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Nudos x y
1 0 0
2 5 7 b 0.1 m L= ((Xj‐Xi)^2+(Yj‐Yi)^2)^0.5
3 11 7 h 0.2 m x = (Xj‐Xi)/L
4 11 2 A 0.02 m2 y = (Yj‐Yi)/L
I 6.66667E‐05 m4
E 20000000 Tn/m2
Elementos i j A I E Xi Yi Xj Yj L  x  y 12EI/L 3
1 1 2 0.02 6.67E‐05 20000000 0.0 0.0 5.0 7.0 8.6023 0.5812 0.8137 25.13
2 2 3 0.02 6.67E‐05 20000000 5.0 7.0 11.0 7.0 6.0000 1.0000 0.0000 74.07
3 4 3 0.02 6.67E‐05 20000000 11.0 2.0 11.0 7.0 5.0000 0.0000 1.0000 128.00
K A Vi Mi Mj
Rigideces 1 2 3 4
1  A*E/L 0 0 0 A
2 0  12*E*I/L^3  6*E*I/L^2  6*E*I/L^2 Vi
3 0  6*E*I/L^2  4*E*I/L  2*E*I/L Mi
4 0  6*E*I/L^2  2*E*I/L  4*E*I/L Mj
{q} = [K'] * {d}
n1 46499 0 0 0 0 0 0 0 0 0 0 0
v1i 0 25.13 108.11 108.11 0 0 0 0 0 0 0 0
m1i 0 108.11 619.99 309.99 0 0 0 0 0 0 0 0
m1j  =  0 108.11 309.99 619.99 0 0 0 0 0 0 0 0
n2 0 0 0 0 66667 0 0 0 0 0 0 0
v2i 0 0 0 0 0 74.07 222.22 222.22 0 0 0 0
m2i 0 0 0 0 0 222.22 888.89 444.44 0 0 0 0
m2j 0 0 0 0 0 222.22 444.44 888.89 0 0 0 0
n3 0 0 0 0 0 0 0 0 80000 0 0 0
v3i 0 0 0 0 0 0 0 0 0 128.00 320.00 320.00
m3i 0 0 0 0 0 0 0 0 0 320.00 1066.67 533.33
m3j 0 0 0 0 0 0 0 0 0 320.00 533.33 1066.67
A X1 Y1 G1 X2 Y2 G2
Comp Despl 1 2 3 4 5 6
1 cos sen  ‐ cos  ‐ sen P
2  ‐ sen cos  sen  ‐ cos Vi
3 1 Mi
4 1 Mj
{d} = [T] * {D}
Dx1 Dy1 1 Dx2 Dy2 2 Dx3 Dy3 3 Dx4 Dy4 4
1 2 3 4 5 6 7 8 9 10 11 12
1 0.581 0.814 0 ‐0.581 ‐0.814 0 0 0 0 0 0 0
1i ‐0.814 0.581 0 0.814 ‐0.581 0 0 0 0 0 0 0
1i 0 0 1.000 0 0 0 0 0 0 0 0 0
1j 0 0 0 0 0 1.000 0 0 0 0 0 0
 0 0 0 1.000 0.000 0 ‐1.000 0.000 0 0 0 0
2i  =  0 0 0 0.000 1.000 0 0.000 ‐1.000 0 0 0 0
2i 0 0 0 0 0 1.000 0 0 0 0 0 0
2j 0 0 0 0 0 0 0 0 1.000 0 0 0
 0 0 0 0 0 0 0.000 ‐1.000 0 0.000 1.000 0
3i 0 0 0 0 0 0 1.000 0.000 0 ‐1.000 0.000 0
i 0 0 0 0 0 0 0 0 0 0 0 1.000
j 0 0 0 0 0 0 0 0 1.000 0 0 0
[T] reducida
1 2 3 4 5 6 7
1 ‐0.581 ‐0.814 0.000 0.000 0.000 0.000 0.000 Dx2
1i 0.814 ‐0.581 0.000 0.000 0.000 0.000 0.000  x  Dy2
1i 0.000 0.000 0.000 0.000 0.000 0.000 0.000 
1j  =  0.000 0.000 1.000 0.000 0.000 0.000 0.000 Dx3
 1.000 0.000 0.000 ‐1.000 0.000 0.000 0.000 Dy3
2i 0.000 1.000 0.000 0.000 ‐1.000 0.000 0.000 
2i 0.000 0.000 1.000 0.000 0.000 0.000 0.000 
2j 0.000 0.000 0.000 0.000 0.000 1.000 0.000
