CALCULO ESTRUCTURAL DE CARGAS EN UN PUENTE MEDIANTE LINEAS DE INLUENCIA

Braulio Huayamave 20-21-1944
Jim Gonzalez 9-734-2394
23/04/2014
CALCULO ESTRUCTURAL DE CARGAS EN UN
PUENTE MEDIANTE LINEAS DE INLUENCIA
INFLUENCIA
UNIVERSIDAD TECNOLÓGICA DE
PANAMÁ
FACULTAD DE INGENIERÍA CIVIL
MATERIA:
PUENTES Y ESTRUCTURAS
ESPECIALES

Introducción
El análisis estructural es base fundamental para poder
realizar un buen diseño, a través de este podemos conocer
los esfuerzos a los que estará sometido nuestro elemento
estructural y así poder determinar las configuraciones que
debe tener para soportar dichas cargas
En el siguiente trabajo podremos apreciar los diferentes
tipos de cargas a las que se ve sometida una viga que es
parte de un puente y sus diferentes combinaciones según
sea el caso.
En este caso específico se utilizaron dos herramientas
computacionales diferentes, como lo son los programas de
Excel y Ftool.

CÁLCULO DE ESFUERZOS DEBIDO A CARGA UNITARIA QUE
SE DESPLAZA A TRAVES DE LA VIGA

L (m) 30.00
Δx (m) 1.00
x 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
x1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 0 0.967 0.933 0.900 0.867 0.833 0.800 0.767 0.733 0.700 0.667 0.633 0.600 0.567 0.533 0.500 0.467 0.433 0.400 0.367 0.333 0.300 0.267 0.233 0.200 0.167 0.133 0.100 0.067 0.033 0
2 0 0.933 1.867 1.800 1.733 1.667 1.600 1.533 1.467 1.400 1.333 1.267 1.200 1.133 1.067 1.000 0.933 0.867 0.800 0.733 0.667 0.600 0.533 0.467 0.400 0.333 0.267 0.200 0.133 0.067 0
3 0 0.900 1.800 2.700 2.600 2.500 2.400 2.300 2.200 2.100 2.000 1.900 1.800 1.700 1.600 1.500 1.400 1.300 1.200 1.100 1.000 0.900 0.800 0.700 0.600 0.500 0.400 0.300 0.200 0.100 0
4 0 0.8667 1.7333 2.6 3.4667 3.3333 3.2 3.0667 2.9333 2.8 2.6667 2.5333 2.4 2.2667 2.1333 2 1.8667 1.7333 1.6 1.4667 1.3333 1.2 1.0667 0.9333 0.8 0.6667 0.5333 0.4 0.2667 0.1333 0
5 0 0.8333 1.6667 2.5 3.3333 4.1667 4 3.8333 3.6667 3.5 3.3333 3.1667 3 2.8333 2.6667 2.5 2.3333 2.1667 2 1.8333 1.6667 1.5 1.3333 1.1667 1 0.8333 0.6667 0.5 0.3333 0.1667 0
6 0 0.8 1.6 2.4 3.2 4 4.8 4.6 4.4 4.2 4 3.8 3.6 3.4 3.2 3 2.8 2.6 2.4 2.2 2 1.8 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 0
7 0 0.7667 1.5333 2.3 3.0667 3.8333 4.6 5.3667 5.1333 4.9 4.6667 4.4333 4.2 3.9667 3.7333 3.5 3.2667 3.0333 2.8 2.5667 2.3333 2.1 1.8667 1.6333 1.4 1.1667 0.9333 0.7 0.4667 0.2333 0
8 0 0.7333 1.4667 2.2 2.9333 3.6667 4.4 5.1333 5.8667 5.6 5.3333 5.0667 4.8 4.5333 4.2667 4 3.7333 3.4667 3.2 2.9333 2.6667 2.4 2.1333 1.8667 1.6 1.3333 1.0667 0.8 0.5333 0.2667 0
9 0 0.7 1.4 2.1 2.8 3.5 4.2 4.9 5.6 6.3 6 5.7 5.4 5.1 4.8 4.5 4.2 3.9 3.6 3.3 3 2.7 2.4 2.1 1.8 1.5 1.2 0.9 0.6 0.3 0
10 0 0.6667 1.3333 2 2.6667 3.3333 4 4.6667 5.3333 6 6.6667 6.3333 6 5.6667 5.3333 5 4.6667 4.3333 4 3.6667 3.3333 3 2.6667 2.3333 2 1.6667 1.3333 1 0.6667 0.3333 0
11 0 0.6333 1.2667 1.9 2.5333 3.1667 3.8 4.4333 5.0667 5.7 6.3333 6.9667 6.6 6.2333 5.8667 5.5 5.1333 4.7667 4.4 4.0333 3.6667 3.3 2.9333 2.5667 2.2 1.8333 1.4667 1.1 0.7333 0.3667 0
12 0 0.6 1.2 1.8 2.4 3 3.6 4.2 4.8 5.4 6 6.6 7.2 6.8 6.4 6 5.6 5.2 4.8 4.4 4 3.6 3.2 2.8 2.4 2 1.6 1.2 0.8 0.4 0
13 0 0.5667 1.1333 1.7 2.2667 2.8333 3.4 3.9667 4.5333 5.1 5.6667 6.2333 6.8 7.3667 6.9333 6.5 6.0667 5.6333 5.2 4.7667 4.3333 3.9 3.4667 3.0333 2.6 2.1667 1.7333 1.3 0.8667 0.4333 0
14 0 0.5333 1.0667 1.6 2.1333 2.6667 3.2 3.7333 4.2667 4.8 5.3333 5.8667 6.4 6.9333 7.4667 7 6.5333 6.0667 5.6 5.1333 4.6667 4.2 3.7333 3.2667 2.8 2.3333 1.8667 1.4 0.9333 0.4667 0
15 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 7 6.5 6 5.5 5 4.5 4 3.5 3 2.5 2 1.5 1 0.5 0
16 0 0.4667 0.9333 1.4 1.8667 2.3333 2.8 3.2667 3.7333 4.2 4.6667 5.1333 5.6 6.0667 6.5333 7 7.4667 6.9333 6.4 5.8667 5.3333 4.8 4.2667 3.7333 3.2 2.6667 2.1333 1.6 1.0667 0.5333 0
17 0 0.4333 0.8667 1.3 1.7333 2.1667 2.6 3.0333 3.4667 3.9 4.3333 4.7667 5.2 5.6333 6.0667 6.5 6.9333 7.3667 6.8 6.2333 5.6667 5.1 4.5333 3.9667 3.4 2.8333 2.2667 1.7 1.1333 0.5667 0
18 0 0.4 0.8 1.2 1.6 2 2.4 2.8 3.2 3.6 4 4.4 4.8 5.2 5.6 6 6.4 6.8 7.2 6.6 6 5.4 4.8 4.2 3.6 3 2.4 1.8 1.2 0.6 0
19 0 0.3667 0.7333 1.1 1.4667 1.8333 2.2 2.5667 2.9333 3.3 3.6667 4.0333 4.4 4.7667 5.1333 5.5 5.8667 6.2333 6.6 6.9667 6.3333 5.7 5.0667 4.4333 3.8 3.1667 2.5333 1.9 1.2667 0.6333 0
20 0 0.3333 0.6667 1 1.3333 1.6667 2 2.3333 2.6667 3 3.3333 3.6667 4 4.3333 4.6667 5 5.3333 5.6667 6 6.3333 6.6667 6 5.3333 4.6667 4 3.3333 2.6667 2 1.3333 0.6667 0
21 0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 3 3.3 3.6 3.9 4.2 4.5 4.8 5.1 5.4 5.7 6 6.3 5.6 4.9 4.2 3.5 2.8 2.1 1.4 0.7 0
22 0 0.2667 0.5333 0.8 1.0667 1.3333 1.6 1.8667 2.1333 2.4 2.6667 2.9333 3.2 3.4667 3.7333 4 4.2667 4.5333 4.8 5.0667 5.3333 5.6 5.8667 5.1333 4.4 3.6667 2.9333 2.2 1.4667 0.7333 0
23 0 0.2333 0.4667 0.7 0.9333 1.1667 1.4 1.6333 1.8667 2.1 2.3333 2.5667 2.8 3.0333 3.2667 3.5 3.7333 3.9667 4.2 4.4333 4.6667 4.9 5.1333 5.3667 4.6 3.8333 3.0667 2.3 1.5333 0.7667 0
24 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3 3.2 3.4 3.6 3.8 4 4.2 4.4 4.6 4.8 4 3.2 2.4 1.6 0.8 0
25 0 0.1667 0.3333 0.5 0.6667 0.8333 1 1.1667 1.3333 1.5 1.6667 1.8333 2 2.1667 2.3333 2.5 2.6667 2.8333 3 3.1667 3.3333 3.5 3.6667 3.8333 4 4.1667 3.3333 2.5 1.6667 0.8333 0
26 0 0.1333 0.2667 0.4 0.5333 0.6667 0.8 0.9333 1.0667 1.2 1.3333 1.4667 1.6 1.7333 1.8667 2 2.1333 2.2667 2.4 2.5333 2.6667 2.8 2.9333 3.0667 3.2 3.3333 3.4667 2.6 1.7333 0.8667 0
27 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 2.3 2.4 2.5 2.6 2.7 1.8 0.9 0
28 0 0.0667 0.1333 0.2 0.2667 0.3333 0.4 0.4667 0.5333 0.6 0.6667 0.7333 0.8 0.8667 0.9333 1 1.0667 1.1333 1.2 1.2667 1.3333 1.4 1.4667 1.5333 1.6 1.6667 1.7333 1.8 1.8667 0.9333 0
29 0 0.0333 0.0667 0.1 0.1333 0.1667 0.2 0.2333 0.2667 0.3 0.3333 0.3667 0.4 0.4333 0.4667 0.5 0.5333 0.5667 0.6 0.6333 0.6667 0.7 0.7333 0.7667 0.8 0.8333 0.8667 0.9 0.9333 0.9667 0
30 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Datos
VALORES DE MOMENTO EN CARGA UNITARIA MOVIL

0
1
2
3
4
5
6
7
8
0 5 10 15 20 25 30
MomentoUnitario
POSICIÓN DE LINEA DE INFLUENCÍA (m)
DIAGRAMA DE MOMENTO DE CARGA UNITARIA MOVIL

CAMIÓN DE DISEÑO SEGÚN AASHTO
HL-93

CAMION DE DISEÑO HL-93
Diagrama de cortante
x [m] Shear Force [kN]
Max. Min.
0 391.3 0
1 376.9 -6.4
2 362.4 -12.9
3 348 -19.3
4 333.6 -25.7
5 319.2 -36.6
6 304.8 -49.5
7 290.4 -62.4
8 276 -75.2
9 261.6 -88.7
10 247.2 -103.1
11 232.8 -117.5
12 218.4 -131.9
13 204 -146.3
14 189.5 -160.7
15 175.1 -175.1
16 160.7 -189.5
17 146.3 -204
18 131.9 -218.4
19 117.5 -232.8
20 103.1 -247.2
21 88.7 -261.6
22 75.2 -276
23 62.4 -290.4
24 49.5 -304.8
25 36.6 -319.2
26 25.7 -333.6
27 19.3 -348
28 12.9 -362.4
29 6.4 -376.9
30 0 -391.3

