7.- viga continua

8/17/2019 7.- Viga Continua

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UNIVERSIFACULTAD DE IN

Integrantes:1.- 2.-

.- !.-

Se"estre: S#$t%"& - Seg'n(&

E)ERCICIO: VIGA CONTINUAMETODO: RIGIDECES

1 1 2

0.35 0.45

* 5.50

E + 2.1E * a /+*G + 0.*E * /3*4+ 1.2*

.5*E * 6N7"

Y

1.- Ge&"etr8a (e9 r& 9e"a:

2.- Dat&s:6N7" 2

6N7" 2

6N7" 2

; R+

.- E


2/86

1 1 2

0.35 0.45

* 5.50

j= 4n= 3

NUDO1 0.002 5.50

12.50! 21.00

=ARRA NI NF1 1 22 2 3

3 4

1 1 2

*

!.- N'"era>%?n (e N'(&s @ =arras:

5.- C&&r(ena(as (e 9&s N'(&s:

%

.- In>%(en>%as (e 9as =arras:

.- Des$9aBa"%ent&s (e 9as =arras: +*

( 1


3/86

=ARRA1 0 0 02 0

0

=ARRAY L%

9% "%" " "

1 5.50 0 5.50 1 0 0.2 7.00 0 7.00 1 0 0.

8.50 0 8.50 1 0 0.

=ARRA 1: ara /+*

6 + EI7L4 22 4

=ARRA 2: ara /+*

6 + EI7L4 6/L 2

6/L 6/L2 6/L 4

=ARRA : ara /+*

6 + EI7L-6/L -6/L

-6/L 4 2-6/L 2 4

ara /+*NUDO 2 NUDO NUDO !

107142 14260.714 33275 0

14261 13438.931 -10663.16 -24924

V1 H1 V2 H2d 1

d 1 d 2 d 3d 2 d 3 d 4

0.- Cara>ter8st%>as Ge&"#tr%>as @ E9 st%>as (e >a(a =arra:

J.- Matr%B (e R%g%(eB (e >a(a =arra:J.1.- E $res%&nes Genera9es:

H1 H2

H1 V2 H2

12/L 2

V1 H1 H212/L 2

1*.- Matr%B (e R%g%(eB T&ta9: 6

(1

(2

( (!


4/86

33275 -10663.16 207785.29 70617.6

0 -24923.88 70617.647 141235

ara /+*NUDO 2 NUDO NUDO !

1E-005 -1.9E-005 -2.2E-006 -2E-006

-2E-005 0.0001408 2.28E-006 2E-005

-2E-006 2.28E-006 6.20E-006 -3E-006

-2E-006 2.37E-005 -2.7E-006 1E-005

=ARRA 1:-12 .*! T-"12 .*! T-"

V+ 1 .5* T V+VK+ 1 .5* T VK+

-12 .*! 12 .*! -2*!.1

1 .5* 1 .5* 1 5.*

78.13

+-476.0496.88

-301.04

11.- Matr%B (e R%g%(eB In ersa: 6 -1

( 1 ( 2 ( ( !

6 -1 +

12.- Matr%B (e Cargas E ter%&res: 12.1.- F'erBas @ M&"ent&s (e E"$&tra"%ent& er e>t&:

MF+ M F+MKF+ MKF+

12.2.- Ve>t&res (e Cargas :

- MF

F F

MF

M

V F


5/86

0.1

1 1 2

*

00.01073

( +-0.07549

( +0.00015

-0.01553

V% + 6% (%M%

=ARRA 1: ara /+*

6 +91.72

561.57

=ARRA 2: ara /+*

6 +-561.5722.60

-505.22

=ARRA : ara /+*

6 +153.06505.22

0.00

1 .- Res&9'>%?n (e9S%ste"a (e E>'a>%&nes: ( + 6 -1

( 1( 2(( !

