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ESTRUCTURA

GRAFICA DE CERCHA O ARMADURAS EN 2D

PASO 1° DATOS DE LOS COMPONE

N =   4 E =

GDL =   8

gdr =   5 A

gdf =   3 2

A =

PASO 2°

BARRA 1

X Y

Ci 0 0

Cf 4 3

Long. 5.000

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λx   0.800

λy   0.600

DETERMINACION DE LA MATRIZ DE RIGIDES

BARRA 1

(E*A)/L 9600.000 Kg/m

K1 =  9600.0 -9600.0

-9600.0 9600.0

2 x 2

MATRIZ DE TRANFORMACION

=  λx λy

0 0

MATRIZ "K" DE COORDENADAS GLOBALES

BARRA 1

0.800 0.000

K1 =   0.600 0.000 X   9600.000.000 0.800 -9600.00

0.000 0.600   4 x 2

Δ7 Δ8 Δ1

Δ7   6144.00 4608.00 -6144.00

K1 =  Δ8   4608.00 3456.00 -4608.00

Δ1   -6144.00 -4608.00 6144.00

Δ2   -4608.00 -3456.00 4608.00

Δ5

Δ3Δ4

Δ6

BARRA 2

0.000 0.000

K2 =  1.000 0.000

X  16000.00

0.000 0.000 -16000.00

0.000 1.000   4 x 2

Δ1 Δ2 Δ3

]=[ [^  

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Δ1   0.00 0.00 0.00

K2 =  Δ2   0.00 16000.00 0.00

Δ3   0.00 0.00 0.00

Δ6   0.00 -16000.00 0.00

Δ4

Δ5

Δ7

Δ8

BARRA

0.800 0.000

K =  -0.600 0.000

X  9600

0.000 0.800 -9600

0.000 -0.600   4 x 2

Δ1 Δ2 Δ4

Δ1   6144.00 -4608.00 -6144.00

K =  Δ2   -4608.00 3456.00 4608.00

Δ4   -6144.00 4608.00 6144.00

Δ5   4608.00 -3456.00 -4608.00

Δ3

Δ7

Δ8

Δ6

MATRIZ "K" DE DE TODA LA ESTRUCTURA

Δ1 Δ2 Δ3

Δ1   12288 0 0

Δ2   0 22912 0

K =  Δ3   0 0 12000

Δ4   -6144 4608 0

Δ5   4608 -3456 0

Δ6   0 -16000 0

Δ7   -6144 -4608 -12000Δ8   -4608 -3456 0

RESOLUCION DE LA MATRIZ DE TODA LA ESTRUCTURA

!1 -1000 12288.00 0.00!2 -500 0.00 22912.00

!3 0 0.00 0.00

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!4 0 -6144.00 4608.00

!5 0 4608.00 -3456.00

!6 0 0.00 -16000.00

!" 0 -6144.00 -4608.00

!8 0 -4608.00 -3456.00

HALLAMOS LOS DESPLAZAMIENTOS

-1000=

  12288.000 0.000

-500 0.000 22912.000

0 0.000 0.000

-1000=

  12288.000 0.000

-500 0.000 22912.0000 0.000 0.000

#1=

  -1230.4X

#2 -6"2.8

#3 0

0

#1 =   -0.1001#2 -0.0294

#3 0.0000

HALLAMOS LAS REACCIONES

!4 -6144.00 4608.00

!5=

  4608.00 -3456.00

!6 0.00 -16000.00

!" -6144.00 -4608.00

!8 -4608.00 -3456.00

!4   4"9.8882681564

!5 -359.916

!6=

  469.832

!" 520.112

!8 390.084

HALLAMOS LAS FUERZAS INTERNAS

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BARRA 1

f =  0.8 0.6 0 0

0 0 0.8 0.6

f =  481.00 Ci

COMPRECION-481.00 Cf  

BARRA 2

f =  0 1 0 0

0 0 0 1

f =  469.83 Ci

COMPRECION-469.83 Cf  

BARRA

f =  0.8 -0.6 0 0

0 0 0.8 -0.6

f =  88".86 Ci

COMPRECION-88".86 Cf  

     .∆=. 

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FUERZA DE L

!1

!2

!3

!4

!5

!6

!"

!8

DESPLAZAMI

Δ1

Δ2

Δ3

Δ4Δ5

Δ6

Δ7

Δ8

TES

8000 Kg/$m2

H R 

3

6 $m2

BARRA 2

X Y

Ci 4 0

Cf 4 3

Long. 3.000

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λx   0.000

λy   1.000

BARRA 2

(E*A)/L 16000.000 Kg/m

K1 =  16000.0 -16000.0

-16000.0 16000.0

2 x 2

0 0

λx λy   2 x 4

-9600.00 X   0.800 0.600 0.0009600.00 0.000 0.000 0.800

2 x2

Δ2 Δ5 Δ3 Δ4 Δ6

-4608.00

-3456.00

4608.00

3456.00

-16000.00X

  0.000 1.000 0.000

16000.00 0.000 0.000 0.000

2 x2

Δ6 Δ4 Δ5 Δ7 Δ8

]. ]. ][ [ 

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0.00

-16000.00

0.00

16000.00

-9600X

  0.800 -0.600 0.000

9600 0.000 0.000 0.800

2 x2

Δ5 Δ3 Δ7 Δ8 Δ6

4608.00

-3456.00

-4608.00

3456.00

Δ4 Δ5 Δ6 Δ7 Δ8

-6144 4608 0 -6144 -4608

4608 -3456 -16000 -4608 -3456

0 0 0 -12000 0

6144 -4608 0 0 0

-4608 3456 0 0 0

0 0 16000 0 0

0 0 0 18144 4608

0 0 0 4608 3456

GDL ! GDL

gdf    3

0.00 -6144.00 4608.00 0.00 -6144.000.00 4608.00 -3456.00 -16000.00 -4608.00

12000.00 0.00 0.00 0.00 -12000.00

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0.00 6144.00 -4608.00 0.00 0.00

