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) 30.00Δx (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

x10 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 01 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 02 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 03 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 04 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 05 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 06 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 07 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 08 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 09 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 011 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 012 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 0.4 013 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 014 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 015 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 0.5 016 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 017 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 018 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 0.6 019 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 020 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 021 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 0.7 022 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 023 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 024 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 0.8 025 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 026 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 027 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 0.9 028 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 029 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 030 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

DatosVALORES DE MOMENTO EN CARGA UNITARIA MOVIL

0

1

2

3

4

5

6

7

8

0 5 10 15 20 25 30

Mom

ento

Uni

tario

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 0.0001 -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 -4.8332 -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 -9.6673 -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 -14.5004 -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 -19.3335 -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 -27.5506 -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 -37.2177 -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 -46.8838 -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 -56.5509 -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 -75.88311 -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 -85.55012 -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 -95.21713 -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 -104.88314 -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 -114.55015 -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 -124.21716 -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 -133.88317 -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 -143.55018 -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 -153.43319 -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 -164.26720 -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 -175.10021 -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 -185.93322 -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 -196.76723 -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 -207.60024 -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 -218.43325 -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 -229.26726 -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 -240.10027 -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 -250.93328 -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 -261.76729 -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 -272.60030 -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. 3ORDENADAS 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

Cort

ante

(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 X10 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 0.01 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 23.8 119.4 140.2 283.4 283.42 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 45.3 229.1 270.7 545.0 545.03 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 64.4 329.2 391.5 785.1 785.14 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 1003.45 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 1200.16 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 1375.17 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 1528.58 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 1660.19 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 1858.511 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 1925.212 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 1970.213 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 1993.614 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 2023.915 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 2050.516 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 2055.417 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 2038.718 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 2000.319 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 1940.220 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 1858.521 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 1755.122 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 1630.023 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 1483.324 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 1314.925 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 1124.826 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 0.0 502.7 502.7 922.227 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 0.0 391.5 391.5 720.728 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 0.0 270.7 270.7 499.829 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 0.0 140.2 140.2 259.630 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

ORDENADASCASO No. 1 CASO No. 2

MOMENTOS ORDENADAS MOMENTOSCASO 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

Mom

ento

(KN

*m)

POSICIÓN DE LINEA DE INFLUENCÍA (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 0.0001 -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 -4.8332 -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 -9.6673 -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 -14.5004 -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 -19.3335 -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 -27.5506 -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 -37.2177 -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 -46.8838 -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 -56.5509 -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 -77.51711 -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 -88.35012 -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 -99.18313 -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 -110.01714 -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 -120.85015 -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 -131.68316 -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 -142.51717 -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 -153.35018 -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 -164.18319 -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 -175.01720 -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 -185.85021 -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 -196.68322 -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 -207.51723 -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 -218.35024 -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 -229.18325 -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 -240.01726 -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 -250.85027 -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 -261.68328 -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 -272.51729 -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 -283.35030 -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

CORTANTECASO No. 1 CASO No. 2 CASO No. 3

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

Cort

ante

(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 X10 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 0.01 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 0.0 140.2 140.2 259.62 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 0.0 270.7 270.7 499.83 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 0.0 391.5 391.5 720.74 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 0.0 502.7 502.7 922.25 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 1124.86 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 1314.97 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 1483.38 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 1630.09 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 1858.511 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 1940.212 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 2000.313 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 2038.714 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 2055.415 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 2050.516 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 2023.917 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 1993.618 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 1970.219 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 1925.220 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 1858.521 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 1770.222 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 1660.123 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 1528.524 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 1375.125 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 1200.126 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 1003.427 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 64.4 329.2 391.5 785.1 785.128 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 45.3 229.1 270.7 545.0 545.029 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 23.8 119.4 140.2 283.4 283.430 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

CASO No. 1 CASO No. 2 CASO No. 3ORDENADAS MOMENTOS ORDENADAS MOMENTOS ORDENADAS

0.0

500.0

1000.0

1500.0

2000.0

2500.0

0 5 10 15 20 25 30

Mom

ento

(KN

*m)

