N° de x y ϕ VA

senϕ cosϕ
Sección (m) (m) (rad)

1 0.00 0.00 1.571 1.000 0.000 42.348

2-0 0.94 3.50 1.047 0.866 0.500 42.348
2+0 0.94 3.50 1.047 0.866 0.500 42.348
3 1.00 3.61 1.030 0.857 0.515 42.348
4 2.00 4.90 0.796 0.714 0.700 42.348
5 3.00 5.74 0.608 0.571 0.821 42.348
6 4.00 6.32 0.443 0.429 0.904 42.348
7 5.00 6.71 0.290 0.286 0.958 42.348
8 6.00 6.93 0.143 0.143 0.990 42.348
9 7.00 7.00 0.000 0.000 1.000 42.348
10 8.00 6.93 -0.143 -0.143 0.990 42.348
11 9.00 6.71 -0.290 -0.286 0.958 42.348
12 10.00 6.32 -0.443 -0.429 0.904 42.348
13 11.00 5.74 -0.608 -0.571 0.821 42.348
14 12.00 4.90 -0.796 -0.714 0.700 42.348
15 13.00 3.61 -1.030 -0.857 0.515 42.348
16 14.00 0.00 -1.571 -1.000 0.000 42.348

DIAGRAMA DE MOMENTO FLECTOR DE LA VIGA

x DIAGRAMA DE MOMEN
(m)
𝑀_𝐾 -Hy 0
^𝑉
0.00 0.00 0.000
0.94 -36.64 -44.282 -10
0.94 -36.64 -44.282
1.00 -38.48 -45.617 -20
2.00 -64.32 -61.981
-30
-36.64
-38.48
-40 -44.282
-45.617
 -20

3.00 -83.17 -72.680 -30

-36.64
-38.48
4.00 -95.02 -80.018
5.00 -99.87 -84.872 -40 -44.282
-45.617
6.00 -97.72 -87.655
7.00 -88.56 -88.563 -50
8.00 -75.91 -87.655 -61.981
-60 -64.32
9.00 -63.26 -84.872
10.00 -50.61 -80.018 -72.680
-70
11.00 -37.96 -72.680
12.00 -25.30 -61.981 -80.018
-80 -83.17 -84.872
13.00 -12.65 -45.617 -87.65
14.00 0.00 0.000
-90 -95.02
-97.7
-99.87

x
DIAGRAMA DE M
MK
(m)

0.00 0.000 -1.085032E-14

0.94 7.645 -7.644949316
0.94 7.645 -7.644949316
1.00 7.142 -7.142041141
2.00 -2.342 2.3417344876
3.00 -10.492 10.491600893
4.00 -15.002 15.001691584
5.00 -14.996 14.995907707
6.00 -10.061 10.060598592
7.00 0.000 0.0003330411 7.6
7.1

0.0
 7.6
7.1
8.00 11.743 -11.74320141
9.00 21.612 -21.61169229
10.00 29.410 -29.40970842 0.0
11.00 34.724 -34.72359911 -2.3
12.00 36.677 -36.67726551
13.00 32.965 -32.96484114
14.00 0.000 0.0003330411 -10.5

-15.0 -1

x
VK
(m)
0.00 0.000
0.00 42.348 42.35
0.94 35.783
35.78
0.94 29.783
1.00 29.348
29.78
29.35
2.00 22.348
3.00 15.348 22.35
4.00 8.348
5.00 1.348 15.35
6.00 -5.652
7.00 -12.652
8.00 -12.652 8.35
9.00 -12.652
10.00 -12.652 1
11.00 -12.652 0.00
12.00 -12.652 0 1 2 3 4
 1
0.00
0 1 2 3 4
13.00 -12.652
14 -12.6519
14.00 0.000

