armadura prueba

8/17/2019 Armadura Prueba

1/48

2

1 4

3

1 3 4

2 5

885

2 2

ESTABILIDAD

INTERNA EXTERNA

J= 4 i= 3m= 5 m= 2

GH= 1

m=2j-3

m= 5

5= 5

COORDENADAS DE LOS NODOS

NODOS 1 2 3 4

X 0 2 2 4

Y 0 1.5 0 0

CONSTANTES DE LAS BARRAS

BARRAS LX LY L l m

1 2 1.5 2.5 0.8 0.6

2 2 0 2 1 0

3 0 1.5 1.5 0 1

4 2 -1.5 2.5 0.8 -0.6

5 2 0 2 1 0

MATRICES DE LAS BARRAS

BARRA 1

KG= 5017.6 3763.2 -5017.6 -3763.2


2/48

3763.2 2822.4 -3763.2 -2822.4

-5017.6 -3763.2 5017.6 3763.2

-3763.2 -2822.4 3763.2 2822.4

DESPLAZAMIETOS

BARRA N. INICIAL N.FINAL

Δyf

1 0 0 Δy2

2 0 0 Δy3

3 Δy2 Δy3

4 Δy2 0

5 Δy3 0

Δxi Δf i Δxf

Δx2

Δx3

Δx2 Δx3

Δx2 Δx4

Δx3 Δx4

ΔX1=0

ΔX2≠

ΔX3≠0

ΔY1=0

ΔY2≠0

ΔY3≠0


3/48

A= 8

E= 2450

1.5

INSIDENCIAS DE LAS BARRAS

BARRAS 1 2 3 4

N.INICIAL 1 1 2 2

N.FINAL 2 3 3 4

AE/L

7840

9800

13066.6667

7840

9800

BARRA 2 Y 5

KG= 9800 0 -9800 0


4/48

0 0 0 0

-9800 0 9800 0

0 0 0 0

MATRIZ GENE

NU

KG= 10035.2

0

0

0

-5017.6

MATRIZ INVER

0.0001506696

-6.80272E-005

-5.10204E-005

-6.80272E-005

= 0.0001020408

BARRA

1

2

3

4

5

Δx2

0

ΔY4=0

ΔX4≠0


5/48

5

3

4

7840

BARRA 3

KG= 0 0 0 0


6/48

0 13066.66667 0 -13066.6667

0 0 0 0

0 -13066.66667 0 13066.6667

AL

! 1 NU! 2 NU! 3Δy2 Δy3

0 0 0 -5017.6

18711.466667 0 -13066.66667 3763.2

0 19600 0 9800

-13066.66667 0 13066.66667 0

3763.2 9800 0 14817.6

0

SA P

-6.80272E-005 -5.1020E-005 -6.8027E-005 0.000102041 0

0.0002678571 6.80272E-005 0.000267857 -0.000136054 15500

6.80272E-005 0.000102041 6.80272E-005 -0.000102041 0

0.0002678571 6.80272E-005 0.000344388 -0.000136054 0

-0.000136054 -0.000102041 -0.000136054 0.000204082 0

AE/L Δxf-Δxi l Δyf-Δyi m Fi

7840.000 -1.054 0.800 4.152 0.600 12916.667

9800.000 1.054 1.000 4.152 0.000 10333.333

13066.667 2.109 0.000 0.000 1.000 0.000

7840.000 -1.054 0.800 -4.152 -0.600 12916.667

9800.000 -3.163 1.000 -4.152 0.000 -31000.000

Δx3 Δx4


7/48

BARRA4

KG= 5017.6 -3763.2 -5017.6 3763.2


8/48

-3763.2 2822.4 3763.2 -2822.4

-5017.6 3763.2 5017.6 -3763.2

3763.2 -2822.4 -3763.2 2822.4

DESPLAZAMIENTOS

-1.054 Δx2

4.152 Δy2

1.054 Δx3

4.152 Δy3

-2.109 Δx4

OBS. !"/C#

"

"

#

"