POSICIÓN DE LINEA DE INFLUENCÍA (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 0.0001 283.350 -4.833 259.550 -4.833 283.350 -4.833 376.856 -6.4282 272.517 -9.667 249.883 -9.667 272.517 -9.667 362.447 -12.8573 261.683 -14.500 240.217 -14.500 261.683 -14.500 348.039 -19.2854 250.850 -19.333 230.550 -19.333 250.850 -19.333 333.631 -25.7135 240.017 -27.550 220.883 -27.550 240.017 -27.550 319.222 -36.6426 229.183 -37.217 211.217 -37.217 229.183 -37.217 304.814 -49.4987 218.350 -46.883 201.550 -46.883 218.350 -46.883 290.406 -62.3558 207.517 -56.550 191.883 -56.550 207.517 -56.550 275.997 -75.2129 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 -103.09711 175.017 -85.550 162.883 -88.350 175.017 -88.350 232.772 -117.50612 164.183 -95.217 153.217 -99.183 164.183 -99.183 218.364 -131.91413 153.350 -104.883 143.550 -110.017 153.350 -110.017 203.956 -146.32214 142.517 -114.550 133.883 -120.850 142.517 -120.850 189.547 -160.73115 131.683 -124.217 124.217 -131.683 131.683 -131.683 175.139 -175.13916 120.850 -133.883 114.550 -142.517 120.850 -142.517 160.731 -189.54717 110.017 -143.550 104.883 -153.350 110.017 -153.350 146.322 -203.95618 99.183 -153.433 95.217 -164.183 99.183 -164.183 131.914 -218.36419 88.350 -164.267 85.550 -175.017 88.350 -175.017 117.506 -232.77220 77.517 -175.100 75.883 -185.850 77.517 -185.850 103.097 -247.18121 66.683 -185.933 66.217 -196.683 66.683 -196.683 88.689 -261.58922 56.550 -196.767 56.550 -207.517 56.550 -207.517 75.212 -275.99723 46.883 -207.600 46.883 -218.350 46.883 -218.350 62.355 -290.40624 37.217 -218.433 37.217 -229.183 37.217 -229.183 49.498 -304.81425 27.550 -229.267 27.550 -240.017 27.550 -240.017 36.642 -319.22226 19.333 -240.100 19.333 -250.850 19.333 -250.850 25.713 -333.63127 14.500 -250.933 14.500 -261.683 14.500 -261.683 19.285 -348.03928 9.667 -261.767 9.667 -272.517 9.667 -272.517 12.857 -362.44729 4.833 -272.600 4.833 -283.350 4.833 -283.350 6.428 -376.85630 0.000 -283.433 0.000 -294.183 0.000 -294.183 0.000 -391.264

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Posición en Viga (m)

DIAGRAMA DE CORTANTE CAMION HL-93 EN DOS DIRECCIONES

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Cort

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Posición en Viga (m)

DIAGRAMA DE CORTANTE CAMION HL-93 EN DOS DIRECCIONES + IM

x1 MX1 Derecha MX1 Izquierda MX1 - 2 DIR.0 0.00 0.00 0.001 283.35 259.55 283.352 545.03 499.77 545.033 785.05 720.65 785.054 1003.40 922.20 1003.405 1200.08 1124.83 1200.086 1375.10 1314.90 1375.107 1528.45 1483.30 1528.458 1660.13 1630.03 1660.139 1770.15 1755.10 1770.15

10 1858.50 1858.50 1858.5011 1925.18 1940.23 1940.2312 1970.20 2000.30 2000.3013 1993.55 2038.70 2038.7014 2023.90 2055.43 2055.4315 2050.50 2050.50 2050.5016 2055.43 2023.90 2055.4317 2038.70 1993.55 2038.7018 2000.30 1970.20 2000.3019 1940.23 1925.18 1940.2320 1858.50 1858.50 1858.5021 1755.10 1770.15 1770.1522 1630.03 1660.13 1660.1323 1483.30 1528.45 1528.4524 1314.90 1375.10 1375.1025 1124.83 1200.08 1200.0826 922.20 1003.40 1003.4027 720.65 785.05 785.0528 499.77 545.03 545.0329 259.55 283.35 283.3530 0.00 0.00 0.00

