METODO DE CROSS EN VIGAS

8/16/2019 METODO DE CROSS EN VIGAS

1/78

ING. La

J.R.T.G. METODO DE CROSS

Datos:

= 3.00 Tn/m Dimensione

1 2 3 = 5.00 Tn/m Tramo

= 7.00 m.L1 L2 = 5.00 m. 12 3

Sección de viga 23 3

Tramo b h I

cm cm cm4 Momento de inercia Vigas de secci12 3 . ! . "#!$# . 23 3 . ! . "#!$# .

%oe&iciente de 'igide( 'elatava modi&icada )*+ K i! " #r.Ki!

Momento de em,otramiento -er&ecto )M i + %argas distri0uidas

%oe&iciente de 'igide( 'elativa )*+ Ki! " Ii!$%i! lementos con nudos r gidos

actor de reducci n 1 # " &.00 5tremo no articulado

'()DR* D+ RIGID+'+S R+%)TI,)S - * +/T* D+ + *TR) I+/T* +R#+'T*

Tramo 1 % I Ki! #actor K i! 2i! 2!i Tn/m m. cm4 cm2 cm2 Tn6m Tn6m

12 3. !. "#!$# . 122# & 122# 612.2# 12.2# 23 #. #. "#!$# . 1!1# & 1!1# 61 .41! 1 .41!

/ do Tramo Ki! 'i!

i i cm2 cm2 actor de distri0uci n de un e5tremo 7i 7

112 122#. 122#. 61.

61. actor de distri0uci n de un nudo

%alcular las uer z as %ortantes 8 Momentos de la viga de secci n rectangular ad unta9

: 2 : 1

: 1: 2 L1L2

&. * +/T* D+ I/+R'I) 4 I

I " bh 3 $&6

6. RIGID+'+S R+%)TI,)S - * +/T* D+ + *TR) I+/T* +R#+'T*

i! " 1i!. % 6 i!

3. #)'T*R+S D+ DISTRI8('I*/

'i! "

∑ 'i

∑ Ki

∑Ci

h

b

d


2/78

2 21 122#. 2;4 . 6 .41!

61. 23 1!1#. 2;4 . 6 .#"3 Nota 9De0e cum,lir


3/78

DI)GR) ) D+ #(+R?imos ositivos

?,licamos un corte en el ,unto de in&le5i n del cortanteen el tramo 12 8 23

V : 1

1 L >

@. DI)GR) ) D+ #(+R


4/78

%onvenci n de signosTramo > V : L

; 12 2. " ". 4 . 3. 1 .!! #.3 23 3.1; 1#.;# 61!.23 #. ".2 3. 2

9

; " , . A ; 99 1.A 6 $6 % " 6 46 ; $ 1 &$6

M 6 M @


5/78

ina

MC-01

s de la viga

b hcm cm

0.00 70.00 0.00 70.00

n rectangular

9 Ki!$ ∑ " 9&.000


6/78

istri0uci n


7/78

3

6;. #

. 3


8/78


9/78

ING. Lami


Datos:

= 6.00 Tn/m Dimensiones d

a 0 c = 6.00 Tn/m Tramo b= @.00 m. cm

L1 L2 = @.00 m. a0 30.0 Sección de viga 0c 30.0

Tramo b h I

cm cm cm4 Momento de inercia Vigas de seccion ra0 3 . ! . "#!$# . 0c 3 . ! . "#!$# .

%oe&iciente de 'igide( 'elatIva modi&icada )*+ K i! " #r.Ki!






a0 2. . "#!$# . 142;.1 ! 0.75 1 !1."!# 6 . . 0c 2. . "#!$# . 142;.1 ! 0.75 1 !1."!# 6 . .

/ do Tramo Ki! 'i!

i i cm2 cm2 actor de distri0uci n de un e5tremo 7i 7 a

a0 1 !1."" 1 !1."" 61. 61.

actor de distri0uci n de un nudo


: 1 : 2 : 1: 2 L1L2

&. * +/T* D+ I/+R'I) 4 I

I " bh 3 $&6


i! " 1i!. % 6 i!


'i! " 9∑ "

∑ Ki ∑ Ci

h

b

d


10/78

00a 1 !1."" 2143.!# 6 .#

61. 0c 1 !1."" 2143.!# 6 .# Nota 9De0e cum,lir


11/78


12/78

a

C-05

la viga

hcm

0 70.00 0 70.00

ectangular

i!$ ∑ 9 .