CAMION DE DISEÑO HL-93
Diagrama de Momento
x [m] Bending Moment
[kNm]
Max. Min.
0 0 0
1 376.8 0
2 724.8 0
3 1044.1 0
4 1334.4 0
5 1596.1 0
6 1828.8 0
7 2032.8 0
8 2208 0
9 2354.2 0
10 2472.4 0
11 2580.5 0
12 2660.3 0
13 2711.4 0
14 2733.7 0
15 2728.7 0
16 2733.7 0
17 2711.4 0
18 2660.3 0
19 2580.5 0
20 2472.4 0
21 2354.2 0
22 2208 0
23 2032.8 0
24 1828.8 0
25 1596.1 0
26 1334.4 0
27 1044.1 0
28 724.8 0
29 376.8 0
30 0 0

V-(x1) V+(x1) Y1 Y2 Y3 V1 V2 V3 V4 ΣV+ ΣV- Y1 Y2 Y3 V1 V2 V3 V4 ΣV+ ΣV- Y1 Y2 Y3 V1 V2 V3 V4 ΣV+ ΣV- Vmàx + Vmàx -
0 0.000 1.000 1.000 0.000 0.000 35.00 0.00 0.00 0.000 35.000 0.000 0.857 1.000 0.000 29.98 145.00 0.00 0.00 174.983 0.000 0.713 0.857 1.000 24.97 124.22 145.00 0.00 294.183 0.000 294.183 0.000
1 -0.033 0.967 0.967 0.000 0.000 33.83 0.00 0.00 -1.167 33.833 -1.167 0.823 0.967 0.000 28.82 140.17 0.00 -4.83 168.983 -4.833 0.680 0.823 0.967 23.80 119.38 140.17 -4.83 283.350 -4.833 283.350 -4.833
2 -0.067 0.933 0.933 0.000 0.000 32.67 0.00 0.00 -2.333 32.667 -2.333 0.790 0.933 0.000 27.65 135.33 0.00 -9.67 162.983 -9.667 0.647 0.790 0.933 22.63 114.55 135.33 -9.67 272.517 -9.667 272.517 -9.667
3 -0.100 0.900 0.900 0.000 0.000 31.50 0.00 0.00 -3.500 31.500 -3.500 0.757 0.900 0.000 26.48 130.50 0.00 -14.50 156.983 -14.500 0.613 0.757 0.900 21.47 109.72 130.50 -14.50 261.683 -14.500 261.683 -14.500
4 -0.133 0.867 0.867 0.000 0.000 30.33 0.00 0.00 -4.667 30.333 -4.667 0.723 0.867 0.000 25.32 125.67 0.00 -19.33 150.983 -19.333 0.580 0.723 0.867 20.30 104.88 125.67 -19.33 250.850 -19.333 250.850 -19.333
5 -0.167 0.833 0.833 -0.023 0.000 29.17 -3.38 0.00 -5.833 29.167 -9.217 0.690 0.833 -0.023 24.15 120.83 -3.38 -24.17 144.983 -27.550 0.547 0.690 0.833 19.13 100.05 120.83 -24.17 240.017 -24.167 240.017 -27.550
6 -0.200 0.800 0.800 -0.057 0.000 28.00 -8.22 0.00 -7.000 28.000 -15.217 0.657 0.800 -0.057 22.98 116.00 -8.22 -29.00 138.983 -37.217 0.513 0.657 0.800 17.97 95.22 116.00 -29.00 229.183 -29.000 229.183 -37.217
7 -0.233 0.767 0.767 -0.090 0.000 26.83 -13.05 0.00 -8.167 26.833 -21.217 0.623 0.767 -0.090 21.82 111.17 -13.05 -33.83 132.983 -46.883 0.480 0.623 0.767 16.80 90.38 111.17 -33.83 218.350 -33.833 218.350 -46.883
8 -0.267 0.733 0.733 -0.123 0.000 25.67 -17.88 0.00 -9.333 25.667 -27.217 0.590 0.733 -0.123 20.65 106.33 -17.88 -38.67 126.983 -56.550 0.447 0.590 0.733 15.63 85.55 106.33 -38.67 207.517 -38.667 207.517 -56.550
9 -0.300 0.700 0.700 -0.157 -0.157 24.50 -22.72 -22.72 -10.500 24.500 -55.933 0.557 0.700 -0.157 19.48 101.50 -22.72 -43.50 120.983 -66.217 0.413 0.557 0.700 14.47 80.72 101.50 -43.50 196.683 -43.500 196.683 -66.217
10 -0.333 0.667 0.667 -0.190 -0.190 23.33 -27.55 -27.55 -11.667 23.333 -66.767 0.523 0.667 -0.190 18.32 96.67 -27.55 -48.33 114.983 -75.883 0.380 0.523 0.667 13.30 75.88 96.67 -48.33 185.850 -48.333 185.850 -75.883
11 -0.367 0.633 0.633 -0.223 -0.223 22.17 -32.38 -32.38 -12.833 22.167 -77.600 0.490 0.633 -0.223 17.15 91.83 -32.38 -53.17 108.983 -85.550 0.347 0.490 0.633 12.13 71.05 91.83 -53.17 175.017 -53.167 175.017 -85.550
12 -0.400 0.600 0.600 -0.257 -0.257 21.00 -37.22 -37.22 -14.000 21.000 -88.433 0.457 0.600 -0.257 15.98 87.00 -37.22 -58.00 102.983 -95.217 0.313 0.457 0.600 10.97 66.22 87.00 -58.00 164.183 -58.000 164.183 -95.217
13 -0.433 0.567 0.567 -0.290 -0.290 19.83 -42.05 -42.05 -15.167 19.833 -99.267 0.423 0.567 -0.290 14.82 82.17 -42.05 -62.83 96.983 -104.883 0.280 0.423 0.567 9.80 61.38 82.17 -62.83 153.350 -62.833 153.350 -104.883
14 -0.467 0.533 0.533 -0.323 -0.323 18.67 -46.88 -46.88 -16.333 18.667 -110.100 0.390 0.533 -0.323 13.65 77.33 -46.88 -67.67 90.983 -114.550 0.247 0.390 0.533 8.63 56.55 77.33 -67.67 142.517 -67.667 142.517 -114.550
15 -0.500 0.500 0.500 -0.357 -0.357 17.50 -51.72 -51.72 -17.500 17.500 -120.933 0.357 0.500 -0.357 12.48 72.50 -51.72 -72.50 84.983 -124.217 0.213 0.357 0.500 7.47 51.72 72.50 -72.50 131.683 -72.500 131.683 -124.217
16 -0.533 0.467 0.467 -0.390 -0.390 16.33 -56.55 -56.55 -18.667 16.333 -131.767 0.323 0.467 -0.390 11.32 67.67 -56.55 -77.33 78.983 -133.883 0.180 0.323 0.467 6.30 46.88 67.67 -77.33 120.850 -77.333 120.850 -133.883
17 -0.567 0.433 0.433 -0.423 -0.423 15.17 -61.38 -61.38 -19.833 15.167 -142.600 0.290 0.433 -0.423 10.15 62.83 -61.38 -82.17 72.983 -143.550 0.147 0.290 0.433 5.13 42.05 62.83 -82.17 110.017 -82.167 110.017 -143.550
18 -0.600 0.400 0.400 -0.457 -0.457 14.00 -66.22 -66.22 -21.000 14.000 -153.433 0.257 0.400 -0.457 8.98 58.00 -66.22 -87.00 66.983 -153.217 0.113 0.257 0.400 3.97 37.22 58.00 -87.00 99.183 -87.000 99.183 -153.433
19 -0.633 0.367 0.367 -0.490 -0.490 12.83 -71.05 -71.05 -22.167 12.833 -164.267 0.223 0.367 -0.490 7.82 53.17 -71.05 -91.83 60.983 -162.883 0.080 0.223 0.367 2.80 32.38 53.17 -91.83 88.350 -91.833 88.350 -164.267
20 -0.667 0.333 0.333 -0.523 -0.523 11.67 -75.88 -75.88 -23.333 11.667 -175.100 0.190 0.333 -0.523 6.65 48.33 -75.88 -96.67 54.983 -172.550 0.047 0.190 0.333 1.63 27.55 48.33 -96.67 77.517 -96.667 77.517 -175.100
21 -0.700 0.300 0.300 -0.557 -0.557 10.50 -80.72 -80.72 -24.500 10.500 -185.933 0.157 0.300 -0.557 5.48 43.50 -80.72 -101.50 48.983 -182.217 0.013 0.157 0.300 0.47 22.72 43.50 -101.50 66.683 -101.500 66.683 -185.933
22 -0.733 0.267 0.267 -0.590 -0.590 9.33 -85.55 -85.55 -25.667 9.333 -196.767 0.123 0.267 -0.590 4.32 38.67 -85.55 -106.33 42.983 -191.883 0.000 0.123 0.267 0.00 17.88 38.67 -106.33 56.550 -106.333 56.550 -196.767
23 -0.767 0.233 0.233 -0.623 -0.623 8.17 -90.38 -90.38 -26.833 8.167 -207.600 0.090 0.233 -0.623 3.15 33.83 -90.38 -111.17 36.983 -201.550 0.000 0.090 0.233 0.00 13.05 33.83 -111.17 46.883 -111.167 46.883 -207.600
24 -0.800 0.200 0.200 -0.657 -0.657 7.00 -95.22 -95.22 -28.000 7.000 -218.433 0.057 0.200 -0.657 1.98 29.00 -95.22 -116.00 30.983 -211.217 0.000 0.057 0.200 0.00 8.22 29.00 -116.00 37.217 -116.000 37.217 -218.433
25 -0.833 0.167 0.167 -0.690 -0.690 5.83 -100.05 -100.05 -29.167 5.833 -229.267 0.023 0.167 -0.690 0.82 24.17 -100.05 -120.83 24.983 -220.883 0.000 0.023 0.167 0.00 3.38 24.17 -120.83 27.550 -120.833 27.550 -229.267
26 -0.867 0.133 0.133 -0.723 -0.723 4.67 -104.88 -104.88 -30.333 4.667 -240.100 0.000 0.133 -0.723 0.00 19.33 -104.88 -125.67 19.333 -230.550 0.000 0.000 0.133 0.00 0.00 19.33 -125.67 19.333 -125.667 19.333 -240.100
27 -0.900 0.100 0.100 -0.757 -0.757 3.50 -109.72 -109.72 -31.500 3.500 -250.933 0.000 0.100 -0.757 0.00 14.50 -109.72 -130.50 14.500 -240.217 0.000 0.000 0.100 0.00 0.00 14.50 -130.50 14.500 -130.500 14.500 -250.933
28 -0.933 0.067 0.067 -0.790 -0.790 2.33 -114.55 -114.55 -32.667 2.333 -261.767 0.000 0.067 -0.790 0.00 9.67 -114.55 -135.33 9.667 -249.883 0.000 0.000 0.067 0.00 0.00 9.67 -135.33 9.667 -135.333 9.667 -261.767
29 -0.967 0.033 0.033 -0.823 -0.823 1.17 -119.38 -119.38 -33.833 1.167 -272.600 0.000 0.033 -0.823 0.00 4.83 -119.38 -140.17 4.833 -259.550 0.000 0.000 0.033 0.00 0.00 4.83 -140.17 4.833 -140.167 4.833 -272.600
30 -1.000 0.000 0.000 -0.857 -0.857 0.00 -124.22 -124.22 -35.000 0.000 -283.433 0.000 0.000 -0.857 0.00 0.00 -124.22 -145.00 0.000 -269.217 0.000 0.000 0.000 0.00 0.00 0.00 -145.00 0.000 -145.000 0.000 -283.433
CORTANTE
x1
CASO No. 1 CASO No. 2 CASO No. 3
ORDENADAS CORTANTE ORDENADAS CORTANTE ORDENADAS
CALCULO DE CORTANTE CAMIÒN HL-93 HACIA LA DERECHA
CORTANTE

