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ANALISIS ESTRUCTURAL I RESOLUCION DEL EXAMEN PARCIAL INTEGRANTES: -HINOSTROZA GARCIA CRISTIAN -PAREZ PALOMINO JOSE MANUEL -EVARISTO DIESTRA EDDY

EAP: INGENIERIA CIVIL

2019 - I

PROBLEMA 1 SOLUCION: *Enumeramos los elementos de la cercha y ponemos los grados de libertad, el sentido empieza desde A y desde B hacia los puntos C y D.

HALLAMOS LAS MATRICES GLOBALES DE CADA ELEMENTO DE LA CERCHA ELEMENTO 1 Propiedades geométricas E= 200000000 Kpa A= 0.000127 m2 L= 2.617250466 m θ= 316.5481577 ° θ= 5.524807593 rad E*A/L= 9704.841143 kN/m

K1=

T=

T'=

Kglobal1=

MATRIZ LOCAL 1 2 3 4 9704.841143 0 -9704.84114 0 0 0 0 0 -9704.841143 0 9704.84114 0 0 0 0 0 MATRIZ DE ROTACION 0.725952684 -0.68774465 0 0 0.687744648 0.72595268 0 0 0 0 0.72595268 -0.68774465 0 0 0.68774465 0.72595268 0.725952684 0.68774465 0 0 -0.687744648 0.72595268 0 0 0 0 0.72595268 0.68774465 0 0 -0.68774465 0.72595268 1 2 5 6 5114.522121 -4845.33675 -5114.52212 4845.33675 1 -4845.336746 4590.31902 4845.33675 -4590.31902 2 -5114.522121 4845.33675 5114.52212 -4845.33675 5 4845.336746 -4590.31902 -4845.33675 4590.31902 6

ELEMENTO 2 Propiedades geométricas E= 200000000 Kpa A= 0.000127 m2 L= 2.343074903 m θ= 230.1944289 ° θ= 4.017650704 rad E*A/L= 10840.45583 kN/m

K2=

T=

MATRIZ LOCAL 1 2 3 10840.45583 0 -10840.4558 0 0 0 -10840.45583 0 10840.4558 0 0 0

4 0 0 0 0

MATRIZ DE ROTACION -0.6401844 -0.76822128 0 0 0.76822128 -0.6401844 0 0 0 0 -0.6401844 -0.76822128 0 0 0.76822128 -0.6401844

T'=

-0.6401844 -0.76822128 0 0

0.76822128 0 -0.6401844 0 0 -0.6401844 0 -0.76822128

3 Kglobal2=

4

5

0 0 0.76822128 -0.6401844 6

4442.80977

5331.37172 -4442.80977 -5331.37172 3

5331.371722

6397.64606 -5331.37172 -6397.64606 4

-4442.80977 -5331.37172

4442.80977

5331.37172 5

-5331.371722 -6397.64606

5331.37172

6397.64606 6

ELEMENTO 3 Propiedades geométricas E= 200000000 Kpa A= 0.000127 m2 L= 3.992492956 m θ= 247.9321004 ° θ= 4.327231473 rad E*A/L= 6361.939841 kN/m

K3=

T=

T'=

MATRIZ LOCAL 1 2 3 4 6361.939841 0 -6361.939841 0 0 0 0 0 -6361.939841 0 6361.939841 0 0 0 0 0 MATRIZ DE ROTACION -0.375705109 -0.926739268 0 0 0.926739268 -0.375705109 0 0 0 0 -0.375705109 -0.92673927 0 0 0.926739268 -0.37570511

-0.375705109 0.926739268 0 0 -0.926739268 -0.375705109 0 0 0 0 -0.375705109 0.92673927 0 0 -0.926739268 -0.37570511

1 2 3 4

3 Kglobal3=

4

7

8

898.0153506

2215.104527

-898.0153506 -2215.10453 3

2215.104527

5463.924491

-2215.104527 -5463.92449 4

-898.0153506

-2215.104527

898.0153506

2215.10453 7

-2215.104527

-5463.924491

2215.104527

5463.92449 8

ELEMENTO 4 Propiedades geométricas E= 200000000 Kpa A= 0.000127 m2 L= 1.9 m θ= 270 ° θ= 4.71238898 rad E*A/L= 13368.42105 kN/m

K4=

T=

MATRIZ LOCAL 1 2 3 13368.4211 0 -13368.4211 0 0 0 -13368.4211 0 13368.4211 0 0 0 MATRIZ DE ROTACION 0 -1 0 1 0 0 0 0 0 0 0 1 0 -1 0 0