#


9/48

Y 10

2 4 50

1 3 5

3 3 3 3

ESTABILIDAD

INTERNA EXTERNA

j= 5 i=4

m= 7 $=3

m=2j-3

m= 2%5&-3 GH= 1

7= 7


NODOS 1 2 3 4 5

X 0 3 6 9 12

Y 0 4 0 4 0

CONS"AN"ES DE LAS BARRAS

BARRAS LX LY L l m

1 3 4 5 0.6 0.8

2 6 0 6 1 0

3 6 0 6 1 0

4 3 -4 5 0.6 -0.8

5 3 4 5 0.6 0.8

$ 6 0 6 1 0

% 3 -4 5 0.6 -0.8

MATRICES

ARRA 1 Y 5

KG= 6804 9072 -6804 -9072

9072 12096 -9072 -12096

-6804 -9072 6804 9072

-9072 -12096 9072 12096

1

2

4 5

3

6

7


10/48

DESPLAZAMIETOS


Δyf

1 0 0 Δy22 0 0 Δy3

3 Δy2 Δy4

4 Δy2 Δy3

5 Δy3 Δy4

$ Δy3 0 0

% Δy4 0 0

Fuerza A!"a#e e$ #a Barra

B&& AE'( )x* - )xi + )y* - )yi m

N

1 7840.000 0.002 0.6 0.000 0.8

2 9800.000 0.001 1 0.001 0

3 13066.670 0.001 1 0.001 0

4 7840.000 -0.001 0.6 0.001 -0.8

5 9800.000 0.002 0.6 0.000 0.8

6 15750.000 -0.001 1 -0.001 0

7 18900.000 -0.003 0.6 -0.001 -0.8

Δxi Δf i Δxf

Δx2Δx3

Δx2 Δx4

Δx2 Δx3

Δx3 Δx4

Δx3

Δx4

ΔY1=0 ΔY5=0

ΔX1=0

ΔX5=

ΔX2≠0

ΔX3≠0

ΔX4≠0

ΔY2≠0

ΔY3≠0

ΔY4≠0

ΔX1=0


11/48

A=450

E=210

4

X

INSIDEMCIA DE LAS BARRAS

BARRAS 1 2

N.INICIAL 1 1

N.FINAL 2 3

AE/L

18900

15750

15750

18900

18900

15750

18900

BARRA 2%3 Y &

KG= 15750 0 -15750

0 0 0

-15750 0 15750

0 0 0


12/48

MATRIZ GENERAL

Δy2

KG= 29358 0 -6804

0 24192 9072-6804 9072 45108

9072 -12096 0

-15750 0 -6804

0 0 -9072

6.055262E-005 -1.78571E-005 0.000015873

-1.78571E-005 7.539683E-005 -1.19048E-005

0.000015873 -1.19048E-005 0.000031746

-2.38095E-005 5.919312E-005 -1.94879E-021

2.880658E-005 5.952381E-006 0.000015873-5.95238E-006 2.513228E-005 1.190476E-005

Y 10

2 4

1 3

3 3 3

,i "'# 0.002 Δx2

0.000Δy2

4.753 " 0.001 Δx3

8.944 " 0.001 Δy3

17.630 " 0.003 Δx4

-7.076 # 0.001 Δy4

12.423 "

-14.375 #

-23.958 #

Δx2 Δx3

0

1

2

4 5

3

6


13/48

3 4 5 $ %

2 2 3 3 4

4 3 4 5 5

BARRA 4 Y '