-400.000
-300.000
-200.000
-100.000
0.000
100.000
200.000
300.000
400.000
0 5 10 15 20 25 30
Cortante(KN)
Posición en viga (m)
CORTANTE DE CAMIÓN HL-93 DERECHA

x1 M(x1) Y1 Y2 Y3 M1 M2 M3 ΣM1 Y1 Y2 Y3 M1 M2 M3 ΣM2 Y1 Y2 Y3 M1 M2 M3 ΣM3 Mmàx X1
0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
1 1.0 1.0 0.0 0.0 33.8 0.0 0.0 33.8 0.8 1.0 0.0 28.8 140.2 0.0 169.0 0.7 0.8 1.0 23.8 119.4 140.2 283.4 283.4
2 1.9 1.9 0.0 0.0 65.3 0.0 0.0 65.3 1.6 1.9 0.0 55.3 270.7 0.0 326.0 1.3 1.6 1.9 45.3 229.1 270.7 545.0 545.0
3 2.7 2.7 0.0 0.0 94.5 0.0 0.0 94.5 2.3 2.7 0.0 79.5 391.5 0.0 471.0 1.8 2.3 2.7 64.4 329.2 391.5 785.1 785.1
4 3.5 3.5 0.0 0.0 121.3 0.0 0.0 121.3 2.9 3.5 0.0 101.3 502.7 0.0 603.9 2.3 2.9 3.5 81.2 419.5 502.7 1003.4 1003.4
5 4.2 4.2 0.6 0.0 145.8 84.6 0.0 230.4 3.5 4.2 0.6 120.8 604.2 84.6 809.5 2.7 3.5 4.2 95.7 500.3 604.2 1200.1 1200.1
6 4.8 4.8 1.4 0.0 168.0 197.2 0.0 365.2 3.9 4.8 1.4 137.9 696.0 197.2 1031.1 3.1 3.9 4.8 107.8 571.3 696.0 1375.1 1375.1
7 5.4 5.4 2.1 0.0 187.8 300.2 0.0 488.0 4.4 5.4 2.1 152.7 778.2 300.2 1231.0 3.4 4.4 5.4 117.6 632.7 778.2 1528.5 1528.5
8 5.9 5.9 2.7 0.0 205.3 393.4 0.0 598.8 4.7 5.9 2.7 165.2 850.7 393.4 1409.3 3.6 4.7 5.9 125.1 684.4 850.7 1660.1 1660.1
9 6.3 6.3 3.3 0.3 220.5 477.1 40.6 738.2 5.0 6.3 3.3 175.4 913.5 477.1 1565.9 3.7 5.0 6.3 130.2 726.5 913.5 1770.2 1770.2
10 6.7 6.7 3.8 0.9 233.3 551.0 135.3 919.7 5.2 6.7 3.8 183.2 966.7 551.0 1700.8 3.8 5.2 6.7 133.0 758.8 966.7 1858.5 1858.5
11 7.0 7.0 4.2 1.5 243.8 615.3 220.4 1079.5 5.4 7.0 4.2 188.7 1010.2 615.3 1814.1 3.8 5.4 7.0 133.5 781.6 1010.2 1925.2 1925.2
12 7.2 7.2 4.6 2.0 252.0 669.9 295.8 1217.7 5.5 7.2 4.6 191.8 1044.0 669.9 1905.7 3.8 5.5 7.2 131.6 794.6 1044.0 1970.2 1970.2
13 7.4 7.4 4.9 2.5 257.8 714.9 361.5 1334.2 5.5 7.4 4.9 192.6 1068.2 714.9 1975.6 3.6 5.5 7.4 127.4 798.0 1068.2 1993.6 1993.6
14 7.5 7.5 5.2 2.9 261.3 750.1 417.6 1429.1 5.5 7.5 5.2 191.1 1082.7 750.1 2023.9 3.5 5.5 7.5 120.9 791.7 1082.7 1995.2 2023.9
15 7.5 7.5 5.4 3.2 262.5 775.8 464.0 1502.3 5.4 7.5 5.4 187.3 1087.5 775.8 2050.5 3.2 5.4 7.5 112.0 775.8 1087.5 1975.3 2050.5
16 7.5 7.5 5.5 3.5 261.3 791.7 500.7 1553.8 5.2 7.5 5.5 181.1 1082.7 791.7 2055.4 2.9 5.2 7.5 100.8 750.1 1082.7 1933.6 2055.4
17 7.4 7.4 5.5 3.6 257.8 798.0 527.8 1583.6 4.9 7.4 5.5 172.6 1068.2 798.0 2038.7 2.5 4.9 7.4 87.3 714.9 1068.2 1870.3 2038.7
18 7.2 7.2 5.5 3.8 252.0 794.6 545.2 1591.8 4.6 7.2 5.5 161.7 1044.0 794.6 2000.3 2.0 4.6 7.2 71.4 669.9 1044.0 1785.3 2000.3
19 7.0 7.0 5.4 3.8 243.8 781.6 552.9 1578.3 4.2 7.0 5.4 148.5 1010.2 781.6 1940.2 1.5 4.2 7.0 53.2 615.3 1010.2 1678.7 1940.2
20 6.7 6.7 5.2 3.8 233.3 758.8 551.0 1543.2 3.8 6.7 5.2 133.0 966.7 758.8 1858.5 0.9 3.8 6.7 32.7 551.0 966.7 1550.3 1858.5
21 6.3 6.3 5.0 3.7 220.5 726.5 539.4 1486.4 3.3 6.3 5.0 115.2 913.5 726.5 1755.1 0.3 3.3 6.3 9.8 477.1 913.5 1400.4 1755.1
22 5.9 5.9 4.7 3.6 205.3 684.4 518.1 1407.9 2.7 5.9 4.7 95.0 850.7 684.4 1630.0 0.0 2.7 5.9 0.0 393.4 850.7 1244.1 1630.0
23 5.4 5.4 4.4 3.4 187.8 632.7 487.2 1307.7 2.1 5.4 4.4 72.5 778.2 632.7 1483.3 0.0 2.1 5.4 0.0 300.2 778.2 1078.3 1483.3
24 4.8 4.8 3.9 3.1 168.0 571.3 446.6 1185.9 1.4 4.8 3.9 47.6 696.0 571.3 1314.9 0.0 1.4 4.8 0.0 197.2 696.0 893.2 1314.9
25 4.2 4.2 3.5 2.7 145.8 500.3 396.3 1042.4 0.6 4.2 3.5 20.4 604.2 500.3 1124.8 0.0 0.6 4.2 0.0 84.6 604.2 688.8 1124.8
26 3.5 3.5 2.9 2.3 121.3 419.5 336.4 877.3 0.0 3.5 2.9 0.0 502.7 419.5 922.2 0.0 0.0 3.5 0.0 0.0 502.7 502.7 922.2
27 2.7 2.7 2.3 1.8 94.5 329.2 266.8 690.5 0.0 2.7 2.3 0.0 391.5 329.2 720.7 0.0 0.0 2.7 0.0 0.0 391.5 391.5 720.7
28 1.9 1.9 1.6 1.3 65.3 229.1 187.5 482.0 0.0 1.9 1.6 0.0 270.7 229.1 499.8 0.0 0.0 1.9 0.0 0.0 270.7 270.7 499.8
29 1.0 1.0 0.8 0.7 33.8 119.4 98.6 251.8 0.0 1.0 0.8 0.0 140.2 119.4 259.6 0.0 0.0 1.0 0.0 0.0 140.2 140.2 259.6
30 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
ORDENADAS
CASO No. 1 CASO No. 2
MOMENTOS ORDENADAS MOMENTOS
CASO No. 3
ORDENADAS MOMENTOS
CALCULOS DE MOMENTOS CAMIÒN HL-93 HACIA LA DERECHA

0.0
500.0
1000.0
1500.0
2000.0
2500.0
0 5 10 15 20 25 30
Momento(KN*m)
DIAGRAMA DE MOMENTO DE CAMIÒN HL-93 HACIA LA DERECHA

