metodo flexibilidad en armaduras-ok.xls

METODO DE FLEXIBILIDADES PARA ARMADURAS

6

4

6

8 8 8 8 8

PRIMER ESTADO CONSIDERANDO FUERZAS6

4

" F "

FUERZAS UNITARIAS EN DIRECCION 1 " U1 "

r1 = 1

" U1 "

FUERZAS UNITARIAS EN DIRECCION 2 " U2"

r2=1

r2=1

1

2 3 4

9 8 710

6

511 1

4

15 1612 13

18

17

BARRA E A L F U1 U2

1 2.10E+07 1 5.00 14 1

2 2.10E+07 1 5.00 14 -0.7071 1

3 2.10E+07 1 5.00 12 1

4 2.10E+07 1 7.07 -16.9706

5 2.10E+07 1 5.00 -12 -0.7071

6 2.10E+07 1 7.07 -11.3137

7 2.10E+07 1 5.00 -0.7071

8 2.10E+07 1 7.07 1 9 2.10E+07 1 7.07 -2.8284 1

10 2.10E+07 1 5.00 2 -0.7071

11 2.10E+07 112 2.10E+07 1 6 1 1 113 2.10E+07 114 2.10E+07 115 2.10E+07 116 2.10E+07 117 2.10E+07 118 2.10E+07 1

-1.3399E-06 1.4352E-06

9.8095E-06 0.000001

1.1736E-07

-1

{ R } = -1.4352E-06 1.1736E-07

*1.1736E-07 0.000001

{ R } = -703503.883 82561.205782561.2057 -1009689.15

{ R } = 1.75254

-10.0151970

" U2 "

∑total=

ΔL1 = F11 =

ΔL2 = F22 =

F12 =

{ R } =- [ F ]-1 * { ΔL }

R1

R2


Grado de indeterminacion :

m = 18r = 4n = 10

ECUACIONES ESTATICAS = 3Redundandes a eliminar EN TOTAL : 2

Redundandes a eliminar EXTERNO : 1

Redundandes a eliminar INTERNO : 1

H8

paty arocutipa: numero de barras

H9

paty arocutipa: numero de reacciones por los apoyos

H10

paty arocutipa: numero de nudos

(F*U1*L)/(E*A) (F*U2*L)/(E*A) (U1^2*L)/(E*A) (U2^2*L)/(E*A) (U1*U2*L)/(E*A)

0 3.333333333E-06 0 2.380952381E-07 0-0.000002357 3.333333333E-06 1.190453357E-07 2.380952381E-07 -1.68357143E-07

0 2.857142857E-06 0 2.380952381E-07 00 0 0 0 0

2.020285714E-06 0 1.190453357E-07 0 00 0 0 0 00 0 1.190453357E-07 0 00 0 3.366666667E-07 0 0

-0.000000952228 0 3.366666667E-07 0 0-3.36714286E-07 0 1.190453357E-07 0 0

0 0 0 0 02.857142857E-07 2.857142857E-07 2.857142857E-07 2.857142857E-07 2.857142857E-07

0 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 0

-1.33994229E-06 9.80952381E-06 1.435228962E-06 0.000001 1.173571429E-07

0.7071067811865

-1.33994229E-069.80952381E-06

-1.33994229E-069.80952381E-06

ΔL1 = ΔL2 = F11 = F22 = F12 =


6

4

6

ECUACIONES ESTATICAS =

8 8 8 8 8

PRIMER ESTADO CONSIDERANDO FUERZAS6

4

" F "


r1=1

" U1 "


r2=1

r2=1

" U2 "

1

2 3 4

9 8 710

6

511 1

4

15 1612 13

18

17

19

BARRA E A L F U1 U2

1 1 1 10 -1 0 02 1 1 8 -4.8 0 03 1 1 8 -5.6 0 -0.84 1 1 8 -6.4 0 05 1 1 10 -9 0 06 1 1 8 7.2 1 17 1 1 8 7.2 1 18 1 1 8 6.4 1 0.29 1 1 8 5.6 1 1

