topografia_proyecto_camino2

I) Alineamiento Horizontal 1) Línea a pelo de tierra 1) Calculo de la abertura del compás

E. A PI1 PI2 PI3 PI4 B

ΔX 313 288 190 270 22

ΔY 105 488 -54 -150 -556

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P.V. PI1 PI2 PI3 PI4 B

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X 164 477 765 955 1225 1247

Y 275 380 868 814 664 108

Distancia 330.14 566.64 197.52 308.86 556.43

RMC N 71° 27' E N 30° 33' E S 74° 08' E S 60° 56' E S 02° 16' E

3) Calculo de las curvas horizontales 3.1) Calculo de la primera curva horizontal

Curva Horizontales

Δ = Deflexion R = Radio St = Subtangente LC = Longitud de la curva M = Ordenada media E = Externa Gc = Grado de curvatura PI = Punto de Inflexión PC = Punto de comienzo PT = Punto de terminación

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2) Calculo de los elementos topográficos del eje

Δ

- 40° 54' + 75° 19' + 13° 12' + 58° 40'

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Se utilizo un radio de curvatura máxima de 30° Gc = 1145.92 = 1145.92 = 24.91° ≈ 24° R prop.

46

R definitivo = 1145.92 = 1145.92 = 47.75m Gc 24

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Datos: Cad. = PC + PI1 = 0 + 330.14 Radio propuesto = 46m Δ = 40° 54'

St = R Tg Δ/2 = 47.75 Tg 40°54'/2 = 17.81m LC = 20 Δ = 20(40°54') = 34.08m Gc 24

E = R (Sec Δ - 1) = 47.75 ( Sec 40°54' - 1) = 3.21m 2 2 M = R (1 - Cos Δ ) = 47.75 (1 - Cos 40°54') = 3.00m 2 2

PC = PI - St = 330.14 - 17.81 = 0 + 312.33 PT = PC + LC = 312.33 + 34.08 = 0 + 346.41

3.2) Calculo de la segunda curva horizontal Datos: Cad. = (Distancia del PI1 al PI2) - St R1 Cad. = 566.64 - 17.81 = 0 + 548.83 Radio propuesto = 39m Δ = 75°19'

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Se utilizo un radio de curvatura máxima de 30° Gc = 1145.92 = 1145.92 = 29.38° ≈ 29° R prop.

39 R definitivo = 1145.92 = 1145.92 = 39.51m Gc 29

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St = R Tg Δ/2 = 39.51 Tg 75°19'/2 = 30.49m LC = 20 (Δ) = 20(75°19') = 51.94m Gc 29

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E = R (Sec Δ - 1) = 39.51 (Sec 75°19' - 1) = 10.39m 2 2

M = R (1 - Cos Δ ) = 39.51 (1 - Cos 75°19') = 8.23m 2 2

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PC = PI - St = 548.83 - 30.49 = 0 + 518.34 PT = PC + LC = 518.34 + 51.94 = 0 + 570.28

3.3) Calculo de la tercera curva horizontal

Datos:

Cad. = (Distancia del PI2 al PI3) - St R2 Cad. = 197.52 - 30.49 = 0 + 167.03 Radio propuesto = 82m Δ = 13°12' Se utilizo un radio de curvatura máxima de 30° Gc = 1145.92 = 1145.92 = 13.97° ≈ 13° R prop.

82

R definitivo = 1145.92 = 1145.92 = 88.15m Gc 13 St = R Tg Δ/2 = 88.15 Tg 13°12'/2 = 10.19m LC = 20 (Δ) = 20(13°12') = 20.31m Gc 13 E = R (Sec Δ - 1) = 88.15 (Sec 13°12' - 1) = 0.58m 2 2

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M = R (1 - Cos Δ ) = 88.15 (1 - Cos 13°12') = 0.58m 2 2 PC = PI - St = 167.03 - 10.19 = 0 + 156.84 PT = PC + LC = 156.84 + 20.31 = 0 + 177.15

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3.4) Calculo de la cuarta curva horizontal Datos: Cad. = (Distancia del PI3 al PI4) - St R3 Cad. = 308.86 -10.19 = 0 + 298.67 Radio propuesto = 40m Δ = 58°40'

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Se utilizo un radio de curvatura máxima de 30° Gc = 1145.92 = 1145.92 = 28.64° ≈ 28° R prop.

