 0.00

-48.5 28142.85 -28425.6 565.6 5 -12.00

1332.68 -565.6 -565.6 1508.4 6 -8.00

-30.05 - - - 1 -

48.5 - - - 2 -

2665.3 - - - 6 -

- 28425.6 -28142.85 -565.6 7 0.00

- -28142.85 28425.6 -565.6 8 -12.00

- -565.6 -565.6 3016. 9 8.00

0.00 6.62E-06 4

-12.00 9D7 -2.4E-04 5

-8.00 -1.41E-03 6

9D7 (,* -1; 9


17/155

9


18/155

1.1 5

-4.38 6

8.4

-8.4 8

-8.00

8.4 4

-8.4 5

8.00 6

18.63

-.66 8

-10.26

-1.66 4

-.31 5

3.62 6


19/155


20/155


21/155


22/155


23/155


24/155


25/155

9


26/155


27/155


28/155


29/155


30/155


31/155


32/155


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34/155


35/155


36/155


37/155


38/155


39/155


40/155


41/155


42/155


43/155


44/155


45/155


46/155

E = 10000000 Tn/m2

ELEM B H AX AY L

m m m m m

1 0.4 0.4 0 4 4

2 0.4 0.4 5 0 5

3 0.4 0.4 3 -4 5


47/155


1 2 3 4 5

1 0 0 0 0

0 1 0 0 0

[A]1 = 0 0 1 0 0

0 0 0 1 0

0 0 0 0 1

0 0 0 0 0

1 2 3 4 5

0 0 0 1 0

0 0 0 0 1

[A]2 = 0 0 0 0 0

0 0 0 0 0

0 0 0 0 0

0 0 0 0 0

1 2 3 4 5

0 0 0 0 0

0 0 0 0 0

[A]6 = 0 0 0 0 0

0 0 0 0 0

0 0 0 0 0

0 0 0 0 0



48/155

()*i

(,* !$ !$!m!n% !n '%%!n""s $%'"$!s30000 0 0 -30000

0 18.5 38 0

()*1 0 38 100 0

-30000 0 0 30000

0 -18.5 -3.5 0

0 38 50 0

24000 0 0 -240000 .6 24 0

()*2 0 24 80 0

-24000 0 0 24000

0 -.6 -24 0

0 24 40 0


49/155

24000 0 0 -24000

0 .6 24 0

()*3 0 24 80 0

-24000 0 0 24000

0 -.6 -24 0

0 24 40 0

MATRIZ DE TRANSFORMACION [R]i !s $" m"i ! "ns%m"'i%

0 0

0 0

(R*i 0 0 1 0

0 0 0

0 0 0

0 0 0 0

0.00 1.00 0 0

-1.00 0.00 0 0

(R*1 0 0 1 0

0 0 0 0.00

0 0 0 -1.00

0 0 0 0

1.00 0.00 0 0

0.00 1.00 0 0

(R*2 0 0 1 0

0 0 0 1.00

0 0 0 0.00

0 0 0 0

0.60 -0.80 0 0

0.80 0.60 0 0

(R*3 0 0 1 0

0 0 0 0.60

0 0 0 0.80

0 0 0 0

COS α SEN α

-SEN α COS α

COS α

-SEN α


50/155

MATRIZ DE RIGIDEZ DEL ELEMENTO [k*]i !n i!''i%n !$ sis!m" #$%&

1 2 3 4

18.5 - -3.50 -18.5

- 30000.00 - -()*1 -3.50 - 100.00 3.50

-18.5 - 3.50 18.5

- -30000.00 - -

-3.50 - 50.00 3.50

4 5 6

24000.00 - - -24000.00

- .60 24.00 -()*2 - 24.00 80.00 -

-24000.00 - - 24000.00

- -.60 -24.00 -

- 24.00 40.00 -

8 10

8646.14 -11515.3 1.20 -8646.14

-11515.3 15363.46 14.40 11515.3

()*3 1.20 14.40 80.00 -1.20

-8646.14 11515.3 -1.20 8646.14

11515.3 -15363.46 -14.40 -11515.3

1.20 14.40 40.00 -1.20


1 2 3 4

18.5 0 -3.5 -18.5

0 30000 0 0

-3.5 0 100 3.5

-18.5 0 3.5 18.5

0 -30000 0 0

[!]1 = -3.5 0 50 3.5


51/155

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 2 3 4