V-(x1) V+(x1) Y1 Y2 Y3 V1 V2 V3 V4 ΣV+ ΣV- Y1 Y2 Y3 V1 V2 V3 V4 ΣV+ ΣV- Y1 Y2 Y3 V1 V2 V3 V4 ΣV+ ΣV- Vmàx + Vmàx -
0 0.000 1.000 1.000 0.857 0.713 35.000 124.217 103.433 0.000 262.650 0.000 0.000 1.000 0.857 0.000 145.000 124.217 0.000 269.217 0.000 0.000 0.000 1.000 0.000 0.000 145.000 0.000 145.000 0.000 269.217 0.000
1 -0.033 0.967 0.967 0.823 0.680 33.833 119.383 98.600 -1.167 251.817 -1.167 0.000 0.967 0.823 0.000 140.167 119.383 -4.833 259.550 -4.833 0.000 0.000 0.967 0.000 0.000 140.167 -4.833 140.167 -4.833 259.550 -4.833
2 -0.067 0.933 0.933 0.790 0.647 32.667 114.550 93.767 -2.333 240.983 -2.333 0.000 0.933 0.790 0.000 135.333 114.550 -9.667 249.883 -9.667 0.000 0.000 0.933 0.000 0.000 135.333 -9.667 135.333 -9.667 249.883 -9.667
3 -0.100 0.900 0.900 0.757 0.613 31.500 109.717 88.933 -3.500 230.150 -3.500 0.000 0.900 0.757 0.000 130.500 109.717 -14.500 240.217 -14.500 0.000 0.000 0.900 0.000 0.000 130.500 -14.500 130.500 -14.500 240.217 -14.500
4 -0.133 0.867 0.867 0.723 0.580 30.333 104.883 84.100 -4.667 219.317 -4.667 0.000 0.867 0.723 0.000 125.667 104.883 -19.333 230.550 -19.333 0.000 0.000 0.867 0.000 0.000 125.667 -19.333 125.667 -19.333 230.550 -19.333
5 -0.167 0.833 0.833 0.690 0.547 29.167 100.050 79.267 -5.833 208.483 -5.833 -0.023 0.833 0.690 -0.817 120.833 100.050 -24.167 220.883 -24.983 0.000 -0.023 0.833 0.000 -3.383 120.833 -24.167 120.833 -27.550 220.883 -27.550
6 -0.200 0.800 0.800 0.657 0.513 28.000 95.217 74.433 -7.000 197.650 -7.000 -0.057 0.800 0.657 -1.983 116.000 95.217 -29.000 211.217 -30.983 0.000 -0.057 0.800 0.000 -8.217 116.000 -29.000 116.000 -37.217 211.217 -37.217
7 -0.233 0.767 0.767 0.623 0.480 26.833 90.383 69.600 -8.167 186.817 -8.167 -0.090 0.767 0.623 -3.150 111.167 90.383 -33.833 201.550 -36.983 0.000 -0.090 0.767 0.000 -13.050 111.167 -33.833 111.167 -46.883 201.550 -46.883
8 -0.267 0.733 0.733 0.590 0.447 25.667 85.550 64.767 -9.333 175.983 -9.333 -0.123 0.733 0.590 -4.317 106.333 85.550 -38.667 191.883 -42.983 0.000 -0.123 0.733 0.000 -17.883 106.333 -38.667 106.333 -56.550 191.883 -56.550
9 -0.300 0.700 0.700 0.557 0.413 24.500 80.717 59.933 -10.500 165.150 -10.500 -0.157 0.700 0.557 -5.483 101.500 80.717 -43.500 182.217 -48.983 -0.013 -0.157 0.700 -0.467 -22.717 101.500 -43.500 101.500 -66.683 182.217 -66.683
10 -0.333 0.667 0.667 0.523 0.380 23.333 75.883 55.100 -11.667 154.317 -11.667 -0.190 0.667 0.523 -6.650 96.667 75.883 -48.333 172.550 -54.983 -0.047 -0.190 0.667 -1.633 -27.550 96.667 -48.333 96.667 -77.517 172.550 -77.517
11 -0.367 0.633 0.633 0.490 0.347 22.167 71.050 50.267 -12.833 143.483 -12.833 -0.223 0.633 0.490 -7.817 91.833 71.050 -53.167 162.883 -60.983 -0.080 -0.223 0.633 -2.800 -32.383 91.833 -53.167 91.833 -88.350 162.883 -88.350
12 -0.400 0.600 0.600 0.457 0.313 21.000 66.217 45.433 -14.000 132.650 -14.000 -0.257 0.600 0.457 -8.983 87.000 66.217 -58.000 153.217 -66.983 -0.113 -0.257 0.600 -3.967 -37.217 87.000 -58.000 87.000 -99.183 153.217 -99.183
13 -0.433 0.567 0.567 0.423 0.280 19.833 61.383 40.600 -15.167 121.817 -15.167 -0.290 0.567 0.423 -10.150 82.167 61.383 -62.833 143.550 -72.983 -0.147 -0.290 0.567 -5.133 -42.050 82.167 -62.833 82.167 -110.017 143.550 -110.017
14 -0.467 0.533 0.533 0.390 0.247 18.667 56.550 35.767 -16.333 110.983 -16.333 -0.323 0.533 0.390 -11.317 77.333 56.550 -67.667 133.883 -78.983 -0.180 -0.323 0.533 -6.300 -46.883 77.333 -67.667 77.333 -120.850 133.883 -120.850
15 -0.500 0.500 0.500 0.357 0.213 17.500 51.717 30.933 -17.500 100.150 -17.500 -0.357 0.500 0.357 -12.483 72.500 51.717 -72.500 124.217 -84.983 -0.213 -0.357 0.500 -7.467 -51.717 72.500 -72.500 72.500 -131.683 124.217 -131.683
16 -0.533 0.467 0.467 0.323 0.180 16.333 46.883 26.100 -18.667 89.317 -18.667 -0.390 0.467 0.323 -13.650 67.667 46.883 -77.333 114.550 -90.983 -0.247 -0.390 0.467 -8.633 -56.550 67.667 -77.333 67.667 -142.517 114.550 -142.517
17 -0.567 0.433 0.433 0.290 0.147 15.167 42.050 21.267 -19.833 78.483 -19.833 -0.423 0.433 0.290 -14.817 62.833 42.050 -82.167 104.883 -96.983 -0.280 -0.423 0.433 -9.800 -61.383 62.833 -82.167 62.833 -153.350 104.883 -153.350
18 -0.600 0.400 0.400 0.257 0.113 14.000 37.217 16.433 -21.000 67.650 -21.000 -0.457 0.400 0.257 -15.983 58.000 37.217 -87.000 95.217 -102.983 -0.313 -0.457 0.400 -10.967 -66.217 58.000 -87.000 58.000 -164.183 95.217 -164.183
19 -0.633 0.367 0.367 0.223 0.080 12.833 32.383 11.600 -22.167 56.817 -22.167 -0.490 0.367 0.223 -17.150 53.167 32.383 -91.833 85.550 -108.983 -0.347 -0.490 0.367 -12.133 -71.050 53.167 -91.833 53.167 -175.017 85.550 -175.017
20 -0.667 0.333 0.333 0.190 0.047 11.667 27.550 6.767 -23.333 45.983 -23.333 -0.523 0.333 0.190 -18.317 48.333 27.550 -96.667 75.883 -114.983 -0.380 -0.523 0.333 -13.300 -75.883 48.333 -96.667 48.333 -185.850 75.883 -185.850
21 -0.700 0.300 0.300 0.157 0.013 10.500 22.717 1.933 -24.500 35.150 -24.500 -0.557 0.300 0.157 -19.483 43.500 22.717 -101.500 66.217 -120.983 -0.413 -0.557 0.300 -14.467 -80.717 43.500 -101.500 43.500 -196.683 66.217 -196.683
22 -0.733 0.267 0.267 0.123 0.000 9.333 17.883 0.000 -25.667 27.217 -25.667 -0.590 0.267 0.123 -20.650 38.667 17.883 -106.333 56.550 -126.983 -0.447 -0.590 0.267 -15.633 -85.550 38.667 -106.333 38.667 -207.517 56.550 -207.517
23 -0.767 0.233 0.233 0.090 0.000 8.167 13.050 0.000 -26.833 21.217 -26.833 -0.623 0.233 0.090 -21.817 33.833 13.050 -111.167 46.883 -132.983 -0.480 -0.623 0.233 -16.800 -90.383 33.833 -111.167 33.833 -218.350 46.883 -218.350
24 -0.800 0.200 0.200 0.057 0.000 7.000 8.217 0.000 -28.000 15.217 -28.000 -0.657 0.200 0.057 -22.983 29.000 8.217 -116.000 37.217 -138.983 -0.513 -0.657 0.200 -17.967 -95.217 29.000 -116.000 29.000 -229.183 37.217 -229.183
25 -0.833 0.167 0.167 0.023 0.000 5.833 3.383 0.000 -29.167 9.217 -29.167 -0.690 0.167 0.023 -24.150 24.167 3.383 -120.833 27.550 -144.983 -0.547 -0.690 0.167 -19.133 -100.050 24.167 -120.833 24.167 -240.017 27.550 -240.017
26 -0.867 0.133 0.133 0.000 0.000 4.667 0.000 0.000 -30.333 4.667 -30.333 -0.723 0.133 0.000 -25.317 19.333 0.000 -125.667 19.333 -150.983 -0.580 -0.723 0.133 -20.300 -104.883 19.333 -125.667 19.333 -250.850 19.333 -250.850
27 -0.900 0.100 0.100 0.000 0.000 3.500 0.000 0.000 -31.500 3.500 -31.500 -0.757 0.100 0.000 -26.483 14.500 0.000 -130.500 14.500 -156.983 -0.613 -0.757 0.100 -21.467 -109.717 14.500 -130.500 14.500 -261.683 14.500 -261.683
28 -0.933 0.067 0.067 0.000 0.000 2.333 0.000 0.000 -32.667 2.333 -32.667 -0.790 0.067 0.000 -27.650 9.667 0.000 -135.333 9.667 -162.983 -0.647 -0.790 0.067 -22.633 -114.550 9.667 -135.333 9.667 -272.517 9.667 -272.517
29 -0.967 0.033 0.033 0.000 0.000 1.167 0.000 0.000 -33.833 1.167 -33.833 -0.823 0.033 0.000 -28.817 4.833 0.000 -140.167 4.833 -168.983 -0.680 -0.823 0.033 -23.800 -119.383 4.833 -140.167 4.833 -283.350 4.833 -283.350
30 -1.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 -35.000 0.000 -35.000 -0.857 0.000 0.000 -29.983 0.000 0.000 -145.000 0.000 -174.983 -0.713 -0.857 0.000 -24.967 -124.217 0.000 -145.000 0.000 -294.183 0.000 -294.183
CORTANTE ORDENADAS CORTANTE
CALCULO DE CORTANTE CAMIÒN HL-93 HACIA LA IZQUIERDA
x1
CORTANTE
ORDENADAS CORTANTE ORDENADAS