x VVK
Hsenϕ
(m) COS(PSI)
0.00 0.000 0.000
0.00 0.000 12.652
0.94 17.892 10.957
0.94 14.892 10.957
1.00 15.117 10.844
2.00 15.640 9.037
3.00 12.595 7.230
4.00 7.543 5.422
5.00 1.292 3.615 17.9
6.00 -5.594 1.807 15.1 15.6
14.9
7.00 -12.652 0.000 12.7 12.6
8.00 -12.522 -1.807 11.0
10.8
9.0
9.00 -12.125 -3.615 7.2 7.5
5.4
10.00 -11.431 -5.422 3.6
11.00 -10.383 -7.230 1.3
12.00 -8.854 -9.037
13.00 -6.517 -10.844 0 1 2 3 4 5
14.00 0.000 -12.652
14.00 0.000 0.000
 𝑀_𝐾 -Hy MK 𝑉_𝐾 𝑉_𝐾^𝑉 -Hsenϕ VK
^𝑉 ^𝑉 𝑐𝑜𝑠ϕ
0.00 0.000 0.000 42.348 0.000 -12.652 -12.652
36.64 -44.282 -7.645 35.783 17.892 -10.957 6.935
36.64 -44.282 -7.645 29.783 14.892 -10.957 3.935
38.48 -45.617 -7.142 29.348 15.117 -10.844 4.272
64.32 -61.981 2.342 22.348 15.640 -9.037 6.603
83.17 -72.680 10.492 15.348 12.595 -7.230 5.366
95.02 -80.018 15.002 8.348 7.543 -5.422 2.120
99.87 -84.872 14.996 1.348 1.292 -3.615 -2.323
97.72 -87.655 10.061 -5.652 -5.594 -1.807 -7.401
88.56 -88.563 0.000 -12.652 -12.652 0.000 -12.652
75.91 -87.655 -11.743 -12.652 -12.522 1.807 -10.715
63.26 -84.872 -21.612 -12.652 -12.125 3.615 -8.510
50.61 -80.018 -29.410 -12.652 -11.431 5.422 -6.009
37.96 -72.680 -34.724 -12.652 -10.383 7.230 -3.153
25.30 -61.981 -36.677 -12.652 -8.854 9.037 0.183
12.65 -45.617 -32.965 -12.652 -6.517 10.844 4.328
0.00 0.000 0.000 -12.652 0.000 12.652 12.652

MA DE MOMENTO FLECTOR DE LA VIGA

-12.65

-25.30

-37.96
-45.617
 -25.30

-37.96
-45.617
-50.61

81 -63.26 -61.981
32

-72.680 -72.680
-75.91
-80.018 -80.018
-83.17 -84.872 -84.872
-87.655 -87.655
-88.56
-95.02
-97.72
-99.87

IAGRAMA DE MOMENTO FLECTOR DEL ARCO

36.7
34.7
33.0
29.4

21.6

11.7

0.0 0.0
 11.7

0.0 0.0
-2.3

-10.5 -10.1

-15.0 -15.0

22.35

15.35

8.35

1.35
0.00
2 3 4 5 6
-5.65 7 8 9 10 11 12 13 14

-12.65 -12.65
 1.35
0.00
2 3 4 5 6
-5.65 7 8 9 10 11 12 13 14

-12.65 -12.65

15.6
12.6
9.0
7.2 7.5
5.4
3.6
1.3 1.8
0.0 0.0
-1.8
2 3 4 5 6 7 8 -3.6
9 10 11 12 13 14 15
-5.6 -5.4 -6.5
-7.2
-8.9
-9.0
-11.4 -10.4 -10.8
-12.7 -12.5 -12.1 -12.7
 -8.9
-9.0
-11.4 -10.4 -10.8
-12.7 -12.5 -12.1 -12.7
𝑉_𝐾^𝑉se Hcosϕ NK
nϕ
42.348 0.000 -42.348
30.989 6.326 -37.315
25.793 6.326 -32.119
25.156 6.517 -31.672
15.963 8.854 -24.817
8.770 10.383 -19.153
3.578 11.431 -15.009
0.385 12.125 -12.510
-0.807 12.522 -11.715
0.000 12.652 -12.652
1.807 12.522 -14.330
3.615 12.125 -15.739
5.422 11.431 -16.853
7.230 10.383 -17.612
9.037 8.854 -17.892
10.844 6.517 -17.361
12.652 0.000 -12.652

DIAGRAMA VK

x
VK
(m)

0.00 -12.65
0.94 6.93 6.93
0.94 3.93
1.00 4.27 4.27
3.93
 6.93

4.27
3.93
2.00 6.60
3.00 5.37
4.00 2.12
5.00 -2.32 -1 0 1
6.00 -7.40
7.00 -12.65
8.00 -10.71
9.00 -8.51
10.00 -6.01
11.00 -3.15
12.00 0.18
13.00 4.33
14.00 12.65 -12.65