T'=

5 Kglobal4=

1 0 0 0

4 0 0 0 0 0 0 -1 0

0 0 0 -1

6

7

0

0

0

13368.4211

1 2 3 4

0 0 1 0

8 0

0 5

0 -13368.4211 6

0

0

0

0 7

0 -13368.4211

0

13368.4211 8

ELEMENTO 5 Propiedades geométricas E= 200000000 Kpa A= 0.000127 m2 L= 4.159326869 m θ= 297.1811111 ° θ= 5.186788863 rad E*A/L= 6106.757368 kN/m

K5=

T=

T'=

Kglobal5=

MATRIZ LOCAL 1 2 3 4 6106.75737 0 -6106.75737 0 0 0 0 0 -6106.75737 0 6106.75737 0 0 0 0 0 MATRIZ DE ROTACION 0.45680469 -0.88956702 0 0 0.88956702 0.45680469 0 0 0 0 0.45680469 -0.88956702 0 0 0.88956702 0.45680469 0.45680469 -0.88956702 0 0

0.88956702 0 0.45680469 0 0 0.45680469 0 -0.88956702

1 2 3 4

0 0 0.88956702 0.45680469

1 2 7 8 1274.30024 -2481.53204 -1274.30024 2481.53204 1 -2481.53204 4832.45713 2481.53204 -4832.45713 2 -1274.30024 2481.53204 1274.30024 -2481.53204 7 2481.53204 -4832.45713 -2481.53204 4832.45713 8

ENSAMBLAMOS LA MATRIZ GLOBAL DE LA CERCHA

1 Kglobal=

2

3

6388.82236

-7326.86879

-7326.86879

9422.77615

0

0

4 0

5

6

7 -1274.300238

8

0

-5114.522121

4845.336746

2481.532041

0

0

4845.336746

-4590.319022

2481.532041

-4832.45713

5340.82512

7546.47625

-4442.80977

-5331.371722

-898.0153506

-2215.104527

1 2 3

0

0

7546.47625

11861.5706

-5331.371722

-6397.646065

-2215.104527

-5463.924491

-5114.52212

4845.33675

-4442.80977

-5331.37172

9557.33189

486.0349764

0

0

4845.33675

-4590.31902

-5331.37172

-6397.64606

486.0349764

24356.38614

0

-13368.42105

-1274.30024

2481.53204

-898.015351

-2215.10453

0

0

2172.315589

-266.4275137

2481.53204

-4832.45713

-2215.10453

-5463.92449

0

-13368.42105

-266.4275137

23664.80267

HALLAMOS LOS DESPLAZAMIENTOS

[U]=[K]¯¹x[F] U1=U2=U3=U4=0; puesto que están empotradas no tienen desplazamientos. -1 U5 U6 U7 U8

U5 U6 U7 U8

= = = =

=

9557.33189 486.034976

486.034976 24356.3861

0 0

0 -13368.4211

0 0

0 -13368.4211

2172.315589 -266.4275137

-266.427514 23664.80267

0.000154396 -0.003036021 -0.000677724 -0.005525817

X

0 0 0 -90

m m m m

HALLANDO LAS FUERZAS

[F]=[K]x[U] RAx RAy RBx RBy 0 0 0 -90

=

Rax = Ray = RBx= RBY= F5 = F6 = F7 = F8 =

-28.349 39.706 28.349 50.294 0 0 0 -90

KGlobal

kN kN kN kN kN kN kN kN

X

0 0 0 0 0.000154396 -0.003036021 -0.000677724 -0.005525817

4 5 6 7 8

COMPROBAMOS CON EXCEL

2.-Para la cercha mostrada en la siguiente figura. Calcular desplazamientos globales y reacciones del Sistema, Considere A=1.27 cm2 y E=200 000 MPa.