-400.000
-300.000
-200.000
-100.000
0.000
100.000
200.000
300.000
0 5 10 15 20 25 30 35
Cortante(KN)
Posición en viga (m)
CORTANTE DE CAMIÓN HL-93 IZQUIERDA

x1 M(x1) Y1 Y2 Y3 M1 M2 M3 ΣM1 Y1 Y2 Y3 M1 M2 M3 ΣM2 Y1 Y2 Y3 M1 M2 M3 ΣM3 Mmàx X1
0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
1 1.0 1.0 0.8 0.7 33.8 119.4 98.6 251.8 0.0 1.0 0.8 0.0 140.2 119.4 259.6 0.0 0.0 1.0 0.0 0.0 140.2 140.2 259.6
2 1.9 1.9 1.6 1.3 65.3 229.1 187.5 482.0 0.0 1.9 1.6 0.0 270.7 229.1 499.8 0.0 0.0 1.9 0.0 0.0 270.7 270.7 499.8
3 2.7 2.7 2.3 1.8 94.5 329.2 266.8 690.5 0.0 2.7 2.3 0.0 391.5 329.2 720.7 0.0 0.0 2.7 0.0 0.0 391.5 391.5 720.7
4 3.5 3.5 2.9 2.3 121.3 419.5 336.4 877.3 0.0 3.5 2.9 0.0 502.7 419.5 922.2 0.0 0.0 3.5 0.0 0.0 502.7 502.7 922.2
5 4.2 4.2 3.5 2.7 145.8 500.3 396.3 1042.4 0.6 4.2 3.5 20.4 604.2 500.3 1124.8 0.0 0.6 4.2 0.0 84.6 604.2 688.8 1124.8
6 4.8 4.8 3.9 3.1 168.0 571.3 446.6 1185.9 1.4 4.8 3.9 47.6 696.0 571.3 1314.9 0.0 1.4 4.8 0.0 197.2 696.0 893.2 1314.9
7 5.4 5.4 4.4 3.4 187.8 632.7 487.2 1307.7 2.1 5.4 4.4 72.5 778.2 632.7 1483.3 0.0 2.1 5.4 0.0 300.2 778.2 1078.3 1483.3
8 5.9 5.9 4.7 3.6 205.3 684.4 518.1 1407.9 2.7 5.9 4.7 95.0 850.7 684.4 1630.0 0.0 2.7 5.9 0.0 393.4 850.7 1244.1 1630.0
9 6.3 6.3 5.0 3.7 220.5 726.5 539.4 1486.4 3.3 6.3 5.0 115.2 913.5 726.5 1755.1 0.3 3.3 6.3 9.8 477.1 913.5 1400.4 1755.1
10 6.7 6.7 5.2 3.8 233.3 758.8 551.0 1543.2 3.8 6.7 5.2 133.0 966.7 758.8 1858.5 0.9 3.8 6.7 32.7 551.0 966.7 1550.3 1858.5
11 7.0 7.0 5.4 3.8 243.8 781.6 552.9 1578.3 4.2 7.0 5.4 148.5 1010.2 781.6 1940.2 1.5 4.2 7.0 53.2 615.3 1010.2 1678.7 1940.2
12 7.2 7.2 5.5 3.8 252.0 794.6 545.2 1591.8 4.6 7.2 5.5 161.7 1044.0 794.6 2000.3 2.0 4.6 7.2 71.4 669.9 1044.0 1785.3 2000.3
13 7.4 7.4 5.5 3.6 257.8 798.0 527.8 1583.6 4.9 7.4 5.5 172.6 1068.2 798.0 2038.7 2.5 4.9 7.4 87.3 714.9 1068.2 1870.3 2038.7
14 7.5 7.5 5.5 3.5 261.3 791.7 500.7 1553.8 5.2 7.5 5.5 181.1 1082.7 791.7 2055.4 2.9 5.2 7.5 100.8 750.1 1082.7 1933.6 2055.4
15 7.5 7.5 5.4 3.2 262.5 775.8 464.0 1502.3 5.4 7.5 5.4 187.3 1087.5 775.8 2050.5 3.2 5.4 7.5 112.0 775.8 1087.5 1975.3 2050.5
16 7.5 7.5 5.2 2.9 261.3 750.1 417.6 1429.1 5.5 7.5 5.2 191.1 1082.7 750.1 2023.9 3.5 5.5 7.5 120.9 791.7 1082.7 1995.2 2023.9
17 7.4 7.4 4.9 2.5 257.8 714.9 361.5 1334.2 5.5 7.4 4.9 192.6 1068.2 714.9 1975.6 3.6 5.5 7.4 127.4 798.0 1068.2 1993.6 1993.6
18 7.2 7.2 4.6 2.0 252.0 669.9 295.8 1217.7 5.5 7.2 4.6 191.8 1044.0 669.9 1905.7 3.8 5.5 7.2 131.6 794.6 1044.0 1970.2 1970.2
19 7.0 7.0 4.2 1.5 243.8 615.3 220.4 1079.5 5.4 7.0 4.2 188.7 1010.2 615.3 1814.1 3.8 5.4 7.0 133.5 781.6 1010.2 1925.2 1925.2
20 6.7 6.7 3.8 0.9 233.3 551.0 135.3 919.7 5.2 6.7 3.8 183.2 966.7 551.0 1700.8 3.8 5.2 6.7 133.0 758.8 966.7 1858.5 1858.5
21 6.3 6.3 3.3 0.3 220.5 477.1 40.6 738.2 5.0 6.3 3.3 175.4 913.5 477.1 1565.9 3.7 5.0 6.3 130.2 726.5 913.5 1770.2 1770.2
22 5.9 5.9 2.7 0.0 205.3 393.4 0.0 598.8 4.7 5.9 2.7 165.2 850.7 393.4 1409.3 3.6 4.7 5.9 125.1 684.4 850.7 1660.1 1660.1
23 5.4 5.4 2.1 0.0 187.8 300.2 0.0 488.0 4.4 5.4 2.1 152.7 778.2 300.2 1231.0 3.4 4.4 5.4 117.6 632.7 778.2 1528.5 1528.5
24 4.8 4.8 1.4 0.0 168.0 197.2 0.0 365.2 3.9 4.8 1.4 137.9 696.0 197.2 1031.1 3.1 3.9 4.8 107.8 571.3 696.0 1375.1 1375.1
25 4.2 4.2 0.6 0.0 145.8 84.6 0.0 230.4 3.5 4.2 0.6 120.8 604.2 84.6 809.5 2.7 3.5 4.2 95.7 500.3 604.2 1200.1 1200.1
26 3.5 3.5 0.0 0.0 121.3 0.0 0.0 121.3 2.9 3.5 0.0 101.3 502.7 0.0 603.9 2.3 2.9 3.5 81.2 419.5 502.7 1003.4 1003.4
27 2.7 2.7 0.0 0.0 94.5 0.0 0.0 94.5 2.3 2.7 0.0 79.5 391.5 0.0 471.0 1.8 2.3 2.7 64.4 329.2 391.5 785.1 785.1
28 1.9 1.9 0.0 0.0 65.3 0.0 0.0 65.3 1.6 1.9 0.0 55.3 270.7 0.0 326.0 1.3 1.6 1.9 45.3 229.1 270.7 545.0 545.0
29 1.0 1.0 0.0 0.0 33.8 0.0 0.0 33.8 0.8 1.0 0.0 28.8 140.2 0.0 169.0 0.7 0.8 1.0 23.8 119.4 140.2 283.4 283.4
30 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
MOMENTOS
CALCULOS DE MOMENTOS EN CAMIÒN HL-93 HACIA LA IZQUIERDA
ORDENADAS MOMENTOS ORDENADAS MOMENTOS ORDENADAS

0.0
500.0
1000.0
1500.0
2000.0
2500.0
0 5 10 15 20 25 30
Momento(KN*m)
DIAGRAMA DE MOMENTO DE CAMIÒN HL-93 HACIA LA IZQUIERDA

DIAGRAMAS DE CAMION DE DISEÑO
EN AMBAS DIRECCIONES

x1 V(+) derecha V(-) derecha V(+) izquierda V(-) izquierda V(+) Max V(-) Min IM *V(+) Max IM *V(-) Min
0 294.183 0.000 269.217 0.000 294.183 0.000 391.264 0.000
1 283.350 -4.833 259.550 -4.833 283.350 -4.833 376.856 -6.428
2 272.517 -9.667 249.883 -9.667 272.517 -9.667 362.447 -12.857
3 261.683 -14.500 240.217 -14.500 261.683 -14.500 348.039 -19.285
4 250.850 -19.333 230.550 -19.333 250.850 -19.333 333.631 -25.713
5 240.017 -27.550 220.883 -27.550 240.017 -27.550 319.222 -36.642
6 229.183 -37.217 211.217 -37.217 229.183 -37.217 304.814 -49.498
7 218.350 -46.883 201.550 -46.883 218.350 -46.883 290.406 -62.355
8 207.517 -56.550 191.883 -56.550 207.517 -56.550 275.997 -75.212
9 196.683 -66.217 182.217 -66.683 196.683 -66.683 261.589 -88.689
10 185.850 -75.883 172.550 -77.517 185.850 -77.517 247.181 -103.097
11 175.017 -85.550 162.883 -88.350 175.017 -88.350 232.772 -117.506
12 164.183 -95.217 153.217 -99.183 164.183 -99.183 218.364 -131.914
13 153.350 -104.883 143.550 -110.017 153.350 -110.017 203.956 -146.322
14 142.517 -114.550 133.883 -120.850 142.517 -120.850 189.547 -160.731
15 131.683 -124.217 124.217 -131.683 131.683 -131.683 175.139 -175.139
16 120.850 -133.883 114.550 -142.517 120.850 -142.517 160.731 -189.547
17 110.017 -143.550 104.883 -153.350 110.017 -153.350 146.322 -203.956
18 99.183 -153.433 95.217 -164.183 99.183 -164.183 131.914 -218.364
19 88.350 -164.267 85.550 -175.017 88.350 -175.017 117.506 -232.772
20 77.517 -175.100 75.883 -185.850 77.517 -185.850 103.097 -247.181
21 66.683 -185.933 66.217 -196.683 66.683 -196.683 88.689 -261.589
22 56.550 -196.767 56.550 -207.517 56.550 -207.517 75.212 -275.997
23 46.883 -207.600 46.883 -218.350 46.883 -218.350 62.355 -290.406
24 37.217 -218.433 37.217 -229.183 37.217 -229.183 49.498 -304.814
25 27.550 -229.267 27.550 -240.017 27.550 -240.017 36.642 -319.222
26 19.333 -240.100 19.333 -250.850 19.333 -250.850 25.713 -333.631
27 14.500 -250.933 14.500 -261.683 14.500 -261.683 19.285 -348.039
28 9.667 -261.767 9.667 -272.517 9.667 -272.517 12.857 -362.447
29 4.833 -272.600 4.833 -283.350 4.833 -283.350 6.428 -376.856
30 0.000 -283.433 0.000 -294.183 0.000 -294.183 0.000 -391.264

-400.000
-300.000
-200.000
-100.000
0.000
100.000
200.000
300.000
400.000
0 5 10 15 20 25 30
Cortante(KN)
Posición en Viga (m)
DIAGRAMA DE CORTANTE CAMION HL-93 EN DOS DIRECCIONES

-400.000
-300.000
-200.000
-100.000
0.000
100.000
200.000
300.000
400.000
0 5 10 15 20 25 30
Cortante(KN)
DIAGRAMA DE CORTANTE CAMION HL-93 EN DOS DIRECCIONES + IM

x1 MX1 Derecha MX1 Izquierda MX1 - 2 DIR.
0 0.00 0.00 0.00
1 283.35 259.55 283.35
2 545.03 499.77 545.03
3 785.05 720.65 785.05
4 1003.40 922.20 1003.40
5 1200.08 1124.83 1200.08
6 1375.10 1314.90 1375.10
7 1528.45 1483.30 1528.45
8 1660.13 1630.03 1660.13
9 1770.15 1755.10 1770.15
10 1858.50 1858.50 1858.50
11 1925.18 1940.23 1940.23
12 1970.20 2000.30 2000.30
13 1993.55 2038.70 2038.70
14 2023.90 2055.43 2055.43
15 2050.50 2050.50 2050.50
16 2055.43 2023.90 2055.43
17 2038.70 1993.55 2038.70
18 2000.30 1970.20 2000.30
19 1940.23 1925.18 1940.23
20 1858.50 1858.50 1858.50
21 1755.10 1770.15 1770.15
22 1630.03 1660.13 1660.13
23 1483.30 1528.45 1528.45
24 1314.90 1375.10 1375.10
25 1124.83 1200.08 1200.08
26 922.20 1003.40 1003.40
27 720.65 785.05 785.05
28 499.77 545.03 545.03
29 259.55 283.35 283.35
30 0.00 0.00 0.00