0.00

500.00

1000.00

1500.00

2000.00

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Mom

ento

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POSICIÓN DE LINEA DE INFLUENCÍA (m)

DIAGRAMA DE MOMENTO DE CAMIÓN HL-93 EN AMBAS DIRECCIONES

TÁNDEM DE DISEÑO

CARGA DE TAMDEM

Diagrama de Cortante

x [m] Shear Force [kN] 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

x [m] Bending Moment [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 (-) +IM0 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 0.0001 -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 -4.8772 -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 -13.6553 -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 -23.4084 -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 -33.1615 -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 -42.9156 -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 -52.6687 -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 -62.4218 -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 -72.1759 -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 -91.68111 -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 -101.43512 -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 -111.18813 -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 -120.94114 -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 -130.69515 -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 -140.44816 -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 -150.20117 -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 -159.95518 -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 -169.70819 -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 -179.46120 -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 -189.21521 -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 -198.96822 -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 -208.72123 -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 -218.47524 -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 -228.22825 -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 -237.98126 -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 -247.73527 -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 -257.48828 -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 -267.24129 -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 -276.99530 -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

CORTANTECASO No. 1 CASO No. 2

ORDENADAS CORTANTE ORDENADAS CORTANTE

CALCULO DE CORTANTE DE TAMDEN

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CORTANTE DE TAMDEN

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CORTANTE DE TAMDEN + IM (%)

x1 M(x1) Y1 Y2 M1 M2 ΣM1 Y1 Y2 M1 M2 ΣM2 Mmàx X10 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.01 1.0 1.0 0.0 106.3 0.0 106.3 0.9 1.0 101.9 106.3 208.3 208.32 1.9 1.9 0.7 205.3 82.1 287.5 1.8 1.9 196.5 205.3 401.9 401.93 2.7 2.7 1.6 297.0 178.2 475.2 2.6 2.7 283.8 297.0 580.8 580.84 3.5 3.5 2.4 381.3 266.9 648.3 3.3 3.5 363.7 381.3 745.1 745.15 4.2 4.2 3.2 458.3 348.3 806.7 4.0 4.2 436.3 458.3 894.7 894.76 4.8 4.8 3.8 528.0 422.4 950.4 4.6 4.8 501.6 528.0 1029.6 1029.67 5.4 5.4 4.4 590.3 489.1 1079.5 5.1 5.4 559.5 590.3 1149.9 1149.98 5.9 5.9 5.0 645.3 548.5 1193.9 5.5 5.9 610.1 645.3 1255.5 1255.59 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 1422.711 7.0 7.0 6.2 766.3 682.7 1449.1 6.5 7.0 717.9 766.3 1484.3 1484.312 7.2 7.2 6.5 792.0 712.8 1504.8 6.7 7.2 739.2 792.0 1531.2 1531.213 7.4 7.4 6.7 810.3 735.5 1545.9 6.8 7.4 753.1 810.3 1563.5 1563.514 7.5 7.5 6.8 821.3 750.9 1572.3 6.9 7.5 759.7 821.3 1581.1 1581.115 7.5 7.5 6.9 825.0 759.0 1584.0 6.9 7.5 759.0 825.0 1584.0 1584.016 7.5 7.5 6.9 821.3 759.7 1581.1 6.8 7.5 750.9 821.3 1572.3 1581.117 7.4 7.4 6.8 810.3 753.1 1563.5 6.7 7.4 735.5 810.3 1545.9 1563.518 7.2 7.2 6.7 792.0 739.2 1531.2 6.5 7.2 712.8 792.0 1504.8 1531.219 7.0 7.0 6.5 766.3 717.9 1484.3 6.2 7.0 682.7 766.3 1449.1 1484.320 6.7 6.7 6.3 733.3 689.3 1422.7 5.9 6.7 645.3 733.3 1378.7 1422.721 6.3 6.3 5.9 693.0 653.4 1346.4 5.5 6.3 600.6 693.0 1293.6 1346.422 5.9 5.9 5.5 645.3 610.1 1255.5 5.0 5.9 548.5 645.3 1193.9 1255.523 5.4 5.4 5.1 590.3 559.5 1149.9 4.4 5.4 489.1 590.3 1079.5 1149.924 4.8 4.8 4.6 528.0 501.6 1029.6 3.8 4.8 422.4 528.0 950.4 1029.625 4.2 4.2 4.0 458.3 436.3 894.7 3.2 4.2 348.3 458.3 806.7 894.726 3.5 3.5 3.3 381.3 363.7 745.1 2.4 3.5 266.9 381.3 648.3 745.127 2.7 2.7 2.6 297.0 283.8 580.8 1.6 2.7 178.2 297.0 475.2 580.828 1.9 1.9 1.8 205.3 196.5 401.9 0.7 1.9 82.1 205.3 287.5 401.929 1.0 1.0 0.9 106.3 101.9 208.3 0.0 1.0 0.0 106.3 106.3 208.330 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