13/78


14/78


15/78

ING. La


:1 Datos::2 Sección

= 5.00 Tn/m Dimensionea 0 c d = 6.00 Tn/m Tramo

= @.00 m.L1 L2 L3 = @.00 m. a0 3

= @.00 m. 0c 3cd 3

Tramo b h I

cm cm cm4 Momento de inercia Vigas de seccioa0 3 . ! . "#!$# . 0c 3 . ! . "#!$# . cd 3 . ! . "#!$# .







a0 #. . "#!$# . 142;.1 ! & 142;.1 ! 61#. 1#. 0c #. . "#!$# . 142;.1 ! & 142;.1 ! 61#. 1#. cd 2. . "#!$# . 142;.1 ! & 142;.1 ! 6 . .

/ do Tramo Ki! 'i!

i i cm2 cm2 actor de distri0uci n de un e5tremo 7i 7 a

a0 142;.1! 142;.1! 61. 61.

actor de distri0uci n de un nudo

%alcular las uer z as %ortantes 8 Momentos de la viga de secci n rectangular ad unta9 %onsiderar I constante

: 1: 2 L1L2 L3

&. * +/T* D+ I/+R'I) 4 I

I " bh 3 $&6


i! " 1i!. % 6 i!


'i! "∑ 'i

∑ Ki ∑ Ci

h


16/78

00a 142;.1! 2"#".33 6 .#

61. 0c 142;.1! 2"#".33 6 .# Nota 9De0e cum,lir


17/78

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

DI)GR) ) D+ #(+R


18/78

ina

MC-05

de vigas de la vigab h

cm cm

0.00 70.00 0.00 70.00 0.00 70.00

n rectangular

9 Ki!$ ∑ Ki " 9&.000

d


19/78

istri0uci n

0.000

90.0C6

0.0C6

6 .1"!# .1"" 1.# 61.# 6 .

. 61.

d


20/78


21/78

ING.


Datos:

= 3.00 Tn/m Di

a 0 c = 5.00 Tn/m T

= 7.00 m.L1 L2 = 5.00 m.

Sección de viga = 3.00 Tn

= 3.00 Tn

Tramo b h I

cm cm cm4 Momento de inercia Vigasa0 3 . ! . "#!$# . 0c 3 . ! . "#!$# .







a0 3. !. "#!$# . 122# & 122# 612.2# 12.2#

0c #. #. "#!$# . 1!1# & 1!1# 61 .41! 1 .41! Tramo % I Ki! #actor K i! 2i! 2!i

Tn/m m. cm4 cm2 cm2 Tn6m Tn6m

a0 3. !. "#!$# . 122# & 122# 62. 2# 2. 2# 0c 3. #. "#!$# . 1!1# & 1!1# 61."!# 1."!#

/ do Tramo Ki! 'i! i i cm2 cm2 actor de distri0uci n de un e5tremo 7i 7

a0 122#. 122#. .


- 1 : 2 - 2 : 1

: 1: 2 L1L2 - 1- 2

&. * +/T* D+ I/+R'I) 4 I

I " bh 3 $&6


i! " 1i!. % 6 i!


∑ Ki∑ Ci

h

b

d


22/78

.actor de distri0uci n de un nudo

00a 122#. 2;4 . 6 .41!

61. 0c 1!1#. 2;4 . 6 .#"3 Nota 9De0e cum,lir


23/78

0 1 2 3 4 5 6 7 8 9 10 11

-20

-15

-10

-5

0

5

10

15

20

25

1; 0.00

1; -16.36

11; 11.20

21; 0.00

1; -14.13

11; 8.38

-16.36

0.00

DI)GR) ) D+ * +/T*S#%+'T*R+S

4Tn9m +

%4m.


24/78

Lamina

MC-05

ensiones de la vigaamo b h

cm cm

a0 30.00 70.00

0c 30.00 70.00

de seccion rectangular

14."!#

614."!#

12.2;612.2;

'i! " 9 Ki!$ ∑


25/78

s de distri0uci n

∑ 'i " 9&.000

12

-9.18; -9.96


26/78

12

; 2.530.00


27/78

ING.


Datos:

= 3.00 Tn/m1 2I 2 I 3 I 4 = @.00 Tn/m

.#L1 .#L2 = 5.00 m.L1 L2 L3 = 3.00 m.

Sección de viga = 5.00 Tn

= 3.00 Tn

Tramo b h I

cm cm cm4 Momento de inercia12 3 . ! . "#!$# . 23 3 . ! . "#!$# . 34 3 . ! . "#!$# .



%oe&iciente de 'igide( 'elativa )*+ Ki! " Ii!$%i! lementos con nudos



Tramo 1 % I Ki! #actor K i! 2i! 2! Tn/m m. cm4 cm2 cm2 Tn6m Tn6

23 3. #. "#!$# . 1!1# & 1!1# 6 .2# 34 3. 3. "#!$# . 2"#".3333 & 2"#".3333333 613.# 1

Tramo % I Ki! #actor K i! 2i! 2! Tn/m m. cm4 cm2 cm2 Tn6m Tn6

12 #. . "#!$# . 142;.1 ! 6 2"#".3333333 63.!# 23 3. #. "#!$# . 1!1# & 1!1# 61."!#

/ do Tramo Ki! 'i!

i i cm2 cm2 actor de distri0uci n de un e5tremo 7i 7 12 2"#".33 2"#".33 .