1!.- Ca9>'9& (e F'erBas @ M&"ent&s F%na9es:

VM

M1M2

M1V2M

V1M1M2


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arJ1. 2 5 1.5 -5 1.5

*.** *.** 2 .!

ar05. 0 55 .2 -55 .2

*.** *.** 2 .2

ara /+*

-2 !.21 ;N

15.- Ca9>'9& (e F'erBa en e9 Res&rte:

F R+ 6 RP( 2 F R+F R+ F R+


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AD CENTRAL DEL ECUADOR GENIERIA, CIENCIAS FISICAS Y MATEMATICA

SCUELA DE INGENIERIA CIVIL

ESTRUCTURAS III

5*6n7"

2 !

0.40 0.55 0.50 0.70

7.00 8.50

+*


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5*6n7"

2 !0

0.40 0.55 0.50 0.70

7.00 8.50

2 !0

( 2( !

(


12/86

/+* /3*% I%

/% /%EI7L EI7LQ1 /+++++++++++

158 0.0027 1.20 0.021 10148 9938.4220 0.0055 1.20 0.019 16638 16320.1350 0.0143 1.20 0.021 35309 34570.3

=ARRA 1: ara /3*

6 + EI7LQ1 /+++++++++++4 + 2 -2 - 4 +

=ARRA 2: ara /3*

6 + EI7LQ1 /+++++++++++4 + 6/L 2 -6/L 6/L2 - 6/L 4 +

=ARRA : ara /3*

6 + EI7LQ1 /+++++++++++-6/L -6/L

-6/L 4 + 2 --6/L 2 - 4 +

ara /3*NUDO 2 NUDO NUDO !

105561 13989 32323 0

13989 13239 -10414 -24403

2 " !

H1 H2

H1 V2 H2

12/L 2

V1 H1 H212/L 2

(1

(2

( (!


13/86

32323 -10414 204618 68402

0 -24403 68402 139020

ara /3*NUDO 2 NUDO NUDO !

1.3E-005 -2E-005 -2E-006 -2E-006

-2E-005 0.00014 2E-006 2E-005

-2E-006 2E-006 6E-006 -3E-006

-2E-006 2E-005 -3E-006 1E-005

=ARRA 2: =ARRA :-2*!.1 T-" - *1.*! T-"2*!.1 T-" *1.*! T-"1 5.** T V+ 212.5* T1 5.** T VK+ 212.5* T

2*!.1 - *1.*! *

* 1 5.** 212.5* 212.5*

( 1 ( 2 ( ( !

6 -1 +

MF+MKF+

simétricacargaser por

0y0 para 12

2

≠== β β pL

2

pL=


14/86

-! .*!

- *1.*!J .00

2 !0

00.01077

-0.07589

0.00010

-0.01554

=ARRA 1: ara /3*

6 +85.68

556.26

=ARRA 2: ara /+*

6 +-556.26

23.73

-502.66

=ARRA : ara /+*

6 +153.36502.66

0.00

( 1( 2(( !

M1M2

M1V2M

V1M1M2


15/86

a /+*-5*5.22 5*5.22 *.

* 22. * 15 .* 2 1.J!

-2 !.21a /3*

-5*2. 5*2. *.

2 . 15 . 2 1. !

-2 5.

ara /3*

-2 5. ;N

F R+

F R+

6 RP( 2


16/86


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21/86

=ARRA 1: ara /+*

*

6 +40592.05 20296.0220296.02 40592.05

=ARRA 2: ara /+*

6 +66550 14260.71 33275

14260.71 4074.49 14260.7133275 14260.71 66550

=ARRA : ara /+*

6 +5864.441 -24923.88 -24923.88-24923.88 141235.3 70617.65-24923.88 70617.65 141235.3

J.2.- Va9&res Ca9>'9a(&s:

( 1

( 1 ( 2 (

( 2 ( ( !


22/86

.*!


23/86


24/86

*

*


25/86


26/86


27/86


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30/86

=ARRA 1: ara /3*

*

6 +39963.3363 19667.313619667.3136 39963.3363

=ARRA 2: ara /3*

6 +65598 13989 3232313989 3997 1398932323 13989 65598

=ARRA : ara /3*

6 +5741.77783 -24402.5558 -24402.5558-24402.5558 139019.686 68402.0385-24402.5558 68402.0385 139019.686

( 1

( 1 ( 2 (

( 2 ( ( !