 0.000 0.000 0.000 0.000 ‐1.000 0.000 0.000
3i 0.000 0.000 0.000 1.000 0.000 0.000 0.000
i 0.000 0.000 0.000 0.000 0.000 0.000 1.000
j 0.000 0.000 0.000 0.000 0.000 1.000 0.000
[12x7]
{Q} = [TT
]*{q}
1 2 3 4 5 6 7 8 9 10 11 12
Fx2 ‐0.581 0.814 0.000 0.000 1.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
Fy2 ‐0.814 ‐0.581 0.000 0.000 0.000 1.000 0.000 0.000 0.000 0.000 0.000 0.000
M2 0.000 0.000 0.000 1.000 0.000 0.000 1.000 0.000 0.000 0.000 0.000 0.000
Fx3 0.000 0.000 0.000 0.000 ‐1.000 0.000 0.000 0.000 0.000 1.000 0.000 0.000
Fy3 0.000 0.000 0.000 0.000 0.000 ‐1.000 0.000 0.000 ‐1.000 0.000 0.000 0.000
M3 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.000 0.000 0.000 0.000 1.000
M4 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.000 0.000
[7x12]
{q} = [k']*[T]*{D}
1 2 3 4 5 6 7
n1 ‐27027.0 ‐37837.8 0.0 0.0 0.0 0.0 0.0 Dx2
v1 20.5 ‐14.6 108.1 0.0 0.0 0.0 0.0  x  Dy2
m1i 88.0 ‐62.8 310.0 0.0 0.0 0.0 0.0 
m1j  =  88.0 ‐62.8 620.0 0.0 0.0 0.0 0.0 Dx3
n2 66666.7 0.0 0.0 ‐66666.7 0.0 0.0 0.0 Dy3
v2 0.0 74.1 222.2 0.0 ‐74.1 222.2 0.0 
m2i 0.0 222.2 888.9 0.0 ‐222.2 444.4 0.0 
m2j 0.0 222.2 444.4 0.0 ‐222.2 888.9 0.0
n3 0.0 0.0 0.0 0.0 ‐80000.0 0.0 0.0
v3 0.0 0.0 0.0 128.0 0.0 320.0 320.0
m3i 0.0 0.0 0.0 320.0 0.0 533.3 1066.7
m3j 0.0 0.0 0.0 320.0 0.0 1066.7 533.3
[12x12]x[12x7]=[12x7]
{Q} = [TT
][k']*[T]*{D} {Q} = [K]*{D}
[K] = [TT
][k']*[T]
1 2 3 4 5 6 7
Fx2 82392.5 21980.9 88.0 ‐66666.7 0.0 0.0 0.0 Dx2
Fy2 21980.9 30872.5 159.4 0.0 ‐74.1 222.2 0.0 Dy2
M2  =  88.0 159.4 1508.9 0.0 ‐222.2 444.4 0.0  x  
Fx3 ‐66666.7 0.0 0.0 66794.7 0.0 320.0 320.0 Dx3
Fy3 0.0 ‐74.1 ‐222.2 0.0 80074.1 ‐222.2 0.0 Dy3
M3 0.0 222.2 444.4 320.0 ‐222.2 1955.6 533.3 
M4 0.0 0.0 0.0 320.0 0.0 533.3 1066.7 
[7x12]x[12x7]=[7x7]
{D}=[K‐1
]*{Q}
1 2 3 4 5 6 7
Dx2 0.009 ‐0.007 0.000 0.009 0.000 0.000 ‐0.003  x  14.00 Fx2
Dy2 ‐0.007 0.005 0.000 ‐0.007 0.000 0.000 0.002 ‐12.59 Fy2
  =  0.000 0.000 0.001 0.000 0.000 0.000 0.000 20.22 M2
4
Dx3 0.009 ‐0.007 0.000 0.009 0.000 0.000 ‐0.003 0.00 Fx3
Dy3 0.000 0.000 0.000 0.000 0.000 0.000 0.000 ‐7.41 Fy3
 0.000 0.000 0.000 0.000 0.000 0.001 0.000 8.89 M3
 ‐0.003 0.002 0.000 ‐0.003 0.000 0.000 0.002 0 M4