0.00
500.00
1000.00
1500.00
2000.00
2500.00
0 5 10 15 20 25 30
Momento(KN*m)
DIAGRAMA DE MOMENTO DE CAMIÓN HL-93 EN AMBAS DIRECCIONES

CARGA DE TAMDEM
Diagrama de Cortante
Max. Min.
0 286.7 0
1 277 -4.9
2 267.2 -13.7
3 257.5 -23.4
4 247.7 -33.2
5 238 -42.9
6 228.2 -52.7
7 218.5 -62.4
8 208.7 -72.2
9 199 -81.9
10 189.2 -91.7
11 179.5 -101.4
12 169.7 -111.2
13 160 -120.9
14 150.2 -130.7
15 140.4 -140.4
16 130.7 -150.2
17 120.9 -160
18 111.2 -169.7
19 101.4 -179.5
20 91.7 -189.2
21 81.9 -199
22 72.2 -208.7
23 62.4 -218.5
24 52.7 -228.2
25 42.9 -238
26 33.2 -247.7
27 23.4 -257.5
28 13.7 -267.2
29 4.9 -277
30 0 -286.7

CARGA DE TAMDEM
Diagrama de Momento
[kNm]
Max. Min.
0 0 0
1 276.9 0
2 534.4 0
3 772.4 0
4 990.9 0
5 1189.9 0
6 1369.3 0
7 1529.3 0
8 1669.8 0
9 1790.7 0
10 1892.1 0
11 1974.1 0
12 2036.4 0
13 2079.4 0
14 2102.8 0
15 2107.1 0
16 2102.8 0
17 2079.4 0
18 2036.4 0
19 1974.1 0
20 1892.1 0
21 1790.7 0
22 1669.8 0
23 1529.3 0
24 1369.3 0
25 1189.9 0
26 990.9 0
27 772.4 0
28 534.4 0
29 276.9 0
30 0 0

x1 V-(x1) V+(x1) Y1 Y2 V1 V2 V3 ΣV+ ΣV- Y1 Y2 V1 V2 V3 ΣV+ ΣV- Vmàx + Vmàx - Vmàx (+) +IM Vmàx (-) +IM
0 0.000 1.000 1.000 0.000 110.000 0.000 0.000 110.000 0.000 0.960 1.000 105.600 110.000 0.000 215.600 0.000 215.600 0.000 286.748 0.000
1 -0.033 0.967 0.967 0.000 106.333 0.000 -3.667 106.333 -3.667 0.927 0.967 101.933 106.333 -3.667 208.267 -3.667 208.267 -3.667 276.995 -4.877
2 -0.067 0.933 0.933 -0.027 102.667 -2.933 -7.333 102.667 -10.267 0.893 0.933 98.267 102.667 -7.333 200.933 -7.333 200.933 -10.267 267.241 -13.655
3 -0.100 0.900 0.900 -0.060 99.000 -6.600 -11.000 99.000 -17.600 0.860 0.900 94.600 99.000 -11.000 193.600 -11.000 193.600 -17.600 257.488 -23.408
4 -0.133 0.867 0.867 -0.093 95.333 -10.267 -14.667 95.333 -24.933 0.827 0.867 90.933 95.333 -14.667 186.267 -14.667 186.267 -24.933 247.735 -33.161
5 -0.167 0.833 0.833 -0.127 91.667 -13.933 -18.333 91.667 -32.267 0.793 0.833 87.267 91.667 -18.333 178.933 -18.333 178.933 -32.267 237.981 -42.915
6 -0.200 0.800 0.800 -0.160 88.000 -17.600 -22.000 88.000 -39.600 0.760 0.800 83.600 88.000 -22.000 171.600 -22.000 171.600 -39.600 228.228 -52.668
7 -0.233 0.767 0.767 -0.193 84.333 -21.267 -25.667 84.333 -46.933 0.727 0.767 79.933 84.333 -25.667 164.267 -25.667 164.267 -46.933 218.475 -62.421
8 -0.267 0.733 0.733 -0.227 80.667 -24.933 -29.333 80.667 -54.267 0.693 0.733 76.267 80.667 -29.333 156.933 -29.333 156.933 -54.267 208.721 -72.175
9 -0.300 0.700 0.700 -0.260 77.000 -28.600 -33.000 77.000 -61.600 0.660 0.700 72.600 77.000 -33.000 149.600 -33.000 149.600 -61.600 198.968 -81.928
10 -0.333 0.667 0.667 -0.293 73.333 -32.267 -36.667 73.333 -68.933 0.627 0.667 68.933 73.333 -36.667 142.267 -36.667 142.267 -68.933 189.215 -91.681
11 -0.367 0.633 0.633 -0.327 69.667 -35.933 -40.333 69.667 -76.267 0.593 0.633 65.267 69.667 -40.333 134.933 -40.333 134.933 -76.267 179.461 -101.435
12 -0.400 0.600 0.600 -0.360 66.000 -39.600 -44.000 66.000 -83.600 0.560 0.600 61.600 66.000 -44.000 127.600 -44.000 127.600 -83.600 169.708 -111.188
13 -0.433 0.567 0.567 -0.393 62.333 -43.267 -47.667 62.333 -90.933 0.527 0.567 57.933 62.333 -47.667 120.267 -47.667 120.267 -90.933 159.955 -120.941
14 -0.467 0.533 0.533 -0.427 58.667 -46.933 -51.333 58.667 -98.267 0.493 0.533 54.267 58.667 -51.333 112.933 -51.333 112.933 -98.267 150.201 -130.695
15 -0.500 0.500 0.500 -0.460 55.000 -50.600 -55.000 55.000 -105.600 0.460 0.500 50.600 55.000 -55.000 105.600 -55.000 105.600 -105.600 140.448 -140.448
16 -0.533 0.467 0.467 -0.493 51.333 -54.267 -58.667 51.333 -112.933 0.427 0.467 46.933 51.333 -58.667 98.267 -58.667 98.267 -112.933 130.695 -150.201
17 -0.567 0.433 0.433 -0.527 47.667 -57.933 -62.333 47.667 -120.267 0.393 0.433 43.267 47.667 -62.333 90.933 -62.333 90.933 -120.267 120.941 -159.955
18 -0.600 0.400 0.400 -0.560 44.000 -61.600 -66.000 44.000 -127.600 0.360 0.400 39.600 44.000 -66.000 83.600 -66.000 83.600 -127.600 111.188 -169.708
19 -0.633 0.367 0.367 -0.593 40.333 -65.267 -69.667 40.333 -134.933 0.327 0.367 35.933 40.333 -69.667 76.267 -69.667 76.267 -134.933 101.435 -179.461
20 -0.667 0.333 0.333 -0.627 36.667 -68.933 -73.333 36.667 -142.267 0.293 0.333 32.267 36.667 -73.333 68.933 -73.333 68.933 -142.267 91.681 -189.215
21 -0.700 0.300 0.300 -0.660 33.000 -72.600 -77.000 33.000 -149.600 0.260 0.300 28.600 33.000 -77.000 61.600 -77.000 61.600 -149.600 81.928 -198.968
22 -0.733 0.267 0.267 -0.693 29.333 -76.267 -80.667 29.333 -156.933 0.227 0.267 24.933 29.333 -80.667 54.267 -80.667 54.267 -156.933 72.175 -208.721
23 -0.767 0.233 0.233 -0.727 25.667 -79.933 -84.333 25.667 -164.267 0.193 0.233 21.267 25.667 -84.333 46.933 -84.333 46.933 -164.267 62.421 -218.475
24 -0.800 0.200 0.200 -0.760 22.000 -83.600 -88.000 22.000 -171.600 0.160 0.200 17.600 22.000 -88.000 39.600 -88.000 39.600 -171.600 52.668 -228.228
25 -0.833 0.167 0.167 -0.793 18.333 -87.267 -91.667 18.333 -178.933 0.127 0.167 13.933 18.333 -91.667 32.267 -91.667 32.267 -178.933 42.915 -237.981
26 -0.867 0.133 0.133 -0.827 14.667 -90.933 -95.333 14.667 -186.267 0.093 0.133 10.267 14.667 -95.333 24.933 -95.333 24.933 -186.267 33.161 -247.735
27 -0.900 0.100 0.100 -0.860 11.000 -94.600 -99.000 11.000 -193.600 0.060 0.100 6.600 11.000 -99.000 17.600 -99.000 17.600 -193.600 23.408 -257.488
28 -0.933 0.067 0.067 -0.893 7.333 -98.267 -102.667 7.333 -200.933 0.027 0.067 2.933 7.333 -102.667 10.267 -102.667 10.267 -200.933 13.655 -267.241
29 -0.967 0.033 0.033 -0.927 3.667 -101.933 -106.333 3.667 -208.267 0.000 0.033 0.000 3.667 -106.333 3.667 -106.333 3.667 -208.267 4.877 -276.995
30 -1.000 0.000 0.000 -0.960 0.000 -105.600 -110.000 0.000 -215.600 0.000 0.000 0.000 0.000 -110.000 0.000 -110.000 0.000 -215.600 0.000 -286.748
CORTANTE
ORDENADAS CORTANTE ORDENADAS CORTANTE
CALCULO DE CORTANTE DE TAMDEN