CASO No. 1 CASO No. 2ORDENADAS 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

Mom

ento

(KN

*m)

POSICIÓN DE LINEA DE INFLUENCÍA (m)

DIAGRAMA DE MOMENTO DE TAMDEN

CARRIL DE DISEÑO

CARGA DE CARRIL

Diagrama de Cortante

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 15.0 139.51 -0.033 0.967 -0.017 14.017 14.0 130.22 -0.067 0.933 -0.067 13.067 13.0 120.93 -0.100 0.900 -0.150 12.150 12.0 111.64 -0.133 0.867 -0.267 11.267 11.0 102.35 -0.167 0.833 -0.417 10.417 10.0 93.06 -0.200 0.800 -0.600 9.600 9.0 83.77 -0.233 0.767 -0.817 8.817 8.0 74.48 -0.267 0.733 -1.067 8.067 7.0 65.19 -0.300 0.700 -1.350 7.350 6.0 55.8

10 -0.333 0.667 -1.667 6.667 5.0 46.511 -0.367 0.633 -2.017 6.017 4.0 37.212 -0.400 0.600 -2.400 5.400 3.0 27.913 -0.433 0.567 -2.817 4.817 2.0 18.614 -0.467 0.533 -3.267 4.267 1.0 9.315 -0.500 0.500 -3.750 3.750 0.0 0.016 -0.533 0.467 -4.267 3.267 -1.0 -9.317 -0.567 0.433 -4.817 2.817 -2.0 -18.618 -0.600 0.400 -5.400 2.400 -3.0 -27.919 -0.633 0.367 -6.017 2.017 -4.0 -37.220 -0.667 0.333 -6.667 1.667 -5.0 -46.521 -0.700 0.300 -7.350 1.350 -6.0 -55.822 -0.733 0.267 -8.067 1.067 -7.0 -65.123 -0.767 0.233 -8.817 0.817 -8.0 -74.424 -0.800 0.200 -9.600 0.600 -9.0 -83.725 -0.833 0.167 -10.417 0.417 -10.0 -93.026 -0.867 0.133 -11.267 0.267 -11.0 -102.327 -0.900 0.100 -12.150 0.150 -12.0 -111.628 -0.933 0.067 -13.067 0.067 -13.0 -120.929 -0.967 0.033 -14.017 0.017 -14.0 -130.230 -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

Cort

ante

(KN

)

Posición en Viga (m)

CORTANTE DE CARRIL DE DISEÑO

x1 M(x1) Àrea Mmàx X10 0.0 0.0 0.01 1.0 14.5 134.92 1.9 28.0 260.43 2.7 40.5 376.74 3.5 52.0 483.65 4.2 62.5 581.36 4.8 72.0 669.67 5.4 80.5 748.78 5.9 88.0 818.49 6.3 94.5 878.9

10 6.7 100.0 930.011 7.0 104.5 971.912 7.2 108.0 1004.413 7.4 110.5 1027.714 7.5 112.0 1041.615 7.5 112.5 1046.316 7.5 112.0 1041.617 7.4 110.5 1027.718 7.2 108.0 1004.419 7.0 104.5 971.920 6.7 100.0 930.021 6.3 94.5 878.922 5.9 88.0 818.423 5.4 80.5 748.724 4.8 72.0 669.625 4.2 62.5 581.326 3.5 52.0 483.627 2.7 40.5 376.728 1.9 28.0 260.429 1.0 14.5 134.930 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