VVK
x
SEN HCOSPSI
(m)
PSI
.0 42.3
0.00 42.348 0.000
0.94 30.989 6.326
0.94 25.793 6.326
1.00 25.156 6.517
31.0
2.00 15.963 8.854
3.00 8.770 10.383 25.8
25.2
4.00 3.578 11.431
5.00 0.385 12.125
6.00 -0.807 12.522
7.00 0.000 12.652

0.0 6.5
6.3
 8.00 1.807 12.522
9.00 3.615 12.125
0.0 10.00 5.422 11.431 6.5
6.3
11.00 7.230 10.383
12.00 9.037 8.854
13.00 10.844 6.517
0 1
14.00 12.652 0.000

x
NK
(m)
0.00 -42.348
0.94 -37.315
0.94 -32.119
1.00 -31.672
2.00 -24.817
3.00 -19.153
4.00 -15.009
5.00 -12.510
0.00
6.00 -11.715
14 7.00 -12.652

65
 0.00
14
8.00 -14.330
9.00 -15.739
65
10.00 -16.853
11.00 -17.612
12.00 -17.892
13.00 -17.361
14.00 -12.652

0
4 15

.7
.7
6.93 6.60
5.37
4.27 4.33
3.93

2.12

0.18
 6.93 6.60
5.37
4.27 4.33
3.93

2.12

0.18

-1 0 1 2 3 4 5 6 7 8 9 10 11 12 13
-2.32
-3.15

-6.01

-7.40
-8.51

-10.71

-12.65 -12.65

42.3

31.0

25.8
25.2

16.0
12.1 12.5 12.7 12.5 12.1
10.4 11.4 11.4 10.4
8.9 8.8
6.5
6.3 7.2
5.4
 16.0
12.1 12.5 12.7 12.5 12.1
10.4 11.4 11.4 10.4
8.9 8.8
6.5
6.3 7.2
5.4
3.6 3.6
1.8
0.4 0.0
-0.8
0 1 2 3 4 5 6 7 8 9 10 11

0 1 2 3 4 5 6 7 8 9 1

-11.71
-12.51 -12.65
-15.01 -14.33
-15.74
-16
-19.15

-24.82
 -19.15

-24.82

-31.67
-32.12

-37.32

-42.35
 12.65

4.33

0.18
 4.33

0.18

10 11 12 13 14 15
-3.15

.01

12.1 12.7
11.4 10.4 10.8
9.0
8.9
7.2 6.5
5.4
 12.1 12.7
11.4 10.4 10.8
9.0
8.9
7.2 6.5
5.4
3.6

9 10 11 12 13 14 15

8 9 10 11 12 13 14 15

65 -12.65
-14.33
-15.74
-16.85 -17.61
-17.89 -17.36
-17.61 -17.89
 N° de x y ϕ
senϕ
Sección (m) (m) (rad)

1 0.00 0.00 1.043 0.864

2 2.00 3.18 0.973 0.827
3 4.00 5.88 0.886 0.775
4 6.00 8.08 0.775 0.700
5-0 8.00 9.80 0.634 0.592
5+0 8.00 9.80 0.634 0.592
6 10.00 11.02 0.455 0.440
7 12.00 11.76 0.240 0.238
8 14.00 12.00 0.000 0.000
9 16.00 11.76 -0.240 -0.238
10 18.00 11.02 -0.455 -0.440
11-0 20.00 9.80 -0.634 -0.592
11+0 20.00 9.80 -0.634 -0.592
12 22.00 8.08 -0.775 -0.700
13-0 24.00 5.88 -0.886 -0.775
13+0 24.00 5.88 -0.886 -0.775
14 26.00 3.18 -0.973 -0.827
15 28.00 0.00 -1.043 -0.864