- 1 : 1 - 2

: 1L1L2 L3- 1- 2

&. * +/T* D+ I/+R'I) 4 I

I " bh 3 $&6


i! " 1i!. % 6 i!


∑ Ki

∑Ci

h

b

d


28/78

.actor de distri0uci n de un nudo

2 21 2"#".33 4#!3.33 6 . 2#

61. 23 1!1#. 4#!3.33 6 .3!# Nota 9De0e cum,lir


29/78

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

-15

DI)GR) ) D+ #(+R


30/78

Lamina

MC-05

Dimensiones de la vigaTramo b h

cm cm

12 30.00 70.00

23 30.00 70.00

34 30.00 70.00

Vigas de seccion rectangular

gidos

i Mto. Tn6m

.2# 23 6".12# 3.# 32 ".12#

i

3.!# 1."!#

'i! " 9 Ki!$ ∑ Ki


31/78

ctores de distri0uci n

9&3.@ = 0.000

. 34

6 . 4# 6 . ";!#

.1" 0.0 0

6 .234 6 .4 ;

.;3" .4 ;61.";# 63.!";

!.#!" 3.!";

6 .!# 613.# 613.# 13.#

6 . 2# 61.

!i n.

96.77&0.77

0.0@

∑ 'i " 9&.000


32/78

13 14


33/78

ING. Lami

J.R.T.G. METODO DEFORMACIONES ANGULARES D

rob ema & rob ema 7 Datos: Datos:

= 5.00 Tn/m =

= 3.00 Tn/m =

1 2 3 = 7.00 m. 1 2 3 == 5.00 m. .# L1 .# L2 =

L1 L2 L1 L2 ==

rob ema 6 rob ema C Datos: Datos:

= =.00 Tn/m =

= 3.00 Tn/m =1 2 3 = 7.00 m. 1 2 3 =

.# L1 = @.00 m. .# L1 .# L2 =L1 L2 = =.00 Tn L1 L2 =

=

rob ema 3 rob ema Datos:

Datos:=

= 3.00 Tn/m =

1 2 3 = 9 Tn/m 1 2 3 == 7.00 m. .# L1 .# L2 =

L1 L2 = 5.00 m. L1 L2 ==

rob ema = rob ema &0 Datos:

Datos:=

= 3.00 Tn/m =

1 2 3 = 9 Tn/m 1 2 3 == 7.00 m. .# L1 .# L2 =

L1 L2 = 5.00 m. L1 L2 ==

rob ema 5 rob ema &&

Datos: Datos:

= 3.00 Tn/m =

1 2 3 = 9 Tn/m 1 2 3 =.# L2 = 7.00 m. .# L1 .# L2 =

L1 L2 = 5.00 m. L1 L2 == 5.00 Tn =

=

rob ema @ rob ema &6

Di0u ar el diagrama de uer z as %ortantes 8 Momentos de la estructura ad unta. %onsiderar I constante9

- 1 - 2 : 1 : 1

: 2 : 1 : 2 : 1: 2 : 2 L1 L1L2 L2

- 1- 2

- 1 - 1 - 2 : 1 : 2

: 2 : 1 : 1 : 1: 2 : 2 L1 L1L2 L2 - 1 - 1

- 2

- 1 - 2 : 1 : 1

: 1: 1 : 2 : 2 L1L1 L2 L2 - 1

- 2

- 1 - 2

: 1 : 1 : 1: 1 : 2 : 2 L1L1 L2 L

2 -

1- 2

- 1 - 1 - 2 : 1 : 1

: 1 : 1: 2 : 2 L1 L1L2 L2 - 1 - 1

- 2

- 1 - 1 - 2


34/78

Datos: Datos:

= 3.00 Tn/m =

1 2 3 = 9 Tn/m 1 2 3 =.# L2 = 7.00 m. .# L1 .# L2 =

L1 L2 = 5.00 m. L1 L2 == 5.00 Tn =

: 1 : 1

: 1 : 1: 2 L1L1 L2 L2 - 1- 1 - 2


35/78

a

A-01

5.00 Tn/m

3.00 Tn/m

7.00 m. 5.00 m. 5.00 Tn 5.00 Tn

3.00 Tn/m

5.00 Tn/m 7.00 m. 5.00 m. 5.00 Tn 5.00 Tn

3.00 Tn/m

9 Tn/m

7.00 m. 5.00 m. 5.00 Tn 5.00 Tn

3.00 Tn/m

9 Tn/m

7.00 m. 5.00 m.