Mom

ento

(KN

*m)

POSICIÓN DE LINEA DE INFLUENCÍA (m)

DIAGRAMA DE MOMENTOS DE CARRIL DE DISEÑO

CARRIL DE DISEÑO + CAMIÓN DE DISEÑO

CARGA DE CAMIO + CARRIL

Diagrama de cortante

x [m] Shear Force [kN] 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

x [m] Bending Moment [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 0.000 139.500 530.76 139.501 376.856 -6.428 130.200 507.06 123.772 362.447 -12.857 120.900 483.35 108.043 348.039 -19.285 111.600 459.64 92.324 333.631 -25.713 102.300 435.93 76.595 319.222 -36.642 93.000 412.22 56.366 304.814 -49.498 83.700 388.51 34.207 290.406 -62.355 74.400 364.81 12.058 275.997 -75.212 65.100 341.10 -10.119 261.589 -88.689 55.800 317.39 -32.89

10 247.181 -103.097 46.500 293.68 -56.6011 232.772 -117.506 37.200 269.97 -80.3112 218.364 -131.914 27.900 246.26 -104.0113 203.956 -146.322 18.600 222.56 -127.7214 189.547 -160.731 9.300 198.85 -151.4315 175.139 -175.139 0.000 175.14 -175.1416 160.731 -189.547 -9.300 151.43 -198.8517 146.322 -203.956 -18.600 127.72 -222.5618 131.914 -218.364 -27.900 104.01 -246.2619 117.506 -232.772 -37.200 80.31 -269.9720 103.097 -247.181 -46.500 56.60 -293.6821 88.689 -261.589 -55.800 32.89 -317.3922 75.212 -275.997 -65.100 10.11 -341.1023 62.355 -290.406 -74.400 -12.05 -364.8124 49.498 -304.814 -83.700 -34.20 -388.5125 36.642 -319.222 -93.000 -56.36 -412.2226 25.713 -333.631 -102.300 -76.59 -435.9327 19.285 -348.039 -111.600 -92.32 -459.6428 12.857 -362.447 -120.900 -108.04 -483.3529 6.428 -376.856 -130.200 -123.77 -507.0630 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

Cort

ante

(KN

)

Posición en Viga (m)

ENVOLVENTE DE CORTANTE(1+IM) HL-93 + CARRIL

x1 HL-93 AMPLIFICADO POR IMPACTO CARRIL DE DISEÑO ENVOLVENTE0 0.00 0.00 0.00 0.001 283.35 376.86 134.85 511.712 545.03 724.89 260.40 985.293 785.05 1044.12 376.65 1420.774 1003.40 1334.52 483.60 1818.125 1200.08 1596.11 581.25 2177.366 1375.10 1828.88 669.60 2498.487 1528.45 2032.84 748.65 2781.498 1660.13 2207.98 818.40 3026.389 1770.15 2354.30 878.85 3233.15

10 1858.50 2471.81 930.00 3401.8111 1940.23 2580.51 971.85 3552.3612 2000.30 2660.40 1004.40 3664.8013 2038.70 2711.47 1027.65 3739.1214 2055.43 2733.73 1041.60 3775.3315 2050.50 2727.17 1046.25 3773.4216 2055.43 2733.73 1041.60 3775.3317 2038.70 2711.47 1027.65 3739.1218 2000.30 2660.40 1004.40 3664.8019 1940.23 2580.51 971.85 3552.3620 1858.50 2471.81 930.00 3401.8121 1770.15 2354.30 878.85 3233.1522 1660.13 2207.98 818.40 3026.3823 1528.45 2032.84 748.65 2781.4924 1375.10 1828.88 669.60 2498.4825 1200.08 1596.11 581.25 2177.3626 1003.40 1334.52 483.60 1818.1227 785.05 1044.12 376.65 1420.7728 545.03 724.89 260.40 985.2929 283.35 376.86 134.85 511.7130 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