-250.000
-200.000
-150.000
-100.000
-50.000
0.000
50.000
100.000
150.000
200.000
250.000
0 5 10 15 20 25 30
Cortante(KN)
CORTANTE DE TAMDEN
-400.000
-300.000
-200.000
-100.000
0.000
100.000
200.000
300.000
400.000
0 5 10 15 20 25 30
Cortante(KN)
CORTANTE DE TAMDEN + IM (%)

x1 M(x1) Y1 Y2 M1 M2 ΣM1 Y1 Y2 M1 M2 ΣM2 Mmàx X1
0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
1 1.0 1.0 0.0 106.3 0.0 106.3 0.9 1.0 101.9 106.3 208.3 208.3
2 1.9 1.9 0.7 205.3 82.1 287.5 1.8 1.9 196.5 205.3 401.9 401.9
3 2.7 2.7 1.6 297.0 178.2 475.2 2.6 2.7 283.8 297.0 580.8 580.8
4 3.5 3.5 2.4 381.3 266.9 648.3 3.3 3.5 363.7 381.3 745.1 745.1
5 4.2 4.2 3.2 458.3 348.3 806.7 4.0 4.2 436.3 458.3 894.7 894.7
6 4.8 4.8 3.8 528.0 422.4 950.4 4.6 4.8 501.6 528.0 1029.6 1029.6
7 5.4 5.4 4.4 590.3 489.1 1079.5 5.1 5.4 559.5 590.3 1149.9 1149.9
8 5.9 5.9 5.0 645.3 548.5 1193.9 5.5 5.9 610.1 645.3 1255.5 1255.5
9 6.3 6.3 5.5 693.0 600.6 1293.6 5.9 6.3 653.4 693.0 1346.4 1346.4
10 6.7 6.7 5.9 733.3 645.3 1378.7 6.3 6.7 689.3 733.3 1422.7 1422.7
11 7.0 7.0 6.2 766.3 682.7 1449.1 6.5 7.0 717.9 766.3 1484.3 1484.3
12 7.2 7.2 6.5 792.0 712.8 1504.8 6.7 7.2 739.2 792.0 1531.2 1531.2
13 7.4 7.4 6.7 810.3 735.5 1545.9 6.8 7.4 753.1 810.3 1563.5 1563.5
14 7.5 7.5 6.8 821.3 750.9 1572.3 6.9 7.5 759.7 821.3 1581.1 1581.1
15 7.5 7.5 6.9 825.0 759.0 1584.0 6.9 7.5 759.0 825.0 1584.0 1584.0
16 7.5 7.5 6.9 821.3 759.7 1581.1 6.8 7.5 750.9 821.3 1572.3 1581.1
17 7.4 7.4 6.8 810.3 753.1 1563.5 6.7 7.4 735.5 810.3 1545.9 1563.5
18 7.2 7.2 6.7 792.0 739.2 1531.2 6.5 7.2 712.8 792.0 1504.8 1531.2
19 7.0 7.0 6.5 766.3 717.9 1484.3 6.2 7.0 682.7 766.3 1449.1 1484.3
20 6.7 6.7 6.3 733.3 689.3 1422.7 5.9 6.7 645.3 733.3 1378.7 1422.7
21 6.3 6.3 5.9 693.0 653.4 1346.4 5.5 6.3 600.6 693.0 1293.6 1346.4
22 5.9 5.9 5.5 645.3 610.1 1255.5 5.0 5.9 548.5 645.3 1193.9 1255.5
23 5.4 5.4 5.1 590.3 559.5 1149.9 4.4 5.4 489.1 590.3 1079.5 1149.9
24 4.8 4.8 4.6 528.0 501.6 1029.6 3.8 4.8 422.4 528.0 950.4 1029.6
25 4.2 4.2 4.0 458.3 436.3 894.7 3.2 4.2 348.3 458.3 806.7 894.7
26 3.5 3.5 3.3 381.3 363.7 745.1 2.4 3.5 266.9 381.3 648.3 745.1
27 2.7 2.7 2.6 297.0 283.8 580.8 1.6 2.7 178.2 297.0 475.2 580.8
28 1.9 1.9 1.8 205.3 196.5 401.9 0.7 1.9 82.1 205.3 287.5 401.9
29 1.0 1.0 0.9 106.3 101.9 208.3 0.0 1.0 0.0 106.3 106.3 208.3
30 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
CALCULOS DE MOMENTOS DE TAMDEN
ORDENADAS MOMENTOS ORDENADAS MOMENTOS

0.0
200.0
400.0
600.0
800.0
1000.0
1200.0
1400.0
1600.0
1800.0
0 5 10 15 20 25 30
Momento(KN*m)
DIAGRAMA DE MOMENTO DE TAMDEN

CARGA DE CARRIL
x [m] Shear
Force [kN]
0 139.5
1 130.2
2 120.9
3 111.6
4 102.3
5 93
6 83.7
7 74.4
8 65.1
9 55.8
10 46.5
11 37.2
12 27.9
13 18.6
14 9.3
15 0
16 -9.3
17 -18.6
18 -27.9
19 -37.2
20 -46.5
21 -55.8
22 -65.1
23 -74.4
24 -83.7
25 -93
26 -102.3
27 -111.6
28 -120.9
29 -130.2
30 -139.5

CARGA DE CARRIL
Diagrama de ;Momento
x [m] Bending
Moment
[kNm]
0 0
1 134.8
2 260.4
3 376.6
4 483.6
5 581.3
6 669.6
7 748.6
8 818.4
9 878.8
10 930
11 971.8
12 1004.4
13 1027.7
14 1041.6
15 1046.3
16 1041.6
17 1027.6
18 1004.4
19 971.8
20 930
21 878.8
22 818.4
23 748.7
24 669.6
25 581.2
26 483.6
27 376.6
28 260.4
29 134.8
30 0

x1 V-(x1) V+(x1) A 1 A 2 A T V(x1)
0 0.000 1.000 0.000 15.000 15.0 139.5
1 -0.033 0.967 -0.017 14.017 14.0 130.2
2 -0.067 0.933 -0.067 13.067 13.0 120.9
3 -0.100 0.900 -0.150 12.150 12.0 111.6
4 -0.133 0.867 -0.267 11.267 11.0 102.3
5 -0.167 0.833 -0.417 10.417 10.0 93.0
6 -0.200 0.800 -0.600 9.600 9.0 83.7
7 -0.233 0.767 -0.817 8.817 8.0 74.4
8 -0.267 0.733 -1.067 8.067 7.0 65.1
9 -0.300 0.700 -1.350 7.350 6.0 55.8
10 -0.333 0.667 -1.667 6.667 5.0 46.5
11 -0.367 0.633 -2.017 6.017 4.0 37.2
12 -0.400 0.600 -2.400 5.400 3.0 27.9
13 -0.433 0.567 -2.817 4.817 2.0 18.6
14 -0.467 0.533 -3.267 4.267 1.0 9.3
15 -0.500 0.500 -3.750 3.750 0.0 0.0
16 -0.533 0.467 -4.267 3.267 -1.0 -9.3
17 -0.567 0.433 -4.817 2.817 -2.0 -18.6
18 -0.600 0.400 -5.400 2.400 -3.0 -27.9
19 -0.633 0.367 -6.017 2.017 -4.0 -37.2
20 -0.667 0.333 -6.667 1.667 -5.0 -46.5
21 -0.700 0.300 -7.350 1.350 -6.0 -55.8
22 -0.733 0.267 -8.067 1.067 -7.0 -65.1
23 -0.767 0.233 -8.817 0.817 -8.0 -74.4
24 -0.800 0.200 -9.600 0.600 -9.0 -83.7
25 -0.833 0.167 -10.417 0.417 -10.0 -93.0
26 -0.867 0.133 -11.267 0.267 -11.0 -102.3
27 -0.900 0.100 -12.150 0.150 -12.0 -111.6
28 -0.933 0.067 -13.067 0.067 -13.0 -120.9
29 -0.967 0.033 -14.017 0.017 -14.0 -130.2
30 -1.000 0.000 -15.000 0.000 -15.0 -139.5
CALCULOS DE CORTANTES DE CARRIL DE DISEÑO

-200.0
-150.0
-100.0
-50.0
0.0
50.0
100.0
150.0
200.0
0 5 10 15 20 25 30
Cortante(KN)
CORTANTE DE CARRIL DE DISEÑO

x1 M(x1) Àrea Mmàx X1
0 0.0 0.0 0.0
1 1.0 14.5 134.9
2 1.9 28.0 260.4
3 2.7 40.5 376.7
4 3.5 52.0 483.6
5 4.2 62.5 581.3
6 4.8 72.0 669.6
7 5.4 80.5 748.7
8 5.9 88.0 818.4
9 6.3 94.5 878.9
10 6.7 100.0 930.0
11 7.0 104.5 971.9
12 7.2 108.0 1004.4
13 7.4 110.5 1027.7
14 7.5 112.0 1041.6
15 7.5 112.5 1046.3
16 7.5 112.0 1041.6
17 7.4 110.5 1027.7
18 7.2 108.0 1004.4
19 7.0 104.5 971.9
20 6.7 100.0 930.0
21 6.3 94.5 878.9
22 5.9 88.0 818.4
23 5.4 80.5 748.7
24 4.8 72.0 669.6
25 4.2 62.5 581.3
26 3.5 52.0 483.6
27 2.7 40.5 376.7
28 1.9 28.0 260.4
29 1.0 14.5 134.9
30 0.0 0.0 0.0
CALCULOS DE MOMENTOS DE CARRIL DE DISEÑO

0.0
200.0
400.0
600.0
800.0
1000.0
1200.0
0 5 10 15 20 25 30
Momento(KN*m)
DIAGRAMA DE MOMENTOS DE CARRIL DE DISEÑO

CARRIL DE DISEÑO + CAMIÓN DE DISEÑO

CARGA DE CAMIO + CARRIL
Diagrama de cortante
Max. Min.
0 530.8 139.5
1 507.1 123.8
2 483.3 108
3 459.6 92.3
4 435.9 76.6
5 412.2 56.4
6 388.5 34.2
7 364.8 12
8 341.1 -10.1
9 317.4 -32.9
10 293.7 -56.6
11 270 -80.3
12 246.3 -104
13 222.6 -127.7
14 198.8 -151.4
15 175.1 -175.1
16 151.4 -198.8
17 127.7 -222.6
18 104 -246.3
19 80.3 -270
20 56.6 -293.7
21 32.9 -317.4
22 10.1 -341.1
23 -12 -364.8
24 -34.2 -388.5
25 -56.4 -412.2
26 -76.6 -435.9
27 -92.3 -459.6
28 -108 -483.3
29 -123.8 -507.1
30 -139.5 -530.8

CARGA DE CAMIO + CARRIL
Diagrama de Momento
[kNm]
Max. Min.
0 0 0
1 511.6 134.8
2 985.2 260.4
3 1420.7 376.6
4 1818 483.6
5 2177.3 581.2
6 2498.4 669.6
7 2781.4 748.6
8 3026.4 818.4
9 3233.1 878.8
10 3402.4 930
11 3552.3 971.8
12 3664.7 1004.4
13 3739 1027.6
14 3775.3 1041.6
15 3774.9 1046.2
16 3775.3 1041.6
17 3739 1027.6
18 3664.7 1004.4
19 3552.3 971.8
20 3402.4 930
21 3233.1 878.8
22 3026.4 818.4
23 2781.4 748.6
24 2498.4 669.6
25 2177.3 581.2
26 1818 483.6
27 1420.7 376.6
28 985.2 260.4
29 511.6 134.8
30 0 0

x1 HL-93 (+) HL-93 (-) CARRIL DE DISEÑO ENVOLVENTE V(+) ENVOLVENTE (V-)
0 391.264 0.000 139.500 530.76 139.50
1 376.856 -6.428 130.200 507.06 123.77
2 362.447 -12.857 120.900 483.35 108.04
3 348.039 -19.285 111.600 459.64 92.32
4 333.631 -25.713 102.300 435.93 76.59
5 319.222 -36.642 93.000 412.22 56.36
6 304.814 -49.498 83.700 388.51 34.20
7 290.406 -62.355 74.400 364.81 12.05
8 275.997 -75.212 65.100 341.10 -10.11
9 261.589 -88.689 55.800 317.39 -32.89
10 247.181 -103.097 46.500 293.68 -56.60
11 232.772 -117.506 37.200 269.97 -80.31
12 218.364 -131.914 27.900 246.26 -104.01
13 203.956 -146.322 18.600 222.56 -127.72
14 189.547 -160.731 9.300 198.85 -151.43
15 175.139 -175.139 0.000 175.14 -175.14
16 160.731 -189.547 -9.300 151.43 -198.85
17 146.322 -203.956 -18.600 127.72 -222.56
18 131.914 -218.364 -27.900 104.01 -246.26
19 117.506 -232.772 -37.200 80.31 -269.97
20 103.097 -247.181 -46.500 56.60 -293.68
21 88.689 -261.589 -55.800 32.89 -317.39
22 75.212 -275.997 -65.100 10.11 -341.10
23 62.355 -290.406 -74.400 -12.05 -364.81
24 49.498 -304.814 -83.700 -34.20 -388.51
25 36.642 -319.222 -93.000 -56.36 -412.22
26 25.713 -333.631 -102.300 -76.59 -435.93
27 19.285 -348.039 -111.600 -92.32 -459.64
28 12.857 -362.447 -120.900 -108.04 -483.35
29 6.428 -376.856 -130.200 -123.77 -507.06
30 0.000 -391.264 -139.500 -139.50 -530.76
CORTANTE