0 KG= 6804 -9072

0 -9072 12096

0 -6804 9072

0 9072 -12096


14/48

Δy3 Δy4

9072 -15750 0

-12096 0 0 Δy20 -6804 -9072 X

24192 -9072 -12096 Δy3

-9072 29358 0

-12096 0 24192 Δy4

-2.38095E-005 2.88066E-005 -5.95238E-006 0.002

5.919312E-005 5.95238E-006 2.513228E-005 0.000

2.766628E-021 0.000015873 1.190476E-005 0.001

0.0001183862 2.38095E-005 5.919312E-005 0.001

2.380952E-005 6.05526E-005 1.785714E-005 0.0035.919312E-005 1.78571E-005 7.539683E-005 0.001

50

4

5 X

3

Δx4

Δ= Δx2

Δx3

Δx4

7


15/48

-6804 9072

9072 -12096

6804 -9072

-9072 12096


16/48

0

-10= 0

0

50

0


17/48

Y

2

3

3

3

1 4

4.5 4.5

ESTABILIDAD

INTERNA EXTERNA

j= 5 i=3

m= 7 $=3

m=2j-3

m= 2%5&-3 GH= 0

7= 7


NODOS 1 2 3 4 5

X 0 0 4.5 4.5 9

Y 0 6 3 0 0

CONS"AN"ES DE LAS BARRAS

BARRAS LX LY L l m

1 0.000 6.000 6.000 0.000 1.000

2 4.500 -3.000 5.408 0.832 -0.555

3 4.500 3.000 5.408 0.832 0.555

4 4.500 0.000 4.500 1.000 0.000

1

2

5

4

$

%

3


18/48

5 0.000 3.000 3.000 0.000 1.000

$ 4.500 -3.000 5.408 0.832 -0.555

% 4.500 0.000 4.500 1.000 0.000

MATRICES

BARRA 1

KG= 0 0 0 0

0 15750 0 -15750

0 0 0 0

0 -15750 0 15750

ARRA 4 Y '