31/86


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=ARRA 1: ara /+*

6 ( +217.7662

435.53231

=ARRA 2: ara /+*

6 ( +-357.4073

-152.398925-709.385165

=ARRA : ara /+*

6 ( +-59.4375

806.260165-301.041667


33/86


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M +-126.04

6 ( +211.7256

126.04 430.219506

V +-204.17

6 ( +-352.0945

175.00 -151.273881204.17 -706.822662

V +212.50

6 ( +-59.1360

-301.04 803.697662301.04 -301.041667


42/86


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=ARRA 1: ara /3*

V +-126.04126.04

=ARRA 2: ara /3*

V +-204.17175.00204.17

=ARRA : ara /3*

V +212.50-301.04301.04


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! .- Estabilidad y determinación est"tica e#terna de la estructura

= 6

C*%"# + nN" L# #"%#d$"#

.D.I. = 3L# #"%#d$"# !# ' n $ *n: $"# + n ;!

$ .- Estabilidad interna de la armadura

.2.- N = 3 - 12 15

% .- Estabilidad y determinación est"tica total de la armadura

N! = N < N" 21! = 3 21

C*%"# + nN! = !

& .- 'oordenadas de los nudos

NUDO1 0.00 0.00 0.002 5.00 0.00 9.00

10.00 0.00 0.00! 2.50 4.00 2.005 5.00 4.00 6.00

7.50 4.00 2.005.00 8.00 4.00

( .- )ncidencias de las barras

NUDO DIAMETRO

N" > .

?A@ 0

.1.- CB $ * >+ $#' d '# '$'# , + #% n! d '# #"%#d$"# + *n !"+#n $'#

N! > . !

% @% B%


57/86

Q""1 1 4 25 490.872 1 5 25 490.87

2 5 25 490.87! 2 6 25 490.875 3 6 25 490.87

3 4 25 490.874 5 25 490.87

0 5 6 25 490.87J 6 4 25 490.87

1* 4 7 25 490.8711 5 7 25 490.8712 6 7 25 490.87

1* .- +espla amientos de los nudos y en cada una de las barras

NUDO INICIAL=ARRA

1 0 0 0 d12 0 0 0 d4

0 0 0 d4! 0 0 0 d75 0 0 0 d7

0 0 0 d1d1 d2 d3 d4

0 d4 d5 d6 d7J d7 d8 d9 d1

1* d1 d2 d3 d1011 d4 d5 d6 d1012 d7 d8 d9 d10

11 .- '"lculo de longitudes, cosenos directores y rigide a#ial en cada

=ARRA@ B L

Q" Q" Q" Q"1 2.5 4 2 5.122 5 4 6 8.77

0 4 -3 5.00! 2.5 4 -7 8.445 -2.5 4 2 5.12

-7.5 4 2 8.732.5 0 4 4.72

0 2.5 0 -4 4.72

INICIAL Qn % FINAL Qn

% @% B%


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J -5 0 0 5.001* 2.5 4 2 5.1211 0 4 -2 4.4712 -2.5 4 2 5.12

12 .- atri de rigide para cada barra de la armadura

=ARRA 14.79 7.66 3.83 -4.797.66 12.26 6.13 -7.663.83 6.13 3.07 -3.83

-4.79 -7.66 -3.83 4.79-7.66 -12.26 -6.13 7.66-3.83 -6.13 -3.07 3.83

=ARRA 0.00 0.00 0.00 0.000.00 13.19 -9.90 0.000.00 -9.90 7.42 0.000.00 0.00 0.00 0.000.00 -13.19 9.90 0.000.00 9.90 -7.42 0.00

=ARRA 54.79 -7.66 -3.83 -4.79

-7.66 12.26 6.13 7.66-3.83 6.13 3.07 3.83-4.79 7.66 3.83 4.797.66 -12.26 -6.13 -7.663.83 -6.13 -3.07 -3.83

