CURVAS HORIZONTALES

CURVAS HORIZONTALES

1.- CALCULO DEL RADIO

a) DISEÑO POR DESLIZAMIENTO

R = 65.35 metros

Velocidad directriz = 45 km/hPeralte = 8 %

Coef. De Friccion = 0.164

b) DISEÑO POR VOLCAMIENTO

b =RADIO = 13.6 m.

Entonces : R = 65.35 m.

2.- CALCULO DE LOS ELEMENTOS DE LA CURVA

CURVA N°2

DATOS :

𝑅= ^2/(127( + ))𝑉 𝑃 𝑓

𝑅=( ^2 (ℎ − /2 ))/(127( /2+ℎ ))𝑉 𝑏 𝑥𝑝 𝑏 𝑥𝑝

CARRITO

R = 40 metrosIo = 136 ° 7 47

ELEMENTOS DE LA CURVA

T = 99.33 m.Lc = 95.04 m.E = 67.08 m.

CURVA5

DATOS :

R = 50 metrosIo = 66 ° 37 56


T = 32.86 m.Lc = 58.15 m.E = 9.83 m.

3.- CALCULO DEL SOBREANCHO

0 '

0 '

𝑆= ( −√( ^2− ^2 ))+ /(10√ )𝑚 𝑥 𝑅 𝑅 𝐿 𝑉 𝑅

S = 2.86449445 m.

