Matrices de Rigidez

BARRA BARRA 1 - 2

MATRIZ DE RIGIDEZ - COORDENADAS LOCALES MATRIZ DE RIGIDEZ - COORDENADAS GLOBALES

1 2 3 4 5 6 7 8 9 10 11 12

= cm = cm = cm 1 0 -1 0 0 0 0 0 0 0 0 0 6 0 0 0 0 0 -6 0 0 0 0 0 4 3 0 0 0 -9 -4 -3 0 0 0 -9 1

1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 15 0 0 0 0 0 15 3 2 0 0 0 12 -3 -2 0 0 0 12 2

= cm2 E = kg/cm2 G = *E 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -15 0 0 0 0 0 -15 0 0 0 0 9 -12 0 0 0 0 9 -12 0 3

0 0 0 1 0 -1 0 0 0 0 0 0 0 0 0 1003 0 0 0 0 0 -1003 0 0 0 0 9 1230 -313 0 0 0 -9 -369 -872 0 4

0 0 0 1 0 1 0 0 0 0 0 0 0 0 -15 0 1662 0 0 0 15 0 831 0 0 0 -12 -313 1434 0 0 0 12 -872 197 0 5

= cm4i = ( ; ; ) cm 0 0 0 0 -1 0 0 0 0 0 0 0 0 15 0 0 0 1662 0 -15 0 0 0 831 -9 12 0 0 0 1662 9 -12 0 0 0 831 6

= cm4j = ( ; ; ) cm 0 0 0 0 0 0 1 0 -1 0 0 0 -6 0 0 0 0 0 6 0 0 0 0 0 -4 -3 0 0 0 9 4 3 0 0 0 9 7

= cm4P = ( ; ; ) cm 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 -15 0 0 0 0 0 -15 -3 -2 0 0 0 -12 3 2 0 0 0 -12 8

0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 15 0 0 0 0 0 15 0 0 0 0 -9 12 0 0 0 0 -9 12 0 9

= = = 0 0 0 0 0 0 0 0 0 1 0 -1 0 0 0 -1003 0 0 0 0 0 1003 0 0 0 0 9 -369 -872 0 0 0 -9 1230 -313 0 10

= = = 0 0 0 0 0 0 0 0 0 1 0 1 0 0 -15 0 831 0 0 0 15 0 1662 0 0 0 -12 -872 197 0 0 0 12 -313 1434 0 11

= = = 12x12 0 0 0 0 0 0 0 0 0 0 -1 0 12x12 0 15 0 0 0 831 0 -15 0 0 0 1662 12x12 -9 12 0 0 0 831 9 -12 0 0 0 1662 12

12x12

= =

MATRIZ DE ROTACIÓN FUERZAS DE FIJACIÓN {f°} FUERZAS DE FIJACIÓN {f°} - COORDENADAS GLOBALES

= kg/cm 1 1 0 0 0 0 0 0 0 0 0 0 4 0 0 0 8 -4 -4 0 0 0 8 -4 0 -0.032137029 1

0 0 -1 0 0 0 0 0 0 0 0 0 3 0 0 0 -11 6 -3 0 0 0 -11 6 0.122850705 0.044232826 2

X -1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -7 -14 0 0 0 0 -7 -14 0 -0.110013472 3

0 0 0 1 1 0 0 0 0 0 0 0 0 -8 4 811 -435 -875 0 8 -4 -811 -217 -437 0 -1.751324702 4

Z 0 0 0 0 0 -1 0 0 0 0 0 0 0 11 -6 589 598 1204 0 -11 6 -589 299 602 0 2.410491656 5

* 104(kg)(cm) 0 0 0 -1 1 0 0 0 0 0 0 0 0 7 14 0 -1488 739 0 -7 -14 0 -744 370 3.327206584 1.480775277 6

0 0 0 0 0 0 1 1 0 0 0 0 -4 0 0 0 -8 4 4 0 0 0 -8 4 0 -0.032137029 7

0 0 0 0 0 0 0 0 -1 0 0 0 -3 0 0 0 11 -6 3 0 0 0 11 -6 0.122850705 0.044232826 8

0 0 0 0 0 0 -1 1 0 0 0 0 0 0 0 0 7 14 0 0 0 0 7 14 0 -0.110013472 9

0 0 0 0 0 0 0 0 0 1 1 0 0 -8 4 -811 -217 -437 0 8 -4 811 -435 -875 0 1.751324702 10

0 0 0 0 0 0 0 0 0 0 0 -1 0 11 -6 -589 299 602 0 -11 6 589 598 1204 0 -2.410491656 11

12x12 0 0 0 0 0 0 0 0 0 -1 1 0 12x12 0 7 14 0 -744 370 0 -7 -13.7 0 -1488 739 12x12 -3.327206584 -1.480775277 12

=_

[K]=

[A] = * E [AT]*[K] =_

{f°}= [AT]* _ {f°} =

[AT] = [K]

Cx

Cy

Cz

0.81

0.59

0

Dy

1 - 2

900 217370.65

Iy

Iz

131 0 300

67500

[K]=

-0.9 0.45senα cosα

Ix

30 DZ

0.45

X Y Z

30 L 163

365625

67500

Xpγ 33.3

Ypγ 99.4

Zpγ -200

Xps -31.465

Yps 100

Zps -200

30095.5263

100 100 100

15.337

0

0

0.189

0

-15.337

0

0

0.189

0

0

0

5.538

0

0

0

0

0

0 1661.54 0

0 0 1661.5

0 -15.337 0

1003 0 0

0 0 0

0 0 15.337

-15.337

0 0 -0.189 0 15.337 0

0 -0.189 0 0 0

0 0 0 0 0-5.538

0 15.337 0 0 0

0

0 0 -15.337 0 830.769 0

0 0 0 -1003 0

-15.337 0

0 0 0 -1003 0 0

0 0

0 -0.189 0 0 0 15.337

830.77

-5.538 0 0 0

0 0 -0.189 0

0 0 15.337 0

5.538 0 0

0

0 0 0.189 0 15.337

0 0 0

0 0.189 0 0 0 -15.337

830.76923 0

0 -15.337 0 0 0 830.77* E

1 1 0 0 0 0 0 0 0 0 0 0

0

0 -15.337 0 0 0 1661.5

0 0 15.337 0 1661.5385

0

0 0 0 1003 0

-1 1 0 0 0 0 0 0 0 0 0 0

0 0 0 0 00 0 -1 0 0

0 0 0 0 0 -1 0 0 0 0 0 0

0 0 0 0 00 0 0 1 1

0 0 0 0 0 0 1 1 0 0 0 0

0 0 0 0 00 0 0 -1 1

0 0 0 0 0

0 0

0 0 0 0 0 0 -1 1 0 0 0 0

0 0 0 -1 00 0 0 0 0

Y

W 15.12

0 0

1 0

A

[a] =

0 0 0 0 -10 0 0 0 0

1 0

0 0 0 0 0 0 0 0 0 0

3 -3

{f°} =

0

0.1

0

0

0

3.3

0

0 -1

0 0 0 0 1

0 0

0 0

0 0

0.1

0

0

0

-3.3

BARRA BARRA 5 - 10


25 26 27 28 29 30 55 56 57 58 59 60

= cm = cm = cm 0 1 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 -3 0 0 0 0 0 0 0 0 0 5 0 0 0 0 0 5 0 25

0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 0 0 0 0 0 5 0 0 0 -5 0 0 0 0 0 -5 0 0 26

= cm2 E = kg/cm2 G = *E 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -5 0 0 0 0 0 -5 0 0 0 3 0 0 0 0 0 -3 0 0 0 27

0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1003 0 0 0 0 0 -1003 0 0 0 -5 0 900 0 0 0 5 0 450 0 0 28

0 0 0 0 0 1 0 0 0 0 0 0 0 0 -5 0 900 0 0 0 5 0 450 0 5 0 0 0 900 0 -5 0 0 0 450 0 29

= cm4i = ( ; ; ) cm 0 0 0 1 0 0 0 0 0 0 0 0 0 5 0 0 0 900 0 -5 0 0 0 450 0 0 0 0 0 1003 0 0 0 0 0 -1003 30

= cm4j = ( ; ; ) cm 0 0 0 0 0 0 0 1 0 0 0 0 -3 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 -5 0 0 0 0 0 -5 0 55

= cm4P = ( ; ; ) cm 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 -5 0 0 0 0 0 -5 0 0 0 5 0 0 0 0 0 5 0 0 56

0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 5 0 0 0 0 0 5 0 0 0 -3 0 0 0 0 0 3 0 0 0 57

= = = 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 -1003 0 0 0 0 0 1003 0 0 0 -5 0 450 0 0 0 5 0 900 0 0 58

= = = 0 0 0 0 0 0 0 0 0 0 0 1 0 0 -5 0 450 0 0 0 5 0 900 0 5 0 0 0 450 0 -5 0 0 0 900 0 59

= = = 12x12 0 0 0 0 0 0 0 0 0 1 0 0 12x12 0 5 0 0 0 450 0 -5 0 0 0 900 12x12 0 0 0 0 0 -1003 0 0 0 0 0 1003 60

12x12

= =


= kg/cm 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 4 0 0 25

1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -4 0 0 0 0 0 -4 0 0 0 26

X 0 1 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 -3 0 0 0 0 0 0 0 27

0 0 0 0 0 1 0 0 0 0 0 0 0 0 -4 0 899 -40 0 0 4 0 450 -20 0 0 28

Z 0 0 0 1 0 0 0 0 0 0 0 0 0 4 0 0 40 899 0 -4 0 0 20 450 0 0 29

* 104(kg)(cm) 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1003 0 0 0 0 0 -1003 0 0 0 0 30

0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 -4 0 0 0 0 0 -4 0 0 55

0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 4 0 0 0 56

0 0 0 0 0 0 0 1 0 0 0 0 -3 0 0 0 0 0 3 0 0 0 0 0 0 0 57

0 0 0 0 0 0 0 0 0 0 0 1 0 0 -4 0 450 -20 0 0 4 0 899 -40 0 0 58

0 0 0 0 0 0 0 0 0 1 0 0 0 4 0 0 20 450 0 -4 0 0 40 899 0 0 59

12x12 0 0 0 0 0 0 0 0 0 0 1 0 12x12 0 0 0 -1003 0 0 0 0 0 1003 0 0 12x12 0 0 60

=_

{f°}= [AT]* _ {f°} =

=_

[K]=

0 0 0.0

0

= * E [AT]*[K]

0 0 0 0 0 0 1 0 0 0

0

X

0 0 0 1003 0 0 0 0 0

Ix 675000 95.5 300[K]=

0 4.500 0 0 0 900 0 -4.500 0

Iy 67500 95.5 600

5 - 10

Dy 30 DZ 30 L 300 3.000 0 0 0 0 0 -3.000 0 0 0 0

0 0.030 0 0 0 4.500 0 -0.030 0 0 0 4.500

A 900 217370.65 0.45 0 0 0.030 0 -4.500 0 0 -0.030 0 -4.500 00

0

-1003 0 0

Y Z 0 0 -4.500 0 900 0 0 0 4.500 0 450 0

0 0 450* E [AT] = [K]

-4.500

0 0 -0.030 0 4.500 0 0 0 0.030 0 4.500 0

-3.000 0 0 0 0 0 3.000 0 0 0 0 0

0 0 -1003 0 0 0 0 0 1003 0

Iz 67500 100 100 0 -0.030 0 0 0 -4.500 0 0.030 0 0 0100

0

450 0 -4.500 0 0 0

0

Cy 0 Yps 4.4849 Ypγ 4.48 0 0 -4.500 0 450 0 0 0 4.500 0 900 0

Cx 0 Xps 100 Xpγ -200 0

900

senα -1 cosα 0.04

Y

0 0 1 0 0 0 0 0 0 0 0 0 W 0 0

Cz 1 Zps -200 Zpγ -100 0 4.500 0 0 0

1 0 0 0 0 0 0 0 0 0 0 0 0 0 0.0

0 1 0 0 0 0 0 0 0 0 0 00

0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 1 0 0 0 0 0 0 0 0 00 0

1

[a] =0 0 0 0 1 0 0 0 0 0 0

{f°} =0.0

[A]0 0 0 0 0 0 0 0 1 0 0 0 0

0

0 1 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 1 0

0 0 0 0 0 0 0 0 0 1 0 0 0

0 0 0 0 0 0 0 0 0 1 0 0.0

0 0 0 0 0 0

BARRA BARRA 2 - 3


7 8 9 10 11 12 13 14 15 16 17 18

= cm = cm = cm 0 -1 -1 0 0 0 0 0 0 0 0 0 6 0 0 0 0 0 -6 0 0 0 0 0 1 -2 0 0 0 -15 -1 2 0 0 0 -15 7

1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 15 0 0 0 0 0 15 -2 5 0 0 0 -5 2 -5 0 0 0 -5 8

= cm2 E = kg/cm2 G = *E 0 -1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 -15 0 0 0 0 0 -15 0 0 0 0 15 5 0 0 0 0 15 5 0 9

0 0 0 0 -1 -1 0 0 0 0 0 0 0 0 0 1003 0 0 0 0 0 -1003 0 0 0 0 15 1599 194 0 0 0 -15 656 539 0 10

0 0 0 1 0 0 0 0 0 0 0 0 0 0 -15 0 1662 0 0 0 15 0 831 0 0 0 5 194 1066 0 0 0 -5 539 -828 0 11

= cm4i = ( ; ; ) cm 0 0 0 0 -1 1 0 0 0 0 0 0 0 15 0 0 0 1662 0 -15 0 0 0 831 -15 -5 0 0 0 1662 15 5 0 0 0 831 12

= cm4j = ( ; ; ) cm 0 0 0 0 0 0 0 -1 -1 0 0 0 -6 0 0 0 0 0 6 0 0 0 0 0 -1 2 0 0 0 15 1 -2 0 0 0 15 13

= cm4P = ( ; ; ) cm 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 -15 0 0 0 0 0 -15 2 -5 0 0 0 5 -2 5 0 0 0 5 14

0 0 0 0 0 0 0 -1 1 0 0 0 0 0 0 0 15 0 0 0 0 0 15 0 0 0 0 -15 -5 0 0 0 0 -15 -5 0 15

= = = 0 0 0 0 0 0 0 0 0 0 -1 -1 0 0 0 -1003 0 0 0 0 0 1003 0 0 0 0 15 656 539 0 0 0 -15 1599 194 0 16

= = = 0 0 0 0 0 0 0 0 0 1 0 0 0 0 -15 0 831 0 0 0 15 0 1662 0 0 0 5 539 -828 0 0 0 -5 194 1066 0 17

= = = 12x12 0 0 0 0 0 0 0 0 0 0 -1 1 12x12 0 15 0 0 0 831 0 -15 0 0 0 1662 12x12 -15 -5 0 0 0 831 15 5 0 0 0 1662 18

12x12

= =


= kg/cm 0 1 0 0 0 0 0 0 0 0 0 0 -2 0 0 0 12 -9 2 0 0 0 12 -9 0 -0.071157014 7

-1 0 -1 0 0 0 0 0 0 0 0 0 5 0 0 0 4 -3 -5 0 0 0 4 -3 0.122850705 -0.023120315 8

X -1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 -9 -12 0 0 0 0 -9 -12 0 -0.097439346 9