=ARRA 6.14 0.00 9.82 -6.140.00 0.00 0.00 0.009.82 0.00 15.71 -9.82

-6.14 0.00 -9.82 6.140.00 0.00 0.00 0.00

-9.82 0.00 -15.71 9.82

=ARRA J20.62 0.00 0.00 -20.62

0.00 0.00 0.00 0.00

6 G +

6 G +

6 G +

6 G +


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0.00 0.00 0.00 0.00-20.62 0.00 0.00 20.62

0.00 0.00 0.00 0.000.00 0.00 0.00 0.00

=ARRA 110.00 0.00 0.00 0.000.00 18.44 -9.22 0.000.00 -9.22 4.61 0.000.00 0.00 0.00 0.000.00 -18.44 9.22 0.000.00 9.22 -4.61 0.00

13 .- atri de rigide total para la armadura

NUDO !(1 (2

NUDO !(1 45.04 10.68(2 10.68 27.00( 15.16 13.50

NUDO 5(! -6.14 0.00(5 0.00 0.00

( -9.82 0.00

NUDO ( -20.62 0.00(0 0.00 0.00(J 0.00 0.00

NUDO (1* -4.79 -7.66(11 -7.66 -12.26(12 -3.83 -6.13

0.0776 0.00820.0082 0.1116

-0.0482 -0.09090.0046 -0.0463

-0.0019 -0.0009-0.0025 -0.02500.0776 0.00810.0270 0.00260.0431 0.00710.0261 0.05620.0078 0.02390.0169 0.0246

6 G +

6 G +

6 T +

6 T-1

+


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1! .- Matr%B (e >argas

"#d* d '+ "!#d % = 12!#d* d #" # n = 1

0 1 NNUDO 40 2 N

0 3 N10 4 N

NUDO 50 5 N + 0 6 N

0 7 NNUDO 60 8 N

0 9 N0 10 N

NUDO 7-15 11 N0 12 N

1! .- esolución del sistema de ecuaciones

)$ "F# +n! "n# < )$ "F# ;! "n# = 0 ?G@H?d@ < ? @ =

-0.0719d1 %%NUDO 4-0.8212d2 %%

1.1630 d3 %%2.1365 d4 %%

NUDO 5-0.9832d5 %%( + -0.2173d6 %%

-0.0404d7 %%

NUDO 6-0.1787d8 %%-0.9827d9 %%0.2881 d10 %%

NUDO 7-1.0259d11 %%0.5109 d12 %%

1$ .- '"lculo de fuer as internas en cada barra

=ARRA 9Q;N7"" Q" Q"

?d@ = ?G@-1H?- @

A%PE%7L% Q - % Q@ - @%


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1 20.120 -0.072 0.488 -0.8212 11.747 2.137 0.570 -0.983

20.617 2.137 0.000 -0.983! 12.212 -0.040 0.296 -0.1795 20.120 -0.040 -0.488 -0.179

11.805 -0.072 -0.859 -0.82121.854 2.208 0.530 -0.162

0 21.854 -2.177 0.530 0.805J 20.617 -0.032 -1.000 -0.643

1* 20.120 0.360 0.488 -0.20511 23.050 -1.848 0.000 -0.04312 20.120 0.329 -0.488 -0.847

1% .- '"lculo de fuer as de reacción y comprobación del e/uilibrio est"

FUER A

F1 -4.47 0.49 0.78 0.39F2 7.29 0.57 0.46 0.68F -13.53 0.00 0.80 -0.60F! 8.77 0.30 0.47 -0.83F5 -10.13 -0.49 0.78 0.39F -0.57 -0.86 0.46 0.23

R; =

9 + >&s " + >&s n + >&s

REACCIONES +

2 3

15 kN

R 2 R 5 R 8

R 1

R 3

R 4

R 6

R 7

R 9

10 kN

1 2 3

z

4 5 6

7

1 2 34

5

6

7 8

9

1011

12

y

x1


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R =RF =


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64/86

!,!+ #% n! +nd ! "%+n#d#

"n#

COORDENADASNUDO INICIAL

" .