10 1 1 8 4.8 1 111 1 1 6 0.6 0 012 1 1 6 0.6 0 -0.613 1 1 6 0.6 0 -0.614 1 1 6 0 0 015 1 1 10 -1 0 016 1 1 10 -1 0 017 1 1 10 -1 0 018 1 1 10 0 0 019 1 1 8

249.6 40

240.16 41.76

38.04 12.06

33.6

10.4

5.56


r3=1 r3=1

" U3 "

ΔL1 = F11 =

ΔL2 = F22 =

ΔL3 = F33 =

F12 =

F13 =

F23 =

{ R } =- [ F ]-1 * { ΔL }

{ R } = -40 33.6 10.4

33.6 41.76 5.5610.4 5.56 12.06

{ R } = -0.101392 0.074512 0.0530840.074512 -0.080271 -0.0272490.053084 -0.027249 -0.116133

{ R } =

-5.39330

-1.71614

2.28789

R1

R2

R3



m = 19r = 4n = 10




U3

0 0 0 0 0 0 00.2 0 0 -7.68 0 0 0.320.6 0 35.84 -26.88 0 5.12 2.880 0 0 0 0 0 00 0 0 0 0 0 01 57.6 57.6 57.6 8 8 8

0.2 57.6 57.6 11.52 8 8 0.320.1 51.2 10.24 5.12 8 0.32 0.080 44.8 44.8 0 8 8 00 38.4 38.4 0 8 8 00 0 0 0 0 0 00 0 -2.16 0 0 2.16 0

0.1 0 -2.16 0.36 0 2.16 0.060 0 0 0 0 0 00 0 0 0 0 0 00 0 0 0 0 0 0

0.2 0 0 -2 0 0 0.40 0 0 0 0 0 00

249.6 240.16 38.04 40 41.76 12.06

(F*U1*L) / (E*A)

(F*U2*L) / (E*A)

(F*U3*L) / (E*A)

(U1^2*L) / (E*A)

(U2^2*L) / (E*A)

(U3^2*L) / (E*A)

∑total=

249.6* 240.16

38.04

249.6* 240.16

38.04

0 0 00 0 00 0 -3.840 0 00 0 08 8 88 1.6 1.6

1.6 0.8 0.168 0 08 0 00 0 00 0 00 0 -0.360 0 00 0 00 0 00 0 00 0 00 0 0

33.6 10.4 5.56

(U1*U2*L) / (E*A)

(U1*U3*L) / (E*A)

(U2*U3*L) / (E*A)


62

1

3

ECUACIONES ESTATICAS =

4 4 4 4 4

PRIMER ESTADO CONSIDERANDO FUERZAS

2 61

" F "


r1=1

" U1 "


r2=1

r2=1

" U2 "

1

2 3 4

9 8 710

6

511 1

4

15

16

12 1318

17

19

r3=1

r3=1

BARRA E A L F U1 U2

1 1 1 5 -4.4167 0 02 1 1 4 -4.5333 0 03 1 1 4 -5.4 0 -0.84 1 1 4 -6.2667 0 05 1 1 5 -8.9167 0 06 1 1 4 7.1333 1 07 1 1 4 7.1333 1 08 1 1 4 6.2667 1 -0.89 1 1 4 5.4 1 0

10 1 1 4 4.5333 1 011 1 1 3 0.65 0 012 1 1 3 0.65 0 -0.613 1 1 3 0.65 0 -0.614 1 1 3 0 0 015 1 1 5 -1.0833 0 016 1 1 5 -1.0833 0 117 1 1 5 -1.0833 0 018 1 1 5 0 0 019 1 1 5 0 0

121.8664 20

-10.52994 12.28

-10.52994 12.28

-3.2

-3.2

1.08


" U3 "

ΔL1 = F11 =

ΔL2 = F22 =

ΔL3 = F33 =

F12 =

F13 =

F23 =

{ R } =- [ F ]-1 * { ΔL }

{ R } = -20 -3.2 -3.2

-3.2 12.28 1.08-3.2 1.08 12.28

{ R } = -0.054150 -0.012970 -0.012970-0.012970 -0.085175 0.004111-0.012970 0.004111 -0.085175

{ R } =

-6.32597

-0.72703

-0.72703

R1

R2

R3



m = 19 numero de barras

r = 4 numero de reacciones

n = 10 numero de nudos




U3

0 0 0 0 0 0 0-0.8 0 0 14.50656 0 0 2.56

0 0 17.28 0 0 2.56 00 0 0 0 0 0 00 0 0 0 0 0 00 28.5332 0 0 4 0 00 28.5332 0 0 4 0 00 25.0668 -20.05344 0 4 2.56 0