0 0 0 0 1 0 0 0 0 0 0 0 0 -12 9 -310 -962 -1253 0 12 -9 310 -481 -627 0 -2.50982129 10

Z 0 0 0 -1 0 -1 0 0 0 0 0 0 0 -4 3 954 -313 -407 0 4 -3 -954 -156 -204 0 -0.815490371 11

* 104(kg)(cm) 0 0 0 -1 0 1 0 0 0 0 0 0 0 9 12 0 -1318 1012 0 -9 -12 0 -659 506 3.327206584 2.026345529 12

0 0 0 0 0 0 0 1 0 0 0 0 2 0 0 0 -12 9 -2 0 0 0 -12 9 0 -0.071157014 13

0 0 0 0 0 0 -1 0 -1 0 0 0 -5 0 0 0 -4 3 5 0 0 0 -4 3 0.122850705 -0.023120315 14

0 0 0 0 0 0 -1 0 1 0 0 0 0 0 0 0 9 12 0 0 0 0 9 12 0 -0.097439346 15

0 0 0 0 0 0 0 0 0 0 1 0 0 -12 9 310 -481 -627 0 12 -9 -310 -962 -1253 0 2.50982129 16

0 0 0 0 0 0 0 0 0 -1 0 -1 0 -4 3 -954 -156 -204 0 4 -3 954 -313 -407 0 0.815490371 17

12x12 0 0 0 0 0 0 0 0 0 -1 0 1 12x12 0 9 12 0 -659 506 0 -9 -12 0 -1318 1012 12x12 -3.327206584 -2.026345529 18

=_

{f°}= [AT]* _ {f°} =

[AT] = [K] =_

[K]=

* E [AT]*[K]

0 0 15.3370

5.538 0 0 0 0 0 -5.538 0 0 0 0 0

0 0 -1003 0 00 1003 0 0 00 0

15.337

0 0 0.189 0 -15.337 0 0 0 -0.189 0 -15.337 0

0 -0.189 0 0 00.189 0

0 0

15.337 0 830.76923 0

0 830.77

0 1661.54 0 0 00 0 -15.337X Y Z

0 0.189 0 0 0 -15.337

0 5.538 0 0 0-5.538 0 0 0 0Iy 67500 213 250 300

Iz 67500 100 100 100 0 -0.189 0 0 0 -15.337

0 0 1003 0 0

0 15.337 0

Cx -0.31 Xps -162.93 Xpγ 54.6 0 0 0 -1003 0 0 0

15.337 0 0 0 0.1890 0 -0.189 0

0 1661.5385 0830.769 0 0 0 15.337-154 0 0 -15.337 0

0 -15.337 0 0 0 1661.5

0-1 0 1 0 0

0

-1 0 -1 0 0 0 0 0 0 0 0 0 0.1

0 1 0 0 0 0 0 0 0 0 0 0

0

0 0 0 -1 0 -1 0 0 0 0 0 0

0 0 0

0 0 0 0 1 0 0 0 0 0 0 0

0 0 0 0

1 00 0 0 0 0

0 0 0

0 0 0 0 0 0 -1 0 -1 0 0 0 0.1

0 0 1 0 00 0 0 0

0 -1 00 0 0 0 -10 0 0 0 0

0 0 0

0 0 0 0 0 0 0 0 0 0 1 0 0

0 -1 0

2 - 3

Dy 30 DZ 30 L 163

A 900 217370.65 0.45

[K]= * E0 0

Ix 365625 263 95.5 300 0 15.337 0 0 0 1661.5 0 -15.337

Cz 0 Zps -200 Zpγ 200 0 15.337 0 0 0 830.77

Cy 0.95 Yps 4.4849 Ypγ

senα 0.793 cosα -0.6

Y

W 15.12

3 -3

0 0

[a] = {f°} = [A] =0

0

0 0 0 -1 0 1 0 0 0 0 0 0 3.3

0 0 0 0 0 0 0 0 0 -1 0 1 -3.3

BARRA BARRA 3 - 4


13 14 15 16 17 18 19 20 21 22 23 24

= cm = cm = cm -1 0 0 0 0 0 0 0 0 0 0 0 6 0 0 0 0 0 -6 0 0 0 0 0 6 0 0 0 0 0 -6 0 0 0 0 0 13

0 -1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 15 0 0 0 0 0 15 0 0 0 0 0 -15 0 0 0 0 0 -15 14

= cm2 E = kg/cm2 G = *E 0 -1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 -15 0 0 0 0 0 -15 0 0 0 0 0 15 0 0 0 0 0 15 0 15

0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 1003 0 0 0 0 0 -1003 0 0 0 0 0 1003 0 0 0 0 0 -1003 0 0 16

0 0 0 0 -1 -1 0 0 0 0 0 0 0 0 -15 0 1662 0 0 0 15 0 831 0 0 0 15 0 1662 0 0 0 -15 0 831 0 17

= cm4i = ( ; ; ) cm 0 0 0 0 -1 1 0 0 0 0 0 0 0 15 0 0 0 1662 0 -15 0 0 0 831 0 -15 0 0 0 1662 0 15 0 0 0 831 18

= cm4j = ( ; ; ) cm 0 0 0 0 0 0 -1 0 0 0 0 0 -6 0 0 0 0 0 6 0 0 0 0 0 -6 0 0 0 0 0 6 0 0 0 0 0 19

= cm4P = ( ; ; ) cm 0 0 0 0 0 0 0 -1 -1 0 0 0 0 0 0 0 0 -15 0 0 0 0 0 -15 0 0 0 0 0 15 0 0 0 0 0 15 20

0 0 0 0 0 0 0 -1 1 0 0 0 0 0 0 0 15 0 0 0 0 0 15 0 0 0 0 0 -15 0 0 0 0 0 -15 0 21

= = = 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 -1003 0 0 0 0 0 1003 0 0 0 0 0 -1003 0 0 0 0 0 1003 0 0 22

= = = 0 0 0 0 0 0 0 0 0 0 -1 -1 0 0 -15 0 831 0 0 0 15 0 1662 0 0 0 15 0 831 0 0 0 -15 0 1662 0 23

= = = 12x12 0 0 0 0 0 0 0 0 0 0 -1 1 12x12 0 15 0 0 0 831 0 -15 0 0 0 1662 12x12 0 -15 0 0 0 831 0 15 0 0 0 1662 24

12x12

= =


= kg/cm -1 0 0 0 0 0 0 0 0 0 0 0 -6 0 0 0 0 0 6 0 0 0 0 0 0 0 13

0 -1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 12 -9 0 0 0 0 12 -9 0.122850705 -0.07372985 14

X 0 -1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 -9 -12 0 0 0 0 -9 -12 0 -0.09826599 15

0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 -1003 0 0 0 0 0 1003 0 0 0 0 16

Z 0 0 0 0 -1 -1 0 0 0 0 0 0 0 -12 9 0 -997 -1329 0 12 -9 0 -499 -665 0 -2.661370562 17

* 104(kg)(cm) 0 0 0 0 -1 1 0 0 0 0 0 0 0 9 12 0 -1329 997 0 -9 -12 0 -665 499 3.327206584 1.996850117 18

0 0 0 0 0 0 -1 0 0 0 0 0 6 0 0 0 0 0 -6 0 0 0 0 0 0 0 19

0 0 0 0 0 0 0 -1 -1 0 0 0 0 0 0 0 -12 9 0 0 0 0 -12 9 0.122850705 -0.07372985 20

0 0 0 0 0 0 0 -1 1 0 0 0 0 0 0 0 9 12 0 0 0 0 9 12 0 -0.09826599 21

0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 1003 0 0 0 0 0 -1003 0 0 0 0 22

0 0 0 0 0 0 0 0 0 0 -1 -1 0 -12 9 0 -499 -665 0 12 -9 0 -997 -1329 0 2.661370562 23

12x12 0 0 0 0 0 0 0 0 0 0 -1 1 12x12 0 9 12 0 -665 499 0 -9 -12 0 -1329 997 12x12 -3.327206584 -1.996850117 24

* E [AT]*[K] =_

{f°}= [AT]* _ {f°}

0.45 0 0A 900 217370.65

0 0

0 0.189 0 0 0 15.337 0 -0.189 0 0 0 15.337

30 5.538 0 0 0 0 0 -5.538 0 0 0

0 -1003 0 0

830.76923 0

1003 0 0 0 00 0 0

0 -0.189 0 -15.337 00.189 0 -15.337 0 0

0 -15.337 0 00 15.337 0 0 0Ix 365625 213 250 300

X Y Z 0 0 -15.337 0 1661.54 0 0 0 15.337 0

[K]=

Cx -1 Xps -112.72 Xpγ

0 0.189 0 15.337 0

0 0 -15.337

0 0 -0.189 0 15.337 0 0

0 -15.337 0 0.189 00 -0.189 0 0Iz

0 0

1003 0 0

-200

0 0 0 0 0113 0 0 0 -1003

0

00 -1 -1 0 0

-1 0 0 0 0 0 0 0 0 0 0

0

0 0 0 -1 0 0 0 0 0 0 0 0

0 0 0.1

0 -1 1 0 0 0 0 0 0 0 0 0

0 0 0 0

0

1 0 0 0 00 0 0 0 -1

0

0 0 0 0 -1 -1 0 0 0 0 0 0 0

0 0 0 0 0 -1 1 0 0 0 0

0 0 -1 -1 00 0 0 0 0

3 - 4

Dy DZ 30 L 163

* E [AT] = [K] =_

[K]=

Iy 67500 50.2 250 300

67500 100 100 100

0 830.77

-5.538 0 0 0 0 0 5.538 0 0 0 0 0

1661.5

Cy 0 Yps -150.06 Ypγ -150 0 0 -15.337 0 830.769 0 0 0 15.337 0 1661.5385

Cz 0 Zps Zpγ 200 0 15.337 0 0 0 830.77 0 -15.337 0 0 0 1661.5


Y

W 15.12

3 -3

0 0

[a] = {f°} = [A] =0 0 3.3

0 0 0 0 0 0 -1 0 0 0 0 0=

0 0 0 0 0 0 0 0 0 0 -1 -1 0

0 0 00 0 0 0 -10 0 0 0 0

0 0 0.1

0 0

0 0 0 0 0 0 0 0 0 0 -1 1 -3.3

BARRA BARRA 4 - 5


19 20 21 22 23 24 25 26 27 28 29 30

= cm = cm = cm 0 0 1 0 0 0 0 0 0 0 0 0 6 0 0 0 0 0 -6 0 0 0 0 0 1 2 0 0 0 15 -1 -2 0 0 0 15 19

-1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 15 0 0 0 0 0 15 2 5 0 0 0 -5 -2 -5 0 0 0 -5 20

= cm2 E = kg/cm2 G = *E 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -15 0 0 0 0 0 -15 0 0 0 0 -15 5 0 0 0 0 -15 5 0 21

0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1003 0 0 0 0 0 -1003 0 0 0 0 -15 1599 -194 0 0 0 15 656 -539 0 22

0 0 0 -1 0 0 0 0 0 0 0 0 0 0 -15 0 1662 0 0 0 15 0 831 0 0 0 5 -194 1066 0 0 0 -5 -539 -828 0 23

= cm4i = ( ; ; ) cm 0 0 0 0 -1 0 0 0 0 0 0 0 0 15 0 0 0 1662 0 -15 0 0 0 831 15 -5 0 0 0 1662 -15 5 0 0 0 831 24

= cm4j = ( ; ; ) cm 0 0 0 0 0 0 0 0 1 0 0 0 -6 0 0 0 0 0 6 0 0 0 0 0 -1 -2 0 0 0 -15 1 2 0 0 0 -15 25

= cm4P = ( ; ; ) cm 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 -15 0 0 0 0 0 -15 -2 -5 0 0 0 5 2 5 0 0 0 5 26

0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 15 0 0 0 0 0 15 0 0 0 0 15 -5 0 0 0 0 15 -5 0 27

= = = 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 -1003 0 0 0 0 0 1003 0 0 0 0 -15 656 -539 0 0 0 15 1599 -194 0 28

= = = 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 -15 0 831 0 0 0 15 0 1662 0 0 0 5 -539 -828 0 0 0 -5 -194 1066 0 29

= = = 12x12 0 0 0 0 0 0 0 0 0 0 -1 0 12x12 0 15 0 0 0 831 0 -15 0 0 0 1662 12x12 15 -5 0 0 0 831 -15 5 0 0 0 1662 30

12x12

= =


= kg/cm 0 -1 0 0 0 0 0 0 0 0 0 0 -2 0 0 0 -13 6 2 0 0 0 -13 6 0 0.049576867 19

0 0 -1 0 0 0 0 0 0 0 0 0 -5 0 0 0 4 -2 5 0 0 0 4 -2 0.122850705 -0.0161085 20

X 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -7 -14 0 0 0 0 -7 -14 0 -0.111242735 21

0 0 0 0 -1 0 0 0 0 0 0 0 0 13 -6 -310 671 1431 0 -13 6 310 335 715 0 2.865365973 22

Z 0 0 0 0 0 -1 0 0 0 0 0 0 0 -4 2 -954 -218 -465 0 4 -2 954 -109 -232 0 -0.931013842 23

* 104(kg)(cm) 0 0 0 1 0 0 0 0 0 0 0 0 0 7 14 0 -1505 705 0 -7 -14 0 -752 353 3.327206584 1.411805483 24

0 0 0 0 0 0 0 -1 0 0 0 0 2 0 0 0 13 -6 -2 0 0 0 13 -6 0 0.049576867 25

0 0 0 0 0 0 0 0 -1 0 0 0 5 0 0 0 -4 2 -5 0 0 0 -4 2 0.122850705 -0.0161085 26

0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 7 14 0 0 0 0 7 14 0 -0.111242735 27

0 0 0 0 0 0 0 0 0 0 -1 0 0 13 -6 310 335 715 0 -13 6 -310 671 1431 0 -2.865365973 28

0 0 0 0 0 0 0 0 0 0 0 -1 0 -4 2 954 -109 -232 0 4 -2 -954 -218 -465 0 0.931013842 29

12x12 0 0 0 0 0 0 0 0 0 1 0 0 12x12 0 7 14 0 -752 353 0 -7 -14 0 -1505 705 12x12 -3.327206584 -1.411805483 30

-0.189 0 0 0 15.3370 0 0 15.337 00 0.189

A 900 217370.65

5.538 0 0 0 0 0 -5.538 0 0 0 0 0

-0.189 0 -15.337 0

0 0

0 -15.337 0 0 00 0 0.1890.45

830.76923 00 0 0 15.337 00 0 -15.337 0 1661.54X Y Z

0 0 0 1003 0 0 0 0 0 -1003

0 1003 0 0

0.189 0 0 0 -15.337

0 0 0

Iz 0 -0.189 0 0 0 -15.337 0

0 0 5.538 0 0-5.538 0 0 0Iy

0 0 0

0 0 -1 0 0 0 0 0 0 0 0 0

0 0 0 0 00 -1 0 0 0

0

0 0 0 0 -1 0 0 0 0 0 0 0 0

0.1

1 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0

0 0 0

0 0 0 1 0 0 0 0 0 0 0 0 3.3

-1 0 0 0 00 0 0 0 0

0 0 0 0 0 0 0 -1 0 0 0 0.1

0 0 -1 0 0

0 0 00 1 0 0 0

4 - 5

Dy 30 DZ 30 L 163

Ix 365625 50.2 250 300[K]= * E [AT] = [K] =

_

[K]=

67500 0 95.5 300

0 15.337 0 0 0 1661.5 0 -15.337 0 0 0 830.77

0

67500 100 100 100

Cx -0.31 Xps 49.785 Xpγ 127 0 0 0 -1003 0 0 0

0 15.337 0

-150.06

15.337 0 0 0 0.1890 0 -0.189 0

0

0 0

Cy -0.95 Yps Ypγ -93.7 0 0 -15.337 0 830.769 0 0 0 15.337 0 1661.5385

1661.5


Y

W 15.12

3 -3

0 0

[a] = {f°} = [A]