Dx2 0.21758
Dy2 ‐0.15542
  =  0.01692
Dx3 0.21748
Dy3 ‐0.00019
 0.00063
 ‐0.06556 w 4
L 8.6023
M 24.66667
{q}=[k']*[T]*{D} {q} P 17.20465
n1 0.031 0.031
v1 8.550 ‐17.205 25.755
m1i 34.152 ‐24.6667 58.819
m1j  =  39.397 24.6667 14.730
n2 7.060 7.060 x 6.43864
v2 ‐7.598 ‐2.59259 ‐5.005 ‐14.7304
m2i ‐19.175 ‐4.44444 ‐14.730 35.30249
m2j ‐26.414 8.88889 ‐35.302 0
n3 15.005 15.005
v3 7.060 0 7.060 ‐8.65474
m3i 0.000 0 0.000
m3j 35.302 0.00 35.302
{d} = [T] * {D}
1 0.581 0.814 0.000 0.000 0.000 Dx1
24.667 Tn
1i ‐0.814 0.581 0.000 0.000 0.000 Dy1
1i 0.000 0.000 1.000 0.000 0.000 
1j 0.000 0.000 0.000 0.000 0.000 Dx4
 0.000 0.000 0.000 0.000 0.000 Dy4
2i  =  0.000 0.000 0.000 0.000 0.000  x 
2i 0.000 0.000 0.000 0.000 0.000
2j 0.000 0.000 0.000 0.000 0.000
 0.000 0.000 0.000 0.000 1.000
3i 0.000 0.000 0.000 ‐1.000 0.000
i 0.000 0.000 0.000 0.000 0.000
j 0.000 0.000 0.000 0.000 0.000
{Q} = [TT
]*{q}
Fx1 0.581 ‐0.814 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
Fy1 0.814 0.581 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
M1  =  0.000 0.000 1.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
Fx4 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 ‐1.000 0.000 0.000
Fy4 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.000 0.000 0.000 0.000
Fx1 ‐20.940
Fy1 14.995
M1  =  58.819
Fx4 ‐7.060 30.000
Fy4 15.005 ‐28.000
4 Tn/m
1
8,60233 m
17.204 Tn
24.667 Tn


14 Tn
10 Tn
10 Tn
6 m
2 m
5 m
5 m
25.755
8.655
5.005
15.005
7.060
V
5 m
58.819
x
8
.
6
0
2
3
3
-
x
 6EI/L 2
4EI/L 2EI/L AE/L
108.11 619.99 309.99 46499.06
222.22 888.89 444.44 66666.67
320.00 1066.67 533.33 80000.00
1
1i
1i
 x  1j

2i
2i
2j

3i
i
j
Dx1=0 empotrado
Dy1=0
1=0
Dx2
 x  Dy2

Dx3
Dy3

Dx4=0 articulado
Dy4=0

6 m
2 m
5 m
4 Tn/m
1
2
4
10 Tn
5 m
3
4 m
3
2
1
n1
 x  v1i
m1i
m1j
n2
v2i
m2i
m2j
n3
v3i
m3i
m3j
2 m
5 m
Tn/m
2
4
10 Tn
3
4 m
3
2
1
P 10 ra 2.5926
a 4 rb 7.4074
b 2 ma 4.4444
L 6 mb 8.8889
Ra 2.5926 Rb 7.4074
Ma 4.4444 Mb 8.8889 alfa 0.95054684
Psen 14
Pcos 10
10 Tn
4 m
17 204 Tn
n
4.444 Tn 8.889 Tn
14 Tn
6 m
2 m
1
5 m
0.031
25.755
 x  58.819
14.730
7.060
‐5.005
‐14.730
‐35.302
15.005
7.060
0.000
35.302
34.4093
alfa 0.95054684
20
28
17.204 Tn
2.593 Tn 7.407 Tn
n
6 m
2 m