1

4

7

5

2

6

3

1

2

3

4

5

6

7

11

8

1210

9

z

x

2.50

10.00

2.00

9.00

2.00

2.00

3.00

2.50 2.50 2.50

10 kN


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-1.00 0.00 0.00 20.62 20.620.49 0.78 0.39 20.12 4.790.00 0.89 -0.45 23.05 0.00

-0.49 0.78 0.39 20.12 4.79

-7.66 -3.83 3.81-12.26 -6.13 3.05

-6.13 -3.07 4.587.66 3.83 -3.81

12.26 6.13 -3.056.13 3.07 -4.58

0.00 0.00 1.07-13.19 9.90 1.71

9.90 -7.42 -3.000.00 0.00 -1.07

13.19 -9.90 -1.71-9.90 7.42 3.00

7.66 3.83 8.71-12.26 -6.13 -4.64

-6.13 -3.07 -2.32-7.66 -3.83 -8.71

12.26 6.13 4.646.13 3.07 2.32

0.00 -9.82 6.140.00 0.00 0.000.00 -15.71 -9.820.00 9.82 -6.140.00 0.00 0.000.00 15.71 9.82

0.00 0.00 4.790.00 0.00 7.66

6 G +

6 G +

6 G +

6 G +


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0.00 0.00 3.830.00 0.00 -4.790.00 0.00 -7.660.00 0.00 -3.83

0.00 0.00 4.79-18.44 9.22 -7.66

9.22 -4.61 -3.830.00 0.00 -4.79

18.44 -9.22 7.66-9.22 4.61 3.83

NUDO 5( (! (5 ( (

15.16 -6.14 0.00 -9.82 -20.6213.50 0.00 0.00 0.00 0.0022.47 -9.82 0.00 -15.71 0.00-9.82 16.09 3.05 4.58 -6.140.00 3.05 34.08 -15.45 0.00

-15.71 4.58 -15.45 48.95 9.820.00 -6.14 0.00 9.82 37.410.00 0.00 0.00 0.00 -13.620.00 9.82 0.00 -15.71 -20.49

-3.83 0.00 0.00 0.00 -4.79-6.13 0.00 -18.44 9.22 7.66-3.07 0.00 9.22 -4.61 3.83

MATRI INVERSA

-0.0482 0.0046 -0.0019 -0.0025 0.0776-0.0909 -0.0463 -0.0009 -0.0250 0.00810.2016 0.0907 0.0027 0.0511 -0.04800.0907 0.1781 -0.0418 -0.0177 0.00740.0027 -0.0418 0.0831 0.0276 -0.00310.0511 -0.0177 0.0276 0.0606 -0.0041

-0.0480 0.0074 -0.0031 -0.0041 0.1261-0.0162 0.0092 -0.0038 -0.0051 0.0438-0.0319 -0.0705 0.0294 0.0392 0.0701-0.0145 0.0261 -0.0109 -0.0145 0.0261-0.0170 -0.0237 0.0377 0.0027 0.00760.0117 0.0186 -0.0633 0.0107 0.0173

6 G +

6 G +


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69/86

0.781 1.163 0.390 -4.470 C*%&0.456 -0.217 0.684 7.291 T"#0.800 -0.217 -0.600 -13.529 C*%&0.474 -0.983 -0.829 8.772 T"#0.781 -0.983 0.390 -10.128 C*%&0.458 1.163 0.229 -0.567 C*%&0.000 -1.380 0.848 0.000 T"#0.000 -0.765 -0.848 -11.029 C*%&0.000 2.146 0.000 0.650 T"#0.781 -0.652 0.390 -4.803 C*%&0.894 0.728 -0.447 -8.385 C*%&0.781 1.494 0.390 -4.803 C*%&

tico total de la armadura

REACCIONES EN LOSR1 R2 R R! R5

-2.18 -3.49 -1.754.15 3.32 4.99

0.00 -10.822.60 4.16

-1.J *.1 - .2! -2. * .