Resolución: Propiedades de los elementos A=0,000127 m2 E=200 000 000 kPa

 Numeración de los grados de libertad y elementos de la cercha

HALLAMOS LAS MATRICES GLOBALES DE CADA ELEMENTO DE LA CERCHA

ELEMENTO 1 E= A= L= θ= θ= E*A/L=

K1=

200000000 0.000127 1.5 90 1.570796327 16933.33333

1 16933.33333 0 -16933.33333 0

MATRIZ LOCAL 2 0 0 0 0

3 -16933.33333 0 16933.33333 0

4 0 0 0 0

0 0 0 -1

0 0 1 0

MATRIZ DE ROTACION 0 1 -1 0 0 0 0 0

T=

T'=

k1*T=

0 1 0 0

-1 0 0 0

0 0 0 1

0 0 -1 0

0 0 0 0

16933.33333 0 -16933.33333 0

0 0 0 0

-16933.33333 0 16933.33333 0

1 Kglobal1=

Kpa m2 m ° rad kN/m

2 0 0 0 0

0 16933.33333 0 -16933.33333

3

1 2 3 4

4 0 0 0 0

0 -16933.33333 0 16933.33333

1 2 3 4

ELEMENTO 2 E= A= L= θ= θ= E*A/L=

K2=

T=

T'=

k2*T=

Kglobal2=

200000000 0.000127 1.2 0 0 21166.66667

1 21166.66667 0 -21166.66667 0

Kpa m2 m ° rad kN/m MATRIZ LOCAL 2 3 0 -21166.66667 0 0 0 21166.66667 0 0

MATRIZ DE ROTACION 1 0 0 1 0 0 0 0 1 0 0 0

3 21166.66667 0 -21166.66667 0

0 0 1 0

0 0 0 1

0 0 1 0

0 0 0 1

0 -21166.66667 0 0 0 21166.66667 0 0

0 0 0 0

0 1 0 0

21166.66667 0 -21166.66667 0

4 0 0 0 0

4 0 0 0 0

5 -21166.66667 0 21166.66667 0

1 2 3 4

6 0 0 0 0

3 4 5 6

ELEMENTO 3 E= A= L= θ= θ= E*A/L=

K3=

T=

T'=

k3*T=

Kglobal3=

200000000 0.000127 0.9 0 0 28222.2222

Kpa m2 m ° rad kN/m

MATRIZ LOCAL 1 2 3 28222.2222 0 -28222.2222 0 0 0 -28222.2222 0 28222.2222 0 0 0

4 0 0 0 0

MATRIZ DE ROTACION 1 0 0 1 0 0 0 0

0 0 1 0

0 0 0 1

0 0 1 0

0 0 0 1

0 -28222.2222 0 0 0 28222.2222 0 0

0 0 0 0

1 0 0 0

0 1 0 0

28222.2222 0 -28222.2222 0

5 28222.2222 0 -28222.2222 0

6 0 0 0 0

7 -28222.2222 0 28222.2222 0

1 2 3 4

8 0 0 0 0

5 6 7 8

ELEMENTO 4 E= A= L= θ= θ= E*A/L=

K4=

200000000 0.000127 1.5 90 1.570796327 16933.33333

1 16933.33333 0 -16933.3333 0

MATRIZ LOCAL 2 0 0 0 0

3 -16933.33333 0 16933.33333 0

MATRIZ DE ROTACION 0 1 -1 0 0 0 0 0

T=

T'=

k4*T=

4 0 0 0 0

0 0 0 -1

0 0 1 0

0 1 0 0

-1 0 0 0

0 0 0 1

0 0 -1 0

0 0 0 0

16933.33333 0 -16933.33333 0

0 0 0 0

-16933.33333 0 16933.33333 0

9 Kglobal4=

Kpa m2 m ° rad kN/m

10 0 0 0 0

0 16933.33333 0 -16933.33333

7

1 2 3 4

8 0 0 0 0

0 -16933.33333 0 16933.33333

9 10 7 8

ELEMENTO 5 E= A= L= θ= θ= E*A/L=

K5=

T=

T'=

k5*T=

Kglobal5=

200000000 0.000127 0.9 0 0 28222.2222

1 28222.2222 0 -28222.2222 0

Kpa m2 m ° rad kN/m MATRIZ LOCAL 2 3 0 -28222.2222 0 0 0 28222.2222 0 0

MATRIZ DE ROTACION 1 0 0 1 0 0 0 0 1 0 0 0

11 28222.2222 0 -28222.2222 0

0 0 1 0

0 0 0 1

0 0 1 0

0 0 0 1

0 -28222.2222 0 0 0 28222.2222 0 0

0 0 0 0

0 1 0 0

28222.2222 0 -28222.2222 0

4 0 0 0 0

12 0 0 0 0

9 -28222.2222 0 28222.2222 0

1 2 3 4

10 0 0 0 0

11 12 9 10

ELEMENTO 6 E= A= L= θ= θ= E*A/L=

K6=

T=

T'=

k6*T=

Kglobal6=

200000000 0.000127 1.2 0 0 21166.6667

1 21166.6667 0 -21166.6667 0

Kpa m2 m ° rad kN/m

MATRIZ LOCAL 2 0 0 0 0