5 m
14.730
7.060
M
14.730
35.302
35.302

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Ejemplo Rigideces Porticos.pdf

  • 1. Nudos x y 1 0 0 2 5 7 b 0.1 m L= ((Xj‐Xi)^2+(Yj‐Yi)^2)^0.5 3 11 7 h 0.2 m x = (Xj‐Xi)/L 4 11 2 A 0.02 m2 y = (Yj‐Yi)/L I 6.66667E‐05 m4 E 20000000 Tn/m2 Elementos i j A I E Xi Yi Xj Yj L  x  y 12EI/L 3 1 1 2 0.02 6.67E‐05 20000000 0.0 0.0 5.0 7.0 8.6023 0.5812 0.8137 25.13 2 2 3 0.02 6.67E‐05 20000000 5.0 7.0 11.0 7.0 6.0000 1.0000 0.0000 74.07 3 4 3 0.02 6.67E‐05 20000000 11.0 2.0 11.0 7.0 5.0000 0.0000 1.0000 128.00 K A Vi Mi Mj Rigideces 1 2 3 4 1  A*E/L 0 0 0 A 2 0  12*E*I/L^3  6*E*I/L^2  6*E*I/L^2 Vi 3 0  6*E*I/L^2  4*E*I/L  2*E*I/L Mi 4 0  6*E*I/L^2  2*E*I/L  4*E*I/L Mj {q} = [K'] * {d} n1 46499 0 0 0 0 0 0 0 0 0 0 0 v1i 0 25.13 108.11 108.11 0 0 0 0 0 0 0 0 m1i 0 108.11 619.99 309.99 0 0 0 0 0 0 0 0 m1j  =  0 108.11 309.99 619.99 0 0 0 0 0 0 0 0 n2 0 0 0 0 66667 0 0 0 0 0 0 0 v2i 0 0 0 0 0 74.07 222.22 222.22 0 0 0 0 m2i 0 0 0 0 0 222.22 888.89 444.44 0 0 0 0 m2j 0 0 0 0 0 222.22 444.44 888.89 0 0 0 0 n3 0 0 0 0 0 0 0 0 80000 0 0 0
  • 2. v3i 0 0 0 0 0 0 0 0 0 128.00 320.00 320.00 m3i 0 0 0 0 0 0 0 0 0 320.00 1066.67 533.33 m3j 0 0 0 0 0 0 0 0 0 320.00 533.33 1066.67 A X1 Y1 G1 X2 Y2 G2 Comp Despl 1 2 3 4 5 6 1 cos sen  ‐ cos  ‐ sen P 2  ‐ sen cos  sen  ‐ cos Vi 3 1 Mi 4 1 Mj {d} = [T] * {D} Dx1 Dy1 1 Dx2 Dy2 2 Dx3 Dy3 3 Dx4 Dy4 4 1 2 3 4 5 6 7 8 9 10 11 12 1 0.581 0.814 0 ‐0.581 ‐0.814 0 0 0 0 0 0 0 1i ‐0.814 0.581 0 0.814 ‐0.581 0 0 0 0 0 0 0 1i 0 0 1.000 0 0 0 0 0 0 0 0 0 1j 0 0 0 0 0 1.000 0 0 0 0 0 0  0 0 0 1.000 0.000 0 ‐1.000 0.000 0 0 0 0 2i  =  0 0 0 0.000 1.000 0 0.000 ‐1.000 0 0 0 0 2i 0 0 0 0 0 1.000 0 0 0 0 0 0 2j 0 0 0 0 0 0 0 0 1.000 0 0 0  0 0 0 0 0 0 0.000 ‐1.000 0 0.000 1.000 0 3i 0 0 0 0 0 0 1.000 0.000 0 ‐1.000 0.000 0 i 0 0 0 0 0 0 0 0 0 0 0 1.000 j 0 0 0 0 0 0 0 0 1.000 0 0 0 [T] reducida 1 2 3 4 5 6 7 1 ‐0.581 ‐0.814 0.000 0.000 0.000 0.000 0.000 Dx2 1i 0.814 ‐0.581 0.000 0.000 0.000 0.000 0.000  x  Dy2 1i 0.000 0.000 0.000 0.000 0.000 0.000 0.000  1j  =  0.000 0.000 1.000 0.000 0.000 0.000 0.000 Dx3