-0.8 21.6 0 -17.28 4 0 2.560 18.1332 0 0 4 0 0

-0.6 0 0 -1.17 0 0 1.08-0.6 0 -1.17 -1.17 0 1.08 1.08

0 0 -1.17 0 0 1.08 00 0 0 0 0 0 01 0 0 -5.4165 0 0 50 0 -5.4165 0 0 5 00 0 0 0 0 0 00 0 0 0 0 0 00 0 0 0

121.8664 -10.52994 -10.52994 20 12.28 12.28

(F*U1*L) / (E*A)

(F*U2*L) / (E*A)

(F*U3*L) / (E*A)

(U1^2*L) / (E*A)

(U2^2*L) / (E*A)

(U3^2*L) / (E*A)

∑total=

121.8664* -10.52994

-10.52994

121.8664* -10.52994

-10.52994

0 0 00 0 00 0 00 0 00 0 00 0 00 0 0

-3.2 0 00 -3.2 00 0 00 0 00 0 1.080 0 00 0 00 0 00 0 00 0 00 0 00 0 0

-3.2 -3.2 1.08

(U1*U2*L) / (E*A)

(U1*U3*L) / (E*A)

(U2*U3*L) / (E*A)


5

4.5

10

3.5 4.5 5

PRIMER ESTADO CONSIDERANDO FUERZAS

5

10" F "


r1 = 1

r1 = 1

" U1 "


r2 = 1

Tn

Tn

1

2 3

4

9

8

7

10

6 5

11

1213

Tn

Tn

BARRA E A L F U1 U21 21000000 0.0005 4.5 -1.1538 -0.78942 21000000 0.0005 3.5 2.9915 -0.6143 21000000 0.0005 4.5 6.8376 -0.70714 21000000 0.0005 6.72681202 9.19915 21000000 0.0005 5 -6.83766 21000000 0.0005 4.5 -2.99157 21000000 0.0005 3.5 0 -0.6139 -0.70718 21000000 0.0005 5.70087713 09 21000000 0.0005 5.70087713 -4.8725 1

10 21000000 0.0005 4.5 3.8462 -0.7894 -0.707111 21000000 0.0005 6.36396103 012 21000000 0.0005 6.36396103 -5.4393 113 21000000 0.0005 4.5 -6.1538 -0.7071

-0.00416862 0.00132836

-0.0046695 0.0014156

0.00038392

-1

{ R } = -0.00132836 0.000383918

*0.00038392 0.0014156

{ R } = -816.833089 221.529515221.529515 -766.4943291

{ R } = 2.37063

2.65567

r2 = 1

" U2 "

∑total=

ΔL1 = F11 =

ΔL2 = F22 =

F12 =

{ R } =- [ F ]-1 * { ΔL }

R1

R2



m = 13r = 3n = 7




E= 2100000 kg/cm2 21000000 Tn/m2A= 5 cm2 0.0005 m2

(F*U1*L)/(E*A) (F*U2*L)/(E*A(U1^2*L)/(E (U2^2*L)/(E*A) (U1*U2*L)/(E*A)

0.00039034702 0 0.00027 0 0-0.00061226033 0 0.00013 0 0

0 -0.002072 0 0.00021428 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0.00013 0.00016666 0.00014470 0 0 0 0

-0.00264547846 0 0.00054 0 0-0.00130122441 -0.001166 0.00027 0.00021428 0.00023922

0 0 0 0 00 -0.003297 0 0.00060609 00 0.001865 0 0.00021428 0

-0.00416861617 -0.004669 0.00133 0.0014156 0.00038392

-0.00416861617-0.00466949778

-0.00416861617-0.00466949778

metodo flexibilidad en armaduras-ok.xls

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