4.- REPLANTEO DE CURVAS

a) METODO DEFLEXION

RADIO = 80 m < I = 114.8 °L.C = 160.336805 m

T= 125.171382 m₰= 57.4

CURVA 2

RADIO = 40 m < I = 136.1 °L.C = 95.0364745 m

T= 99.3270601 m₰= 68.06

CURVA3

RADIO = 60 m < I = 38.3 °L.C = 40.0992305 m

T= 20.8307926 m₰= 19.1

CURVA 4RADIO = 40 m < I = 75.1 °L.C = 52.4013776 m

T= 30.7260601 m₰= 37.5

C5RADIO = 50 m < I = 66.6 °L.C = 58.1475833 m

T= 32.863991 m₰= 33.3

C6RADIO = 40 m < I = 51.7 °L.C = 36.0893365 m

T= 19.3773236 m₰= 25.8

C7RADIO = 40 m < I = 28.6 °L.C = 19.9648213 m

T= 10.1949428 m₰= 14.3

b) METODO COORDENADAS

RADIO = 80 m < I = 114.8 °L.C = 160.34 m

T= 125.17 mGm= 0.72

2RADIO = 40 m < I = 136.1 °L.C = 95.03647 m

T= 99.33 mGm= 1.43

3RADIO = 60 m < I = 38.3 °L.C = 40.10 m

T= 20.83 mGm= 0.95

4RADIO = 40 m < I = 75.1 °L.C = 52.40 m

T= 30.73 mGm= 1.43

5RADIO = 50 m < I = 66.6 °L.C = 58.15 m

T= 32.86 mGm= 1.15

6RADIO = 40 m Gm= 1.43 < I = 51.7 °L.C = 36.09 m

T= 19.38 m

7RADIO = 40 m Gm= 1.43 < I = 28.6 °L.C = 19.96 m

T= 10.19 m

5.- REPLANTEO DE CURVAS

RESUMEN 1

RADIO = 80.00 m < I = 114.83 °L.C = 160.34 m

T= 125.17 mE = 68.5525997 m

PROGRESIVA ESTACATIPO CURVA

PROGRESIVA ESTACA

ESPI

RAL

223.22 --------230 6.78240 10250 10260 10270 10280 10290 10300 10

312.37 42.37CI

RCUL

AR 312.37 --------320 7.63330 10340 10

347.96 7.96

CIRC

ULAR 347.96 2.04

350 10360 20370380 3.56

383.56 --------

ESPIRA

L

383.56 6.44390 10400 10410 10420 10430 10440 10450 10460 10470 2.71

472.71 --------

RESUMEN 2

RADIO = 40.00 m < I = 136.13 °

CURVA

L.C = 95.04 mT= 99.33 mE = 67.0787788 m

PROGRESIVA ESTACA

ESPIRAL

509.19 --------520 10.81

TIPO CURVA

ESPIRAL

540 20560 20580 20600 20620 20640 20660 20680 20

687.49 7.49

CIRC

ULAR 687.49 --------

700 12.51720 20

729.13 9.13

CIRC

ULAR 729.13 10.87

740 20760 10.76

770.76 --------

ESPI

RAL

770.76 9.24780 20800 20820 20840 20860 20880 20900 20920 20940 9.06

949.06 --------

RESUMEN 3

RADIO = 60.00 m < I = 38.29 °L.C = 40.10 m

T= 20.83 mE = 3.51316335 m

PROGRESIVA ESTACA

ESPIRAL

1093.75 --------1100 6.251110 101120 101130 101140 101150 101160 101170 10

TIPO CURVA

ESPI

RAL

1180 101190 101200 101210 10

1212.61 2.61

CIRC

ULAR

1212.61 --------1220 7.391230 101240 101250 101252 2

CIRC

ULAR 1252 8

1260 101270 101280 101290 1.38

1291.38 --------

ESPI

RAL

1291.38 8.621300 101310 101320 101330 101340 101350 101360 101370 101380 101390 101400 10.25

1410.25 --------

RESUMEN 4

RADIO = 40.00 m < I = 75.06 °L.C = 52.40 m

T= 30.73 mE = 10.4389807 m

PROGRESIVA ESTACA

ESPI

RAL

1147.45 --------1160 12.551180 201200 201220 201240 20

TIPO CURVA

ESPI

RAL

1260 201280 201300 201320 20

1325.75 5.75

CIRC

ULAR 1325.75 --------

1340 14.251360 201380 201388.7 8.7

CIRC

ULAR 1388.7 11.3

1400 201420 201440 11.65

1451.65 --------

ESPIRA

L

1451.65 8.351460 201480 201500 201520 201540 201560 201580 201600 201620 9.95

1629.95 --------

RESUMEN 5

RADIO = 50.00 m < I = 66.63 °L.C = 58.15 m

T= 32.86 mE = 9.83345137 m

PROGRESIVA ESTACA

ESPI

RAL

1311.28 --------1320 8.721340 201360 201380 201400 201420 201440 20

1453.92 13.92

TIPO CURVA

CIRC

ULAR

1453.92 --------1460 6.081470 101480 101490 10

1496.16 6.16

CIRC

ULAR 1496.16 3.84

1500 101510 101520 101530 8.41

1538.41 --------

ESPI

RAL

1538.41 1.591540 201560 201580 201600 201620 201640 201660 201680 1.05

1681.05 --------

RESUMEN 6

RADIO = 40.00 m < I = 51.69 °L.C = 36.09 m

T= 19.38 mE = 4.44637972 m

PROGRESIVA ESTACA

ESPIRA

L

1412.02 --------1420 7.981440 201460 201480 201500 201520 201540 201560 201580 20

1590.32 90.32

CIRC

ULAR

1590.32 --------1600 9.681620 20

TIPO CURVA

CIRC

ULAR

1640 201660 20

1661.42 1.42

CIRCUL

AR 1661.42 18.581680 201700 201720 12.53

1732.53 --------

ESPI

RAL

1732.53 7.471740 201760 201780 201800 201820 201840 201860 201880 30.83

1910.83 --------

RESUMEN 7

RADIO = 40.00 m < I = 28.60 °L.C = 19.96 m

T= 10.19 mE = 1.27877007 m

PROGRESIVA ESTACA

ESPI

RAL

1493.87 --------1500 6.131520 201540 201560 201580 201600 201620 201640 201660 20

1672.17 12.17

CIRC

ULAR

1672.17 --------1680 7.831700 201720 201740 20

1751.33 11.33

CIRCULAR 1751.33 8.67

TIPO CURVA

CIRCUL

AR 1760 201780 201800 201820 10.51830.5 --------

ESPIRA

L

1830.5 9.51840 201860 201880 201900 201920 201940 201960 201980 202000 8.82008.8 --------

h= 1.30m

2.60m

CURVA N°1

P.I : PUNTO DE INTERSECCIONP.T : PUNTO DE TANGENCIAP.C : PRINCIPIO DE CURVA

E : EXTERNAT : TANGENTER : RADIO

Lc : LONG. DE CIRCF.


T = 125.17Lc = 160.34E = 68.55

CURVA N°3

DATOS :

metros R =" Io =


T =Lc =E =

CURVA6

DATOS :

metros R = 40" Io = 51


T = 19.38Lc = 36.09E = 4.45

m: Número de carrilesL : Longitud máxima del veh.

