Date post: | 25-Dec-2015 |
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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
MATRIZ DE RIGIDEZ - COORDENADAS LOCALES MATRIZ DE RIGIDEZ - COORDENADAS GLOBALES
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
= =
MATRIZ DE ROTACIÓN FUERZAS DE FIJACIÓN {f°} FUERZAS DE FIJACIÓN {f°} - COORDENADAS GLOBALES
= 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
MATRIZ DE RIGIDEZ - COORDENADAS LOCALES MATRIZ DE RIGIDEZ - COORDENADAS GLOBALES
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
= =
MATRIZ DE ROTACIÓN FUERZAS DE FIJACIÓN {f°} FUERZAS DE FIJACIÓN {f°} - COORDENADAS GLOBALES
= 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
MATRIZ DE RIGIDEZ - COORDENADAS LOCALES MATRIZ DE RIGIDEZ - COORDENADAS GLOBALES
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
= =
MATRIZ DE ROTACIÓN FUERZAS DE FIJACIÓN {f°} FUERZAS DE FIJACIÓN {f°} - COORDENADAS GLOBALES
= 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
senα 0.8 cosα -0.6
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
MATRIZ DE RIGIDEZ - COORDENADAS LOCALES MATRIZ DE RIGIDEZ - COORDENADAS GLOBALES
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
= =
MATRIZ DE ROTACIÓN FUERZAS DE FIJACIÓN {f°} FUERZAS DE FIJACIÓN {f°} - COORDENADAS GLOBALES
= 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
senα 0.906 cosα -0.4
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
MATRIZ DE RIGIDEZ - COORDENADAS LOCALES MATRIZ DE RIGIDEZ - COORDENADAS GLOBALES
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
= =
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 -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
MATRIZ DE RIGIDEZ - COORDENADAS LOCALES MATRIZ DE RIGIDEZ - COORDENADAS GLOBALES
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
= =
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 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
MATRIZ DE RIGIDEZ - COORDENADAS LOCALES MATRIZ DE RIGIDEZ - COORDENADAS GLOBALES
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
= =
MATRIZ DE ROTACIÓN FUERZAS DE FIJACIÓN {f°} FUERZAS DE FIJACIÓN {f°} - COORDENADAS GLOBALES
= 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
senα 0.956 cosα -0.3
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
MATRIZ DE RIGIDEZ - COORDENADAS LOCALES MATRIZ DE RIGIDEZ - COORDENADAS GLOBALES
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
= =
MATRIZ DE ROTACIÓN FUERZAS DE FIJACIÓN {f°} FUERZAS DE FIJACIÓN {f°} - COORDENADAS GLOBALES
= 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
MATRIZ DE RIGIDEZ - COORDENADAS LOCALES MATRIZ DE RIGIDEZ - COORDENADAS GLOBALES
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
= =
MATRIZ DE ROTACIÓN FUERZAS DE FIJACIÓN {f°} FUERZAS DE FIJACIÓN {f°} - COORDENADAS GLOBALES
= 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
senα 0.983 cosα -0.2
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
MATRIZ DE RIGIDEZ - COORDENADAS LOCALES MATRIZ DE RIGIDEZ - COORDENADAS GLOBALES
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
= =
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 -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
MATRIZ DE RIGIDEZ - COORDENADAS LOCALES MATRIZ DE RIGIDEZ - COORDENADAS GLOBALES
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
= =
MATRIZ DE ROTACIÓN FUERZAS DE FIJACIÓN {f°} FUERZAS DE FIJACIÓN {f°} - COORDENADAS GLOBALES
= 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
MATRIZ DE RIGIDEZ - COORDENADAS LOCALES MATRIZ DE RIGIDEZ - COORDENADAS GLOBALES
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
= =
MATRIZ DE ROTACIÓN FUERZAS DE FIJACIÓN {f°} FUERZAS DE FIJACIÓN {f°} - COORDENADAS GLOBALES
= 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
MATRIZ DE RIGIDEZ - COORDENADAS LOCALES MATRIZ DE RIGIDEZ - COORDENADAS GLOBALES
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
= =
MATRIZ DE ROTACIÓN FUERZAS DE FIJACIÓN {f°} FUERZAS DE FIJACIÓN {f°} - COORDENADAS GLOBALES
= 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
MATRIZ DE RIGIDEZ - COORDENADAS LOCALES MATRIZ DE RIGIDEZ - COORDENADAS GLOBALES
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
= =
MATRIZ DE ROTACIÓN FUERZAS DE FIJACIÓN {f°} FUERZAS DE FIJACIÓN {f°} - COORDENADAS GLOBALES
= 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
MATRIZ DE RIGIDEZ - COORDENADAS LOCALES MATRIZ DE RIGIDEZ - COORDENADAS GLOBALES
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
= =
MATRIZ DE ROTACIÓN FUERZAS DE FIJACIÓN {f°} FUERZAS DE FIJACIÓN {f°} - COORDENADAS GLOBALES
= 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
MATRIZ DE RIGIDEZ - COORDENADAS LOCALES MATRIZ DE RIGIDEZ - COORDENADAS GLOBALES
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
= =
MATRIZ DE ROTACIÓN FUERZAS DE FIJACIÓN {f°} FUERZAS DE FIJACIÓN {f°} - COORDENADAS GLOBALES
= 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
MATRIZ DE RIGIDEZ - COORDENADAS LOCALES MATRIZ DE RIGIDEZ - COORDENADAS GLOBALES
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
= =
MATRIZ DE ROTACIÓN FUERZAS DE FIJACIÓN {f°} FUERZAS DE FIJACIÓN {f°} - COORDENADAS GLOBALES
= 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
MATRIZ DE RIGIDEZ - COORDENADAS LOCALES MATRIZ DE RIGIDEZ - COORDENADAS GLOBALES
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
= =
MATRIZ DE ROTACIÓN FUERZAS DE FIJACIÓN {f°} FUERZAS DE FIJACIÓN {f°} - COORDENADAS GLOBALES
= 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
senα 0.601 cosα -0.8
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
MATRIZ DE RIGIDEZ - COORDENADAS LOCALES MATRIZ DE RIGIDEZ - COORDENADAS GLOBALES
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
= =
MATRIZ DE ROTACIÓN FUERZAS DE FIJACIÓN {f°} FUERZAS DE FIJACIÓN {f°} - COORDENADAS GLOBALES
= 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
620
630
640
650
660
670
680
690
700
710
720
730
740
750
760
770
780
790
800
810
820
830
840
850
860
870
880
890
900