DIAGRAMA DE MOMENTO FLECTOR DE LA VIGA

x 𝑀_𝐾 H(y-a)
(m) ^𝑉
0.00 0.00 0.000
2.00 183.71 0.000
4.00 339.43 0.000
6.00 467.14 0.000
 8.00 566.86 0.000
8.00 566.86 0.000
10.00 638.57 387.778
12.00 682.29 620.444
14.00 698.00 698.000
16.00 685.71 620.444
18.00 645.43 387.778
20.00 577.14 0.000
20.00 577.14 0.000
22.00 480.86 0.000
24.00 356.57 0.000
24.00 356.57 0.000
26.00 192.29 0.000
28.00 0.00 0.00

x
MK
(m)
0.00 0.000 0
2.00 183.714
4.00 339.429
6.00 467.143
8.00 566.857 183.7
8.00 566.857
10.00 250.794
12.00 61.841
14.00 0.000
16.00 65.270
18.00 257.651
20.00 577.143
20.00 577.143
22.00 480.857
24.00 356.571
24.00 356.571
26.00 192.286
28.00 0.00

x 98.857
VVK
(m) 8
0.00 98.857
2.00 84.857
4.00 70.857
6.00 56.857
8.00 42.857
8.00 42.857
10.00 28.857
12.00 14.857
14.00 0.857
16.00 -13.143
18.00 -27.143 -2 0
20.00 -41.143
20.00 -41.143
22.00 -55.143
24.00 -69.143
24.00 -75.143
26.00 -89.143
28.00 -103.143

x
Hsenϕ
(m)
0.00 49.811 0.000
2.00 47.743 0.000
4.00 44.820 0.000
6.00 40.616 0.000
8.00 34.538 0.000
8.00 34.538 187.502
10.00 25.916 139.300 49.8 4
12.00 14.431 75.330
14.00 0.857 0.000
16.00 -12.766 -75.330 0.0
18.00 -24.376 -139.300
20.00 -33.156 -187.502
20.00 -33.156 0.000
22.00 -39.392 0.000
24.00 -43.735 0.000
24.00 -47.530 0.000
26.00 -50.15 0.000
28.00 -51.97 0.000
 Long
cosϕ VA H P W Carga 𝑀_𝐾
Distrib ^𝑉
0.504 98.857 0.000 0.000 7.000 28.000 0.00
0.563 98.857 0.000 0.000 7.000 28.000 183.71
0.633 98.857 0.000 0.000 7.000 28.000 339.43
0.714 98.857 0.000 0.000 7.000 28.000 467.14
0.806 98.857 0.000 0.000 7.000 28.000 566.86
0.806 98.857 316.685 0.000 7.000 28.000 566.86
0.898 98.857 316.685 0.000 7.000 28.000 638.57
0.971 98.857 316.685 0.000 7.000 28.000 682.29
1.000 98.857 316.685 0.000 7.000 28.000 698.00
0.971 98.857 316.685 0.000 7.000 28.000 685.71
0.898 98.857 316.685 0.000 7.000 28.000 645.43
0.806 98.857 316.685 0.000 7.000 28.000 577.14
0.806 98.857 0.000 0.000 7.000 28.000 577.14
0.714 98.857 0.000 0.000 7.000 28.000 480.86
0.633 98.857 0.000 0.000 7.000 28.000 356.57
0.633 98.857 0.000 6.000 7.000 28.000 356.57
0.563 98.857 0.000 6.000 7.000 28.000 192.29
0.504 98.857 0.000 6.000 7.000 28.000 0.00
 387.8 387.8

620.4 620.4

698.0

0.0

61.8 65.3

183.7

250.8

339.4
 250.8

339.4

467.1

566.9

98.857
84.857
70.857
56.857
42.857
28.857
14.857
0.857

-2 0 2 4 6 8 10 12 14 -1
 187.5

139.3

75.3
49.8 47.7 44.8 40.6 34.5
25.9
14.4
0.0 0.9
0.0
-12.

-75.
-H(y-a) MK 𝑉_𝐾 𝑉_𝐾^𝑉 -Hsenϕ
^𝑉 𝑐𝑜𝑠ϕ
0.000 0.000 98.857 49.811 0.000
0.000 183.714 84.857 47.743 0.000
0.000 339.429 70.857 44.820 0.000
0.000 467.143 56.857 40.616 0.000
0.000 566.857 42.857 34.538 0.000
0.000 566.857 42.857 34.538 -187.502
-387.778 250.794 28.857 25.916 -139.300
-620.444 61.841 14.857 14.431 -75.330
-698.000 0.000 0.857 0.857 0.000
-620.444 65.270 -13.143 -12.766 75.330
-387.778 257.651 -27.143 -24.376 139.300
0.000 577.143 -41.143 -33.156 187.502
0.000 577.143 -41.143 -33.156 0.000
0.000 480.857 -55.143 -39.392 0.000
0.000 356.571 -69.143 -43.735 0.000
0.000 356.571 -75.143 -47.530 0.000
0.000 192.286 -89.143 -50.154 0.000
0.000 0.000 -103.143 -51.971 0.000
 387.8