Cz 0 Zps -200 Zpγ 200 0 15.337 0 0 0 830.77 0 -15.337 0

= * E [AT]*[K] =_

{f°}= [AT]* _ {f°} =

0 0 0 0 0 0 0 0 0 0 -1 0 0

0 0 0 0 0

0 0 0

0

0 0 0 0 0 0 0 0 0 0 0 -1 0

0 0 0 0 0 0 0 0 0 1 0 0 -3.3

BARRA BARRA 5 - 1


25 26 27 28 29 30 1 2 3 4 5 6

= cm = cm = cm 1 0 1 0 0 0 0 0 0 0 0 0 6 0 0 0 0 0 -6 0 0 0 0 0 4 -3 0 0 0 9 -4 3 0 0 0 9 25

-1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 15 0 0 0 0 0 15 -3 2 0 0 0 12 3 -2 0 0 0 12 26

= cm2 E = kg/cm2 G = *E 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -15 0 0 0 0 0 -15 0 0 0 0 -9 -12 0 0 0 0 -9 -12 0 27

0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 1003 0 0 0 0 0 -1003 0 0 0 0 -9 1230 313 0 0 0 9 -369 872 0 28

0 0 0 -1 0 1 0 0 0 0 0 0 0 0 -15 0 1662 0 0 0 15 0 831 0 0 0 -12 313 1434 0 0 0 12 872 197 0 29

= cm4i = ( ; ; ) cm 0 0 0 0 -1 0 0 0 0 0 0 0 0 15 0 0 0 1662 0 -15 0 0 0 831 9 12 0 0 0 1662 -9 -12 0 0 0 831 30

= cm4j = ( ; ; ) cm 0 0 0 0 0 0 1 0 1 0 0 0 -6 0 0 0 0 0 6 0 0 0 0 0 -4 3 0 0 0 -9 4 -3 0 0 0 -9 1

= cm4P = ( ; ; ) cm 0 0 0 0 0 0 -1 0 1 0 0 0 0 0 0 0 0 -15 0 0 0 0 0 -15 3 -2 0 0 0 -12 -3 2 0 0 0 -12 2

0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 15 0 0 0 0 0 15 0 0 0 0 9 12 0 0 0 0 9 12 0 3

= = = 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 -1003 0 0 0 0 0 1003 0 0 0 0 -9 -369 872 0 0 0 9 1230 313 0 4

= = = 0 0 0 0 0 0 0 0 0 -1 0 1 0 0 -15 0 831 0 0 0 15 0 1662 0 0 0 -12 872 197 0 0 0 12 313 1434 0 5

= = = 12x12 0 0 0 0 0 0 0 0 0 0 -1 0 12x12 0 15 0 0 0 831 0 -15 0 0 0 1662 12x12 9 12 0 0 0 831 -9 -12 0 0 0 1662 6

12x12

= =


= kg/cm 1 -1 0 0 0 0 0 0 0 0 0 0 4 0 0 0 -9 3 -4 0 0 0 -9 3 0 0.021509147 25

0 0 -1 0 0 0 0 0 0 0 0 0 -3 0 0 0 -12 4 3 0 0 0 -12 4 0.122850705 0.029604801 26

X 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -5 -15 0 0 0 0 -5 -15 0 -0.117274072 27

0 0 0 1 -1 0 0 0 0 0 0 0 0 9 -3 811 291 932 0 -9 3 -811 145 466 0 1.866907523 28

Z 0 0 0 0 0 -1 0 0 0 0 0 0 0 12 -4 -589 400 1283 0 -12 4 589 200 642 0 2.569577762 29

* 104(kg)(cm) 0 0 0 1 1 0 0 0 0 0 0 0 0 5 15 0 -1586 495 0 -5 -15 0 -793 247 3.327206584 0.991075213 30

0 0 0 0 0 0 1 -1 0 0 0 0 -4 0 0 0 9 -3 4 0 0 0 9 -3 0 0.021509147 1

0 0 0 0 0 0 0 0 -1 0 0 0 3 0 0 0 12 -4 -3 0 0 0 12 -4 0.122850705 0.029604801 2

0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 5 15 0 0 0 0 5 15 0 -0.117274072 3

0 0 0 0 0 0 0 0 0 1 -1 0 0 9 -3 -811 145 466 0 -9 3 811 291 932 0 -1.866907523 4

0 0 0 0 0 0 0 0 0 0 0 -1 0 12 -4 589 200 642 0 -12 4 -589 400 1283 0 -2.569577762 5

12x12 0 0 0 0 0 0 0 0 0 1 1 0 12x12 0 5 15 0 -793 247 0 -5 -15 0 -1586 495 12x12 -3.327206584 -0.991075213 6

0 0 0 0 00 0 0 0 -5.538163 5.538 0

0 0 0.189 0 -15.337 0 0 0 -0.189 0

0 0 0 15.337

-15.337 0

0 0 15.337 0 -0.1890 0.189 0

0 0

0 0 -15.337 0 1661.54 0 0 0 15.337 0 830.76923 0

0 0 0 0 -10030 0 0 1003 0

Iz

0 0 0 0 0

0 0 830.77

Iy -5.538 0 0 0 0 0 5.538

0 1661.5 0 -15.337 00 15.337 0 0Ix

-1 0 0 0 0 0 0 0 0 0 0

Y

0.3senα -0.95 cosα

0

100

0 -15.337 0 0.189 00 -0.189 0 0

0 0 -0.189 0 15.337

0.1

1 1 0 0 0 0 0 0 0 0 0 0 0

0W 15.12

3 -30 0 -1 0 0 0 0 0 0 0 0 0

1

0 0 0

0 0 0 0 0 -1 0 0 0 0 0 0 0

0 0 0 0 00 0 0 1 -1

0 0

1 -1 0 0 0 0 0

0 0 0 0 00 0 0 1 1

5 - 1

Dy 30 DZ 30 L

A 900 217370.65

X Y Z

365625 0 95.5 300

0.45

0

[K]= * E [AT] = [K] =_

[K]=

67500 131 0 300

67500 100 100 100 0 -15.337

0 0 0 0.189 0 15.337 0

0 15.337 0 1661.5385

Cx 0.81 Xps Xpγ 78.3 0 0 0 -1003 0 0 0 0 0 1003 0

0

Cz 0 Zps -200 Zpγ -200 0 15.337 0 0 0 830.77 0 -15.337 0 0 0 1661.5

Cy -0.59 Yps 4.4849 Ypγ 62.4 0 0 -15.337 0 830.769 0 0

[A] = * E [AT]*[K] =_

{f°}= [AT]* _ {f°} =

0 0 0 0 0 0 1 1 0 0 0 0 0

0 0 0.10 0 0 -1 0

0

0 0 0 0 0 0 0 0 0 0 0 -1 0

[a] = {f°} =

0 0 0 0 0

0 0 3.3

0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 1 -1 0

0 0 0 0 0 0 0 0 0 1 1 0 -3.3

BARRA BARRA 6 - 7


31 32 33 34 35 36 37 38 39 40 41 42

= cm = cm = cm 1 0 -1 0 0 0 0 0 0 0 0 0 6 0 0 0 0 0 -6 0 0 0 0 0 4 3 0 0 0 -9 -4 -3 0 0 0 -9 31

1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 15 0 0 0 0 0 15 3 2 0 0 0 12 -3 -2 0 0 0 12 32

= cm2 E = kg/cm2 G = *E 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -15 0 0 0 0 0 -15 0 0 0 0 9 -12 0 0 0 0 9 -12 0 33

0 0 0 1 0 -1 0 0 0 0 0 0 0 0 0 1003 0 0 0 0 0 -1003 0 0 0 0 9 1230 -313 0 0 0 -9 -369 -872 0 34

0 0 0 1 0 1 0 0 0 0 0 0 0 0 -15 0 1662 0 0 0 15 0 831 0 0 0 -12 -313 1434 0 0 0 12 -872 197 0 35

= cm4i = ( ; ; ) cm 0 0 0 0 -1 0 0 0 0 0 0 0 0 15 0 0 0 1662 0 -15 0 0 0 831 -9 12 0 0 0 1662 9 -12 0 0 0 831 36

= cm4j = ( ; ; ) cm 0 0 0 0 0 0 1 0 -1 0 0 0 -6 0 0 0 0 0 6 0 0 0 0 0 -4 -3 0 0 0 9 4 3 0 0 0 9 37

= cm4P = ( ; ; ) cm 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 -15 0 0 0 0 0 -15 -3 -2 0 0 0 -12 3 2 0 0 0 -12 38

0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 15 0 0 0 0 0 15 0 0 0 0 -9 12 0 0 0 0 -9 12 0 39

= = = 0 0 0 0 0 0 0 0 0 1 0 -1 0 0 0 -1003 0 0 0 0 0 1003 0 0 0 0 9 -369 -872 0 0 0 -9 1230 -313 0 40

= = = 0 0 0 0 0 0 0 0 0 1 0 1 0 0 -15 0 831 0 0 0 15 0 1662 0 0 0 -12 -872 197 0 0 0 12 -313 1434 0 41

= = = 12x12 0 0 0 0 0 0 0 0 0 0 -1 0 12x12 0 15 0 0 0 831 0 -15 0 0 0 1662 12x12 -9 12 0 0 0 831 9 -12 0 0 0 1662 42

12x12

= =


= kg/cm 1 1 0 0 0 0 0 0 0 0 0 0 4 0 0 0 9 -2 -4 0 0 0 9 -2 0 -0.014924027 31

0 0 -1 0 0 0 0 0 0 0 0 0 3 0 0 0 -12 2 -3 0 0 0 -12 2 0.130221387 0.02054116 32

X -1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -3 -15 0 0 0 0 -3 -15 0 -0.127722135 33

0 0 0 1 1 0 0 0 0 0 0 0 0 -9 2 811 -190 -958 0 9 -2 -811 -95 -479 0 -2.033232156 34

Z 0 0 0 0 0 -1 0 0 0 0 0 0 0 12 -2 589 262 1318 0 -12 2 -589 131 659 0 2.79850398 35

* 104(kg)(cm) 0 0 0 -1 1 0 0 0 0 0 0 0 0 3 15 0 -1630 324 0 -3 -15 0 -815 162 3.526829227 0.687653159 36

0 0 0 0 0 0 1 1 0 0 0 0 -4 0 0 0 -9 2 4 0 0 0 -9 2 0 -0.014924027 37

0 0 0 0 0 0 0 0 -1 0 0 0 -3 0 0 0 12 -2 3 0 0 0 12 -2 0.130221387 0.02054116 38

0 0 0 0 0 0 -1 1 0 0 0 0 0 0 0 0 3 15 0 0 0 0 3 15 0 -0.127722135 39

0 0 0 0 0 0 0 0 0 1 1 0 0 -9 2 -811 -95 -479 0 9 -2 811 -190 -958 0 2.033232156 40

0 0 0 0 0 0 0 0 0 0 0 -1 0 12 -2 -589 131 659 0 -12 2 589 262 1318 0 -2.79850398 41

12x12 0 0 0 0 0 0 0 0 0 -1 1 0 12x12 0 3 15 0 -815 162 0 -3 -15 0 -1630 324 12x12 -3.526829227 -0.687653159 42

=_

[K]=

0.45

0 0.189 0 0 0 15.337 0 -0.189 0 0

0 0 0 0

0 15.337

0 0 0 -5.538 05.538 0 0

0

0 0 1003 0 0 0 0 0 -1003 0 0

0 0 0 -0.189 00 0 0.189 0 -15.337

Cz 0 Zps

0 0 00 0 5.538 0 0-5.538 0 0 0

0 0 -0.189 0 15.337 0 0 0 0.189 0 15.337 0

Iy

-15.337

0 0 1003

0

0 0 -1 0 0 0 0 0 0 0 0 0 0.1

Y

W 16.03

4 -4

1 1 0 0 0 0 0 0 0 0 0 0

0 0 0

0 0 0 1 1 0 0 0 0 0 0 0 0

0 0 0 0 0-1 1 0 0 0

0

0 0 0

0 0 0 -1 1 0 0 0 0 0 0 0 3.5

-1 0 0 0 00 0 0 0 0 0 0

0 0 00 1 1 0 0

Dy 30 DZ 30 L 163

[K]67500 263 95.5 600

6 - 7

-15.337 0 0 0 830.77

0 830.76923 0

Ix 0 15.337

A 900 217370.65

X Y Z

365625 131 0 600[K]= * E [AT] =

0 0 0 1661.5 0

1661.54 0 0 0 15.3370 0 -15.337 0

-15.337

0

0

Iz 67500 100 100 100 0 -0.189 0 0 0 -15.337 0 0.189 0 0 0

0

Cy 0.59 Yps 100 Ypγ 99.4 0 0 -15.337 0 830.769 0 0 0 15.337 0 1661.5385 0

Cx 0.81 Xps -31.465 Xpγ 33.3 0 0 0 -1003 0 0 0

-500 Zpγ -500 0 15.337 0 0 0 830.77 0 -15.337 0 0 0 1661.5

senα -0.98 cosα 0.19

[a] = {f°} = [A] = * E [AT]*[K] =_

{f°}= [AT]* _ {f°} =

0 0 0 0 0 0 0 0 -1 0 0 0 0.1

0 0 0 0

0 0 0 0 0 0 -1 1 0 0 0 0 0

0 0 0 0 0 0 0 0 0 1 1 0 0

0 0 0 0 0 0 0 0 0 0 0 -1 0

0 0 0 0 0 0 0 0 0 -1 1 0 -3.5

BARRA BARRA 7 - 8


37 38 39 40 41 42 43 44 45 46 47 48

= cm = cm = cm 0 0 -1 0 0 0 0 0 0 0 0 0 6 0 0 0 0 0 -6 0 0 0 0 0 1 -2 0 0 0 -15 -1 2 0 0 0 -15 37

1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 15 0 0 0 0 0 15 -2 5 0 0 0 -5 2 -5 0 0 0 -5 38

= cm2 E = kg/cm2 G = *E 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -15 0 0 0 0 0 -15 0 0 0 0 15 5 0 0 0 0 15 5 0 39

0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 1003 0 0 0 0 0 -1003 0 0 0 0 15 1599 194 0 0 0 -15 656 539 0 40

0 0 0 1 0 0 0 0 0 0 0 0 0 0 -15 0 1662 0 0 0 15 0 831 0 0 0 5 194 1066 0 0 0 -5 539 -828 0 41