-600.00
-400.00
-200.00
0.00
200.00
400.00
600.00
0 5 10 15 20 25 30
Cortante(KN)
ENVOLVENTE DE CORTANTE(1+IM) HL-93 + CARRIL

x1 HL-93 AMPLIFICADO POR IMPACTO CARRIL DE DISEÑO ENVOLVENTE
0 0.00 0.00 0.00 0.00
1 283.35 376.86 134.85 511.71
2 545.03 724.89 260.40 985.29
3 785.05 1044.12 376.65 1420.77
4 1003.40 1334.52 483.60 1818.12
5 1200.08 1596.11 581.25 2177.36
6 1375.10 1828.88 669.60 2498.48
7 1528.45 2032.84 748.65 2781.49
8 1660.13 2207.98 818.40 3026.38
9 1770.15 2354.30 878.85 3233.15
10 1858.50 2471.81 930.00 3401.81
11 1940.23 2580.51 971.85 3552.36
12 2000.30 2660.40 1004.40 3664.80
13 2038.70 2711.47 1027.65 3739.12
14 2055.43 2733.73 1041.60 3775.33
15 2050.50 2727.17 1046.25 3773.42
16 2055.43 2733.73 1041.60 3775.33
17 2038.70 2711.47 1027.65 3739.12
18 2000.30 2660.40 1004.40 3664.80
19 1940.23 2580.51 971.85 3552.36
20 1858.50 2471.81 930.00 3401.81
21 1770.15 2354.30 878.85 3233.15
22 1660.13 2207.98 818.40 3026.38
23 1528.45 2032.84 748.65 2781.49
24 1375.10 1828.88 669.60 2498.48
25 1200.08 1596.11 581.25 2177.36
26 1003.40 1334.52 483.60 1818.12
27 785.05 1044.12 376.65 1420.77
28 545.03 724.89 260.40 985.29
29 283.35 376.86 134.85 511.71
30 0.00 0.00 0.00 0.00
MOMENTOS

0.00
500.00
1000.00
1500.00
2000.00
2500.00
3000.00
3500.00
4000.00
0 5 10 15 20 25 30 35
Momento(KN*m)
ENVOLVENTE DE MOMENTO

CARRIL DE DISEÑO + TÁNDEM DE DISEÑO

CARGA DE TAMDEM + CARRIL
Max. Min.
0 426.2 139.5
1 407.2 125.3
2 388.1 107.2
3 369.1 88.2
4 350 69.1
5 331 50.1
6 311.9 31
7 292.9 12
8 273.8 -7.1
9 254.8 -26.1
10 235.7 -45.2
11 216.7 -64.2
12 197.6 -83.3
13 178.6 -102.3
14 159.5 -121.4
15 140.4 -140.4
16 121.4 -159.5
17 102.3 -178.6
18 83.3 -197.6
19 64.2 -216.7
20 45.2 -235.7
21 26.1 -254.8
22 7.1 -273.8
23 -12 -292.9
24 -31 -311.9
25 -50.1 -331
26 -69.1 -350
27 -88.2 -369.1
28 -107.2 -388.1
29 -125.3 -407.2
30 -139.5 -426.2

CARGA DE TAMDEM + CARRIL
Diagrama de Momento
x [m] Bending
Momen
t [kNm]
Max. Min.
0 0 0
1 411.8 134.8
2 794.8 260.4
3 1149.1 376.6
4 1474.5 483.6
5 1771.1 581.2
6 2038.9 669.6
7 2277.9 748.6
8 2488.2 818.4
9 2669.5 878.8
10 2822.1 930
11 2945.9 971.8
12 3040.8 1004.4
13 3107 1027.6
14 3144.4 1041.6
15 3153.3 1046.2
16 3144.4 1041.6
17 3107 1027.6
18 3040.8 1004.4
19 2945.9 971.8
20 2822.1 930
21 2669.5 878.8
22 2488.2 818.4
23 2277.9 748.6
24 2038.9 669.6
25 1771.1 581.2
26 1474.5 483.6
27 1149.1 376.6
28 794.8 260.4
29 411.8 134.8
30 0 0

x1 TAMDEN V(+) TAMDEN V(-) CARRIL DE DISEÑO ENVOLVENTE V(+) ENVOLVENTE (V-)
0 286.748 0.000 139.500 426.25 139.50
1 276.995 -4.877 130.200 407.19 125.32
2 267.241 -13.655 120.900 388.14 107.25
3 257.488 -23.408 111.600 369.09 88.19
4 247.735 -33.161 102.300 350.03 69.14
5 237.981 -42.915 93.000 330.98 50.09
6 228.228 -52.668 83.700 311.93 31.03
7 218.475 -62.421 74.400 292.87 11.98
8 208.721 -72.175 65.100 273.82 -7.07
9 198.968 -81.928 55.800 254.77 -26.13
10 189.215 -91.681 46.500 235.71 -45.18
11 179.461 -101.435 37.200 216.66 -64.23
12 169.708 -111.188 27.900 197.61 -83.29
13 159.955 -120.941 18.600 178.55 -102.34
14 150.201 -130.695 9.300 159.50 -121.39
15 140.448 -140.448 0.000 140.45 -140.45
16 130.695 -150.201 -9.300 121.39 -159.50
17 120.941 -159.955 -18.600 102.34 -178.55
18 111.188 -169.708 -27.900 83.29 -197.61
19 101.435 -179.461 -37.200 64.23 -216.66
20 91.681 -189.215 -46.500 45.18 -235.71
21 81.928 -198.968 -55.800 26.13 -254.77
22 72.175 -208.721 -65.100 7.07 -273.82
23 62.421 -218.475 -74.400 -11.98 -292.87
24 52.668 -228.228 -83.700 -31.03 -311.93
25 42.915 -237.981 -93.000 -50.09 -330.98
26 33.161 -247.735 -102.300 -69.14 -350.03
27 23.408 -257.488 -111.600 -88.19 -369.09
28 13.655 -267.241 -120.900 -107.25 -388.14
29 4.877 -276.995 -130.200 -125.32 -407.19
30 0.000 -286.748 -139.500 -139.50 -426.25
CORTANTE

-500.00
-400.00
-300.00
-200.00
-100.00
0.00
100.00
200.00
300.00
400.00
500.00
0 5 10 15 20 25 30
Cortante(KN)
ENVOLVENTE DE CORTANTE(1+IM) TAMDEN + CARRIL

x1 TAMDEN AMPLIFICADO POR IMPACTO CARRIL DE DISEÑO ENVOLVENTE
0 0.00 0.00 0.00 0.00
1 208.27 276.99 134.85 411.84
2 401.87 534.48 260.40 794.88
3 580.80 772.46 376.65 1149.11
4 745.07 990.94 483.60 1474.54
5 894.67 1189.91 581.25 1771.16
6 1029.60 1369.37 669.60 2038.97
7 1149.87 1529.32 748.65 2277.97
8 1255.47 1669.77 818.40 2488.17
9 1346.40 1790.71 878.85 2669.56
10 1422.67 1892.15 930.00 2822.15
11 1484.27 1974.07 971.85 2945.92
12 1531.20 2036.50 1004.40 3040.90
13 1563.47 2079.41 1027.65 3107.06
14 1581.07 2102.82 1041.60 3144.42
15 1584.00 2106.72 1046.25 3152.97
16 1581.07 2102.82 1041.60 3144.42
17 1563.47 2079.41 1027.65 3107.06
18 1531.20 2036.50 1004.40 3040.90
19 1484.27 1974.07 971.85 2945.92
20 1422.67 1892.15 930.00 2822.15
21 1346.40 1790.71 878.85 2669.56
22 1255.47 1669.77 818.40 2488.17
23 1149.87 1529.32 748.65 2277.97
24 1029.60 1369.37 669.60 2038.97
25 894.67 1189.91 581.25 1771.16
26 745.07 990.94 483.60 1474.54
27 580.80 772.46 376.65 1149.11
28 401.87 534.48 260.40 794.88
29 208.27 276.99 134.85 411.84
30 0.00 0.00 0.00 0.00
MOMENTOS

0.00
500.00
1000.00
1500.00
2000.00
2500.00
3000.00
3500.00
0 5 10 15 20 25 30
Momento(KN*m)
ENVOLVENTE DE MOMENTO

PROCEDIMIENTO PARA EL ANÁLISIS ESTRUCTURAL EN FTOOL
1. Al abrir el programa se debe configurar para el sistema de unidades que vayamos a utilizar.
2. Dibujar los elementos que vayamos a analizar incluyendo los tipos de apoyo que tengan.
3. Dar propiedades al material que utilizaremos en los elementos.
4. Introducir las características geométricas de la sección transversal del elemento.
5. Definir la carga muerta, en este caso la del carril de diseño.
6. Definir las Loads train, para esta ocasión son las del camión de diseño y las del tándem de diseño.
7. Proceder a correr el programa, para que determine las líneas de influencia en cada una de las
cargas y de la combinación de cargas.
8. Determinar la envolvente para cada uno de los diagramas.
9. Imprimir diagramas y tablas de datos.

CONCLUSIÓN
Luego de realizar la creación de una hoja electrónica en el programa MICROSOFT EXCEL
para lograr obtener los valores de momentos y cortantes, y con estos graficar y a la misma
vez lograr las envolventes con las combinaciones de cargas dadas, y compararlos con los
resultados al usar el programa F TOOLS se observa una muy mínima diferencia casi del
99.00 % idénticos los resultados, estos nos hace plantear una conclusión de que la
programación interna del proceso en F TOOLS se hace con los mismos principios con lo
cual se programó el Excel.

CALCULO ESTRUCTURAL DE CARGAS EN UN PUENTE MEDIANTE LINEAS DE INLUENCIA

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