  • 3.  1.000 0.000 0.000 ‐1.000 0.000 0.000 0.000 Dy3 2i 0.000 1.000 0.000 0.000 ‐1.000 0.000 0.000  2i 0.000 0.000 1.000 0.000 0.000 0.000 0.000  2j 0.000 0.000 0.000 0.000 0.000 1.000 0.000  0.000 0.000 0.000 0.000 ‐1.000 0.000 0.000 3i 0.000 0.000 0.000 1.000 0.000 0.000 0.000 i 0.000 0.000 0.000 0.000 0.000 0.000 1.000 j 0.000 0.000 0.000 0.000 0.000 1.000 0.000 [12x7] {Q} = [TT ]*{q} 1 2 3 4 5 6 7 8 9 10 11 12 Fx2 ‐0.581 0.814 0.000 0.000 1.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 Fy2 ‐0.814 ‐0.581 0.000 0.000 0.000 1.000 0.000 0.000 0.000 0.000 0.000 0.000 M2 0.000 0.000 0.000 1.000 0.000 0.000 1.000 0.000 0.000 0.000 0.000 0.000 Fx3 0.000 0.000 0.000 0.000 ‐1.000 0.000 0.000 0.000 0.000 1.000 0.000 0.000 Fy3 0.000 0.000 0.000 0.000 0.000 ‐1.000 0.000 0.000 ‐1.000 0.000 0.000 0.000 M3 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.000 0.000 0.000 0.000 1.000 M4 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.000 0.000 [7x12] {q} = [k']*[T]*{D} 1 2 3 4 5 6 7 n1 ‐27027.0 ‐37837.8 0.0 0.0 0.0 0.0 0.0 Dx2 v1 20.5 ‐14.6 108.1 0.0 0.0 0.0 0.0  x  Dy2 m1i 88.0 ‐62.8 310.0 0.0 0.0 0.0 0.0  m1j  =  88.0 ‐62.8 620.0 0.0 0.0 0.0 0.0 Dx3
  • 4. n2 66666.7 0.0 0.0 ‐66666.7 0.0 0.0 0.0 Dy3 v2 0.0 74.1 222.2 0.0 ‐74.1 222.2 0.0  m2i 0.0 222.2 888.9 0.0 ‐222.2 444.4 0.0  m2j 0.0 222.2 444.4 0.0 ‐222.2 888.9 0.0 n3 0.0 0.0 0.0 0.0 ‐80000.0 0.0 0.0 v3 0.0 0.0 0.0 128.0 0.0 320.0 320.0 m3i 0.0 0.0 0.0 320.0 0.0 533.3 1066.7 m3j 0.0 0.0 0.0 320.0 0.0 1066.7 533.3 [12x12]x[12x7]=[12x7] {Q} = [TT ][k']*[T]*{D} {Q} = [K]*{D} [K] = [TT ][k']*[T] 1 2 3 4 5 6 7 Fx2 82392.5 21980.9 88.0 ‐66666.7 0.0 0.0 0.0 Dx2 Fy2 21980.9 30872.5 159.4 0.0 ‐74.1 222.2 0.0 Dy2 M2  =  88.0 159.4 1508.9 0.0 ‐222.2 444.4 0.0  x   Fx3 ‐66666.7 0.0 0.0 66794.7 0.0 320.0 320.0 Dx3 Fy3 0.0 ‐74.1 ‐222.2 0.0 80074.1 ‐222.2 0.0 Dy3 M3 0.0 222.2 444.4 320.0 ‐222.2 1955.6 533.3  M4 0.0 0.0 0.0 320.0 0.0 533.3 1066.7  [7x12]x[12x7]=[7x7] {D}=[K‐1 ]*{Q} 1 2 3 4 5 6 7 Dx2 0.009 ‐0.007 0.000 0.009 0.000 0.000 ‐0.003  x  14.00 Fx2 Dy2 ‐0.007 0.005 0.000 ‐0.007 0.000 0.000 0.002 ‐12.59 Fy2   =  0.000 0.000 0.001 0.000 0.000 0.000 0.000 20.22 M2 4