Mom

ento

(KN

*m)

POSICIÓN DE LINEA DE INFLUENCÍA (m)

ENVOLVENTE DE MOMENTO

CARRIL DE DISEÑO + TÁNDEM DE DISEÑO

CARGA DE TAMDEM + CARRIL

Diagrama de Cortante

x [m] Shear Force [kN] 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 Moment [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 0.000 139.500 426.25 139.501 276.995 -4.877 130.200 407.19 125.322 267.241 -13.655 120.900 388.14 107.253 257.488 -23.408 111.600 369.09 88.194 247.735 -33.161 102.300 350.03 69.145 237.981 -42.915 93.000 330.98 50.096 228.228 -52.668 83.700 311.93 31.037 218.475 -62.421 74.400 292.87 11.988 208.721 -72.175 65.100 273.82 -7.079 198.968 -81.928 55.800 254.77 -26.13

10 189.215 -91.681 46.500 235.71 -45.1811 179.461 -101.435 37.200 216.66 -64.2312 169.708 -111.188 27.900 197.61 -83.2913 159.955 -120.941 18.600 178.55 -102.3414 150.201 -130.695 9.300 159.50 -121.3915 140.448 -140.448 0.000 140.45 -140.4516 130.695 -150.201 -9.300 121.39 -159.5017 120.941 -159.955 -18.600 102.34 -178.5518 111.188 -169.708 -27.900 83.29 -197.6119 101.435 -179.461 -37.200 64.23 -216.6620 91.681 -189.215 -46.500 45.18 -235.7121 81.928 -198.968 -55.800 26.13 -254.7722 72.175 -208.721 -65.100 7.07 -273.8223 62.421 -218.475 -74.400 -11.98 -292.8724 52.668 -228.228 -83.700 -31.03 -311.9325 42.915 -237.981 -93.000 -50.09 -330.9826 33.161 -247.735 -102.300 -69.14 -350.0327 23.408 -257.488 -111.600 -88.19 -369.0928 13.655 -267.241 -120.900 -107.25 -388.1429 4.877 -276.995 -130.200 -125.32 -407.1930 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

Cort

ante

(KN

)

Posición en Viga (m)

ENVOLVENTE DE CORTANTE(1+IM) TAMDEN + CARRIL

x1 TAMDEN AMPLIFICADO POR IMPACTO CARRIL DE DISEÑO ENVOLVENTE0 0.00 0.00 0.00 0.001 208.27 276.99 134.85 411.842 401.87 534.48 260.40 794.883 580.80 772.46 376.65 1149.114 745.07 990.94 483.60 1474.545 894.67 1189.91 581.25 1771.166 1029.60 1369.37 669.60 2038.977 1149.87 1529.32 748.65 2277.978 1255.47 1669.77 818.40 2488.179 1346.40 1790.71 878.85 2669.56

10 1422.67 1892.15 930.00 2822.1511 1484.27 1974.07 971.85 2945.9212 1531.20 2036.50 1004.40 3040.9013 1563.47 2079.41 1027.65 3107.0614 1581.07 2102.82 1041.60 3144.4215 1584.00 2106.72 1046.25 3152.9716 1581.07 2102.82 1041.60 3144.4217 1563.47 2079.41 1027.65 3107.0618 1531.20 2036.50 1004.40 3040.9019 1484.27 1974.07 971.85 2945.9220 1422.67 1892.15 930.00 2822.1521 1346.40 1790.71 878.85 2669.5622 1255.47 1669.77 818.40 2488.1723 1149.87 1529.32 748.65 2277.9724 1029.60 1369.37 669.60 2038.9725 894.67 1189.91 581.25 1771.1626 745.07 990.94 483.60 1474.5427 580.80 772.46 376.65 1149.1128 401.87 534.48 260.40 794.8829 208.27 276.99 134.85 411.8430 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

Mom

ento

(KN

*m)

POSICIÓN DE LINEA DE INFLUENCÍA (m)

ENVOLVENTE DE MOMENTO

ANEXOS

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 lascargas 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.