40

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R definitivo = 1145.92 = 1145.92 = 40.92m Gc 28 St = R Tg Δ/2 = 40.92 Tg 58°40'/2 = 22.99m LC = 20 (Δ) = 20(58°40') = 41.90m Gc 28

E = R (Sec Δ - 1) = 40.92 (Sec 58°40' - 1) = 6.01m 2 2 M = R (1 - Cos Δ ) = 40.92 (1 - Cos 58°40') = 5.24m 2 2

PC = PI - St = 298.67 - 22.99 = 0 + 275.68 PT = PC + LC = 275.68 + 41.90 = 0 + 317.58

II)

Alineamiento Vertical

1) Perfil deducido del eje CADENAMIENTO COTA 0 + 000 2482 0 + 020 2478 0 + 040 2476 0 + 060 2473 0 + 080 2474 0 + 100 2474 0 + 120 2474 0 + 140 2472 0 + 160 2472 0 + 180 2470 0 + 200 2469 0 + 220 2468 0 + 240 2466 0 + 260 2465 0 + 280 2463 0 + 300 2462 0 + 320 2462 0 + 340 2462 0 + 360 2460 0 + 380 2458 0 + 400 2454 0 + 420 2458 0 + 440 2458 0 + 460 2451 0 + 480 2445 0 + 500 2446 0 + 520 2445 0 + 540 2442 0 + 560 2440 0 + 580 2438 0 + 600 2438 0 + 620 2439 0 + 640 2438 0 + 660 2435 0 + 680 2432 0 + 700 2432 0 + 720 2432 0 + 740 2430 0 + 760 2428 0 + 780 2426 0 + 800 2426

CADENAMIENTO 0 + 820 0 + 840 0 + 860 0 + 880 0 + 900 0 + 920 0 + 940 0 + 960 0 + 980 1 + 000 1 + 020 1 + 040 1 + 060 1 + 080 1 + 100 1 + 120 1 + 140 1 + 160 1 + 180 1 + 200 1 + 220 1 + 240 1 + 260 1 + 280 1 + 300 1 + 320 1 + 340 1 + 360 1 + 380 1 + 400 1 + 420 1 + 440 1 + 460 1 + 480 1 + 500 1 + 520 1 + 540 1 + 560 1 + 580 1 + 600

CADENAMIENTO 1 + 620 1 + 640 1 + 660 1 + 680 1 + 700 1 + 720 1 + 740 1 + 760 1 + 780 1 + 800 1 + 820 1 + 840 1 + 860 1 + 880 1 + 900 1 + 920 1 + 940 1 + 960 1 + 980 2 + 000

COTA 2391 2392 2393 2393 2396 2398 2398 2400 2401 2401 2401 2401 2400 2400 2398 2401 2401 2401 2400 2400

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COTA 2425 2423 2420 2418 2416 2112 2113 2116 2417 2114 2411 2409 2408 2408 2408 2406 2406 2404 2402 2400 2400 2400 2398 2397 2396 2395 2393 2391 2390 2388 2386 2387 2389 2391 2392 2391 2390 2388 2391 2390

2) Proyecto de subrasante Criterios o recomendaciones para proyecto de un camino: 1) Compensar lo más posible cortes y terraplenes longitudinalmente, sin sobrepasar la pendiente máxima permitida.

2) Por construcción se recomienda que en curva en cresta, el punto de inflexión vertical quede en corte.

3) Por cuestión de drenaje, se recomienda que en curvas en columpio, el punto de inflexión vertical quede en terraplén.

4) Por facilidad de calculo, se pide que el punto de inflexión vertical quede en cadenamiento cerrado

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3) Calculo de las pendientes de las tangentes verticales A = Diferencia algebraica de pendientes PIV = Punto de Inflexión Vertical PCV = Punto de Comienzo de la Vertical PTV = Punto de Terminación de la Vertical P = Pendiente H = Altura D = Distancia N = Longitud de la curva en estaciones

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Se utilizo una pendiente gobernadora del 7%.

P1 = H1 (100) = 2407 - 2482 (100) = - 6.94% D1 1080

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P2 = H2 (100) = 2390 - 2407 (100) = - 5.66% D2 1380 - 1080

P3 = H3 (100) = 2400 - 2390 (100) = + 1.61% D3 2000 - 1380 4) Calculo de las curvas verticales 4.1) Curva vertical 1

Se utilizo un valor de curvatura (K) para una velocidad en camino de 40 km./h donde K = 9.