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 24000

0 0 0 0

[!]2 = 0 0 0 00 0 0 -24000

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

1 2 3 40 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

[!]6= 0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 00 0 0 0

0 0 0 0

1 2 3 4

18.5 0 -3.5 -18.5

0 30000 0 0


52/155

-3.5 0 100 3.5

-18.5 0 3.5 24018.5

0 -30000 0 0

-3.5 0 50 3.5

[!] = 0 0 0 -24000

0 0 0 0

0 0 0 00 0 0 0

0 0 0 0

0 0 0 0

REORDENANDO LAS FILAS Y COLUMNAS

($$)&'++, -i3)&,

< 7 8

24018.5 0 3.5 -24000 0

0 3000.6 24 0 -.63.5 24 180 0 -24

-24000 0 0 32646.144 -11515.32

0 -.6 -24 -11515.32 1533.056

[!] = 0 24 40 1.2 -.6

-18.5 0 -3.5 0 0

0 -30000 0 0 0

3.5 0 50 0 0

0 0 0 -8646.144 11515.32

0 0 0 11515.32 -15363.456

0 0 0 1.2 14.4

HALLAMOS EL 5ECTOR DE CARGA "%

+--+m$, &- &(4$) & (+)+, )im+)i+, &m$4)+mi&'4$, "R%1

"" $" &"" 1

10 1

6 2

9:071 4 3

0 4

6 5

-4 6


53/155

FUERZAS DE EMPOTRAMIENTO "#*$%

1

-6 1

0 2

4 39:%71 -6 4

0 5

-4 6

FUERZAS DE FIACION "R%

1

-6 1

0 2

4 3-6 4

0 5

9R71 -4 6

0

0 8

0

0 10

0 11

0 12

1

-6 1

0 2

4 3

-6 4

0.416 5"R%1= -3.36 6

2

5.084 8

0.565

2 10

1.5 11

-3.125 12

9:07

! (R* T

! ; 9:

07

!

!n%n'!s "R%1 9R71 + 9R72 + 9R73


54/155

+--+m$, &- &(4$) & (+)+, ($m-&m&'4+)i+, '$+-&, "R%2

1

0 10 2

0 3

-4 4

0 5

"R%2= 0 6

0

0 8

3

0 10

0 110 12

"%= > ["R%2 ; "R%1]

1

6 1

0 2

-4 310 <

-0.416

3.36

TOTAL "%= -2 7

-5.084 8

-3.565 9

-2 10

-1.5 11

3.125 12

CALCULO DE LOS DESPLAZAMIENTOS

9,7

4 5 6

24018.5 0 3.5 -24000


55/155

0 3000.6 24 0

3.5 24 180 0

[!]= -24000 0 0 32646.144

0 -.6 -24 -11515.32

0 24 40 1.2

5ECTOR DE DESPLAZAMIENTOS

1

0 1

0 2

0 3

0.1106123 4

2.84440E-005 50.014160448 6

9D7 0.11036061

0.082343528 8

-0.0341314535

0 10

0 11

0 12

CALCULO DE REACCIONES

9

1

-2.606535236 1

-0.853322623 2

9


56/155

0 2

0 3

971 0.1106123 4 972

2.84441E-005 5

0.01416045 6

DESPLAZAMIENTO EN ELEMENTOS "% &' ($$)&'

"%& = [R]& / "*%&

0 1

0 2

0 3

971 2.84441E-005 4 972

-0.1106123 5

0.01416045 6

?@ERZAS INTERNAS COMPLEMENTARIAS 9:7 &' ($$)&'

"#%& = [!]& / "%&

-0.853322623 1

2.606535236 2

4.858844351 3

9:71 0.853322623 4 9:72

-2.606535236 5

5.562651 6


0 1

6 2

9:071 4 3 9:072

0 4

6 5

-4 6

?@ERZAS INTERNAS TOTALES 9:7 '%%!n""s $%'"

"#4%& = "#:%& ; "

-0.853 1 ";i"$

8.60 2 '%"n!


57/155

8.85 3 m%m!n%

9:71 0.853 4 ";i"$ 9:72

3.33 5 '%"n!