  • 5. Dx3 0.009 ‐0.007 0.000 0.009 0.000 0.000 ‐0.003 0.00 Fx3 Dy3 0.000 0.000 0.000 0.000 0.000 0.000 0.000 ‐7.41 Fy3  0.000 0.000 0.000 0.000 0.000 0.001 0.000 8.89 M3  ‐0.003 0.002 0.000 ‐0.003 0.000 0.000 0.002 0 M4 Dx2 0.21758 Dy2 ‐0.15542   =  0.01692 Dx3 0.21748 Dy3 ‐0.00019  0.00063  ‐0.06556 w 4 L 8.6023 M 24.66667 {q}=[k']*[T]*{D} {q} P 17.20465 n1 0.031 0.031 v1 8.550 ‐17.205 25.755 m1i 34.152 ‐24.6667 58.819 m1j  =  39.397 24.6667 14.730 n2 7.060 7.060 x 6.43864 v2 ‐7.598 ‐2.59259 ‐5.005 ‐14.7304 m2i ‐19.175 ‐4.44444 ‐14.730 35.30249 m2j ‐26.414 8.88889 ‐35.302 0 n3 15.005 15.005 v3 7.060 0 7.060 ‐8.65474 m3i 0.000 0 0.000 m3j 35.302 0.00 35.302 {d} = [T] * {D} 1 0.581 0.814 0.000 0.000 0.000 Dx1 24.667 Tn
  • 6. 1i ‐0.814 0.581 0.000 0.000 0.000 Dy1 1i 0.000 0.000 1.000 0.000 0.000  1j 0.000 0.000 0.000 0.000 0.000 Dx4  0.000 0.000 0.000 0.000 0.000 Dy4 2i  =  0.000 0.000 0.000 0.000 0.000  x  2i 0.000 0.000 0.000 0.000 0.000 2j 0.000 0.000 0.000 0.000 0.000  0.000 0.000 0.000 0.000 1.000 3i 0.000 0.000 0.000 ‐1.000 0.000 i 0.000 0.000 0.000 0.000 0.000 j 0.000 0.000 0.000 0.000 0.000 {Q} = [TT ]*{q} Fx1 0.581 ‐0.814 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 Fy1 0.814 0.581 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 M1  =  0.000 0.000 1.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 Fx4 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 ‐1.000 0.000 0.000 Fy4 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.000 0.000 0.000 0.000 Fx1 ‐20.940 Fy1 14.995 M1  =  58.819 Fx4 ‐7.060 30.000 Fy4 15.005 ‐28.000 4 Tn/m 1 8,60233 m 17.204 Tn 24.667 Tn   14 Tn 10 Tn 10 Tn
  • 7. 6 m 2 m 5 m 5 m 25.755 8.655 5.005 15.005 7.060 V 5 m 58.819 x 8 . 6 0 2 3 3 - x
  • 8.  6EI/L 2 4EI/L 2EI/L AE/L 108.11 619.99 309.99 46499.06 222.22 888.89 444.44 66666.67 320.00 1066.67 533.33 80000.00 1 1i 1i  x  1j  2i 2i 2j 
  • 9. 3i i j Dx1=0 empotrado Dy1=0 1=0 Dx2  x  Dy2  Dx3 Dy3  Dx4=0 articulado Dy4=0  6 m 2 m 5 m 4 Tn/m 1 2 4 10 Tn 5 m 3 4 m 3 2 1
  • 11. 2 m 5 m Tn/m 2 4 10 Tn 3 4 m 3 2 1
  • 12. P 10 ra 2.5926 a 4 rb 7.4074 b 2 ma 4.4444 L 6 mb 8.8889 Ra 2.5926 Rb 7.4074 Ma 4.4444 Mb 8.8889 alfa 0.95054684 Psen 14 Pcos 10 10 Tn 4 m 17 204 Tn n 4.444 Tn 8.889 Tn 14 Tn 6 m 2 m 1 5 m
  • 14. 6 m 2 m 5 m 14.730 7.060 M 14.730 35.302 35.302