-10.00 K R; = 0.00

9

x


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15.00 K R = 0.000.00 K RF = 0.00


71/86


72/86

NUDO FINAL


73/86


74/86

0.00 0.00 0.00 0.00 0.0012.26 3.07 7.66 3.83 6.1318.44 4.61 0.00 0.00 -9.2212.26 3.07 -7.66 -3.83 6.13

=ARRA 23.05 4.58 -3.81 -3.05 -4.582.44 3.66 -3.05 -2.44 -3.663.66 5.49 -4.58 -3.66 -5.49

-3.05 -4.58 3.81 3.05 4.58-2.44 -3.66 3.05 2.44 3.66-3.66 -5.49 4.58 3.66 5.49

=ARRA !1.71 -3.00 -1.07 -1.71 3.002.74 -4.80 -1.71 -2.74 4.80

-4.80 8.40 3.00 4.80 -8.40-1.71 3.00 1.07 1.71 -3.00-2.74 4.80 1.71 2.74 -4.804.80 -8.40 -3.00 -4.80 8.40

=ARRA -4.64 -2.32 -8.71 4.64 2.322.48 1.24 4.64 -2.48 -1.241.24 0.62 2.32 -1.24 -0.624.64 2.32 8.71 -4.64 -2.32

-2.48 -1.24 -4.64 2.48 1.24-1.24 -0.62 -2.32 1.24 0.62

=ARRA 00.00 -9.82 -6.14 0.00 9.820.00 0.00 0.00 0.00 0.000.00 15.71 9.82 0.00 -15.710.00 9.82 6.14 0.00 -9.820.00 0.00 0.00 0.00 0.000.00 -15.71 -9.82 0.00 15.71

=ARRA 1*7.66 3.83 -4.79 -7.66 -3.83

12.26 6.13 -7.66 -12.26 -6.13


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6.13 3.07 -3.83 -6.13 -3.07-7.66 -3.83 4.79 7.66 3.83

-12.26 -6.13 7.66 12.26 6.13-6.13 -3.07 3.83 6.13 3.07

=ARRA 12-7.66 -3.83 -4.79 7.66 3.83

12.26 6.13 7.66 -12.26 -6.136.13 3.07 3.83 -6.13 -3.077.66 3.83 4.79 -7.66 -3.83

-12.26 -6.13 -7.66 12.26 6.13-6.13 -3.07 -3.83 6.13 3.07

NUDO NUDO (0 (J (1* (11 (12

0.00 0.00 -4.79 -7.66 -3.830.00 0.00 -7.66 -12.26 -6.130.00 0.00 -3.83 -6.13 -3.070.00 9.82 0.00 0.00 0.000.00 0.00 0.00 -18.44 9.22

0.00 -15.71 0.00 9.22 -4.61-13.62 -20.49 -4.79 7.66 3.8327.27 7.46 7.66 -12.26 -6.13

7.46 30.25 3.83 -6.13 -3.077.66 3.83 9.58 0.00 0.00

-12.26 -6.13 0.00 42.97 3.04-6.13 -3.07 0.00 3.04 10.74

0.0270 0.0431 0.0261 0.0078 0.01690.0026 0.0071 0.0562 0.0239 0.0246

-0.0162 -0.0319 -0.0145 -0.0170 0.01170.0092 -0.0705 0.0261 -0.0237 0.0186

-0.0038 0.0294 -0.0109 0.0377 -0.0633-0.0051 0.0392 -0.0145 0.0027 0.01070.0438 0.0701 0.0261 0.0076 0.01730.0825 0.0165 -0.0417 0.0180 0.03870.0165 0.1271 -0.0145 0.0185 0.0174

-0.0417 -0.0145 0.2087 -0.0018 0.00360.0180 0.0185 -0.0018 0.0526 -0.02170.0387 0.0174 0.0036 -0.0217 0.2024


76/86


77/86

" + n+ n

" + n+ n

" + n" + n

+ n" + n

+ n" + n" + n" + n

OYOSR R R0 RJ

8.12-7.27

4.94 -7.91 -3.950.49 -0.26 -0.13

-*.0! -5.! 0.1 !.*0


78/86

C$%&' '# *nd+ + n


79/86


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7.- viga continua

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