1.56 6 m%m!n%

i"#"m" ! !" ";i"$

!s$""mi!n% !$ n% 2


58/155


59/155



0.012 0.00001 30000 100 38 1

0.012 0.00001 24000 80 24 10

0.012 0.00001 24000 80 24 10


60/155

6 8 10 11

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

1 0 0 0 0 0

6 8 10 11

0 0 0 0 0 0

0 0 0 0 0 0

1 0 0 0 0 0

0 1 0 0 0 0

0 0 1 0 0 0

0 0 0 1 0 0

6 8 10 11

0 1 0 0 0 0

0 0 1 0 0 0

0 0 0 1 0 0

0 0 0 0 1 0

0 0 0 0 0 1

0 0 0 0 0 0


61/155

0 0

-18.5 3.5

-3.5 50

0 0

18.5 -3.5

-3.5 100

0 0-.6 24

-24 40

0 0

.6 -24

-24 80


62/155

0 0

-.6 24

-24 40

0 0

.6 -24

-24 80

!s ! !"s

0 0

0 0

0 0

0

0

0 1

0 0

0 0

0 0

1.00 0

0.00 0

0 1

0 0

0 0

0 0

0.00 0

1.00 0

0 1

0 0

0 0

0 0

-0.80 0

0.60 0

0 1

SEN α

COS α


63/155

$ ! '%%!n""s

5 6

- -3.50 1

-30000.00 - 2 - 50.00 3

- 3.50 4

30000.00 - 5

- 100.00 6

8

- - 4

-.60 24.00 5 -24.00 40.00 6

- -

.60 -24.00 8

-24.00 80.00

11 12

11515.3 1.20

-15363.46 14.40 8

-14.40 40.00

-11515.3 -1.20 10

15363.46 -14.40 11

-14.40 80.00 12

5 6 8 10

0 -3.5 0 0 0 0

-30000 0 0 0 0 0

0 50 0 0 0 0

0 3.5 0 0 0 0

30000 0 0 0 0 0

0 100 0 0 0 0

(B* 7 * 7{ ^ [ {

* 7 B* 7[ { ^ [ {


64/155

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

5 6 8 10

0 0 0 0 0 0

0 0 0 0 0 0

0 0 0 0 0 0

0 0 -24000 0 0 0

.6 24 0 -.6 24 0

24 80 0 -24 40 00 0 24000 0 0 0

-.6 -24 0 .6 -24 0

24 40 0 -24 80 0

0 0 0 0 0 0

0 0 0 0 0 0

0 0 0 0 0 0

5 6 8 100 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 8646.144 -11515.32 1.2 -8646.144

0 0 -11515.32 15363.456 14.4 11515.32

0 0 1.2 14.4 80 -1.2

0 0 -8646.144 11515.32 -1.2 8646.1440 0 11515.32 -15363.456 -14.4 -11515.32

0 0 1.2 14.4 40 -1.2

5 6 8 10

0 -3.5 0 0 0 0

-30000 0 0 0 0 0


65/155

0 50 0 0 0 0

0 3.5 -24000 0 0 0

3000.6 24 0 -.6 24 0

24 180 0 -24 40 0

0 0 32646.144 -11515.32 1.2 -8646.144

-.6 -24 -11515.32 1533.056 -.6 11515.32

24 40 1.2 -.6 160 -1.20 0 -8646.144 11515.32 -1.2 8646.144

0 0 11515.32 -15363.456 -14.4 -11515.32

0 0 1.2 14.4 40 -1.2

9 1 2 6 1: 11

0 -18.5 0 3.5 0 0

24 0 -30000 0 0 040 -3.5 0 50 0 0

1.2 0 0 0 -8646.144 11515.32

-.6 0 0 0 11515.32 -15363.456

160 0 0 0 -1.2 -14.4

0 18.5 0 -3.5 0 0

0 0 30000 0 0 0

0 -3.5 0 100 0 0

-1.2 0 0 0 8646.144 -11515.32

-14.4 0 0 0 -11515.32 15363.456

40 0 0 0 -1.2 -14.4

"" $" &"" 2 "" $" &""