Datos: P1 = - 6.94% P2 = - 5.66% K=9 A = - 5.66 - (- 6.94) A = 1.28

Cad. PIV = 1 + 080 Cota PIV = 2407

L = KA L = 9 (1.28) = 11.52 ≈ 11.52 = 0.576 ≈ 2 estaciones = 40 mts.

20 A la longitud mínima de la curva (L) se le expresa en estaciones, en caso de no ser un numero cerrado par, se pasa al siguiente numero mayor par.

Cad. PCV = Cad. PIV - (L/2) Cad. PCV = 1 + 080 - (40/2) Cad. PCV = 1 + 060

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Cad. PTV = Cad. PIV + (L/2) Cad. PTV = 1 + 080 + (40/2) Cad. PTV = 1 + 100

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Cota PCV = Cota PIV - P1 (L/2) Cota PCV = 2407 - (- 0.0694) (40/2) Cota PCV = 2408.38 Cota PTV = Cota PIV + P2 (L/2) Cota PTV = 2407 + (- 0.0566) (40/2) Cota PTV = 2405.87

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L = 2 estaciones A = 1.28

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Si la curva se encuentra en cresta se resta el tirante (t) sobre la cota del primer subrasante; si esta en columpio se suman.

Estación 1 + 060 1 + 080 1 + 100 4.2)

n 0 1 2

n2 0 1 4

A/10N 0.064 0.064 0.064

Curva vertical 2

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t = An2/ 10N 0.00 0.064 0.254

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Cota sobre primer subrasante 2408.38 2407 2405.62

Cota de la curva 2408.38 2407.06 2405.87

Se utilizo un valor de curvatura (K) para una velocidad en camino de 40 km./h donde K = 9.

Datos: P2 = - 5.66% P3 = + 1.61% K=9

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A = 1.61 - (- 5.66) A = 7.27

Cad. PIV = 1 + 380 Cota PIV = 2390

L = KA L = 9 (7.27) = 65.43 ≈ 65.43 = 3.27 ≈ 4 estaciones = 80 mts.

20 Cad. PCV = Cad. PIV - (L/2) Cad. PCV = 1 + 380 - (80/2) Cad. PCV = 1 + 340 Cad. PTV = Cad. PIV + (L/2) Cad. PTV = 1 + 380 + (80/2) Cad. PTV = 1 + 420

Cota PCV = Cota PIV - P2 (L/2) Cota PCV = 2390 - (- 0.0566) (80/2) Cota PCV = 2392.26 Cota PTV = Cota PIV + P3 (L/2) Cota PTV =2390 + (0.0161) (80/2) Cota PTV = 2390.64

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Estaci贸n 1 + 340 1 + 360 1 + 380 1 + 400 1 + 420

g

n 0 1 2 3 4

n2 0 1 4 9 16

A/10N 0.1817 0.1817 0.1817 0.1817 0.1817

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t = An2/ 10N 0.00 0.1817 0.7268 1.6353 2.9072

Cota sobre primer subrasante 2392.26 2391.13 2390 2388.87 2387.74

Cota de la curva 2392.26 2391.31 2390.72 2390.50 2390.64

III) Secciones transversales de construcci贸n 1) Secciones transversales a nivel del Terreno Natural IZQUIERDA 18/2476 10/2478 20/2470 14/2474 18/2470 12/2472 14/2468 10/2470 16/2470 6/2472 18/2470 12/2472 12/2470 4/2472 18/2468 7/2470 18/2468 6/2470 16/2466 8/2468 16/2464 8/2466

6/2480 8/2476 2/2474 2/2472

EJE 0+000/2482 0+020/2478 0+040/2476 0+060/2473 0+080/2474 0+100/2474 0+120/2474 0+140/2472 0+160/2472 0+180/2470 0+200/2469

DERECHA 10/2484 18/2486 4/2480 10/2482 20/2484 8/2478 12/2480 18/2482 2/2474 8/2476 12/2478 18/2480 8/2476 14/2478 18/2480 6/2476 15/2478 19/2480 10/2476 16/2478 4/2474 10/2476 7/2474 13/2476 3/2472 10/2474 16/2476 3/2470 8/2472 14/2474 20/2476

20/2462 16/2462 14/2462 20/2458 10/2460 12/2460 8/2460 10/2458 20/2454 20/2452 20/2454 10/2452 20/2450 18/2440 16/2440 12/2440 20/2436 18/2436 18/2436 18/2432 19/2434 18/2434 18/2432 10/2430 12/2428 16/2428 10/2428 19/2422 16/2424 18/2422 8/2424 18/2420 14/2416 12/2414 14/2112 20/2408 20/2412 18/2410 16/2412 16/2410 12/2408 16/2404 18/2402 18/2404 18/2404