KG= 21000 0 -21000 0

0 0 0 0

-21000 0 21000 0

0 0 0 0

DESPLAZAMIETOS


Δyf

1 0 Δy1 0 0

2 0 0 Δy3

3 0 Δy1 Δy3

4 0 Δy1 Δy4

5 Δy3 Δy4

$ Δy3 Δy5

% Δy4 Δy5

Δxi Δf i Δxf

Δx3

Δx3

Δx4

Δx3 Δx4

Δx3 Δx5

Δx4 Δx5


19/48

N(DO 1 0

0

,X2 150

,X1= 150

,Y1=0


20/48

E 210

A 450

5

X

100 KN

INSIDEMCIA DE LAS BARRAS

BARRAS 1 2 3

N.INICIAL 1 2 1

N.FINAL 2 3 3

AE/L

15750.000

17473.056

17473.056

21000.000


21/48

31500.000

17473.056

21000.000

ARRA 2 Y &

KG= 12096.7312 -8064.48747 -12096.7312 8064.48747

-8064.48747 5376.32498 8064.48747 -5376.32498

-12096.7312 8064.48747 12096.7312 -8064.48747

8064.48747 -5376.32498 -8064.48747 5376.32498

BARRA 1

KG= 0 0 0 0

0 31500 0 -31500

0 0 0 0

0 -31500 0 31500

2

3

3

3

5

1 4

4.5 4.5

100

2

1

2

5

4

$

%

3

ΔY2=0


22/48

3

3

3

5

1 4

4.5 4.5

100

Fuerza A!"a#e e$ #a Barra

B&& AE'( )x* - )xi + )y* - )yi m

N

1 15750.000 0.000 0.000 0.000 1.000

2 17473.056 -0.006 0.832 0.009 -0.555

3 17473.056 -0.006 0.832 0.009 0.555

4 21000.000 0.007 1.000 0.009 0.000

5 31500.000 0.013 0.000 0.000 1.000

6 17473.056 0.020 0.832 0.049 -0.555

7 21000.000 0.007 1.000 0.049 0.000

N(DO 2

,X2

,Y2 -180.278

,X2 150

,Y2 100.00

1

2

5

4

$

%

3

ΔY3≠0

ΔY5≠0

ΔY4≠0

ΔY1≠0

ΔX3≠0

ΔX5ΔX4≠0

=

ΔX1=0


23/48

4 5 $ %

1 3 3 4

4 4 5 5


24/48

BARRA 3

KG= 12096.7312022963 8064.4874681976 -12096.7312023 -8064.4874681976

8064.4874681976 5376.3249787984 -8064.487468198 -5376.3249787984

-12096.731202296 -8064.4874681976 12096.731202296 8064.4874681976

-8064.4874681976 -5376.3249787984 8064.4874681976 5376.3249787984

Δy1 Δy3

21126.3249787984 -8064.4874681976 -5376.324978798 0

-8064.4874681976 36290.193606889 -8064.487468198 0

-5376.3249787984 -8064.4874681976 47628.974936395 0

0 0 0 42000

0 0 -31500 0

0 -12096.731202296 8064.4874681976 -21000

0 8064.4874681976 -5376.324978798 0

6.349206349E-005 0.000021164 0.000031746 -9.81498797E-022

0.000021164 4.838815395E-005 0.000010582 0

0.000031746 0.000010582 0.0001088733 -3.85680974E-021

KN -3.30423519E-022 -4.19309923E-021 1.67723969E-021 0.000047619

0.000031746 0.000010582 0.0001088733 -3.25765236E-021

-6.60847038E-022 -8.38619846E-021 3.35447938E-021 0.000047619

Δx3 Δx4


25/48

4.171284854E-021 -6.20002203E-005 9.30003305E-005 7.142857143E-005

,i "'# 0.000 Δy1

-0.006Δx3

0.000 E"A/(A 0.009 Δy3

-180.278 # 0.007 Δx4

0.000 E"A/(A 0.009 Δy4

150.000 " 0.014 Δx5

0.000 E"A/(A 0.059 Δy5

-180.278 #

150.000 "