=.00 Tn =.00 Tn

3.00 Tn/m

9 Tn/m 7.00 m. 5.00 m. 5.00 Tn =.00 Tn


36/78

3.00 Tn/m

7.00 m. 5.00 m. 5.00 Tn

=.00 Tn


37/78

ING. Lami


rob ema &3 rob ema &Datos: Datos:

= 3.00 Tn/m =

= 5.00 Tn/m =1 2 3 = 7.00 m. 1 2 3 =

= 5.00 m. .# L1 .# L2 =L1 L2 L1 L2 =

=

rob ema &= rob ema 60

Datos: Datos:

= 5.00 Tn/m =

= 3.00 Tn/m =1 2 3 = 7.00 m. 1 2 3 =

.# L1 = 5.00 m. .# L1 .# L2 =L1 L2 = 5.00 Tn L1 L2 =

=

rob ema &5 rob ema 6& Datos:

Datos:=

= 3.00 Tn/m =

1 2 3 = 9 Tn/m 1 2 3 == 7.00 m. .# L1 .# L2 =

L1 L2 = 5.00 m. L1 L2 ==

rob ema &@ rob ema 66 Datos:

Datos:=

= 3.00 Tn/m =

1 2 3 = 9 Tn/m 1 2 3 =

= 7.00 m. .# L1 .# L2 =L1 L2 = 5.00 m. L1 L2 ==

rob ema &7 rob ema 63

Datos: Datos:

= 3.00 Tn/m =

1 2 3 = 9 Tn/m 1 2 3 =.# L2 = 7.00 m. .# L1 .# L2 =

L1 L2 = 7.00 m. L1 L2 == 5.00 Tn =

! =

rob ema &C rob ema 6=


- 1 - 2 : 1 : 1

: 2 : 1 : 2 : 1: 2 : 2 L1 L1L2 L2

- 1- 2

- 1 - 1 - 2 : 1 : 2

: 2 : 1 : 1 : 1: 2 : 2 L1 L1L2 L2 - 1 - 1

- 2

- 1 - 2 : 1 : 1

: 1: 1 : 2 : 2 L1L1 L2 L2 - 1

- 2

- 1 - 2

: 1 : 1 : 1: 1 : 2 : 2 L1L

1L

2 L2 - 1

- 2

- 2 - 1 - 2 : 1 : 1

: 1 : 1: 2 : 2 L1 L1L2 L2 - 1 - 1

- 2


38/78

Datos: Datos:

= 3.00 Tn/m =

1 2 3 = 9 Tn/m 1 2 3 =.# L1 .# L2 = @.00 m. .# L1 .# L2 =

L1 L2 = 5.00 m. L1 L2 == 5.00 Tn =

=

- 1 - 1 - 2 : 1 : 1

: 1 : 1: 2 : 2 L1 L1L2 L2 - 1 - 1

- 2


39/78

a

A-02

=.00 Tn/m

3.00 Tn/m 7.00 m. 5.00 m. 5.00 Tn 5.00 Tn

3.00 Tn/m

5.00 Tn/m 7.00 m. 5.00 m. 5.00 Tn 5.00 Tn

3.00 Tn/m

9 Tn/m

7.00 m. 5.00 m. =.00 Tn =.00 Tn

3.00 Tn/m

5.00 Tn/m

7.00 m.

5.00 m. 3.00 Tn 3.00 Tn

3.00 Tn/m

9 Tn/m 7.00 m. @.00 m. 5.00 Tn

3.00Tn


40/78

3.00 Tn/m

9 Tn/m @.00 m.

5.00 m. 5.00 Tn 3.00 Tn


41/78

ING. Lami


rob ema 65 rob ema 3&Datos: Datos:

= 5.00 Tn/m =

= =.00 Tn/m =

1 2 3 = 7.00 m. 1 2 3 == 5.00 m. .# L1 .# L2 =

L1 L2 L1 L2 ==

rob ema 6@ rob ema 36 Datos: Datos:

= 5.00 Tn/m =

= 3.00 Tn/m =1 2 3 = 7.00 m. 1 2 3 =

.# L1 = 5.00 m. .# L1 .# L2 =L1 L2 L1 L2 =

=

rob ema 67 rob ema 33Datos:

Datos:=

= 3.00 Tn/m =

1 2 3 = 9 Tn/m 1 2 3 == 7.00 m. .# L1 .# L2 =

L1 L2 = 5.00 m. L1 L2 ==

rob ema 6C rob ema 3=Datos:

Datos:=

= 3.00 Tn/m =

1 2 3 = 9 Tn/m 1 2 3 == 7.00 m. .# L1 .# L2 =

L1 L2 = 5.00 m. L1 L2 ==

rob ema 6 rob ema 35

Datos: Datos:

= 3.00 Tn/m =

1 2 3 = 9 Tn/m 1 2 3 =.# L2 = 7.00 m. .# L1 .# L2 =

L1 L2 = @.00 m. L1 L2 == 5.00 Tn =

=

rob ema 30 rob ema 3@


- 1 - 2 : 1 : 1

: 2 : 1 : 2 : 1: 2 : 2 L1 L1L2 L2

- 1- 2

- 1 - 1 - 2 : 1 : 2

: 2 : 1 : 1 : 1: 2 : 2 L1 L1L2 L2

- 1- 2

- 1 - 2 : 1 : 1

: 1: 1 : 2 : 2 L1L1 L2 L2 - 1

- 2

- 1 - 2

: 1 : 1 : 1: 1 : 2 : 2 L1L1 L2 L

2 -

1- 2

- 1 - 1 - 2 : 1 : 1

: 1 : 1: 2 : 2 L1 L1L2 L2 - 1 - 1

- 2

- 1 - 1 - 2


42/78

Datos: Datos:

= 3.00 Tn/m =

1 2 3 = 9 Tn/m 1 2 3 =.# L1 .# L2 = 7.00 m. .# L1 .# L2 =

L1 L2 = 5.00 m. L1 L2 == 5.00 Tn =

=

: 1 : 1

: 1 : 1: 2 : 2 L1 L1L2 L2 - 1 - 1

- 2


43/78

a

A-03

=.00 Tn/m

6.00 Tn/m

7.00 m. 5.00 m. 5.00 Tn 5.00 Tn

6.00 Tn/m

=.00 Tn/m 7.00 m. 5.00 m. 5.00 Tn 5.00 Tn

3.00 Tn/m

9 Tn/m

7.00 m. 5.00 m. 5.00 Tn 5.00 Tn

3.00 Tn/m

9 Tn/m

7.00 m. 5.00 m.

5.00 Tn 5.00 Tn

3.00 Tn/m

9 Tn/m 7.00 m. @.00 m. 5.00 Tn 5.00 Tn


44/78

3.00 Tn/m

9 Tn/m 7.00 m. 5.00 m.

=.00 Tn =.00 Tn


45/78

ING. Lami


rob ema 37 rob ema =&

1 2I 2 I 3 I 4 1 2I 2 I 3 I 4.# L2

L1 L2 L3 L1 L2 L3

Datos: = 3.00 Tn/m Datos: = 3.00 Tn/m

= 5.00 Tn/m = 7.00 m.= 7.00 m. = 5.00 m.

= 5.00 m. = 6.00 m.= 6.00 m. = 5.00 Tn

= @.00 Tn

rob ema 3C rob ema =6

1 2I 2 I 3 I 4 1 2I 2 I 3 I 4.# L1 .# L2

L1 L2 L3 L1 L2 L3

Datos: = =.00 Tn/m Datos: = 3.00 Tn/m

= 3.00 Tn/m = 9 Tn/m= 7.00 m. = 7.00 m.= @.00 m. = 5.00 m.

= 6.00 m. = @.00 m.= =.00 Tn = 5.00 Tn

rob ema 3 rob ema =3

1 2I 2 I 3 I 4 1 2I 2 I 3 I 4.# L1 .# L2

L1 L2 L3 L1 L2 L3

Datos: = 3.00 Tn/m Datos: = 5.00 Tn/m

= 9 Tn/m = 3.00 Tn/m= 7.00 m. = 7.00 m.= 5.00 m. = 5.00 m.

rob ema =0 rob ema ==

1 2I 2 I 3 I 4 1 2I 2 I 3 I 4

Di0u ar el diagrama de uer z as %ortantes 8 Momentos de la estructura ad unta9

- 1 - 2 : 1 : 1

: 2

: 1 : 1: 2 L1L1 L2

L2 L3L3 - 1

- 2

- 1 - 1: 1 : 1

: 2

: 1 : 1: 2 : 2 L1 L1L2 L2 L3 L3- 1 - 1

- 1 - 2 : 1 : 1

: 2

: 1 : 1 L3: 2 : 2 - 1L1 L1 - 2 L2 L2

- 1 - 1 - 2 : 2

: 1 : 1


46/78

.# L1 .# L2

L1 L2 L3 L1 L2 L3

Datos: = 3.00 Tn/m Datos: = 3.00 Tn/m =

= 6.00 Tn/m = 5.00 Tn/m == 7.00 m. = 7.00 m. == 5.00 m. = 5.00 m.

= &.50 m.

rob ema =5

1 2I 2 I 3 I 4.# L1 .# L2

L1 L2

Datos: = 3.00 Tn/m= 7.00 m.= 5.00 m.

