12.- vigas continuas11

8/17/2019 12.- Vigas continuas11

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1.- Geometría del problema

4 m

5 m

6 m

P = 40 KN/mα = 0

E = 210

G = 80

γ = 1.2

3 KN/m

0.2 0.4 m

0.25 0.5 m

0.3 0.6 m

2.- E!e" #oorde$ado"

%1=

%2=

%3=

105 KN/m2

105

K&= 103

'(1=

'(2=

'(3=


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3.- N)merar $)do" * barra"

4.- +oorde$ada" de lo" $)do"

Nudo X

1 0

2 4

3 ,

4 15

5.- $#(de$#(a de la" barra"

Barra Ni Nf

1 1 2

2 2 33 3 4

6.- e"plaam(e$to de la" barra"

Barra

1 0 0 0

2 0

3 0

.- +ara#terí"t(#a" eomtr(#a" * el"t(#a" de #ada barra

Barra

m m

1 4 4 1 0 8 1.1 1.2 0.032

2 5 5 1 0 12.5 2.6 1.2 0.031

3 6 6 1 0 18 5.4 1.2 0.032

8.- atr( de r((de de #ada barra

8.1.- Epre"(o$e" e$erale"

0 d1 0 d1

K1 =22.4 11.2

K1 =21.88 10.6,

11.2 22.4 10.68 21.8,

d1 d2 d3 d1 d2

K1 =43.5 13.125 21.85

K1 =42.6 12.3

13.13 5.25 13.125 12.3 5.0,21

V 1

θ1

V 2

θ2

d1

d1

d2

d3

d2

d3

d4

Δxi

Li

li

mi

Aix

Iix

γi

βi

10-3 m 2 10-3 m 4

Barra 1 β=0 Barra 1 β≠0

103 103


103 103


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21.88 13.125 43.5 20.8, 12.3

d2 d3 d4 d2 d3

K1 = 6.3 -18., -18., K1 = 6.105 -18.31-18., 5.6 3.8 -18.3 3.842

-18., 3.8 5.6 -18.3 36.042

,.- atr( de r((de total

β=0 β≠0

d1 d2 d3 d4 d1

66.15 13.125 21.85 0 64.642

[K] =13.13 14.542 -5.5 -18.,

K =12.3

21.88 -5.5 11,.35 3.8 20.888

0 -18., 3.8 5.6 0

0.022 0.0 -0.004 -0.01 0.0222

-0.03 0.1 0.001 0.034 -0.028

0 0.0 0.010 -0.01 -0.004

-0.01 0.0 -0.005 0.024 -0.005

10.- atr( de #ara" eter(ore" P

10.1.- 7)era" * mome$to" de empotram(e$to pere#to

P

Para 9=0 * 9:

Barra 1 Barra 2

-53.33 p= 40 53.333 -83.33 p= 40

80 80 100

4 5

10.2.- ;e#tore" de #ara" P

30 36. -120


103 103

103 103

[K]-1 = 103 [K]-1 = 103

7


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-220

30

P=-220

36.

-120

β=0 β≠0

d1 d2 d3 d4 d1 d2

.258 .258 .258 .258 .2, .2,2

[d]=-35.4 -35.4 -35.42 -35.42

[d]=-35. -35.4

0.68 0.68 0.68 0.68 0.633 0.6335

-10.8 -10.8 -10.8 -10.8 -10.8 -10.8

d1= .258 d1= .2,2

d2= -35.4 d2= -35.4

d3= 0.68 d3= 0.6335

d4= -10.8 d4= -10.8

12.- +l#)lo de )era" * mome$to" ($ale"

Para 9=0

1=

2

FUERZAS Y MOMENTOS

Frame Joint F F! F" M M! M"

KN KN KN KN-m KN-m KN-m

1 1 0 0 0 0 0 0

1 2 0 0 0 0 0 0

2 2 0 0 0 0 0 0

2 3 0 0 0 0 0 0

3 3 0 0 0 0 0 0

3 4 0 0 0 0 0 0

#ES$LAZAMIENTO #E LOS NU#OS

n%&o' U U! U" R R! R"

m m m Radianes adiane adianes

1 0 0 0 0 0 0

2 0 0 0 0 0 0

3 0 0 0 0 0 0

4 0 0 0 0 0 0

11.- &e"ol)#(@$ del "("tema de e#)a#(o$e" d=K-1P

10-3 10-3

10-3

10-3

10-3

10-3


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REA((IONES

n%&o' F F! F" M M! M"

KN KN KN KN-m KN-m KN-m

1 0 0 0 0 0 0

2 0 0 0 0 0 04 0 0 0 0 0 0


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m-KN m-KN

5.6 5.43

10.,35 10.61

18., 18.31

I II

d3

20.8884

12.3036

EI/Lx103 EIx103/L(1β!


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42.634

d4

-18.3136.04

3.84

d2 d3 d4

12.3036 20.8, 0

14.1, -5.58 -18.3

-5.58 116.61 36.04

-18.3 36.04 3.84

0.0 0.00 -0.01

0.1 0.00 0.03

0.0 0.01 -0.01

0.0 -0.01 0.02

0 por "er #ara "(mtr(#a

Barra 3

83.33333 -120 p= 40 120

100 120 120

6

2/12

/2

%3=


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d3 d4

.2,232 .2,2323856

-35.36, -35.36853662

0.633455 0.633455448

-10.,6 -10.,5880336

10-3

10-3

10-3

10-3


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12.- vigas continuas11

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