3 -21166.6667 0 21166.6667 0

MATRIZ DE ROTACION 1 0 0 1 0 0 0 0

4 0 0 0 0

0 0 1 0

0 0 0 1

1 0 0 0

0 1 0 0

0 0 1 0

0 0 0 1

21166.6667 0 -21166.6667 0

0 0 0 0

-21166.6667 0 21166.6667 0

0 0 0 0

0 0 0 0

11 -21166.6667 0 21166.6667 0

1 21166.6667 0 -21166.6667 0

2

1 2 3 4

12 0 0 0 0

1 2 11 12

ELEMENTO 7 E= A= L= θ= θ= E*A/L=

K7=

T=

T'=

k7*T=

Kglobal7=

200000000 0.000127 1.92093727 51.3401918 0.89605538 13222.7118

1 13222.7118 0 -13222.7118 0

Kpa m2 m ° rad kN/m

MATRIZ LOCAL 2 0 0 0 0

3 -13222.7118 0 13222.7118 0

4 0 0 0 0

MATRIZ DE ROTACION 0.62469505 0.78086881 0 -0.78086881 0.62469505 0 0 0 0.62469505 0 0 -0.78086881

0 0 0.78086881 0.62469505

0.62469505 0.78086881 0 0

-0.78086881 0.62469505 0 0

0 0 0.62469505 0.78086881

0 0 -0.78086881 0.62469505

8260.1626 0 -8260.1626 0

10325.2033 0 -10325.2033 0

-8260.1626 0 8260.1626 0

-10325.2033 0 10325.2033 0

1 5160.08267 6450.10334 -5160.08267 -6450.10334

2 6450.10334 8062.62917 -6450.10334 -8062.62917

5 -5160.08267 -6450.10334 5160.08267 6450.10334

6 -6450.10334 -8062.62917 6450.10334 8062.62917

1 2 3 4

1 2 5 6

ELEMENTO 8 E=

200000000 Kpa

A=

0.000127 m2

L=

1.74928557 m2

θ=

59.0362435 °

θ=

1.03037683 rad

E*A/L=

14520.2135 kN/m

MATRIZ LOCAL 1

2

3

14520.2135

0

-14520.2135

0 1

0

0

0

0 2

-14520.2135 0

0 0

14520.2135 0

0 3 0 4

K8=

4

MATRIZ DE ROTACION T=

T'=

0.51449576 -0.85749293

0.85749293 0.51449576

0 0

0 0

0

0

0.51449576

0.85749293

0

0

-0.85749293

0.51449576

0.51449576

-0.85749293

0

0

0.85749293

0.51449576

0

0

0

0

0.51449576

-0.85749293

0

0

0.85749293

0.51449576

7470.58823

12450.9804

-7470.58823

-12450.9804

0

0

0

0

-7470.58823

-12450.9804

7470.58823

12450.9804

0

0

0

0

k8*T=

11 Kglobal8=

12

7

8

3843.58594 6405.97656

6405.97656 10676.6276

-3843.58594 -6405.97656

-6405.97656 11 -10676.6276 12

-3843.58594

-6405.97656

3843.58594

6405.97656 7

-6405.97656

-10676.6276

6405.97656

10676.6276 8

ELEMENTO 9 E=

200000000 Kpa

A=

0.000127 m2

L=

1.5 m

θ=

90 °

θ=

1.57079633 rad

E*A/L=

16933.3333 kN/m MATRIZ LOCAL 1

2

3

16933.3333

0

-16933.3333

0 1

0

0

0

0 2

-16933.3333

0

16933.3333

0 3

0

0

0

0 4

K9=

4

MATRIZ DE ROTACION T=

T'=

k9*T=

0

1

0

0

-1

0

0

0

0

0

0

1

0

0

-1

0

0

-1

0

0

1

0

0

0

0

0

0

-1

0

0

1

0

0

16933.3333

0

-16933.3333

0

0

0

0

0

-16933.3333

0

16933.3333

0

0

0

0

11 Kglobal9=

12

5

6

0

0

0

0 11

0

16933.3333

0

-16933.3333 12

0

0

0

0 5

0

-16933.3333

0

16933.3333 6

ENSAMBLAMOS LA MATRIZ GLOBAL DE LA CERCHA

1

2

26326.74933 6450.103336 6450.103336

24995.9625

3

4 0

0 0 16933.3333

0 0 21166.66667 0 0 -16933.3333 0 16933.3333 -5160.08266 -6450.10334 -21166.6666 0 -6450.10333 -8062.62917 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -21166.6666 0 0 0 0 0 0 0