14/2464 5/2466 4/2464 6/2464 8/2460 2/2462

4/2456 2/2456 6/2454 1/2456 10/2442 2/2444 8/2442 2/2444 4/2442 3/2444 10/2438 2/2440 8/2438 12/2434 6/2436 10/2436 1/2438 12/2436 2/2434

0+220/2468 0+240/2466 0+260/2465 0+280/2463 0+300/2462 0+320/2462 0+340/2462 0+360/2460 0+380/2458 0+400/2454 0+420/2458 0+440/2458 0+460/2451 0+480/2445 0+500/2446 0+520/2445 0+540/2442 0+560/2440 0+580/2438 0+600/2438 0+620/2439 0+640/2438 0+660/2435 0+680/2432 0+700/2432 0+720/2432 0+740/2430 0+760/2428 0+780/2426 0+800/2426 0+820/2425 0+840/2423 0+880/2420 0+880/2418 0+900/2416 0+720/2412 0+740/2413 0+960/2416 0+980/2417 1+000/2414 1+020/2411 1+040/2409 1+060/2408 1+080/2408 1+100/2408

g

12/2424 6/2426 8/2424 12/2424 6/2422 4/2418 8/2416 6/2414 10/2410

10/2412 12/2114 4/2412 2/2410 10/2406 12/2404 8/2406 8/2406

6/2414 2/2416

2/2408 8/2406

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e l o 2/2430 10/2430

10/2470 17/2472 8/2468 20/2470 8/2466 19/2468 2/2464 10/2466 19/2468 4/2464 13/2466 5/2464 20/2466 6/2464 18/2466 10/2462 1/2460 2/2456 5/2458 10/2460 2/2460 3/2462 9/2464 10/2460 18/2462 4/2452 9/2454 1/2446 3/2448 10/2450 14/2452 18/2454 2/2448 10/2450 14/2452 19/2454 1/2446 10/2448 12/2450 18/2452 4/2444 8/2446 12/2448 4/2442 8/2444 10/2446 16/2448 8/2440 10/2442 12/2474 2/2440 14/2442 14/2440 10/2440 18/2442 1/2436 8/2438 14/2440 4/2434 12/2436 18/2438 14/2434 6/2434 14/2436 4/2432 12/2434 18/2436 12/2430 18/2432 10/2428 16/2430 10/2428 18/2430 10/2426 18/2428 2/2424 18/2426 10/2422 18/2424 8/2420 14/2422 18/2418 20/2420 5/2414 14/2416 8/2414 14/2416 4/2418 14/2420 2/2418 12/2420 18/2422 6/2416 12/2418 6/2412 10/2414 18/2416 2/2410 6/2412 16/2414 6/2410 14/2412 7/2410 10/2412 16/2414 7/2410 10/2412

18/2400 12/2402 2/2404 20/2402 2/2404 14/2400 6/2402 20/2406 14/2408 10/2400 16/2404 12/2406 8/2408 18/2404 14/2406 10/2408 16/2404 12/2406 8/2408 16/2394 10/2396 16/2396 8/2398 18/2392 8/2394 19/2392 8/2394 18/2380 8/2392 12/2389 3/239 18/2386 10/2388 18/2484 10/2386 19/2390 12/2388 14/2400 8/2388 10/2402 2/2400 16/2396 10/2394 4/2392 18/2398 12/2396 4/2394 8/2394 1/2392 16/2394 1/2392 18/2404 12/2402 1/2400 16/2398 14/2396 10/2394 2/2392 16/2396 12/2394 8/2392 18/2396 8/2394 4/2392 16/2396 8/2394 18/2398 10/2396 1/2394 12/2398 8/2396 1/2394 12/2400 6/2398 10/2402 6/2400 16/2402 8/2400 10/2404 4/2402 10/2404 2/2402 12/2404 2/2402 19/2406 12/1404 2/2402 12/2404 2/2402 16/2404 8/2402

1+120/2406 1+140/2406 1+160/2404 1+180/2402 1+200/2400 1+220/2400 1+240/2400 1+260/2398 1+280/2397 1+300/2396 1+320/2395 1+340/2393 1+360/2391 1+380/2390 1+400/2388 1+420/2386 1+440/2387 1+460/2389 1+480/2391 1+500/2392 1+520/2391 1+540/2390 1+560/2388 1+580/2391 1+600/2390 1+620/2391 1+640/2392 1+660/2393 1+680/2393 1+700/2396 1+720/2398 1+740/2398 1+760/2400 1+780/2401 1+800/2401 1+820/2401 1+840/2401 1+860/2400