= &.50 m.= =.00 Tn= =.00 Tn

rob ema =@

1 2I 2 I 3 I 4.# L1 .# L2

L1 L2

Datos: = 3.00 Tn/m= 7.00 m.= 5.00 m.

= &.50 m.= =.00 Tn= =.00 Tn

rob ema =7

1 2I 2 I 3 I 4.# L1 .# L2

L1 L2

Datos: = 3.00 Tn/m= 7.00 Tn/m= 7.00 m.

= &.50 m.

= 5.00 Tn= =.00 Tn

= &.00 Tn

: 1 : 1 L3- 1 : 2 - 1L1 L1 - 2 L2 L2 L3

- 1 - 2 : 1

: 1L1L2 L3- 1- 2

- 1 - 2

: 1

: 1L1L2 L3- 1- 2

- 1 - 2 - 3: 1

: 1L1L1L2 -

1- 2 - 3


47/78

rob ema =C

1 2I 2 I 3 I 4

.# L1 .# L2 L1 L2

Datos: = 3.00 Tn/m= 7.00 m.= 5.00 m.= 5.00 Tn= =.00 Tn

- 1 - 2 : 1

: 1L1L2 - 1- 2


48/78

a

A-04

= &.50 m.

= 5.00 Tn= 5.00 Tn


49/78

6.00 m.

=.00 Tn =.00 Tn


50/78


51/78

ING.

J.R.T.G. METODO DEFORMACIONES ANGULARES

rob ema = rob ema 55 Datos:

= 3.00 Tn/m

= 5.00 Tn/m

1 2I 2 I 3 I 4 = 7.00 m. 1 2I 2 I 3 I = 5.00 m. .# L1 .# L2

L1 L2 L3 L1 L2 L3

rob ema 50 rob ema 5@ Datos:

= 5.00 Tn/m

= 3.00 Tn/m1 2I 2 I 3 I 4 = 7.00 m. 1 2I 2 I 3 I

.# L1 = 5.00 m. .# L1 .# L2 L1 L2 L3 = 5.00 Tn L1 L2 L3

rob ema 5& rob ema 57

Datos:

= 3.00 Tn/m

1 2I 2 I 3 I = 9 Tn/m 1 2I 2 I 3 I = 7.00 m. .# L1 .# L2

L1 L2 L3 = 5.00 m. L1 L2 L3

rob ema 56 rob ema 5C

Datos:

= 3.00 Tn/m

1 2I 2 I 3 I 4 = 9 Tn/m 1 2I 2 I 3 I = 7.00 m. .# L1 .# L2

L1 L2 L3 = 5.00 m. L1 L2 L3


Datos:

= 3.00 Tn/m

1 2I 2 I 3 I 4 = 9 Tn/m 1 2I 2 I 3 I .# L2 = 7.00 m. .# L1 .# L2

L1 L2 L3 = 7.00 m. L1 L2 L3

Di0u ar el diagrama de uer z as %ortantes 8 Momentos de la estructura ad unta9

- 1 - 2 : 1 : 1

: 2 : 1 : 2 : 2 L1L2

- 1 - 1 - 2 : 1 : 2

: 2 : 1 : 1: 2 L1L2 - 1

- 1 - 2 : 1 : 1

: 1: 2 L1L2

- 1 - 2

: 1 : 1: 1: 2 L1L2

- 2 - 3 - 1 - 2 : 1 : 1

: 1:

2 L1L2


52/78

= 5.00 Tn!

rob ema 5= rob ema @0

Datos:

= 3.00 Tn/m

1 2I 2 I 3 I 4 = 9 Tn/m 1 2I 2 I 3 I .# L1 .# L2 = @.00 m. .# L1 .# L2

L1 L2 L3 = 5.00 m. L1 L2 L3= 5.00 Tn

- 1

- 1 - 1 - 2 : 1 : 1

: 1: 2 L1L2 - 1


53/78

Lamina

DA-05

Datos:

= =.00 Tn/m

= 3.00 Tn/m

4 = 7.00 m.= 5.00 m.= 5.00 Tn= 5.00 Tn

Datos:

= 3.00 Tn/m

= 5.00 Tn/m4 = 7.00 m.

= 5.00 m.= 5.00 Tn= 5.00 Tn

Datos:

= 3.00 Tn/m

= 9 Tn/m

4 = 7.00 m.= 5.00 m.= =.00 Tn= =.00 Tn

Datos:

= 3.00 Tn/m

= 5.00 Tn/m

4 = 7.00 m.= 5.00 m.= 3.00 Tn= 3.00 Tn

Datos:

= 3.00 Tn/m

4 = 9 Tn/m= 7.00 m.= @.00 m.