20 4

0.416 5

9:072 0.64 6 9:073

0

3.584 8

-2.56


66/155

&' ($$)&'++, -$3+-&,

2

0 4

0.416 5

0.64 69:%72 0 9:%72

3.584 8

-2.56

2

0 1

0 2

0 30 4

0.416 5

9R72 0.64 6 9R73

0

3.584 8

-2.56

0 10

0 11

0 12


67/155

10 4

-0.416 5

3.36 6-2

-5.084 8

-3.565

6 1

0 2

-4 3

9


68/155

-.6 24 5

-24 40 6 9


69/155

2.84440E-005 5 0.08234353 8

0.014160448 6 -0.03413145

0.11036061 973 0 10

0.082343528 8 0 11

-0.0341314535 0 12

++, -$(+-&,

0.1106123 4 0.00034661

2.84440E-005 5 0.13013 8

0.014160448 6 -0.03413145

0.11036061 973 0 10

0.082343528 8 0 11

-0.0341314535 0 12

++, -$(+-&,

.33464644 4 8.318366

-1.263226231 5 0.502824 8

-2.2026513 6 0.5431652

-.33464644 9:73 -8.318366 10

1.263226231 8 -0.502824 11

-4.13316524 1.35466 12

0 4 0

0.416 5 2.5 8

0.64 6 9:073 3.125

0 0 10

3.584 8 2.5 11

-2.56 -3.125 12

$!s

#%&

.33 4 ";i"$ 8.31

-0.853 5 '%"n! 3.003 8


70/155

-1.56 6 m%m!n% 3.6

-.33 ";i"$ 9:73 -8.31 10

4.853 8 '%"n! 1. 11

-6.6 m%m!n% -1.185 12

i"#"


71/155


72/155

C$,&'$, Di)&(4$)&,

0.00 1.00

1.00 0.00

0.60 -0.80

l = cos( ) m = sen( )


73/155

12

0 1

0 2

0 3

0 4

0 5

0 6

12

0 4

0 5

0 6

0

0 8

0

12

0

0 8

0

0 10

0 11

1 12


74/155


75/155


76/155

11 12

0 0 1

0 0 2

0 0 3

0 0 4

0 0 5

0 0 6


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0 0

0 0 8

0 0

0 0 10

0 0 11

0 0 12

11 12

0 0 1

0 0 2

0 0 3

0 0 4

0 0 5

0 0 60 0

0 0 8

0 0

0 0 10

0 0 11

0 0 12

11 120 0 1

0 0 2

0 0 3

0 0 4

0 0 5

0 0 6

11515.32 1.2

-15363.456 14.4 8

-14.4 40

-11515.32 -1.2 1015363.456 -14.4 11

-14.4 80 12

11 12

0 0 1

0 0 2


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0 0 3

0 0 4

0 0 5

0 0 6

11515.32 1.2

-15363.456 14.4 8

-14.4 40 -11515.32 -1.2 10

15363.456 -14.4 11

-14.4 80 12

12

0 <

0 0

1.2 7

14.4 8

40 9

0 1

0 2

0 6

-1.2 1:

-14.4 11

80 12

3

30

2.5 8

3.125

0 10

2.5 11

-3.125 12


79/155

3

2

1.5 8

3.125 2 10

1.5 11

-3.125 12

3

0 1

0 2

0 30 4

0 5

0 6

2

1.5 8

3.125

2 10

1.5 11

-3.125 12


80/155

10 4 0.110612

9D7 (,* -1; 9


81/155

-0.416 5 2.8444E-005

3.36 6 9D7 0.0141604

-2 0.1103606

-5.084 8 0.08234353

-3.565 -0.03413145

9


82/155

";i"$

'%"n!


83/155

m%m!n%

";i"$

'%"n!

m%m!n%

" ! !" '%"n!