0.00 -4608.00 3456.00 0.00 0.00

0.00 0.00 0.00 16000.00 0.00

-12000.00 0.00 0.00 0.00 18144.00

0.00 0.00 0.00 0.00 4608.00

0.000 #1

0.000 X #2 %

12000.000 #3

0.000 #1

0.000 X #2 %12000.000 #3

0.000081 0.000000 0.000000

0.000000 0.000044 0.000000

0.000000 0.000000 0.000083

0.00 6144.00 -4608.00 0.00 0.00

0.00 -4608.00 3456.00 0.00 0.00

0.00 0.00 0.00 16000.00 0.00

-12000.00 0.00 0.00 0.00 18144.00

0.00 0.00 0.00 0.00 4608.00

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COMPRECION

TRACCION

#"

X  9600 -9600

X  #8

-9600 9600 #1

#2

#1

X  16000 -16000

X  #2

-16000 16000 #3

#6

#1

X  9600 -9600

X  #2

-9600 9600 #4

#5

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ESTRUCTURA

-1000

-500

NTOS DE LAS FUERZAS EXTERNAS

#1

#2

Δ3

00

0

0

-0.05

BARRA

X Y

Ci 4 3

Cf 8 0

Long. 5.000

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λx   0.800

λy   -0.600

BARRA

(E*A)/L 9600.000 Kg/m

K1 =  9600.0 -9600.0

-9600.0 9600.0

2 x 2

BARRA

0.000 K1 =0.600

2 x 4

K1 =

BARRA #

0.000K2 =

1.000

2 x 4

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K2 =

0.000

-0.600

2 x 4

8

-4608.00   Δ1   #1-3456.00   Δ2   #2

0.00   Δ3   #3

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0.00   Δ4   0

0.00   Δ5   0

0.00   Δ6   0

4608.00   Δ7   0

3456.00   Δ8   -0.05

-6144.00 4608.00 0.00 -6144.00

4608.00 -3456.00 -16000.00 -4608.00

0.00 0.00 0.00 -12000.00

230.4

1"2.80

-0.1001

0.00 -0.0294

0.00X

  0.0000

0.00 0.0000

4608.00 0

3456.00 0

0

-0.05

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BARRA

0

-0.05f =

-0.1001

0.0000

f =

BARRA #

0.00000.0000

f =-0.1001

-0.0294

f =

0.0000

-0.0500

-0.1001

-0.0294

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BARRA

X Y

Ci 0 0

Cf 4 0

Long. 4.000

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λx   1.000

λy   0.000

BARRA

(E*A)/L 12000.000 Kg/m

K1 =  12000.0 -12000.0

-12000.0 12000.0

2 x 2

1.000 0.000

0.000 0.000 X   12000.00 -12000.000.000 1.000 -12000.00 12000.00

0.000 0.000   4 x 2

Δ7 Δ8 Δ3 Δ6

Δ7   12000.00 0.00 -12000.00 0.00

Δ8   0.00 0.00 0.00 0.00

Δ3   -12000.00 0.00 12000.00 0.00

Δ6   0.00 0.00 0.00 0.00

Δ4

Δ5Δ1

Δ2

0.000 0.000

0.000 0.000X

  0.000 0.000

0.000 0.000 0.000 0.000

0.000 0.000   4 x 2

Δ7 Δ8 Δ4 Δ6

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Δ7   0.000 0.000 0.000 0.000

Δ8   0.000 0.000 0.000 0.000

Δ4   0.000 0.000 0.000 0.000

Δ6   0.000 0.000 0.000 0.000

Δ1

Δ2

Δ3

Δ5

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0

-4608.00 0

-3456.00 X 0

0.00 0

-0.05

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1 0 0 0X

0 0 1 0

-1201.56 CiTRACCION

1201.56 Cf  

0 0 0 0X

0 0 0 0

0.00 CiCOMPRECION

0.00 Cf  

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BARRA #

X Y

Ci 0 0

Cf 0 0

Long. 0

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λx   0

λy   0

BARRA #

(E*A)/L 0.000 Kg/m

K1 =  0 0

0 0

2 x 2

X   1.000 0.000 0.000 0.0000.000 0.000 1.000 0.000

2 x2 2 x 4

Δ4 Δ5 Δ1 Δ2

X  0.000 0.000 0.000 0.000

0.000 0.000 0.000 0.000

2 x2 2 x 4

Δ1 Δ2 Δ3 Δ5

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#"   -0.1001

12000.000 -12000.000X

  #8   -0.0294

-12000.000 12000.000 #3   0.0000

#6   0.0000

#"   0.00000 0

X  #8   -0.0500

0 0 #4   0.0000

#6   0.0000

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2   C

711.77

1   C   3   T   4   C

100 149.75 432.59

5   T

305.89

PARA ELEMENTOS EN TRACCION

BARRA F. INTERNA

N° ft A Nadm T (Kg)

3 105 6 630 149.75   CU

5 105 6 630 305.89   CU

PARA ELEMENTOS EN TRACCION

LONG. EFECTI!

E"#ELT$

MENO% LONGITU&

C'

L() 110 20.2 #!%%! CO%T

* 2 #!%%! INTE%

λ 15 #!%%! L!%G

#!%%!"

N+

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CUMPLE

NO CUMPLE

* ,

2 3

!%E! 6   -2

 TIPO &E M!&E%! #

PLE

PLE

ME&I!

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