5

6

5160.08267 6450.10334 21166.6667 0 54548.9716 6450.10334 -28222.222 0 0 0 0 0

6450.10334 8062.62917 0 0 6450.10334 24995.9625 0 0 0 0 0 -16933.333

7

8

9

10

11

12

0

0

0

0 -21166.6667

0 1

0

0

0

0

0 2

0 0 -28222.222 0 32065.8082 6405.97656 0 0 -3843.5859 -6405.9765

0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -16933.3333 6405.97656 0 0 -3843.58594 -6405.97656 27609.9609 0 -16933.333 -6405.97656 -10676.6276 0 28222.2222 0 -28222.2222 0 -16933.333 0 16933.3333 0 0 -6405.9765 -28222.222 0 53232.47483 6405.976562 -10676.627 0 0 6405.976562 27609.96094

3 4 5 6 7 8 9 10 11 12

HALLANDO LOS DESPLAZAMIENTOS

[U]=[K]¯¹x[F] -1 U5

54548.97156

6450.10334

-28222.22222

0

0

0

0

0

U6

6450.103336

24995.9625

0

0

0

0

0

-16933.333

U7

-28222.2222

0

32065.80816

6405.976562

0

0

-3843.58594

-6405.97656

0

0

6405.976562

27609.96094

0

-16933.3333

-6405.97656

-10676.6276

0

0

0

0

28222.22222

0

-28222.2222

0

U10

0

0

0

-16933.3333

0

16933.33333

0

0

U11

0

0

-3843.58593

-6405.97656

-28222.2222

0

53232.47483

6405.976562

0

U12

0

-16933.333

-6405.97656

-10676.6276

0

0

6405.976562

27609.96094

0

U8 U9

=

U5 U6 U7 U8 U9 U10 U11 U12

= = = = = = = =

0.004110236 -0.012590366 0.005066929 -0.023268172 -0.001275591 -0.02474455 -0.001275591 -0.015247846

m m m m m m m m

0 -30 0 X

-20 0 -25

HALLANDO LAS FUERZAS

[F]=[K]x[U]

Rax Ray RBx RBy 0 -30 0 -20 0 -25 0 0

Rax Ray RBx RBy F5 F6 F7 F8 F9 F10 F11 F12

=

KGLOBAL

= = = = = = = = = = = =

COMPROBACION CON EXCEL

86.99999999 75 -86.99999999 0 2.84217E-14 -30 0 -20 0 -25 1.42109E-14 1.13687E-13

X

87 75 -87 0 0 -30 0 -20 0 -25 0 0

kN kN kN kN kN kN kN kN kN kN kN kN

0 0 0 0 0.00411024 -0.01259037 0.00506693 -0.02326817 -0.00127559 -0.02474455 -0.00127559 -0.01524785

MATRIZ GLOBAL ENSAMBLADA 1 26326.74933 6450.103336 0 0 -5160.082668 -6450.103336 0 0 0 0 -21166.66667 0

2 3 4 5 6 7 8 9 10 11 6450.103336 0 0 -5160.08267 -6450.10334 0 0 0 0 -21166.6667 24995.9625 0 -16933.3333 -6450.10334 -8062.62917 0 0 0 0 0 0 21166.66667 0 -21166.6667 0 0 0 0 0 0 -16933.3333 0 16933.3333 0 0 0 0 0 0 0 -6450.10334 -21166.66667 0 54548.9716 6450.10334 -28222.2222 0 0 0 0 -8062.62917 0 0 6450.10334 24995.9625 0 0 0 0 0 0 0 0 -28222.2222 0 32065.8082 6405.97656 0 0 -3843.58594 0 0 0 0 0 6405.97656 27609.9609 0 -16933.3333 -6405.97656 0 0 0 0 0 0 0 28222.2222 0 -28222.2222 0 0 0 0 0 0 -16933.3333 0 16933.3333 0 0 0 0 0 0 -3843.58594 -6405.97656 -28222.2222 0 53232.47483 0 0 0 0 -16933.3333 -6405.97656 -10676.6276 0 0 6405.976562

12 01 02 03 04 05 -16933.33333 6 -6405.976562 7 -10676.6276 8 09 0 10 6405.976562 11 27609.96094 12