!s$""mi!n% !$ n%3


84/155


85/155


86/155


87/155


88/155


89/155


90/155


91/155


92/155


93/155

4


94/155

5

6

8


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96/155

i"#"m" ! m%m!n% !'%


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111/155

E = 1 Tn/m2

ELEM B H AX AY L

m m m m m

1 0.4 0.4 0.6 0.8 1


112/155


1 2 3 4 5

1 0 0 0 0

0 1 0 0 0

[A]1 = 0 0 1 0 0

0 0 0 1 0

0 0 0 0 1

0 0 0 0 0


()*i


113/155

(,* !$ !$!m!n% !n '%%!n""s $%'"$!s

5 0 0 -5

0 12.00 6 0

()*1 0 6 4 0

-5 0 0 5

0 -12 -6 0

0 6 2 0

MATRIZ DE TRANSFORMACION [R]i !s $" m"i ! "ns%m"'i%

0 0

0 0

(R*i 0 0 1 0

0 0 0

0 0 0

0 0 0 0

0.60 0.80 0 0

-0.80 0.60 0 0

(R*1 0 0 1 0

0 0 0 0.60

0 0 0 -0.80

0 0 0 0

MATRIZ DE RIGIDEZ DEL ELEMENTO [k*]i !n i!''i%n !$ sis!m" #$%&

1 2 3 4

.48 -3.36 -4.80 -.48

-3.36 .52 3.60 3.36

()*1 -4.80 3.60 4.00 4.80

-.48 3.36 4.80 .48

COS α SEN α

-SEN α COS α

COS α

-SEN α


114/155

3.36 -.52 -3.60 -3.36

-4.80 3.60 2.00 4.80


1 2 3 4

.48 -3.36 -4.8 -.48

-3.36 .52 3.6 3.36

-4.8 3.6 4 4.8

[!]1 = -.48 3.36 4.8 .48

3.36 -.52 -3.6 -3.36

-4.8 3.6 2 4.8

1 2 3 4

1 0 0 0

0 1 0 0

0 0 1 0

0 0 0 0.8

RT 0 0 0 -0.6

0 0 0 0

1 2 3 4

.48 -3.36 -4.8 -5.568

-3.36 .52 3.6 -1.824

-4.8 3.6 4 1.68

[!]*1 = -5.568 -1.824 1.68 5.5488

8.36 -8.032 -5.6 -1.8816

-4.8 3.6 2 1.68

0

0

0

0

-10

0

* = RT


115/155

0

0

0

* -6

-8

0

MATRIZ REDUCIDA

3 4 6

4 1.68 2 3

! 1.68 5.55 1.68 4

2 1.68 4 6

0 3

-6 4

0 6

D = !>1

0.3645 3

D -1.301 4

0.3645 6

0 1

0 2

0.3645 3

%"$ D -1.301 4

0 5

0.3645 6

* = !* D*

3.4 1

4. 2

0.000 3


116/155

%"$ * -5.8 4

-1.50 5 9


117/155

DESPLAZAMIENTO EN ELEMENTOS "*% &' ($$)&'

"*%& = [A]& / "D%

0 1

0 2

0.3644884145 3

971 -1.30144334 4

0 5

0.3644884145 6

DESPLAZAMIENTO EN ELEMENTOS "% &' ($$)&'

"%& = [R]& / "*%&

0.00000 1

0.00000 2

0.3644 3

971 -0.8105 4

1.04140 5

0.3644 6

?@ERZAS INTERNAS COMPLEMENTARIAS 9:7 &' ($$)&'

"#%& = [!]& / "%&

3.052330122 1

-8.1228846655 2

-4.061442332 3

9:71 -3.052330122 4

8.1228846655 5

-4.061442332 6


0 1


118/155

0 2

9:071 0 3

0 4

0 5

0 6

?@ERZAS INTERNAS TOTALES 9:7 '%%!n""s $%'""#4%& = "#:%& ; "#

3.05 1 ";i"$

-8.123 2 '%"n!

-4.061 3 m%m!n%

9:71 -3.05 4 ";i"$

8.123 5 '%"n!

-4.061 6 m%m!n%

i"#"m" ! !" ";i"$

!s$""mi!n% !$ n% 2


119/155


120/155



5 1 5 4 6 12


121/155

6

0 1

0 2

0 3

0 4

0 5

1 6


122/155

0 0

-12 6

-6 2

0 0

12 -6

-6 4

!s ! !"s

0 0

0 0

0 0

0

0

0 1

0 0

0 0

0 0

0.80 0

0.60 0

0 1

$ ! '%%!n""s

5 6

3.36 -4.80 1

-.52 3.60 2

-3.60 2.00 3

-3.36 4.80 4

SEN α

COS α

(B* 9 7 ( * 9 7


123/155

.52 -3.60 5

-3.60 4.00 6

5 6

3.36 -4.8 1

-.52 3.6 2

-3.6 2 3

-3.36 4.8 4

.52 -3.6 5

-3.6 4 6

5 6

0 0 1

0 0 2

0 0 3

0.6 0 4

0.8 0 5

0 1 6

5 6

8.36 -4.8 1

-8.032 3.6 2

-5.6 2 3

-1.8816 1.68 4

11.4512 -5.6 5

-5.6 4 6

( * 9 7 ( B * 9 7


124/155

0.000 3

-5.8 4

0.000 6


125/155

3.4 1

4. 2

-1.50 5

)&,4)i'i+,2 5

3

4

6

1

2

5

0.000 3

9


126/155

+, -$3+-&,

++, -$(+-&,

++, -$(+-&,


127/155


128/155


129/155

C$,&'$, Di)&(4$)&,

0.60 0.80

l = cos( ) m = sen( )


130/155


131/155


132/155


133/155


134/155

0.3644 3

-1.3014 4

0.3644 6

7T 9


135/155


136/155

m" ! !" '%"n!

!s$""mi!n% !$ n%3


137/155


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139/155


140/155


141/155


142/155


143/155


144/155


145/155

i"#"m" ! m%m!n% !'%


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