= cm4i = ( ; ; ) cm 0 0 0 0 -1 0 0 0 0 0 0 0 0 15 0 0 0 1662 0 -15 0 0 0 831 -15 -5 0 0 0 1662 15 5 0 0 0 831 42

= cm4j = ( ; ; ) cm 0 0 0 0 0 0 0 0 -1 0 0 0 -6 0 0 0 0 0 6 0 0 0 0 0 -1 2 0 0 0 15 1 -2 0 0 0 15 43

= cm4P = ( ; ; ) cm 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 -15 0 0 0 0 0 -15 2 -5 0 0 0 5 -2 5 0 0 0 5 44

0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 15 0 0 0 0 0 15 0 0 0 0 -15 -5 0 0 0 0 -15 -5 0 45

= = = 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 -1003 0 0 0 0 0 1003 0 0 0 0 15 656 539 0 0 0 -15 1599 194 0 46

= = = 0 0 0 0 0 0 0 0 0 1 0 0 0 0 -15 0 831 0 0 0 15 0 1662 0 0 0 5 539 -828 0 0 0 -5 194 1066 0 47

= = = 12x12 0 0 0 0 0 0 0 0 0 0 -1 0 12x12 0 15 0 0 0 831 0 -15 0 0 0 1662 12x12 -15 -5 0 0 0 831 15 5 0 0 0 1662 48

12x12

= =


= kg/cm 0 1 0 0 0 0 0 0 0 0 0 0 -2 0 0 0 14 -4 2 0 0 0 14 -4 0 -0.036362226 37

0 0 -1 0 0 0 0 0 0 0 0 0 5 0 0 0 5 -1 -5 0 0 0 5 -1 0.130221387 -0.011814804 38

X -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -5 -15 0 0 0 0 -5 -15 0 -0.124482161 39

0 0 0 0 1 0 0 0 0 0 0 0 0 -14 4 -310 -464 -1511 0 14 -4 310 -232 -755 0 -3.206384207 40

Z 0 0 0 0 0 -1 0 0 0 0 0 0 0 -5 1 954 -151 -491 0 5 -1 -954 -75 -245 0 -1.041817383 41

* 104(kg)(cm) 0 0 0 -1 0 0 0 0 0 0 0 0 0 5 15 0 -1588 488 0 -5 -15 0 -794 244 3.526829227 1.035490826 42

0 0 0 0 0 0 0 1 0 0 0 0 2 0 0 0 -14 4 -2 0 0 0 -14 4 0 -0.036362226 43

0 0 0 0 0 0 0 0 -1 0 0 0 -5 0 0 0 -5 1 5 0 0 0 -5 1 0.130221387 -0.011814804 44

0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 5 15 0 0 0 0 5 15 0 -0.124482161 45

0 0 0 0 0 0 0 0 0 0 1 0 0 -14 4 310 -232 -755 0 14 -4 -310 -464 -1511 0 3.206384207 46

0 0 0 0 0 0 0 0 0 0 0 -1 0 -5 1 -954 -75 -245 0 5 -1 954 -151 -491 0 1.041817383 47

12x12 0 0 0 0 0 0 0 0 0 -1 0 0 12x12 0 5 15 0 -794 244 0 -5 -15 0 -1588 488 12x12 -3.526829227 -1.035490826 48

5.538 0 0 0 0 0 -5.538 0 0 0 0 0

0 15.337

0 0 0.189 0 -15.337 0 0 0 -0.189 0 -15.337 0

15.337 0 -0.189 0 00 0.189 0 0 0

0 15.337 0 830.76923 0

-1003 0 0

0 0 -15.337 0 1661.54 0 0

0 0 0 0 00 0 0 1003

Cz 0 Zps

0 0 830.77

100

0 1661.5 0 -15.337 00 15.337 0 0[K]=

Ix

-15.337

0 0 -0.189 0 15.337 0 0 0 0.189 0 15.337 0

-4

0 1 0 0 0 0 0 0 0 0 0 0 0

Y

W 16.03

0 0 0 0 1

0 0 0.1

-1 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 00 0 -1 0 0 4

3.50 0 0 0 00 0 0 -1 0

0 0 0

0 0 0 0 0 -1 0 0 0 0 0 0 0

0 0 0 0 0

7 - 8

Dy 30 DZ 30 L

A 900 217370.65 0.45

X Y Z

365625 263 95.5 600

163

[K] =_

[K]=

Iy 67500 213 250 600 -5.538 0 0 0 0 0 5.538 0 0 0 0 0* E [AT] =

0 0 1003 0

Iz 67500 100 100 0 -0.189 0 0 0 -15.337 0 0.189 0 0 0

0

Cy 0.95 Yps 4.4849 Ypγ -154 0 0 -15.337 0 830.769 0 0 0 15.337 0 1661.5385 0

Cx -0.31 Xps -162.93 Xpγ 54.6 0 0 0 -1003 0 0 0

-500 Zpγ 500 0 15.337 0 0 0 830.77 0 -15.337 0 0 0 1661.5


0 0

[a] = {f°} = [A] = * E [AT]*[K] =_

{f°}= [AT]* _ {f°} =

0 0 0 0 0 0 0 1 0 0 0 0 0

0 0

0 0 0 0 0 0 0 0 -1 0 0 0 0.1

0 0 0 0 0 0 -1 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 1 0 0

0 0 0 0 0 0 0 0 0 0 0 -1 0

0 0 0 0 0 0 0 0 0 -1 0 0 -3.5

BARRA BARRA 8 - 9


43 44 45 46 47 48 49 50 51 52 53 54

= cm = cm = cm -1 0 0 0 0 0 0 0 0 0 0 0 6 0 0 0 0 0 -6 0 0 0 0 0 6 0 0 0 0 0 -6 0 0 0 0 0 43

0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 15 0 0 0 0 0 15 0 0 0 0 0 -15 0 0 0 0 0 -15 44

= cm2 E = kg/cm2 G = *E 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -15 0 0 0 0 0 -15 0 0 0 0 0 15 0 0 0 0 0 15 0 45

0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 1003 0 0 0 0 0 -1003 0 0 0 0 0 1003 0 0 0 0 0 -1003 0 0 46

0 0 0 0 0 -1 0 0 0 0 0 0 0 0 -15 0 1662 0 0 0 15 0 831 0 0 0 15 0 1662 0 0 0 -15 0 831 0 47

= cm4i = ( ; ; ) cm 0 0 0 0 -1 0 0 0 0 0 0 0 0 15 0 0 0 1662 0 -15 0 0 0 831 0 -15 0 0 0 1662 0 15 0 0 0 831 48

= cm4j = ( ; ; ) cm 0 0 0 0 0 0 -1 0 0 0 0 0 -6 0 0 0 0 0 6 0 0 0 0 0 -6 0 0 0 0 0 6 0 0 0 0 0 49

= cm4P = ( ; ; ) cm 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 -15 0 0 0 0 0 -15 0 0 0 0 0 15 0 0 0 0 0 15 50

0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 15 0 0 0 0 0 15 0 0 0 0 0 -15 0 0 0 0 0 -15 0 51

= = = 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 -1003 0 0 0 0 0 1003 0 0 0 0 0 -1003 0 0 0 0 0 1003 0 0 52

= = = 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 -15 0 831 0 0 0 15 0 1662 0 0 0 15 0 831 0 0 0 -15 0 1662 0 53

= = = 12x12 0 0 0 0 0 0 0 0 0 0 -1 0 12x12 0 15 0 0 0 831 0 -15 0 0 0 1662 12x12 0 -15 0 0 0 831 0 15 0 0 0 1662 54

12x12

= =


= kg/cm -1 0 0 0 0 0 0 0 0 0 0 0 -6 0 0 0 0 0 6 0 0 0 0 0 0 0 43

0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 15 -4 0 0 0 0 15 -4 0.130221387 -0.03743298 44

X 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -4 -15 0 0 0 0 -4 -15 0 -0.124725224 45

0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 -1003 0 0 0 0 0 1003 0 0 0 0 46

Z 0 0 0 0 0 -1 0 0 0 0 0 0 0 -15 4 0 -478 -1591 0 15 -4 0 -239 -796 0 -3.377974826 47

* 104(kg)(cm) 0 0 0 0 -1 0 0 0 0 0 0 0 0 4 15 0 -1591 478 0 -4 -15 0 -796 239 3.526829227 1.01380988 48

0 0 0 0 0 0 -1 0 0 0 0 0 6 0 0 0 0 0 -6 0 0 0 0 0 0 0 49

0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 -15 4 0 0 0 0 -15 4 0.130221387 -0.03743298 50

0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 4 15 0 0 0 0 4 15 0 -0.124725224 51

0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 1003 0 0 0 0 0 -1003 0 0 0 0 52

0 0 0 0 0 0 0 0 0 0 0 -1 0 -15 4 0 -239 -796 0 15 -4 0 -478 -1591 0 3.377974826 53

12x12 0 0 0 0 0 0 0 0 0 0 -1 0 12x12 0 4 15 0 -796 239 0 -4 -15 0 -1591 478 12x12 -3.526829227 -1.01380988 54

0 0

0 0.189 0 0 0 15.337 0 -0.189 0 0 0 15.337

0 -5.538 0 0 05.538 0 0 0 0

0 0 -1003 0 0

0 -15.337 0

0 0 0 1003 0 0 0

-15.337 0 0 0 -0.1890 0 0.189 0

-0.3

Cy 0 Yps

0 830.76923 0

50.2

1661.54 0 0 0 15.3370 0 -15.337 0

0 0 1661.5 0 -15.337 0 0 0 830.77

Iz 67500 100 100 100 0

0 0 0

0 0 -1 0 0 0 0 0 0 0 0 0 0.1

0 0 0 0 0-1 0 0 0 0

0 0 0-1 0 0 0 00 0 0 0 0

0 0 0

0 0 0 -1 0 0 0 0 0 0 0 0 0

8 - 9

Dy 30 DZ 30 L 163

A 900 217370.65 0.45

X Y Z

Ix 365625 213 250 600[K]=

0 15.337 0* E [AT] = [K] =

_

[K]=

Iy 67500 250 600 -5.538 0 0 0 0 0 5.538 0 0 0 0 0

-0.189 0 0 0 -15.337 0 0.189 0 0 0 -15.337

0 0 -0.189 0 15.337 0 0 0 0.189 0 15.337 0

Cx -1 Xps -112.72 Xpγ 113 0 0 0 -1003 0 0 0 0 0 1003 0 0

-150.06 Ypγ -150 0 0 -15.337 0 830.769 0 0 0 15.337 0 1661.5385 0

Cz 0 Zps -500 Zpγ 500 0 15.337 0 0 0 830.77 0 -15.337 0 0 0 1661.5

senα 0.958 cosα

Y

W 16.03

4 -4

0 0

[a] =0 0 0 0 -1 0 0 0 0 0 0 0

{f°} =3.5

0 0 0 0

[A] = * E [AT]*[K] =_

{f°}= [AT]* _ {f°} =

0 0 0 0 0 0 -1 0 0 0 0 0 0

00 -1 0 0 0

0 0 0 0 0 0 0 0 -1 0 0 0 0.1

0 0 0 0 0 0 0 -1 0 0 0 0 0

0 0 0 0 0 0 0 0 0 -1 0 0 0

0 0 0 0 0 0 0 0 0 0 0 -1 0

0 0 0 0 0 0 0 0 0 0 -1 0 -3.5

BARRA BARRA 9 - 10


49 50 51 52 53 54 55 56 57 58 59 60

= cm = cm = cm 0 0 1 0 0 0 0 0 0 0 0 0 6 0 0 0 0 0 -6 0 0 0 0 0 1 2 0 0 0 15 -1 -2 0 0 0 15 49

-1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 15 0 0 0 0 0 15 2 5 0 0 0 -5 -2 -5 0 0 0 -5 50

= cm2 E = kg/cm2 G = *E 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -15 0 0 0 0 0 -15 0 0 0 0 -15 5 0 0 0 0 -15 5 0 51

0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1003 0 0 0 0 0 -1003 0 0 0 0 -15 1599 -194 0 0 0 15 656 -539 0 52

0 0 0 -1 0 0 0 0 0 0 0 0 0 0 -15 0 1662 0 0 0 15 0 831 0 0 0 5 -194 1066 0 0 0 -5 -539 -828 0 53

= cm4i = ( ; ; ) cm 0 0 0 0 -1 0 0 0 0 0 0 0 0 15 0 0 0 1662 0 -15 0 0 0 831 15 -5 0 0 0 1662 -15 5 0 0 0 831 54

= cm4j = ( ; ; ) cm 0 0 0 0 0 0 0 0 1 0 0 0 -6 0 0 0 0 0 6 0 0 0 0 0 -1 -2 0 0 0 -15 1 2 0 0 0 -15 55

= cm4P = ( ; ; ) cm 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 -15 0 0 0 0 0 -15 -2 -5 0 0 0 5 2 5 0 0 0 5 56

0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 15 0 0 0 0 0 15 0 0 0 0 15 -5 0 0 0 0 15 -5 0 57

= = = 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 -1003 0 0 0 0 0 1003 0 0 0 0 -15 656 -539 0 0 0 15 1599 -194 0 58

= = = 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 -15 0 831 0 0 0 15 0 1662 0 0 0 5 -539 -828 0 0 0 -5 -194 1066 0 59

= = = 12x12 0 0 0 0 0 0 0 0 0 0 -1 0 12x12 0 15 0 0 0 831 0 -15 0 0 0 1662 12x12 15 -5 0 0 0 831 -15 5 0 0 0 1662 60

12x12

= =


= kg/cm 0 -1 0 0 0 0 0 0 0 0 0 0 -2 0 0 0 -14 3 2 0 0 0 -14 3 0 0.022816632 49

0 0 -1 0 0 0 0 0 0 0 0 0 -5 0 0 0 5 -1 5 0 0 0 5 -1 0.130221387 -0.007413573 50

X 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -3 -15 0 0 0 0 -3 -15 0 -0.127992382 51

0 0 0 0 -1 0 0 0 0 0 0 0 0 14 -3 -310 291 1553 0 -14 3 310 146 777 0 3.2967997 52

Z 0 0 0 0 0 -1 0 0 0 0 0 0 0 -5 1 -954 -95 -505 0 5 -1 954 -47 -252 0 -1.071195157 53

* 104(kg)(cm) 0 0 0 1 0 0 0 0 0 0 0 0 0 3 15 0 -1633 306 0 -3 -15 0 -817 153 3.526829227 0.649751541 54

0 0 0 0 0 0 0 -1 0 0 0 0 2 0 0 0 14 -3 -2 0 0 0 14 -3 0 0.022816632 55

0 0 0 0 0 0 0 0 -1 0 0 0 5 0 0 0 -5 1 -5 0 0 0 -5 1 0.130221387 -0.007413573 56

0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 3 15 0 0 0 0 3 15 0 -0.127992382 57

0 0 0 0 0 0 0 0 0 0 -1 0 0 14 -3 310 146 777 0 -14 3 -310 291 1553 0 -3.2967997 58

0 0 0 0 0 0 0 0 0 0 0 -1 0 -5 1 954 -47 -252 0 5 -1 -954 -95 -505 0 1.071195157 59

12x12 0 0 0 0 0 0 0 0 0 1 0 0 12x12 0 3 15 0 -817 153 0 -3 -15 0 -1633 306 12x12 -3.526829227 -0.649751541 60