HALLANDO LOS DESPLAZAMIENTOS

[U]=[K]¯¹x[F] -1 U5 U6 U7 U8 U9 U10 U11 U12

=

54548.97156 6450.10334 -28222.22222 0 0 0 0 0 6450.103336 24995.9625 0 0 0 0 0 -16933.33333 -28222.22222 0 32065.80816 6405.976562 0 0 -3843.58594 -6405.976562 0 0 6405.976562 27609.96094 0 -16933.33333 -6405.97656 -10676.6276 0 0 0 0 28222.22222 0 -28222.2222 0 0 0 0 -16933.33333 0 16933.33333 0 0 0 0 -3843.585937 -6405.976562 -28222.22222 0 53232.47483 6405.976562 0 -16933.3333 -6405.976562 -10676.6276 0 0 6405.976562 27609.96094

U5 U6 U7 U8 U9 U10 U11 U12

= = = = = = = =

0.004110236 m -0.012590366 m 0.005066929 m -0.023268172 m -0.001275591 m -0.02474455 m -0.001275591 m -0.015247846 m

4.72441E-05 -3.77953E-05 4.72441E-05 -6.61417E-05 -1.31129E-21 -6.61417E-05 -1.31129E-21 -3.77953E-05

-3.77953E-05 0.000154265 -3.77953E-05 0.000176942 5.24515E-21 0.000176942 5.24515E-21 0.000154265

4.72441E-05 -3.77953E-05 8.26772E-05 -8.74016E-05 -1.31129E-21 -8.74016E-05 -1.31129E-21 -3.77953E-05

-6.61417E-05 0.000176942 -8.74016E-05 0.000399109 2.83465E-05 0.000399109 2.83465E-05 0.000235998

-2.1545E-21 7.42549E-21 -2.4672E-21 2.83465E-05 8.26772E-05 2.83465E-05 4.72441E-05 1.01404E-20

-6.61417E-05 0.000176942 -8.74016E-05 0.000399109 2.83465E-05 0.000458164 2.83465E-05 0.000235998

X

-2.1545E-21 7.42549E-21 -2.4672E-21 2.83465E-05 4.72441E-05 2.83465E-05 4.72441E-05 1.01404E-20

0 -30 0 -20 0 -25 0 0

-3.77953E-05 0.000154265 -3.77953E-05 0.000235998 5.24515E-21 0.000235998 5.24515E-21 0.00021332

HALLANDO LAS FUERZAS

[F]=[K]x[U] Rax Ray RBx RBy 0 -30 0 -20 0 -25 0 0

=

1 26326.74933 6450.103336 0 0 -5160.082668 -6450.103336 0 0 0 0 -21166.66667 0

2 3 4 5 6 6450.10334 0 0 -5160.082668 -6450.103336 24995.9625 0 -16933.33333 -6450.103336 -8062.629172 0 21166.66667 0 -21166.66667 0 -16933.3333 0 16933.33333 0 0 -6450.10334 -21166.66667 0 54548.97156 6450.103336 -8062.62917 0 0 6450.103336 24995.9625 0 0 0 -28222.22222 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -16933.33333

7 0 0 0 0 -28222.2222 0 32065.80816 6405.976562 0 0 -3843.58594 -6405.97656

8

9 10 11 12 0 0 0 -21166.6667 01 0 0 0 0 02 0 0 0 0 03 0 0 0 0 04 0 0 0 0 05 0 0 0 0 -16933.3333 6 6405.976562 0 0 -3843.58594 -6405.97656 7 27609.96094 0 -16933.33333 -6405.97656 -10676.6276 8 0 28222.22222 0 -28222.2222 09 -16933.33333 0 16933.33333 0 0 10 -6405.976562 -28222.2222 0 53232.4748 6405.97656 11 -10676.6276 0 0 6405.97656 27609.9609 12

X

0 0 0 0 0.00411024 -0.01259037 0.00506693 -0.02326817 -0.00127559 -0.02474455 -0.00127559 -0.01524785

Rax Ray RBx RBy F5 F6 F7 F8 F9 F10 F11 F12

= = = = = = = = = = = =

86.99999999 75 -86.99999999 0 2.84217E-14 -30 0 -20 0 -25 1.42109E-14 1.13687E-13

87 kN 75 kN -87 kN 0 kN 0 kN -30 kN 0 kN -20 kN 0 kN -25 kN 0 kN 0 kN