: 1: 2 L1L2 - 1- 2

: 1: 2 L1L2 - 1- 2

: 1: 2 L1L2 - 1- 2

: 1: 2 L1L2 - 1- 2

- 3

: 1

: 2 L1L2


54/78

= 5.00 Tn= 3.00 Tn

Datos:

= 3.00 Tn/m

4 = 9 Tn/m= @.00 m.= 5.00 m.= 5.00 Tn= 3.00 Tn

- 1- 2

: 1: 2 L1L2 - 1- 2


55/78

ING. Lami


rob ema @& rob ema @7 Datos: Datos:

= 5.00 Tn/m =

= 3.00 Tn/m =

1 2 3 = 7.00 m. 1 2 3 == 5.00 m. .# L1 .# L2 =

L1 L2 L1 L2 ==

rob ema @6 rob ema @C Datos: Datos:

= =.00 Tn/m =

= 3.00 Tn/m =1 2 3 = 7.00 m. 1 2 3 =

.# L1 = @.00 m. .# L1 .# L2 =L1 L2 = =.00 Tn L1 L2 =

=

rob ema @3 rob ema @Datos:

Datos:=

= 3.00 Tn/m =

1 2 3 = 9 Tn/m 1 2 3 == 7.00 m. .# L1 .# L2 =

L1 L2 = 5.00 m. L1 L2 ==

rob ema @= rob ema 70 Datos:

Datos:=

= 3.00 Tn/m =

1 2 3 = 9 Tn/m 1 2 3 == 7.00 m. .# L1 .# L2 =

L1 L2 = 5.00 m. L1 L2 ==

rob ema @5 rob ema 7&

Datos: Datos:

= =.00 Tn/m =

1 2 3 = 9 Tn/m 1 2 3 =.# L2 = 7.00 m. .# L1 .# L2 =

L1 L2 = 5.00 m. L1 L2 == 5.00 Tn =

=

rob ema @@ rob ema 76


- 1 - 2 : 1 : 1

: 2 : 1 : 2 : 1: 2 : 2 L1 L1L2 L2

- 1- 2

- 1 - 1 - 2 : 1 : 2

: 2 : 1 : 1 : 1: 2 : 2 L1 L1L2 L2 - 1 - 1

- 2

- 1 - 2 : 1 : 1

: 1: 1 : 2 : 2 L1L1 L2 L2 - 1

- 2

- 1 - 2

: 1 : 1 : 1: 1 : 2 : 2 L1L1 L2 L

2 -

1- 2

- 1 - 1 - 2 : 1 : 1

: 1 : 1: 2 : 2 L1 L1L2 L2 - 1 - 1

- 2

- 1 - 1 - 2


56/78

Datos: Datos:

= =.00 Tn/m =

1 2 3 = 9 Tn/m 1 2 3 =.# L2 = 7.00 m. .# L1 .# L2 =

L1 L2 = 5.00 m. L1 L2 == 5.00 Tn =

: 1 : 1

: 1 : 1: 2 L1L1 L2 L2 - 1- 1 - 2


57/78


58/78

=.00 Tn/m

7.00 m. 5.00 m. 5.00 Tn

=.00 Tn


59/78

ING. Lami



.# L1

4 1.# I # 1.# I Datos: 4 1.# I # 1.# I Datos:

I I I A = =.00 Tn/m I I I A =A = 3.00 m. A =

= 5.00 m. == 5.00 m. =

1 2 3 1 2 2 3 3 =L1 L2 L1 L2

rob ema 7= rob ema 7C

.# L1

4 1.# I # 1.# I Datos: 4 1.# I # 1.# I Datos:

I I I A = 5.00 Tn/m I I I A =

= 6.00 Tn/m =A = 3.00 m. A =

= 5.00 m. =1 2 2 3 3 = 5.00 m. 1 2 2 3 3 =

L1 L2 L1 L2 =


.# L1

4 1.# I # 1.# I Datos: 4 1.# I # 1.# I Datos:

I I I = 6.00 Tn/m I I I =

A = =.00 Tn/m A =A = 3.00 m. A =

= 5.00 m. =1 2 2 3 3 = 5.00 m. 1 2 2 3 3 =

L1 L2 L1 L2

rob ema 7@ rob ema C0

.# L1 .# L1 .# L1 .# L1

4 1.# I # 1.# I Datos: 4 1.# I # 1.# I Datos:

- 1: 1

: 1

: 1 : 1

L1 L1L2 L2

- 1

- 1: 2 : 2

: 1 : 1

: 1 : 1: 2 : 2

L1 L1L2 L2

- 1

- 1: 2

: 1 : 1

: 1 : 1

: 2 - 1

L1 L1L2 L2

- 1 - 1 - 1 - 1

: 1


60/78

I I I = 6.00 Tn I I I =A A =

A = 3.00 m. A == 5.00 m. =

1 2 2 3 3 = 5.00 m. 1 2 2 3 3 =L1 L2 L1 L2

- 1 - 1: 1

L1 L1L2 L2


61/78

a

A-07

=.00 Tn/m 3.00 m. 5.00 m. 5.00 m. 6.00 Tn

3.00 Tn/m

5.00 Tn/m 3.00 m. 5.00 m. 5.00 m. 6.00 Tn

6.00 Tn/m

6.00 Tn 3.00 m. 5.00 m. 5.00 m.


62/78

6.00 Tn 6.00 Tn/m 3.00 m. 5.00 m. 5.00 m.


63/78

ING. Lami


rob ema C& rob ema C5

3 I 4 I # I 3 I 4 I # I

I I I IA

1 2 1 2L1 L2 L1 L1 L2 L1

rob ema C6 rob ema C@

3 I 4 I # I 3 I 4 I # I

I I I I.# L1 .# L1 A .# L1 .# L1

1 2 1 2L1 L2 L1 L1 L2 L1

rob ema C3 rob ema C7

3 I 4 I # I 3 I 4 I # I

I I I I.# L1 A .# L1

1 2 1 2L1 L2 L1 L1 L2 L1

rob ema C= rob ema CC

Di0u ar el diagrama de uer z as %ortantes 8 Momentos de la estructura ad unta. %onsiderar constante9

: 2 : 2 : 1 : 1 : 1 : 1

- 2 - 1 - 2 - 2 - 1 - 2 : 1 : 1

: 2 : 2 : 2 : 2

- 2 - 1 - 2 - 1: 1 : 1

: 2 : 2 : 2 : 2

- 2 - 2 : 1 : 1

M 1 M 1


64/78

3 I 4 I # I 3 I 4 I #

I I I I.# L1 .# L1 A .# L1 .# L1

1 2 1 2L1 L2 L1 L1 L2 L1


65/78

a

A-06

A

A

A


66/78


67/78

ING. Lami


rob ema &

3 I 4 I # I 3 I 4 I #

I I I I.# L1 .# L1 A .# L1 .# L1

1 2 1 2L1 L2 L1 L1 L2 L1

3 I 4 I # I 3 I 4 I # I

I I I I.# L2 A .# L2

1 2 1 2L1 L2 L1 L1 L2 L1

3 I 4 I # I 3 I 4 I #

I I I I.# L2 A .# L2

1 2 1 2L1 L2 L1 L1 L2 L1

M2 M2


: 1 : 1M 1 M 1

: 1 M 1 : 1 : 1 M 1 : 1

: 1 M 1 M 1 : 1 M 1 M 1

M 1 M 1 M 1 M 1


68/78


69/78

a

A-06

I

A

A

I

A


70/78

I

A


71/78

ING. Lami


rob ema &

1 I 2 I 3 I 4 1 I 2 I 3

L1 L2 L1 L1 L2 L1

1 I 2 I 3 I 4 1 I 2 I 3

L1 L2 L1 L1 L2 L1

1 I 2 I 3 I 4 1 I 2 I 3

L1 L2 L1 L1 L2 L1

1 I 2 I 3 I 4 1 I 2 I 3

L1 L2 L1 L1 L2 L1

1 I 2 I 3 I 4 1 I 2 I 3

L1 L2 L1 L1 L2 L1

1 I 2 I 3 I 4 1 I 2 I 3


: 1 : 3 : 1 : 3: 2 : 2

: 1 : 1: 2 : 2

: 2 : 2 : 1 : 1

: 2 : 2 : 1 : 3 : 1 : 3

- 1 - 1 - 1 - 1: 2 : 2

: 1 : 3 : 1 : 3

: 2 : 2 : 1 : 1


72/78

L1 L2 L1 L1 L2 L1

1 I 2 I 3 I 4 1 I 2 I 3

L1 L2 L1 L1 L2 L1

3 I 4 I # I 3 I 4 I # I

I I I I.# L2 A .# L2

1 2 1 2L1 L2 L1 L1 L2 L1

3 I 4 I # I 3 I 4 I #

I I I I.# L2 .# L2

1 2 1 2L1 L2 L1 L1 L2 L1

M2 M2

3 I 4 I # I 3 I 4 I #

: 1 : 1: 2 : 2

: 1 M 1 : 1 : 1 M 1 : 1

: 1 M 1 M 1 : 1 M 1 M 1

M 1 M 1 M 1 M 1


73/78


74/78

a

A-06

I 4

I 4

I 4

I 4

I 4

I 4


75/78

I 4

A

I

A

I


76/78


77/78


78/78

34

33

32

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17

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METODO DE CROSS EN VIGAS