0 0 0

0 0 15.337

0 0 0.189 0 -15.337 0 0

0 15.337 0 -0.189 00 0.189 0 0

0

50.2

0 0 0 0 00 0 0 1003

830.76923 0

830.77

0 -0.189 0 -15.337 0

15.337 0 0 0 1661.5 0 -15.337 0 0 0

0

0 0 0

Y

W 16.03

4 -4


Cy -0.95 Yps -150.06 Ypγ -93.7 0 0 -15.337

0 00 0 -1 0 0

0 -1 0 0 0 0 0 0 0 0

0 0 00 0 0 0 00 0 0 0 -1

0 0 0.1

1 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0

0 0

9 - 10

Dy 30 DZ 30 L 163 5.538 0 0 0 0 0 -5.538 0 0

A 900 217370.65 0.45

X Y Z 0 0 -15.337 0 1661.54 0 0 0 15.337 0

-1003

* E [AT] = [K] =_

[K]=

Iy 67500 0 95.5 600 -5.538 0 0 0 0 0 5.538 0 0 0 0 0

Ix 365625 250 600[K]=

0

Iz 67500 100 100 100 0 -0.189 0 0 0 -15.337 0 0.189 0 0 0 -15.337

0 15.337 0 0 0 0.189 0 15.337 0

Cx -0.31 Xps 49.785 Xpγ 127 0 0 0 -1003 0 0 0 0 0 1003 0 0

0 0 -0.189

0 830.769 0 0 0 15.337 0 1661.5385 0

Cz 0 Zps -500 Zpγ 500 0 15.337 0 0 0 830.77 0 -15.337 0 0 0 1661.5

0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0

[a] =0 0 0 1 0 0 0 0 0 0 0 0

{f°} =3.5

[A] = * E [AT]*[K] =_

{f°}= [AT]* _ {f°} =

0 0 0 0 0 0 0 -1 0 0 0 0 0

-1 0

0 0 0 0 0 0 0 0 -1 0 0 0 0.1

0 0 0 0 0 0 1 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 -1

0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 1 0 0 -3.5

BARRA BARRA 10 - 6


55 56 57 58 59 60 31 32 33 34 35 36

= cm = cm = cm 1 0 1 0 0 0 0 0 0 0 0 0 6 0 0 0 0 0 -6 0 0 0 0 0 4 -3 0 0 0 9 -4 3 0 0 0 9 55

-1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 15 0 0 0 0 0 15 -3 2 0 0 0 12 3 -2 0 0 0 12 56

= cm2 E = kg/cm2 G = *E 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -15 0 0 0 0 0 -15 0 0 0 0 -9 -12 0 0 0 0 -9 -12 0 57

0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 1003 0 0 0 0 0 -1003 0 0 0 0 -9 1230 313 0 0 0 9 -369 872 0 58

0 0 0 -1 0 1 0 0 0 0 0 0 0 0 -15 0 1662 0 0 0 15 0 831 0 0 0 -12 313 1434 0 0 0 12 872 197 0 59

= cm4i = ( ; ; ) cm 0 0 0 0 -1 0 0 0 0 0 0 0 0 15 0 0 0 1662 0 -15 0 0 0 831 9 12 0 0 0 1662 -9 -12 0 0 0 831 60

= cm4j = ( ; ; ) cm 0 0 0 0 0 0 1 0 1 0 0 0 -6 0 0 0 0 0 6 0 0 0 0 0 -4 3 0 0 0 -9 4 -3 0 0 0 -9 31

= cm4P = ( ; ; ) cm 0 0 0 0 0 0 -1 0 1 0 0 0 0 0 0 0 0 -15 0 0 0 0 0 -15 3 -2 0 0 0 -12 -3 2 0 0 0 -12 32

0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 15 0 0 0 0 0 15 0 0 0 0 9 12 0 0 0 0 9 12 0 33

= = = 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 -1003 0 0 0 0 0 1003 0 0 0 0 -9 -369 872 0 0 0 9 1230 313 0 34

= = = 0 0 0 0 0 0 0 0 0 -1 0 1 0 0 -15 0 831 0 0 0 15 0 1662 0 0 0 -12 872 197 0 0 0 12 313 1434 0 35

= = = 12x12 0 0 0 0 0 0 0 0 0 0 -1 0 12x12 0 15 0 0 0 831 0 -15 0 0 0 1662 12x12 9 12 0 0 0 831 -9 -12 0 0 0 1662 36

12x12

= =


= kg/cm 1 -1 0 0 0 0 0 0 0 0 0 0 4 0 0 0 -9 1 -4 0 0 0 -9 1 0 0.009479965 55

0 0 -1 0 0 0 0 0 0 0 0 0 -3 0 0 0 -12 2 3 0 0 0 -12 2 0.130221387 0.013048053 56

X 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -2 -15 0 0 0 0 -2 -15 0 -0.129218761 57

0 0 0 1 -1 0 0 0 0 0 0 0 0 9 -1 811 121 969 0 -9 1 -811 60 485 0 2.05705722 58

Z 0 0 0 0 0 -1 0 0 0 0 0 0 0 12 -2 -589 166 1334 0 -12 2 589 83 667 0 2.831296367 59

* 104(kg)(cm) 0 0 0 1 1 0 0 0 0 0 0 0 0 2 15 0 -1649 206 0 -2 -15 0 -824 103 3.526829227 0.436807586 60

0 0 0 0 0 0 1 -1 0 0 0 0 -4 0 0 0 9 -1 4 0 0 0 9 -1 0 0.009479965 31

0 0 0 0 0 0 0 0 -1 0 0 0 3 0 0 0 12 -2 -3 0 0 0 12 -2 0.130221387 0.013048053 32

0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 2 15 0 0 0 0 2 15 0 -0.129218761 33

0 0 0 0 0 0 0 0 0 1 -1 0 0 9 -1 -811 60 485 0 -9 1 811 121 969 0 -2.05705722 34

0 0 0 0 0 0 0 0 0 0 0 -1 0 12 -2 589 83 667 0 -12 2 -589 166 1334 0 -2.831296367 35

12x12 0 0 0 0 0 0 0 0 0 1 1 0 12x12 0 2 15 0 -824 103 0 -2 -15 0 -1649 206 12x12 -3.526829227 -0.436807586 36

-0.189 0 0 0 15.337

0 0 0

0 0.189 0 0 0 15.337 0

0 0 -5.538 0 05.538 0 0 0

0.12

Cx 0.81 Xps 100 Xpγ 78.3 0 0 0

Iz 67500 100

0 -15.337 0

X

-15.337 0 0 0 -0.1890 0 0.189 0

0 0

Y Z 0 0

0 0 0

0 0 -1 0 0 0 0 0 0 0 0 0 0.1

0 0 0 0 01 -1 0 0 0

0 0 00 0 0 0 01 1 0 0 0

0 0 0 0 0 -1 0 0 0

Dy 30 DZ 30 L 163

15.337 0 830.76923 0

10 - 6

[K]=0 15.337 0 0 0 1661.5 0 -15.337 0 0

A 900 217370.65 0.45

0 0 0 1003 0 0 0 0 0 -1003

-15.337 0 1661.54 0 0 0

0 830.77* E [AT] = [K] =

_

[K]=

Iy 67500 131 0 600 -5.538 0 0 0 0 0 5.538 0 0 0 0 0

Ix 365625 0 95.5 600

1661.5385 0

100 100 0 -0.189 0 0 0 -15.337 0 0.189 0 0 0 -15.337

0 0 -0.189 0 15.337 0 0 0 0.189 0 15.337 0

0 830.77 0 -15.337 0 0 0

-1003 0 0 0 0 0 1003 0 0

Cy -0.59 Yps 4.4849 Ypγ 62.4 0 0 -15.337 0 830.769 0 0 0 15.337 0

1661.5

senα -0.99 cosα

Y

W 16.03

4 -4

0 0 0 1 -1 0 0 0 0 0 0 0 0

Cz 0 Zps -500 Zpγ -500 0 15.337 0 0

0 0 0 0 0 0

[a] =0 0 0 1 1 0 0 0 0 0 0 0

{f°} =3.5

[A] = * E [AT]*[K] =_

{f°}= [AT]* _ {f°} =

0 0 0 0 0 0 1 -1 0 0 0 0 0

0 0 0 0 0 0 0 0 -1 0 0 0 0.1

0 0 0 0 0 0 1 1 0 0 0 0 0

0 0 0 0 0 0 0 0 0 1 -1 0 0

0 0 0 0 0 0 0 0 0 0 0 -1 0

0 0 0 0 0 0 0 0 0 1 1 0 -3.5

BARRA BARRA 11 - 1


61 62 63 64 65 66 1 2 3 4 5 6

= cm = cm = cm 0 0 -1 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 -3 0 0 0 0 0 0 0 0 0 5 0 0 0 0 0 5 0 61

0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 0 0 0 0 0 5 0 0 0 -5 0 0 0 0 0 -5 0 0 62

= cm2 E = kg/cm2 G = *E 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -5 0 0 0 0 0 -5 0 0 0 3 0 0 0 0 0 -3 0 0 0 63

0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 1003 0 0 0 0 0 -1003 0 0 0 -5 0 900 0 0 0 5 0 450 0 0 64

0 0 0 0 1 0 0 0 0 0 0 0 0 0 -5 0 900 0 0 0 5 0 450 0 5 0 0 0 900 0 -5 0 0 0 450 0 65

= cm4i = ( ; ; ) cm 0 0 0 1 0 0 0 0 0 0 0 0 0 5 0 0 0 900 0 -5 0 0 0 450 0 0 0 0 0 1003 0 0 0 0 0 -1003 66

= cm4j = ( ; ; ) cm 0 0 0 0 0 0 0 0 -1 0 0 0 -3 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 -5 0 0 0 0 0 -5 0 1

= cm4P = ( ; ; ) cm 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 -5 0 0 0 0 0 -5 0 0 0 5 0 0 0 0 0 5 0 0 2

0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 5 0 0 0 0 0 5 0 0 0 -3 0 0 0 0 0 3 0 0 0 3

= = = 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 -1003 0 0 0 0 0 1003 0 0 0 -5 0 450 0 0 0 5 0 900 0 0 4

= = = 0 0 0 0 0 0 0 0 0 0 1 0 0 0 -5 0 450 0 0 0 5 0 900 0 5 0 0 0 450 0 -5 0 0 0 900 0 5

= = = 12x12 0 0 0 0 0 0 0 0 0 1 0 0 12x12 0 5 0 0 0 450 0 -5 0 0 0 900 12x12 0 0 0 0 0 -1003 0 0 0 0 0 1003 6

12x12

= =


= kg/cm 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 4 -1 0 0 0 0 4 -1 0 0 61

0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 4 0 0 0 0 1 4 0 0 62

X -1 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 -3 0 0 0 0 0 0 0 63

0 0 0 0 0 1 0 0 0 0 0 0 0 -4 1 0 -270 -859 0 4 -1 0 -135 -429 0 0 64

Z 0 0 0 0 1 0 0 0 0 0 0 0 0 -1 -4 0 859 -270 0 1 4 0 429 -135 0 0 65

* 104(kg)(cm) 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 1003 0 0 0 0 0 -1003 0 0 0 0 66

0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 -4 1 0 0 0 0 -4 1 0 0 1

0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 -1 -4 0 0 0 0 -1 -4 0 0 2

0 0 0 0 0 0 -1 0 0 0 0 0 -3 0 0 0 0 0 3 0 0 0 0 0 0 0 3

0 0 0 0 0 0 0 0 0 0 0 1 0 -4 1 0 -135 -429 0 4 -1 0 -270 -859 0 0 4

0 0 0 0 0 0 0 0 0 0 1 0 0 -1 -4 0 429 -135 0 1 4 0 859 -270 0 0 5

12x12 0 0 0 0 0 0 0 0 0 -1 0 0 12x12 0 0 0 -1003 0 0 0 0 0 1003 0 0 12x12 0 0 6

A 900 217370.65 0.45

3.000 0 0 0 0 0

0 0 4.500

0

0 0.030 0 0 0 4.500 0 -0.030 0

-3.000 0 0 0 0

100Iz 67500 100 100 0 -0.030 0 0 0 -4.500

0 0 -1003 0 0

100 Zpγ 31.5

0 0 1 0 0 W 0

0

Y

0.95

450Cz 1 Zps

Cx 0 Xps -31.465 Xpγ 100 0

1 0 0 0 0 0 0 0 0 0 0 0.0

0 0 0 0 0

00 0 0 0 0 0 0 0 -1 0 0 0.0

11 - 1

Dy 30 DZ 30 L 300

0 0 0.030 0 -4.500 0 0 0 -0.030 0 -4.500 0

0 0 0 1003 0 0 0 0 0 -1003 0 0

X Y Z 0 0 -4.500 0 900 0 0 0 4.500 0 450 0

Ix 675000 131 0 0[K]=

0 4.500 0 0 0 900 0 -4.500 0 0 0 450* E [AT] = [K] =

_

[K]=

Iy 67500 131 0 300 -3.000 0 0 0 0 0 3.000 0 0 0 0 0

0 0.030 0 0 0 -4.500

0 0 -0.030 0 4.500 0 0 0 0.030 0 4.500 0

0 0 0 1003 0 0

Cy 0 Yps 100 Ypγ 100 0 0 -4.500 0 450 0 0 0 4.500 0 900 0

0 4.500 0 0 0 0 -4.500 0 0 0 900

senα 0.3 cosα

0

-1 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0

0

0 0 0 0 0 1 0 0 0 0 0 0 0

0 0 0 0 1 0 0 0 0 0 0 0 0 0 0

[a] =0 0 0 -1 0 0 0 0 0 0 0 0

{f°} =0.0

[A] = * E [AT]*[K] =_

{f°}= [AT]* _ {f°} =

0 0 0 0 0 0 0 0 1 0 0 0 0

0 0 0 0 0 0 0 1 0 0 0 0 0.0

0 0 0 0 0 0 -1 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 1 0

0 0 0 0 0 0 0 0 0 0 1 0 0

BARRA BARRA 12 - 2


67 68 69 70 71 72 7 8 9 10 11 12

= cm = cm = cm 0 -1 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 -3 0 0 0 0 0 0 0 0 0 5 0 0 0 0 0 5 0 67

0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 0 0 0 0 0 5 0 0 0 -5 0 0 0 0 0 -5 0 0 68

= cm2 E = kg/cm2 G = *E 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -5 0 0 0 0 0 -5 0 0 0 3 0 0 0 0 0 -3 0 0 0 69

0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 1003 0 0 0 0 0 -1003 0 0 0 -5 0 900 0 0 0 5 0 450 0 0 70

0 0 0 0 0 -1 0 0 0 0 0 0 0 0 -5 0 900 0 0 0 5 0 450 0 5 0 0 0 900 0 -5 0 0 0 450 0 71

= cm4i = ( ; ; ) cm 0 0 0 1 0 0 0 0 0 0 0 0 0 5 0 0 0 900 0 -5 0 0 0 450 0 0 0 0 0 1003 0 0 0 0 0 -1003 72

= cm4j = ( ; ; ) cm 0 0 0 0 0 0 0 -1 0 0 0 0 -3 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 -5 0 0 0 0 0 -5 0 7