0


26/48


27/48

Δy4 Δy5

0 0 0

0 -12096.731202296 8064.4874681976 X

-31500 8064.4874681976 -5376.3249787984

0 -21000 0

31500 0 0

0 33096.7312022963 -8064.4874681976

0 -8064.4874681976 5376.3249787984

0.000031746 -1.96299759E-021 -5.25516400E-021

0.000010582 0 -6.20002203E-005

0.0001088733 -7.71361948E-021 9.300033052E-005

1.677239691E-021 0.000047619 7.142857143E-005

0.0001406194 -6.51530471E-021 9.300033052E-005

3.354479383E-021 9.523809524E-005 0.0001428571

Δx5 Δ=


28/48

9.300033052E-005 0.0001428571 0.000586287


29/48


30/48

Δy1 0

0

Δy3 = 0

0

Δy4 0

0

Δy5 100

-5.255E-019

-0.00620002

0.00930003

0.00714286

0.00930003

0.01428571

Δx3

Δx4

Δx5


31/48

0.0586287


32/48

2

1 4

3

1 3 4

2 5

885

2 2

ESTABILIDAD

INTERNA EXTERNA

J= 4 i= 3m= 5 m= 2

GH= 1

m=2j-3

m= 5

5= 5


NODOS 1 2 3 4

X 0 2 2 4

Y 0 1.5 0 0


BARRAS LX LY L l m

1 2 1.5 2.5 0.8 0.6

2 2 0 2 1 0

3 0 1.5 1.5 0 1

4 2 -1.5 2.5 0.8 -0.6

5 2 0 2 1 0


BARRA 1

KG= 5017.6 3763.2 -5017.6 -3763.2


33/48

3763.2 2822.4 -3763.2 -2822.4

-5017.6 -3763.2 5017.6 3763.2

-3763.2 -2822.4 3763.2 2822.4

DESPLAZAMIETOS


Δyf

1 0 Δy2

2 0 Δy3

3 Δy2 Δy3

4 Δy2 0 0

5 Δy3 0 0

Δxi Δf i Δxf

Δx1 Δx2

Δx1 Δx3

Δx2 Δx3

Δx2

Δx3

ΔX2≠

ΔY1=0

ΔX3≠0

ΔY2≠0

ΔX1≠0

ΔY3≠0


34/48

A= 8

E= 2450

1.5

INSIDENCIAS DE LAS BARRAS

BARRAS 1 2 3 4

N.INICIAL 1 1 2 2

N.FINAL 2 3 3 4

AE/L

7840

9800 +2 +m -+2 -+m

13066.6667 +m m2 -+m -m2

7840 -+2 -+m +2 +m

9800 -+m -m2 +m m2

BARRA 2 Y 5

KG= 9800 0 -9800 0


35/48

0 0 0 0

-9800 0 9800 0

0 0 0 0

MATRIZ GENE

NU! 1

KG= 14817.6

-5017.6

-3763.2

-9800

0

MATRIZ INVE

0.00020408160.0001020408

0.0001360544

0.0001020408

0.0001360544

=

BARRA

1

2

3

4

5

Δx1

ΔX4=0

0

ΔY4=0


36/48

5

3

4

7840

BARRA 3

KG= 0 0 0 0


37/48

0 13066.6667 0 -13066.6667

0 0 0 0

0 -13066.6667 0 13066.6667

RAL

NU! 2 NU! 3Δx2 Δx3

-5017.6 -3763.2 -9800 0

10035.2 0 0 0

0 18711.4667 0 -13066.6667

0 0 19600 0

0 -13066.6667 0 13066.6667

SA P

0.0001020408 0.00013605 0.00010204 0.00013605 00.0001506696 6.8027E-005 5.1020E-005 6.8027E-005 15500

6.80272E-005 0.00026786 6.8027E-005 0.00026786 0

5.10204E-005 6.8027E-005 0.00010204 6.8027E-005 0

6.80272E-005 0.00026786 6.8027E-005 0.00034439 0

AE/L Δxf-Δxi l Δyf-Δyi m Fi

7840.000 0.754 0.800 1.054 0.600 9687.500

9800.000 -0.791 1.000 1.054 0.000 -7750.000

13066.667 -1.545 0.000 0.000 1.000 0.000

7840.000 -2.335 0.800 -1.054 -0.600 -9687.500

9800.000 -0.791 1.000 -1.054 0.000 -7750.000

Δy2 Δy3


38/48

BARRA4

KG= 5017.6 -3763.2 -5017.6 3763.2


39/48

-3763.2 2822.4 3763.2 -2822.4

-5017.6 3763.2 5017.6 -3763.2

3763.2 -2822.4 -3763.2 2822.4

DESPLAZAMIENTOS

1.582 Δx12.335 Δx2

1.054 Δy2

0.791 Δx3

1.054 Δy3

OBS. !"/C#

"

#

#

#

#


40/48

3

2

3 70000

1 2

1

7 9

ESTABILIDAD

INTERNA EXTERNA

J= 3 i= 3m= 3 m= 2

GH= 1

m=2j-3

m= 3

5= 5


NODOS 1 2 3

X 0 7 16

Y 0 0 12


BARRAS LX LY L l m

1 7 0 7 1 0

2 16 12 20 0.8 0.6

3 9 12 15 0.6 0.8


BARRA 1

KG=

21428.571 0 -21428.571 0


41/48

0 0 0 0

-21428.571 0 21428.571 0

0 0 0 0

DESPLAZAMIETOS

2

3

1


Δyf

1 0 0 0

2 0 0 0 ΔY3

3 0 0 ΔY3

F'(&)* &(+,i* ( l* 0y*

NDO 1 38511.137

x1 35170

y1

0

R)1 * 23106.6823

0

Δxi Δf i Δxf

Δx2

Δx2

,y =

,x =

ΔX1=0

ΔY2=0

ΔX3=0

ΔY1=0

ΔX2≠0

ΔY3≠0


42/48

R!1 *&5+',-,+,

E.u"#"/r"0 e"0 e #a eruura

3

70000

1 2

65978.898

23106.6822977726 46893.3177022274


43/48

A= 5

E= 30000

12

INCIDENCIAS DE LAS BARRAS

BARRAS 1 2 3

N.INICIAL 1 1 2

N.FINAL 2 3 3

AE/L

21428.571

7500 +2 +m -+2 -+m

10000 +m m2 -+m -m2

-+2 -+m +2 +m

-+m -m2 +m m2

BARRA 2

KG=

4800 3600 -4800 -3600


44/48

3600 2700 -3600 -2700

-4800 -3600 4800 3600

-3600 -2700 3600 2700

MATRIZ GENERAL

NDO 2 NDO 3

Δx2 ΔY3

25028.571 -4800 0

-4800 9100 -70000

MATRIZ INVERSA DESPLAZAMIENTOS

4.4451E-005 2.3447E-005 -1.64126612

2.3447E-005 0.00012226 -8.55803048

BARRA AE/L Δxf-Δxi l Δyf-Δyi m

1 21428.571 -1.641 1.000 0.000 0.000

2 7500.000 0.000 0.800 -8.558 0.600

3 10000.000 1.641 0.600 -8.558 0.800

NDO 2 58616.647

y2

0

R)2 * 4&,+3-31,

,y =


45/48

65978.898 0

65978.898 65978.898.=0

0.=0

0

23106.68 46893.32 70000 .=0

0.=0

0

0.=0

,x =

,y =

1 =


46/48

21428.5714

BARRA 3

KG=

3600 4800 -3600 -4800


47/48

4800 6400 -4800 -6400

-3600 -4800 3600 4800

-4800 -6400 4800 6400

Fi OBS. !"/C#

-35169.988 #

-38511.137 #

-58616.647 #

NDO 3

x3

38511.137

58616.647

0

R!3 * &5+',-,+,

,x =


48/48

armadura prueba

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