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2/2408 10/2410 2/2408 10/2410 6/2406 12/2408 10/2404 14/2406 18/2408 10/2402 16/2404 8/2402 14/2404 10/2402 14/2404 8/2400 16/2402 2/2398 8/2400 16/2402 10/2398 16/2400 20/2402 4/2396 10/2398 16/2400 20/2402 4/2394 12/2395 18/2396 2/2392 18/2394 4/2392 16/2394 10/2400 16/2402 12/2384 4/2386 19/2384 8/2388 20/2386 2/2390 12/2388 16/2386 10/2390 19/2392 1/2390 8/2388 6/2388 14/2386 2/2386 12/2384 6/2390 12/2388 18/2386 2/2388 8/2386 14/2384 4/2390 12/2388 18/2386 12/2390 16/2388 1/2392 6/2390 10/2388 1/2392 4/2390 10/2388 16/286 8/2394 12/2392 6/2396 12/2394 14/2392 2/2396 8/2394 14/2392 18/2390 10/2398 18/2396 6/2400 10/2398 14/2396 6/2400 14/2402 19/2404 6/2400 14/2398 20/2396 6/2400 14/2398 20/2396 8/2398 14/2396

2) Datos para secciones transversales de construcción Ancho de corona = 7mts Bombeo = -2% Talud de terraplén = 1:1.5 Talud de corte = 1:1/4 Talud de cuneta = 1:3 3) Listado de áreas CAD AREA DE TERRAPLEN 0 + 000 0.7 0 + 020 44.3 0 + 040 17.7 0 + 060 46.2 0 + 080 32.7 0 + 100 10.2 0 + 120 4.8 0 + 140 5.6 0 + 160 0 + 180 0.7 0 + 200 0.9 0 + 220 0 + 240 1.7 0 + 260 0 + 280 1.6 0 + 300 0 + 320 0 + 340 0 + 360 0 + 380 0 + 400 1.9 0 + 420 0 + 440 0 + 460 0 + 480 40.9 0 + 500 29.6 0 + 520 15.4 0 + 540 53.2 0 + 560 31.8 0 + 580 44.0 0 + 600 28.4 0 + 620 5.1 0 + 640 0 + 660 9.8

1.9

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AREA DE CORTE 2.9

0.7 4.2 5.0 9.8 7.5 7.4 9.

6.9 10.7 7.0 13.5 28.7 42.6 32.1 18.3 9.3 64.2 5.2 13.9 3.8 3.1

0.7 1.9 61 3.9

0 + 680 0 + 700 0 + 720 0 + 740 0 + 760 0 + 780 0 + 800 0 + 820 0 + 840 0 + 860 0 + 880 0 + 900 0 + 920 0 + 940 0 + 960 0 + 980 1 + 000 1 + 020 1 + 040 1 + 060 1 + 080 1 + 100 1 + 120 1 + 140 1 + 160 1 + 180 1 + 200 1 + 220 1 + 240 1 + 260 1 + 280 1 + 300 1 + 320 1 + 340 1 + 360 1 + 380 1 + 400 1 + 420 1 + 440 1 + 460 1 + 480 1 + 500 1 + 520 1 + 540 1 + 560

26.5 24.2 2.0 4.6 14.6 21.8 21.4 1.6 3.5 3.7 35.5 57.5 93.8 31.2 2.4 33.1 0.4 4.0 9.4 3.1 9.5

3.1 3.2

0.7 1.5 2.2 35.3

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3.8 4.6 27.5 65.9 57.7 14.6 8.1 3.1 16 29 82.5

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5.9

14.5 0.9 1.4 2.0

22.2 17.4 18.6 6.7 9.8 22.1 34 11 18.9 12.7 17 8.7 3 0.6

36.4 0.4 4.1 1.1 0.7

1 + 580 1 + 600 1 + 620 1 + 640 1 + 660 1 + 680 1 + 700 1 + 720 1 + 740 1 + 760 1 + 780 1 + 800 1 + 820 1 + 840 1 + 860

34.2 75.3 37.9 12.7 15.9 37.3 10.7 0.5 1.0

0.8

1.8

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24.5 17.5 3.8 49.9 46.9 44.8 41.5 1.9