= cm4P = ( ; ; ) cm 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 -5 0 0 0 0 0 -5 0 0 0 5 0 0 0 0 0 5 0 0 8

0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 5 0 0 0 0 0 5 0 0 0 -3 0 0 0 0 0 3 0 0 0 9

= = = 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 -1003 0 0 0 0 0 1003 0 0 0 -5 0 450 0 0 0 5 0 900 0 0 10

= = = 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 -5 0 450 0 0 0 5 0 900 0 5 0 0 0 450 0 -5 0 0 0 900 0 11

= = = 12x12 0 0 0 0 0 0 0 0 0 1 0 0 12x12 0 5 0 0 0 450 0 -5 0 0 0 900 12x12 0 0 0 0 0 -1003 0 0 0 0 0 1003 12

12x12

= =


= kg/cm 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -4 0 0 0 0 0 -4 0 0 67

-1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 4 0 0 0 68

X 0 -1 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 -3 0 0 0 0 0 0 0 69

0 0 0 0 0 1 0 0 0 0 0 0 0 0 4 0 -900 -25 0 0 -4 0 -450 -12 0 0 70

Z 0 0 0 -1 0 0 0 0 0 0 0 0 0 -4 0 0 25 -900 0 4 0 0 12 -450 0 0 71

* 104(kg)(cm) 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 1003 0 0 0 0 0 -1003 0 0 0 0 72

0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 4 0 0 0 0 0 4 0 0 7

0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 -4 0 0 0 0 0 -4 0 0 0 8

0 0 0 0 0 0 0 -1 0 0 0 0 -3 0 0 0 0 0 3 0 0 0 0 0 0 0 9

0 0 0 0 0 0 0 0 0 0 0 1 0 0 4 0 -450 -12 0 0 -4 0 -900 -25 0 0 10

0 0 0 0 0 0 0 0 0 -1 0 0 0 -4 0 0 12 -450 0 4 0 0 25 -900 0 0 11

12x12 0 0 0 0 0 0 0 0 0 0 -1 0 12x12 0 0 0 -1003 0 0 0 0 0 1003 0 0 12x12 0 0 12

0 0

900

0 0 -3.000 0 03.000 0 0 0

0 0 4.500

12 - 2

0 -4.500

Iz 67500 100 100 0 -0.030 0 0 0100

263

-4.500 0 0.030

0Dy 30 DZ 30 L 300

0 0.030 0 0 0 4.500 0 -0.030 0

00 0 1 0 0

0.03

0

Cz 1 Zps 100 Zpγ 163 0 4.500 0 0 0 450

0

0

0 0 0 0 0 0 0 0 0 -1 0 0.0

A 217370.65 0.45 0 0 0.030 0 -4.500 0 0 0 -0.030 0 -4.500 0

0 0 0 1003 0 0 0 0 0 -1003 0 0

X Y Z 0 0 -4.500 0 900 0 0 0 4.500 0 450 0

Ix 675000 263 95.5 0[K]=

0 4.500 0 0 0 900 0 -4.500 0 0 0 450* E [AT] = [K] =

_

[K]=

Iy 67500 95.5 300 -3.000 0 0 0 0 0 3.000 0 0 0 0 0

0 0 0 -4.500

0 0 -0.030 0 4.500 0 0 0 0.030 0 4.500 0

Cx 0 Xps -162.93 Xpγ 100 0 0 0 -1003 0 0 0 0 0 1003 0 0

Cy 0 Yps 4.4849 Ypγ 4.48 0 0 -4.500 0 450 0 0 4.500 0 900 0

0 0 0 900

senα 1 cosα

Y

W 0

-1 0 0 0 0 0 0 0 0 0 0 0 0 0 0.0

0 0 00 0 0 0

0 -1 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 1 0 0 0 0 0 0 0

0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0

[a] =0 0 0 0 -1 0 0 0 0 0 0 0

{f°} =0.0

[A] = * E [AT]*[K] =_

{f°}= [AT]* _ {f°} =

0 0 0 0 0 0 0 0 1 0 0 0 0

0 0 0 0 0 0 -1 0 0 0 0 0 0.0

0 0 0 0 0 0 0 -1 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 1 0

0 0 0 0 0 0 0 0 -1 0 0 0

BARRA BARRA 13 - 3


73 74 75 76 77 78 13 14 15 16 17 18

= cm = cm = cm 0 -1 1 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 -3 0 0 0 0 0 0 0 0 0 5 0 0 0 0 0 5 0 73

0 -1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 0 0 0 0 0 5 0 0 0 -5 0 0 0 0 0 -5 0 0 74

= cm2 E = kg/cm2 G = *E 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -5 0 0 0 0 0 -5 0 0 0 3 0 0 0 0 0 -3 0 0 0 75

0 0 0 0 -1 1 0 0 0 0 0 0 0 0 0 1003 0 0 0 0 0 -1003 0 0 0 -5 0 900 0 0 0 5 0 450 0 0 76

0 0 0 0 -1 -1 0 0 0 0 0 0 0 0 -5 0 900 0 0 0 5 0 450 0 5 0 0 0 900 0 -5 0 0 0 450 0 77

= cm4i = ( ; ; ) cm 0 0 0 1 0 0 0 0 0 0 0 0 0 5 0 0 0 900 0 -5 0 0 0 450 0 0 0 0 0 1003 0 0 0 0 0 -1003 78

= cm4j = ( ; ; ) cm 0 0 0 0 0 0 0 -1 1 0 0 0 -3 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 -5 0 0 0 0 0 -5 0 13

= cm4P = ( ; ; ) cm 0 0 0 0 0 0 0 -1 -1 0 0 0 0 0 0 0 0 -5 0 0 0 0 0 -5 0 0 0 5 0 0 0 0 0 5 0 0 14

0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 5 0 0 0 0 0 5 0 0 0 -3 0 0 0 0 0 3 0 0 0 15

= = = 0 0 0 0 0 0 0 0 0 0 -1 1 0 0 0 -1003 0 0 0 0 0 1003 0 0 0 -5 0 450 0 0 0 5 0 900 0 0 16

= = = 0 0 0 0 0 0 0 0 0 0 -1 -1 0 0 -5 0 450 0 0 0 5 0 900 0 5 0 0 0 450 0 -5 0 0 0 900 0 17

= = = 12x12 0 0 0 0 0 0 0 0 0 1 0 0 12x12 0 5 0 0 0 450 0 -5 0 0 0 900 12x12 0 0 0 0 0 -1003 0 0 0 0 0 1003 18

12x12

= =


= kg/cm 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 -4 -3 0 0 0 0 -4 -3 0 0 73

-1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 -4 0 0 0 0 3 -4 0 0 74

X 1 -1 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 -3 0 0 0 0 0 0 0 75

0 0 0 0 0 1 0 0 0 0 0 0 0 4 3 0 -541 720 0 -4 -3 0 -270 360 0 0 76

Z 0 0 0 -1 -1 0 0 0 0 0 0 0 0 -3 4 0 -720 -541 0 3 -4 0 -360 -270 0 0 77

* 104(kg)(cm) 0 0 0 1 -1 0 0 0 0 0 0 0 0 0 0 1003 0 0 0 0 0 -1003 0 0 0 0 78

0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 4 3 0 0 0 0 4 3 0 0 13

0 0 0 0 0 0 -1 -1 0 0 0 0 0 0 0 0 -3 4 0 0 0 0 -3 4 0 0 14

0 0 0 0 0 0 1 -1 0 0 0 0 -3 0 0 0 0 0 3 0 0 0 0 0 0 0 15

0 0 0 0 0 0 0 0 0 0 0 1 0 4 3 0 -270 360 0 -4 -3 0 -541 720 0 0 16

0 0 0 0 0 0 0 0 0 -1 -1 0 0 -3 4 0 -360 -270 0 3 -4 0 -720 -541 0 0 17

12x12 0 0 0 0 0 0 0 0 0 1 -1 0 12x12 0 0 0 -1003 0 0 0 0 0 1003 0 0 12x12 0 0 18

0

0 0.030 0 0 0 4.500 0 -0.030 0 0 0 4.500

13 - 3

100Iz 67500 100 100 0 -0.030 0 0 0

213

213

X Y Z

0 0Dy 30 DZ 30 L 300 3.000 0 0 0 0 0 -3.000 0 0

0

0

00 0 0 0 0

-0.8

0Cx 0 Xps -112.72 Xpγ 100 0 0 0 -1003 0 0 0 0

0 -4.500 0 0 0

A 900 217370.65 0.45 0 0 0.030 0 -4.500 0 0 0 -0.030 0 -4.500 0

0 0 0 1003 0 0 0 0 0 -1003 0 0

0 0 -4.500 0 900 0 0 0 4.500 0 450 0

Ix 675000 250 0[K]=

0 4.500 0 0 0 900 0 -4.500 0 0 0 450* E [AT] = [K] =

_

[K]=

Iy 67500 250 300 -3.000 0 0 0 0 0 3.000 0 0 0 0 0

-4.500 0 0.030 0 0 0 -4.500

0 0 -0.030 0 4.500 0 0 0 0.030 0 4.500 0

1003 0 0

Cy 0 Yps -150.06 Ypγ -150 0 0 -4.500 0 450 0 0 0 4.500 0 900 0

900

senα 0.601 cosα

Y

0 0 1 0 0 0 0 0 0 0 0 0 W 0 0

Cz 1 Zps 100 Zpγ 113 0 4.500 0 0 0 450

-1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0.0

1 -1 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 1 0 0 0 0 0 0 0

0 0 0 -1 -1 0 0 0 0 0 0 0 0 0 0

[a] =0 0 0 1 -1 0 0 0 0 0 0 0

{f°} =0.0

[A] = * E [AT]*[K] =_

{f°}= [AT]* _ {f°} =

0 0 0 0 0 0 0 0 1 0 0 0 0

0 0 0 0 0 0 -1 -1 0 0 0 0 0.0

0 0 0 0 0 0 1 -1 0 0 0 0 0

0 0 0 0 0 1 0

0 0 0 0 0 0 0 0 -1 -1 0 0

0 0 0 0 0 0 0 0 1 -1 0 0.0

BARRA BARRA 14 - 4


79 80 81 82 83 84 19 20 21 22 23 24

= cm = cm = cm 0 0 1 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 -3 0 0 0 0 0 0 0 0 0 5 0 0 0 0 0 5 0 79

0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 0 0 0 0 0 5 0 0 0 -5 0 0 0 0 0 -5 0 0 80

= cm2 E = kg/cm2 G = *E 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -5 0 0 0 0 0 -5 0 0 0 3 0 0 0 0 0 -3 0 0 0 81

0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1003 0 0 0 0 0 -1003 0 0 0 -5 0 900 0 0 0 5 0 450 0 0 82

0 0 0 0 -1 0 0 0 0 0 0 0 0 0 -5 0 900 0 0 0 5 0 450 0 5 0 0 0 900 0 -5 0 0 0 450 0 83

= cm4i = ( ; ; ) cm 0 0 0 1 0 0 0 0 0 0 0 0 0 5 0 0 0 900 0 -5 0 0 0 450 0 0 0 0 0 1003 0 0 0 0 0 -1003 84

= cm4j = ( ; ; ) cm 0 0 0 0 0 0 0 0 1 0 0 0 -3 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 -5 0 0 0 0 0 -5 0 19

= cm4P = ( ; ; ) cm 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 -5 0 0 0 0 0 -5 0 0 0 5 0 0 0 0 0 5 0 0 20

0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 5 0 0 0 0 0 5 0 0 0 -3 0 0 0 0 0 3 0 0 0 21

= = = 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 -1003 0 0 0 0 0 1003 0 0 0 -5 0 450 0 0 0 5 0 900 0 0 22

= = = 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 -5 0 450 0 0 0 5 0 900 0 5 0 0 0 450 0 -5 0 0 0 900 0 23

= = = 12x12 0 0 0 0 0 0 0 0 0 1 0 0 12x12 0 5 0 0 0 450 0 -5 0 0 0 900 12x12 0 0 0 0 0 -1003 0 0 0 0 0 1003 24

12x12

= =


= kg/cm 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 -4 1 0 0 0 0 -4 1 0 0 79

0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 -4 0 0 0 0 -1 -4 0 0 80

X 1 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 -3 0 0 0 0 0 0 0 81

0 0 0 0 0 1 0 0 0 0 0 0 0 4 -1 0 283 854 0 -4 1 0 142 427 0 0 82

Z 0 0 0 0 -1 0 0 0 0 0 0 0 0 1 4 0 -854 283 0 -1 -4 0 -427 142 0 0 83

* 104(kg)(cm) 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1003 0 0 0 0 0 -1003 0 0 0 0 84

0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 4 -1 0 0 0 0 4 -1 0 0 19

0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 1 4 0 0 0 0 1 4 0 0 20

0 0 0 0 0 0 1 0 0 0 0 0 -3 0 0 0 0 0 3 0 0 0 0 0 0 0 21

0 0 0 0 0 0 0 0 0 0 0 1 0 4 -1 0 142 427 0 -4 1 0 283 854 0 0 22

0 0 0 0 0 0 0 0 0 0 -1 0 0 1 4 0 -427 142 0 -1 -4 0 -854 283 0 0 23

12x12 0 0 0 0 0 0 0 0 0 1 0 0 12x12 0 0 0 -1003 0 0 0 0 0 1003 0 0 12x12 0 0 24

0 0 0

100

50.2

Ix 675000 250 0[K]=

0 4.500 050.2

X

0 0 0

30

0 0.030 0

Iy 67500 250 300 -3.000 0 0

Iz 67500 100 100 0

0 0 0.030

Cy 0 Yps -150.06 Ypγ -150 0 0 -4.500 0 450 0 0 0 4.500

0 0 0 0 0 1

-0.9senα -0.31 cosα

00 0 -0.030 0 4.500

0

14 - 4

Dy DZ 30 L 300 3.000 0 0 0 0 0 -3.000 0 0

0 0 4.500 0 -0.030 0 0 0 4.500

A 900 217370.65 0.45 0 0 0.030 0 -4.500 0 0 0 -0.030 0 -4.500 0

1003 0 0 0 0 0 -1003 0 0

Y Z 0 0 -4.500 0 900 0 0 0 4.500 0 450 0

0 0 900 0 -4.500 0 0 0 450* E [AT] = [K] =

_

[K]=

0 0 0 3.000 0 0 0 0 0

-0.030 0 0 0 -4.500 0 0.030 0 0 0 -4.500

0 4.500 0

Cx 0 Xps 49.785 Xpγ 100 0 0 0 -1003 0 0 0 0 0 1003 0 0

0 900 0

Cz 1 Zps 100 Zpγ -49.8 0 4.500 0 0 0 450 0 -4.500 0 0 0 900

Y

0 0 1 0 0 0 0 0 0 0 0 0 W 0 0

0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0.0

1 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 1 0 0 0 0 0 0 0

0 0 0 0 -1 0 0 0 0 0 0 0 0 0

[a] =0 0 0 1 0 0 0 0 0 0 0 0

{f°} =0.0

0

[A] = * E [AT]*[K] =_

{f°}= [AT]* _ {f°} =

0 0 0 0 0 0 0 0 1 0 0 0 0

0 0 0 0 0 0 0 -1 0 0 0 0 0.0

0 0 0 0 0 1 0 0 0 0 0 00

0

0 0 0 0 0 0 0 0 0 -1 0 0

0 0 0 0 0 0 0 0 1 0 0 0.0

0

00 0 0 0 0

BARRA BARRA 15 - 5


85 86 87 88 89 90 25 26 27 28 29 30

= cm = cm = cm 0 1 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 -3 0 0 0 0 0 0 0 0 0 5 0 0 0 0 0 5 0 85