620.4

0.0

65.3

192.3

257.7

356.6
 257.7

356.6

480.9

577.1

857
0.857

2 14 -13.143
16 18 20 22 24 26 28
-27.143
-41.143
-55.143
-69.143
-75.143
-89.143
-103.143
 -55.143
-69.143
-75.143
-89.143
-103.143

0.9
0.0 0.0
-12.8
-24.4
-33.2 -39.4 -43.7
-47.5 -50.2 -52.0
-75.3

-139.3

-187.5
-187.5
 VK 𝑉_𝐾^𝑉se Hcosϕ NK
nϕ
49.811 85.391 0.000 -85.391
47.743 70.152 0.000 -70.152
44.820 54.881 0.000 -54.881
40.616 39.787 0.000 -39.787
34.538 25.375 0.000 -25.375
-152.964 25.375 255.211 -280.586
-113.384 12.693 284.403 -297.096
-60.899 3.534 307.595 -311.130
0.857 0.000 316.685 -316.685
62.564 3.126 307.595 -310.722
114.924 11.939 284.403 -296.342
154.346 24.360 255.211 -279.571
-33.156 24.360 0.000 -24.360
-39.392 38.588 0.000 -38.588
-43.735 53.553 0.000 -53.553
-47.530 58.201 0.000 -58.201
-50.154 73.696 0.000 -73.696
-51.971 89.093 0.000 -89.093

DIAGRAMA VK

x VK
(m)
0.00 49.81
2.00 47.74
4.00 44.82
6.00 40.62
 8.00 34.54
8.00 -152.96
10.00 -113.38
12.00 -60.90
14.00 0.86
16.00 62.56
18.00 114.92
20.00 154.35
20.00 -33.16
22.00 -39.39
24.00 -43.74
24.00 -47.53
26.00 -50.15
28.00 -51.97

x
(m)
0.00 85.391
2.00 70.152
4.00 54.881
6.00 39.787
8.00 25.375
3 8.00 25.375
10.00 12.693
12.00 3.534
14.00 0.000
16.00 3.126
 18.00 11.939
20.00 24.360
20.00 24.360
22.00 38.588
24.00 53.553
24.00 58.201
26.00 73.696
28.00 89.093

x
(m)
0.00
2.00
4.00
6.00
26 28 8.00
8.00
10.00
12.00
14.00
16.00
18.00

89.143
-103.143
 20.00
89.143 20.00
-103.143 22.00
24.00
24.00
26.00
28.00

0.0

-52.0
 62
49.8 47.7 44.8 40.6
34.5
 62
49.8 47.7 44.8 40.6
34.5

0.9

-60.9

-113.4

-153.0

0.000
0.000
0.000
0.000
0.000
255.211
284.403
307.595
316.685
307.595
284.403
255.211
0.000
0.000
0.000 255.211
0.000
0.000 284.403
0.000 307.59

NK 0
-85.391 -2 0 2 4 6 8
-25.4 1
-20
-70.152 -39.8
-54.881 -40 -54.9
-39.787 -60 -70.2
-25.375 -85.4
-280.586 -80
-297.096 -10
-311.130
-12
-316.685
-310.722 -14
-296.342 -16
-18
-20
 -14
-16
-279.571
-18
-24.360
-38.588 -20
-53.553 -22
-58.201
-73.696 -24
-89.093 -26
-280.6
-28
-29
-30
-32
 154.3

114.9

62.6

5
 62.6

0.9

-33.2
-39.4
-43.7
-47.5 -50.2 -52.0
-60.9

-113.4

3.0
 255.211 255.211

284.403 284.403
307.595 307.595
316.685

4 6 8
-25.4 10 12 14 16 18 20
-24.4 22 24 26 28
-39.8 -38.6
-54.9 -53.6
-58.2
-73.7
-89.1
-280.6 -279.6
-297.1 -296.3
-311.1 -316.7 -310.7
24 26 28 30

53.6
58.2
-73.7
-89.1