FACULTAD DE INGENIERIA CIVIL

a11.80

ESTACA ACUMULADODEFLEXION

PARCIALESα G

201.66 - - -210 8.34 8.34 2.99 2220 10 18.34 3.58 3230 10 28.34 3.58 3240 10 38.34 3.58 3250 10 48.34 3.58 3260 10 58.34 3.58 3270 10 68.34 3.58 3280 10 78.34 3.58 3290 10 88.34 3.58 3300 10 98.34 3.58 3310 10 108.34 3.58 3390 80 188.34 28.65 28400 10 198.34 3.58 3410 10 208.34 3.58 3420 10 218.34 3.58 3430 10 228.34 3.58 3

434.14 4.14 232.48 1.48 183.25 83

ERROR = 25.83 =


PARCIALESα G

563.2 - - -570 6.8 6.8 4.87 4580 10 16.8 7.16 7590 10 26.8 7.16 7600 10 36.8 7.16 7

LONGITUD DE CURVA

LONGITUD DE CURVA


610 10 46.8 7.16 7620 10 56.8 7.16 7630 10 66.8 7.16 7640 10 76.8 7.16 7650 10 86.8 7.16 7

658.24 8.24 95.04 5.90 568.07 68

ERROR = 0.00 =


PARCIALESα G

960.88 - - -970 9.12 9.12 4.35 4980 10 19.12 4.77 4990 10 29.12 4.77 41000 10 39.12 4.77 4

1000.98 0.98 40.1 0.47 019.15 19

ERROR = 0.00 =


PARCIALESα G

1045.63 - - -1050 4.37 4.37 3.13 31060 10 14.37 7.16 71070 10 24.37 7.16 71080 10 34.37 7.16 71090 10 44.37 7.16 7

1098.03 8.03 52.4 5.75 537.53 37

ERROR = 0.00 =


PARCIALESα G

1183.82 - - -1190 6.18 6.18 3.54 31200 10 16.18 5.73 5

LONGITUD DE CURVA

LONGITUD DE CURVA

LONGITUD DE CURVA

1210 10 26.18 5.73 51220 10 36.18 5.73 51230 10 46.18 5.73 51240 10 56.18 5.73 5

1241.96 1.96 58.14 1.12 133.31 33

ERROR = 0.00 =


PARCIALESα G

1280.66 - - -1290 9.34 9.34 6.69 61300 10 19.34 7.16 71310 10 29.34 7.16 7

1316.75 6.75 36.09 4.83 425.85 25

ERROR = 0.00 =


PARCIALESα G

1357.59 - - -1360 2.41 2.41 1.73 11370 10 10 7.16 7

1377.55 7.55 7.55 5.41 514.30 14

ERROR = 0.00 =

ESTACAS L.C ℓ (METROS) ANGULOSα G

201.66 - - - -280 78.34 78.34 56.107 56290 10 88.34 63.269 63300 10 98.34 70.431 70310 10 108.34 77.593 77320 10 118.34 84.755 84330 10 128.34 91.917 91

LONGITUD DE CURVA

LONGITUD DE CURVA

340 10 138.34 99.079 99350 10 148.34 106.241 106

353.97 3.97 152.31 109.084 109353.97 6.03 80.17 57.418 57

360 10 74.14 53.099 53370 10 64.14 45.937 45380 10 54.14 38.775 38390 10 44.14 31.613 31400 10 34.14 24.451 24410 10 24.14 17.289 17420 10 14.14 10.127 10430 4.14 4.14 2.965 2

434.14 - - - -


563.2 - - - -570 6.8 6.8 9.74 9580 10 16.8 24.06 24590 10 26.8 38.39 38600 10 36.8 52.71 52610 10 46.8 67.04 67

610.72 0.72 47.52 68.07 68610.72 9.28 47.52 68.07 68

620 10 38.24 54.77 54630 10 28.24 40.45 40640 10 18.24 26.13 26650 8.24 8.24 11.80 11

658.24 - - - -


960.88 - - - -970 9.12 9.12 8.7089584848514 8980 10 19.12 18.258255069118 18

980.93 0.93 20.05 19.146339651455 19980.93 9.07 20.05 19.146339651455 19

990 10.98 10.98 10.485127649525 101000.98 - - - -


1045.63 - - - -

1050 4.37 4.37 6.2595639109868 61060 10 14.37 20.583508787387 201070 10 24.37 34.907453663787 34

1071.83 1.83 26.2 37.528735576169 371071.83 8.17 26.2 37.528735576169 37

1080 10 18.03 25.82607261215 251090 8.03 8.03 11.502127735749 11

1098.03 - - - -


1183.82 - - - -1190 6.18 6.18 7.0817583468924 71200 10 16.18 18.540914248013 181210 10 26.18 30.000070149133 30