0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 0 0 0 0 0 5 0 0 0 -5 0 0 0 0 0 -5 0 0 86

= cm2 E = kg/cm2 G = *E 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -5 0 0 0 0 0 -5 0 0 0 3 0 0 0 0 0 -3 0 0 0 87

0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1003 0 0 0 0 0 -1003 0 0 0 -5 0 900 0 0 0 5 0 450 0 0 88

0 0 0 0 0 1 0 0 0 0 0 0 0 0 -5 0 900 0 0 0 5 0 450 0 5 0 0 0 900 0 -5 0 0 0 450 0 89

= cm4i = ( ; ; ) cm 0 0 0 1 0 0 0 0 0 0 0 0 0 5 0 0 0 900 0 -5 0 0 0 450 0 0 0 0 0 1003 0 0 0 0 0 -1003 90

= cm4j = ( ; ; ) cm 0 0 0 0 0 0 0 1 0 0 0 0 -3 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 -5 0 0 0 0 0 -5 0 25

= cm4P = ( ; ; ) cm 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 -5 0 0 0 0 0 -5 0 0 0 5 0 0 0 0 0 5 0 0 26

0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 5 0 0 0 0 0 5 0 0 0 -3 0 0 0 0 0 3 0 0 0 27

= = = 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 -1003 0 0 0 0 0 1003 0 0 0 -5 0 450 0 0 0 5 0 900 0 0 28

= = = 0 0 0 0 0 0 0 0 0 0 0 1 0 0 -5 0 450 0 0 0 5 0 900 0 5 0 0 0 450 0 -5 0 0 0 900 0 29

= = = 12x12 0 0 0 0 0 0 0 0 0 1 0 0 12x12 0 5 0 0 0 450 0 -5 0 0 0 900 12x12 0 0 0 0 0 -1003 0 0 0 0 0 1003 30

12x12

= =


= kg/cm 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 4 0 0 85

1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -4 0 0 0 0 0 -4 0 0 0 86

X 0 1 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 -3 0 0 0 0 0 0 0 87

0 0 0 0 0 1 0 0 0 0 0 0 0 0 -4 0 899 -40 0 0 4 0 450 -20 0 0 88

Z 0 0 0 1 0 0 0 0 0 0 0 0 0 4 0 0 40 899 0 -4 0 0 20 450 0 0 89

* 104(kg)(cm) 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1003 0 0 0 0 0 -1003 0 0 0 0 90

0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 -4 0 0 0 0 0 -4 0 0 25

0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 4 0 0 0 26

0 0 0 0 0 0 0 1 0 0 0 0 -3 0 0 0 0 0 3 0 0 0 0 0 0 0 27

0 0 0 0 0 0 0 0 0 0 0 1 0 0 -4 0 450 -20 0 0 4 0 899 -40 0 0 28

0 0 0 0 0 0 0 0 0 1 0 0 0 4 0 0 20 450 0 -4 0 0 40 899 0 0 29

12x12 0 0 0 0 0 0 0 0 0 0 1 0 12x12 0 0 0 -1003 0 0 0 0 0 1003 0 0 12x12 0 0 30

15 - 5

Dy

0 -4.500 0Ix 675000 95.5 0[K]=

0 4.500 0

X

0 0 0

0

30 DZ 30 L 300 3.000 0 0 0 0 0 -3.000 0 0 0 0 0

0 0.030 0 0 0 4.500 0 -0.030 0 0 0 4.500

A 900 217370.65 0.45 0 0 0.030 0 -4.500 0 0 0 -0.030 0 -4.500 0

1003 0 0 0 0 0 -1003 0 0

Y Z 0 0 -4.500 0 900 0 0 0 4.500 0 450 0

0 0 450* E [AT] = [K] =

_

[K]=

Iy 67500 95.5 300 -3.000 0 0 0 0 0 3.000 0 0 0 0 00

0 0 0 900

Iz 67500 100 100 0 -0.030 0 0 0 0 0.030 0 0 0 -4.500

0 4.500 0

-4.500

0 0 -0.030 0 4.500 0 0 0 0.030

100

Cx 0 Xps 100 Xpγ 100 0 0 0 -1003 0 0 0 0 0 1003 0 0

4.48 0 0 -4.500 0 450 0 0 0 4.500 0 900 0

Cz 1 Zps 100 Zpγ -100 0 4.500 0 0 0 450 0 -4.500 0 0 0 900

Cy

senα -1 cosα

Y

0 0 1 0 0 0 0 0 0 0 0 0

0 Yps 4.4849 Ypγ

W

0.04

0 0

1 0 0 0 0 0 0 0 0 0 0 0 0 0 0.0

0 1 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 1 0 0 0 0 0 0 0

0 0 0 1 0 0 0 0 0 0 0 0 0 0

[a] =0 0 0 0 1 0 0 0 0 0 0 0

{f°} =0.0

0

[A] = * E [AT]*[K] =_

{f°}= [AT]* _ {f°} =

0 0 0 0 0 0 0 0 1 0 0 0 0

1 0 0 0 0 0 0.0

0 0 0 0 0 0 1 0 0 0 0 00

00 0 0 0 0

0 0 0 0 0 0 0 0 0 0 1 0

0 0 0 0 0 0 0 0 1 0 0 0

0

0 0 0 0 0 0 0 0 0 0 1 0 0.0

BARRA BARRA 1 - 6


1 2 3 4 5 6 31 32 33 34 35 36

= cm = cm = cm 0 0 -1 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 -3 0 0 0 0 0 0 0 0 0 5 0 0 0 0 0 5 0 1

0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 0 0 0 0 0 5 0 0 0 -5 0 0 0 0 0 -5 0 0 2

= cm2 E = kg/cm2 G = *E 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -5 0 0 0 0 0 -5 0 0 0 3 0 0 0 0 0 -3 0 0 0 3

0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 1003 0 0 0 0 0 -1003 0 0 0 -5 0 900 0 0 0 5 0 450 0 0 4

0 0 0 0 1 0 0 0 0 0 0 0 0 0 -5 0 900 0 0 0 5 0 450 0 5 0 0 0 900 0 -5 0 0 0 450 0 5

= cm4i = ( ; ; ) cm 0 0 0 1 0 0 0 0 0 0 0 0 0 5 0 0 0 900 0 -5 0 0 0 450 0 0 0 0 0 1003 0 0 0 0 0 -1003 6

= cm4j = ( ; ; ) cm 0 0 0 0 0 0 0 0 -1 0 0 0 -3 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 -5 0 0 0 0 0 -5 0 31

= cm4P = ( ; ; ) cm 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 -5 0 0 0 0 0 -5 0 0 0 5 0 0 0 0 0 5 0 0 32

0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 5 0 0 0 0 0 5 0 0 0 -3 0 0 0 0 0 3 0 0 0 33

= = = 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 -1003 0 0 0 0 0 1003 0 0 0 -5 0 450 0 0 0 5 0 900 0 0 34

= = = 0 0 0 0 0 0 0 0 0 0 1 0 0 0 -5 0 450 0 0 0 5 0 900 0 5 0 0 0 450 0 -5 0 0 0 900 0 35

= = = 12x12 0 0 0 0 0 0 0 0 0 1 0 0 12x12 0 5 0 0 0 450 0 -5 0 0 0 900 12x12 0 0 0 0 0 -1003 0 0 0 0 0 1003 36

12x12

= =


= kg/cm 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 4 -1 0 0 0 0 4 -1 0 0 1

0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 4 0 0 0 0 1 4 0 0 2

X -1 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 -3 0 0 0 0 0 0 0 3

0 0 0 0 0 1 0 0 0 0 0 0 0 -4 1 0 -270 -859 0 4 -1 0 -135 -429 0 0 4

Z 0 0 0 0 1 0 0 0 0 0 0 0 0 -1 -4 0 859 -270 0 1 4 0 429 -135 0 0 5

* 104(kg)(cm) 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 1003 0 0 0 0 0 -1003 0 0 0 0 6

0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 -4 1 0 0 0 0 -4 1 0 0 31

0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 -1 -4 0 0 0 0 -1 -4 0 0 32

0 0 0 0 0 0 -1 0 0 0 0 0 -3 0 0 0 0 0 3 0 0 0 0 0 0 0 33

0 0 0 0 0 0 0 0 0 0 0 1 0 -4 1 0 -135 -429 0 4 -1 0 -270 -859 0 0 34

0 0 0 0 0 0 0 0 0 0 1 0 0 -1 -4 0 429 -135 0 1 4 0 859 -270 0 0 35

12x12 0 0 0 0 0 0 0 0 0 -1 0 0 12x12 0 0 0 -1003 0 0 0 0 0 1003 0 0 12x12 0 0 36

0 0.030 0100

131

131

X

0 0 0 1003 0 0 0 0 0

0 0 0 900 0 -4.500 0

0

Iz 67500 100 100 0 -0.030 0 0 0 -4.500

31.5 0 4.500 0 0 0 450

1 - 6

Dy 30 DZ 30 L 300 3.000 0 0 0 0 0 -3.000 0 0 0 0 0

0 0.030 0 0 0 4.500 0 -0.030 0 0 0 4.500

A 900 217370.65 0.45 0 0 0.030 0 -4.500 0 0 0 -0.030 0 -4.500 0

0

-1003 0 0

Y Z 0 0 -4.500 0 900 0 0 0 4.500 0 450 0

450* E [AT] = [K] =

_

[K]=

Iy 67500 0 600 -3.000 0 0 0 0 3.000 0 0 0 0 0

Ix 675000 0 300[K]=

0 4.500 0

0 0 -4.500

0 0 -0.030 0 4.500 0 0 0 0.030 0 4.500 0

Cx 0 Xps -31.465 Xpγ -200 0 0 0 -1003 0 0 0 0 0 1003 0 0

Cy 0 Yps 100 Ypγ 100 0 0 -4.500 0 450 0 0 0 4.500 0 900 0

0 -4.500 0 0 0 900

senα 0.3 cosα

Y

0 0 1 0 0 0 0 0 0 0 0 0 W 0 0

0.95

Cz 1 Zps -200 Zpγ

0 0 0 0 0 0 0 0.0

-1 0 0 0 0 0 0 0 0 0 0 0 0

0 1 0 0 0 0 0

0 0 0 0 0 1 0 0 0 0 0 0 0

0 0 0 0 1 0 0 0 0 0 0 0 0 00

[a] =0 0 0 -1 0 0 0 0 0 0 0 0

{f°} =0.0

0[A] = * E [AT]*[K] =

_

{f°}= [AT]* _ {f°} =

0 0 0 0 0 0 0 1 0 0 0 0

0 1 0 0 0 0 0.0

0 0 0 0 0 -1 0 0 0 0 0 00

00 0 0 0 0

0 0 0 0 0 0 0 0 0 0 1 0

0 0 0 0 0 0 0 0 0 0 1 0 0

0

0 0 0 0 0 0 0 0 0 -1 0 0 0.0

BARRA BARRA 2 - 7


7 8 9 10 11 12 37 38 39 40 41 42

= cm = cm = cm 0 -1 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 -3 0 0 0 0 0 0 0 0 0 5 0 0 0 0 0 5 0 7

0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 0 0 0 0 0 5 0 0 0 -5 0 0 0 0 0 -5 0 0 8

= cm2 E = kg/cm2 G = *E 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -5 0 0 0 0 0 -5 0 0 0 3 0 0 0 0 0 -3 0 0 0 9

0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 1003 0 0 0 0 0 -1003 0 0 0 -5 0 900 0 0 0 5 0 450 0 0 10

0 0 0 0 0 -1 0 0 0 0 0 0 0 0 -5 0 900 0 0 0 5 0 450 0 5 0 0 0 900 0 -5 0 0 0 450 0 11

= cm4i = ( ; ; ) cm 0 0 0 1 0 0 0 0 0 0 0 0 0 5 0 0 0 900 0 -5 0 0 0 450 0 0 0 0 0 1003 0 0 0 0 0 -1003 12

= cm4j = ( ; ; ) cm 0 0 0 0 0 0 0 -1 0 0 0 0 -3 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 -5 0 0 0 0 0 -5 0 37

= cm4P = ( ; ; ) cm 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 -5 0 0 0 0 0 -5 0 0 0 5 0 0 0 0 0 5 0 0 38

0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 5 0 0 0 0 0 5 0 0 0 -3 0 0 0 0 0 3 0 0 0 39

= = = 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 -1003 0 0 0 0 0 1003 0 0 0 -5 0 450 0 0 0 5 0 900 0 0 40

= = = 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 -5 0 450 0 0 0 5 0 900 0 5 0 0 0 450 0 -5 0 0 0 900 0 41

= = = 12x12 0 0 0 0 0 0 0 0 0 1 0 0 12x12 0 5 0 0 0 450 0 -5 0 0 0 900 12x12 0 0 0 0 0 -1003 0 0 0 0 0 1003 42

12x12

= =


= kg/cm 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -4 0 0 0 0 0 -4 0 0 7

-1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 4 0 0 0 8

X 0 -1 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 -3 0 0 0 0 0 0 0 9

0 0 0 0 0 1 0 0 0 0 0 0 0 0 4 0 -900 -25 0 0 -4 0 -450 -12 0 0 10

Z 0 0 0 -1 0 0 0 0 0 0 0 0 0 -4 0 0 25 -900 0 4 0 0 12 -450 0 0 11

* 104(kg)(cm) 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 1003 0 0 0 0 0 -1003 0 0 0 0 12

0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 4 0 0 0 0 0 4 0 0 37

0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 -4 0 0 0 0 0 -4 0 0 0 38

0 0 0 0 0 0 0 -1 0 0 0 0 -3 0 0 0 0 0 3 0 0 0 0 0 0 0 39

0 0 0 0 0 0 0 0 0 0 0 1 0 0 4 0 -450 -12 0 0 -4 0 -900 -25 0 0 40

0 0 0 0 0 0 0 0 0 -1 0 0 0 -4 0 0 12 -450 0 4 0 0 25 -900 0 0 41

12x12 0 0 0 0 0 0 0 0 0 0 -1 0 12x12 0 0 0 -1003 0 0 0 0 0 1003 0 0 12x12 0 0 42

= * E [AT]*[K] =_

{f°}= [AT]* _ {f°} =

[K]=0 4.500 0 0 0 0 -4.500 0

263

263

X

0 0 0 1003 0 0 0 0 0

0

0

0

0

0 0 0 0 0

0

Cx 0 Xps -162.93 Xpγ

450 0 -4.500 0

Y

0 0 1 0 0 0 0 0 0 0

2 - 7

Dy 30 DZ 30 L 300 3.000 0 0 0 0 0 -3.000 0 0 0 0 0

0 0.030 0 0 0 4.500 0 -0.030 0 0 0 4.500

A 900 217370.65 0.45 0 0 0.030 0 -4.500 0 0 0 -0.030 0 -4.500 0

-1003 0 0

Y Z 0 0 -4.500 0 900 0 0 0 4.500 0 450 0

0 0 450* E [AT] = [K] =

_

[K]=

Iy 67500 95.5 600 -3.000 0 0 0 0 0 3.000 0 0 0 0 0

900Ix 675000 95.5 300

Iz 67500 100 100 0 -0.030 0 0 0 -4.500 0 0.030 0 0 0 -4.500

0 0 -0.030 0 4.500 0 0 0 0.030 0 4.500 0

100

Cy 0 Yps 4.4849 Ypγ 4.48 0 0 -4.500 0 450 0 0 0 4.500 0 900

0 0

-200 0 0 0 -1003 0 0 0 0 0 1003 0

900

senα 1 cosα 0.03

0

0

0 0 W 0 0

Cz 1 Zps -200 Zpγ 163 0 4.500 0 0 0

-1 0 0 0 0 0 0 0 0 0 0 0 0 0 0.0

0 -1 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 1 0 0 0 0 0 0 0

0 0 0 -1 0 0 0 0 0 0 0 0 0 0

[a] =0 0 0 0 -1 0 0 0 0 0 0

{f°} =0.0

[A]0 0 0 0 0 0 0 1 0 0 0 0

-1 0 0 0 0 0 0.0

0 0 0 0 0 0 -1 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 1 0

0 0 0 0 0 0 0 0 0 -1 0 0 0

0 0 0 0 0 0 0 0 0 0 -1 0 0.0

BARRA BARRA 3 - 8


13 14 15 16 17 18 43 44 45 46 47 48

= cm = cm = cm 0 -1 1 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 -3 0 0 0 0 0 0 0 0 0 5 0 0 0 0 0 5 0 13

0 -1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 0 0 0 0 0 5 0 0 0 -5 0 0 0 0 0 -5 0 0 14

= cm2 E = kg/cm2 G = *E 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -5 0 0 0 0 0 -5 0 0 0 3 0 0 0 0 0 -3 0 0 0 15

0 0 0 0 -1 1 0 0 0 0 0 0 0 0 0 1003 0 0 0 0 0 -1003 0 0 0 -5 0 900 0 0 0 5 0 450 0 0 16

0 0 0 0 -1 -1 0 0 0 0 0 0 0 0 -5 0 900 0 0 0 5 0 450 0 5 0 0 0 900 0 -5 0 0 0 450 0 17

= cm4i = ( ; ; ) cm 0 0 0 1 0 0 0 0 0 0 0 0 0 5 0 0 0 900 0 -5 0 0 0 450 0 0 0 0 0 1003 0 0 0 0 0 -1003 18

= cm4j = ( ; ; ) cm 0 0 0 0 0 0 0 -1 1 0 0 0 -3 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 -5 0 0 0 0 0 -5 0 43

= cm4P = ( ; ; ) cm 0 0 0 0 0 0 0 -1 -1 0 0 0 0 0 0 0 0 -5 0 0 0 0 0 -5 0 0 0 5 0 0 0 0 0 5 0 0 44

0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 5 0 0 0 0 0 5 0 0 0 -3 0 0 0 0 0 3 0 0 0 45

= = = 0 0 0 0 0 0 0 0 0 0 -1 1 0 0 0 -1003 0 0 0 0 0 1003 0 0 0 -5 0 450 0 0 0 5 0 900 0 0 46

= = = 0 0 0 0 0 0 0 0 0 0 -1 -1 0 0 -5 0 450 0 0 0 5 0 900 0 5 0 0 0 450 0 -5 0 0 0 900 0 47

= = = 12x12 0 0 0 0 0 0 0 0 0 1 0 0 12x12 0 5 0 0 0 450 0 -5 0 0 0 900 12x12 0 0 0 0 0 -1003 0 0 0 0 0 1003 48

12x12

= =


= kg/cm 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 -4 -3 0 0 0 0 -4 -3 0 0 13

-1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 -4 0 0 0 0 3 -4 0 0 14

X 1 -1 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 -3 0 0 0 0 0 0 0 15

0 0 0 0 0 1 0 0 0 0 0 0 0 4 3 0 -541 720 0 -4 -3 0 -270 360 0 0 16

Z 0 0 0 -1 -1 0 0 0 0 0 0 0 0 -3 4 0 -720 -541 0 3 -4 0 -360 -270 0 0 17

* 104(kg)(cm) 0 0 0 1 -1 0 0 0 0 0 0 0 0 0 0 1003 0 0 0 0 0 -1003 0 0 0 0 18

0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 4 3 0 0 0 0 4 3 0 0 43

0 0 0 0 0 0 -1 -1 0 0 0 0 0 0 0 0 -3 4 0 0 0 0 -3 4 0 0 44

0 0 0 0 0 0 1 -1 0 0 0 0 -3 0 0 0 0 0 3 0 0 0 0 0 0 0 45

0 0 0 0 0 0 0 0 0 0 0 1 0 4 3 0 -270 360 0 -4 -3 0 -541 720 0 0 46

0 0 0 0 0 0 0 0 0 -1 -1 0 0 -3 4 0 -360 -270 0 3 -4 0 -720 -541 0 0 47

12x12 0 0 0 0 0 0 0 0 0 1 -1 0 12x12 0 0 0 -1003 0 0 0 0 0 1003 0 0 12x12 0 0 48

=_

{f°}=E [AT]*[K] [AT]* _ {f°} =

[AT] = =_

[K]=

[A] =

0 0

100Iz 67500 100 100 0

213

0

213

X

0 0 0 1003 0 0 0

0 0 0 0 0 0 0 0 0 1 -1 0 0.0

3 - 8

Dy 30 DZ 30 L 300 3.000 0 0 0 0 0 -3.000 0 0 0 0 0

0 0.030 0 0 0 4.500 0 -0.030 0 0 0 4.500

A 900 217370.65 0.45 0 0 0.030 0 -4.500 0 0 0 -0.030 0 -4.500 0

-1003 0 0

Y Z 0 0 -4.500 0 900 0 0 4.500 0 450 0

Ix 675000 250 300[K]=

0 4.500 0 0 0 900 0 -4.500 0 0[K]

Iy 67500 250 600 -3.000 0 0 0 0 0 3.000 0 0 0 0 0

-4.500

0 0 -0.030 0 4.500 0 0 0 0.030 0 4.500 0

0 450* E

0 0 -1003 0 0 0 0 0 1003 0

-0.030 0 0 0 -4.500 0 0.030 0 0 0

450 0 -4.500 0 0 0

0

Cy 0 Yps -150.06 Ypγ -150 0 0 -4.500 0 450 0 0 0 4.500 0 900 0

Cx 0 Xps -112.72 Xpγ -200 0

900


Y

0 0 1 0 0 0 0 0 0 0 0 0 W 0 0

Cz 1 Zps -200 Zpγ 113 0 4.500 0 0 0

-1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0.0

1 -1 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 1 0 0 0 0 0 0 0

0 0 0 -1 -1 0 0 0 0 0 0 0 000

[a] =0 0 0 1 -1 0 0 0 0 0 0

{f°} =0.0

*0 0 0 0 0 0 0 1 0 0 0 00

0

0 0 0 0 0 -1 -1 0 0 0 0 0.0

0 0 0 0 0 0 1 -1 0 0 0 0 0

0

0 0 0 0 0 0 0 0 0 0 0 1 0

0 0 0 0 0 0 0 0 0 -1 -1 0 0

BARRA BARRA 4 - 9


19 20 21 22 23 24 49 50 51 52 53 54

= cm = cm = cm 0 0 1 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 -3 0 0 0 0 0 0 0 0 0 5 0 0 0 0 0 5 0 19

0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 0 0 0 0 0 5 0 0 0 -5 0 0 0 0 0 -5 0 0 20

= cm2 E = kg/cm2 G = *E 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -5 0 0 0 0 0 -5 0 0 0 3 0 0 0 0 0 -3 0 0 0 21

0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1003 0 0 0 0 0 -1003 0 0 0 -5 0 900 0 0 0 5 0 450 0 0 22

0 0 0 0 -1 0 0 0 0 0 0 0 0 0 -5 0 900 0 0 0 5 0 450 0 5 0 0 0 900 0 -5 0 0 0 450 0 23

= cm4i = ( ; ; ) cm 0 0 0 1 0 0 0 0 0 0 0 0 0 5 0 0 0 900 0 -5 0 0 0 450 0 0 0 0 0 1003 0 0 0 0 0 -1003 24

= cm4j = ( ; ; ) cm 0 0 0 0 0 0 0 0 1 0 0 0 -3 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 -5 0 0 0 0 0 -5 0 49

= cm4P = ( ; ; ) cm 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 -5 0 0 0 0 0 -5 0 0 0 5 0 0 0 0 0 5 0 0 50

0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 5 0 0 0 0 0 5 0 0 0 -3 0 0 0 0 0 3 0 0 0 51

= = = 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 -1003 0 0 0 0 0 1003 0 0 0 -5 0 450 0 0 0 5 0 900 0 0 52

= = = 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 -5 0 450 0 0 0 5 0 900 0 5 0 0 0 450 0 -5 0 0 0 900 0 53

= = = 12x12 0 0 0 0 0 0 0 0 0 1 0 0 12x12 0 5 0 0 0 450 0 -5 0 0 0 900 12x12 0 0 0 0 0 -1003 0 0 0 0 0 1003 54

12x12

= =


= kg/cm 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 -4 1 0 0 0 0 -4 1 0 0 19

0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 -4 0 0 0 0 -1 -4 0 0 20

X 1 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 -3 0 0 0 0 0 0 0 21

0 0 0 0 0 1 0 0 0 0 0 0 0 4 -1 0 283 854 0 -4 1 0 142 427 0 0 22

Z 0 0 0 0 -1 0 0 0 0 0 0 0 0 1 4 0 -854 283 0 -1 -4 0 -427 142 0 0 23

* 104(kg)(cm) 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1003 0 0 0 0 0 -1003 0 0 0 0 24

0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 4 -1 0 0 0 0 4 -1 0 0 49

0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 1 4 0 0 0 0 1 4 0 0 50

0 0 0 0 0 0 1 0 0 0 0 0 -3 0 0 0 0 0 3 0 0 0 0 0 0 0 51

0 0 0 0 0 0 0 0 0 0 0 1 0 4 -1 0 142 427 0 -4 1 0 283 854 0 0 52

0 0 0 0 0 0 0 0 0 0 -1 0 0 1 4 0 -427 142 0 -1 -4 0 -854 283 0 0 53

12x12 0 0 0 0 0 0 0 0 0 1 0 0 12x12 0 0 0 -1003 0 0 0 0 0 1003 0 0 12x12 0 0 54

= * E [AT]*[K] =_

{f°}= [AT]* _ {f°} =

675000 250 300 0 0

X

0

4 - 9

0 0.030 0 0 0 4.500 0 -0.030 0

0 0 0 0 0 0 0 1 0 0 0.0

0

0

00

0 0 0 0 0 0 0 -1 0 0 0 0 0.0

0 0

Dy 30 DZ 30 L 300 3.000 0 0 0 0 0 -3.000 0 0 0 0

0 0 4.500

A 900 217370.65 0.45 0 0 0.030 0 -4.500 0 0 0 -0.030 0 -4.500 0

-1003 0 0

Y Z 0 0 -4.500 0 900 0 0 0 4.500 0 450 0

00 0 0 1003 0 0 0 0

* E [AT] = [K] =_

[K]=

Iy 67500 250 600 -3.000 0 0 0 0 0 3.000 0 0 0 0 050.2[K]=

0 4.500 050.2Ix

-4.500

0 0 -0.030 0 4.500 0 0 0 0.030 0 4.500 0

900 0 -4.500 0 0 0 450

0 0 -1003 0 0 0 0 0 1003 0

Iz 67500 100 100 0 -0.030 0 0 0 -4.500 0 0.030 0 0 0100

450 0 -4.500 0 0 0

0

Cy 0 Yps -150.06 Ypγ -150 0 0 -4.500 0 450 0 0 0 4.500 0 900 0

Cx 0 Xps 49.785 Xpγ -200 0

900

senα -0.31 cosα -0.9

Y

0 0 1 0 0 0 0 0 0 0 0 0 W 0 0

Cz 1 Zps -200 Zpγ -49.8 0 4.500 0 0 0

0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0.0

1 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0

0 0 0 0 -1 0 0 0 0 0 0 0 0

10 0 0 0 0

[a] =0 0 0 1 0 0 0 0 0 0 0

{f°} =0.0

[A]0 0 0 0 0 0 0 1 0 0 0 0

0 0 0 0 1 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 1 0

0 0 0 0 0 0 0 0 0 0 -1 0 0

0 0

FUERZA , DESPLAMIENTOS,FUERZAS

FUERZA

SD

ESPLAZA

MIEN

TOS

REACCIO

NES

1-0.0106279

0.94171

-0.0214533961

20.07383763

1.13392

-0.0279032362

3-0.2272875

0.19053

-0.571461263

4-3.6182322

-0.00144

4.49122373664

5-0.1590861

0.00155

-3.5579228665

60.48970006

-0.00016

0.12619986366

7-0.103294

0.95417

-0.0165423567

80.02111251

1.13768

-0.0275290568

9-0.2074528

0.13949

-0.4183232269

10-0.7584966

-0.001510

4.45923549470

11-3.225982

0.002711

-3.0854094271

120.54557025

-0.000112

0.10113727672

13-0.071157

0.945613

-0.0172117973

14-0.0968502

1.149814

-0.0202401974

15-0.1957053

0.110715

-0.3321349975

162.50982129

-0.003216

3.74868723776

17-1.8458802

0.002517

-3.1396500277

18-0.0294954

0.000018

-0.0036357878

190.04957687

0.931619

-0.0241607879

20-0.0898384

1.154320

-0.0221355380

21-0.2095087

0.144621

-0.4338603281

222.86536597

-0.002822

3.94501589882

231.73035672

0.000823

-3.8134350283

24-0.5850446

0.000124

-0.1138332284

250.07108601

0.933025

-0.0230270585

260.0134963

1.141226

-0.0265783686

27-0.2285168

0.193727

-0.5809728487

28-0.9984584

-0.001728

4.36968990588

293.5005916

0.001129

-3.7021696289

30-0.4207303

0.000130

-0.1098681490

31-0.0054441

1.576331

320.03358921

1.908132

33-0.2569409

0.284033

34-4.0902894

0.001334

35-0.0327924

0.000735

360.25084557

-0.000136

37-0.0512863

1.585037

380.00872636

1.911438

39-0.2522043

0.219839

40-1.1731521

-0.000140

41-3.8403214

0.003141

420.34783767

-0.000142

43-0.0363622

1.580943

44-0.0492478

1.921344

45-0.2492074

0.183645

463.20638421

-0.003146

47-2.3361574

0.002347

48-0.0216809

0.000048

490.02281663

1.570349

50-0.0448466

1.922250

51-0.2527176

0.226351

523.2967997

-0.002952

532.30677967

-0.000753

54-0.3640583

0.000154

550.0322966

1.570155

560.00563448

1.912956

57-0.2572111

0.288057

58-1.2397425

-0.000258

593.90249152

-0.001459

60-0.212944

0.000160

610

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700

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730

740

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Documents

Matrices de Rigidez