1212.895 2.895 29.075 33.317495782507 331212.895 7.105 29.065 33.306036626606 33

1220 10 21.96 25.16430635886 251230 10 11.96 13.70515045774 131240 1.96 1.96 2.2459945566196 2

1241.96 - - - -


1280.66 - - - -1290 9.34 9.34 13.378564514558 13

1298.705 8.705 18.045 25.847558529464 251298.705 1.295 18.045 25.847558529464 25

1300 10 16.75 23.992607667971 231310 6.75 6.75 9.6686627915702 9

1316.75 - - - -


1357.59 - - - -1360 2.41 2.41 3.4520707152126 3

1367.57 7.57 9.98 14.295296986648 141367.57 2.43 9.98 14.295296986648 14

1370 7.55 7.55 10.814578381682 101377.55 - - - -

A) ELEMENTOS DE CURVAS DE TRANSICIONGm= 0.72𝐺𝑚=

/( . )𝐼𝑜 𝐿 𝑐

B) ELEMENTOS DE CURVAS DE TRANSICION

LONGITUD DE ESPIRAL DE TRANSICION

Ls = 48.83 m

β = 17.49 en radianes

ENTONCES : 5.83

HALLAMOS RADIO VECTORCoordenadas Polares

Rv = 48.63

HALLAMOS DESPLAZAMIENTO DE LA TANGENTE O DE RADIO

DR= 1.24

HALLAMOS DESPLAZAMIENTO (k) EN TANGENTE PRINCIPAL (Xm)

Xm = 24.340

HALLAMOS INCREMENTO O DESPLAZAMIENTO DE LA TANGENTE

Dt = 1.943

HALLAMOS INCREMENTO DE EXTERNA

De = 2.306

C) HALLAMOS VALORES DE LA CURVA DESPLAZADA

Ld = LONGITUD DE LA CURVA DEZPLAZADA

HALLAMOS "θ" = β

α =

Ls=(0.04( ^3))/𝑉 𝑅

𝛽= /2 𝐿𝑠 ∗ 𝐺𝑚

𝑅𝑣= (1−0.04444 ^2)𝐿𝑠 ∗ ∗𝐵 𝑋𝑠= cos ( )𝑅𝑣∗ 𝑎Y = sen ( )𝑠 𝑅𝑣∗ 𝑎

𝐺𝑚= /( . )𝐼𝑜 𝐿 𝑐

𝐷𝑅= − (1−cos 𝑌𝑠 𝑅 𝐵〖 ) 〗

𝑋𝑚= −𝑋𝑠 𝑅∗𝑠𝑒𝑛𝐵

𝐷𝑡= tan ( /2)𝐷𝑟∗ 𝐼

𝐷𝑒= sec( /𝐷𝑟∗ 𝐼2)

𝐿𝑑= −𝐿𝑐 𝐿𝑠

Ld= 111.509 m

79.862

HALLAMOS TANGENTE DE LA CURVA DEZPLAZADA

Td= 66.964 m

HALLAMOS EXTERNA DE LA CURVA DESPLAZADA(Ed)

Ed= 24.327 m

D) CALCULO DE LA CURVA TOTAL

Lt= ###m

HALLAMOS TANGENTE TOTAL (Tt)

Tt= ###mHALLAMOS EXTERNA TOTAL (Et)

ET= ###mHALLAMOS DIFERENCIA DE EXTERNAS (ZZ')

ZZ'= ###m

PI= KM 0 398.97 -Tt 151.454

TS= KM 0 247.52 +Ls 48.83

SC= KM 0 296.34 +LD/2 55.7543

PM= KM 0 352.10 +LD/2 55.7543

CS= KM 0 407.85 +Ls 48.83

ST= KM 0 456.68

CUERDA ℓ (METROS)

HALLAMOS ANGULO DE INTERSECCION êd

êd=

θ (β)

𝑑= 𝐿𝑑 ∗𝐺𝑚

T = (𝑑 𝑅∗𝑇𝑎𝑛 )/2𝑑

E = ( (𝑑 𝑅∗ 𝑆𝐸𝐶 )/2 𝑑−1)

Lt=Ld+2Ls

Tt=T+Xm+Dt

Et=Eb+De

ZZ′= −𝐸𝑡 𝐸𝑑

CUERDA ℓ (METROS) θ (β) G M---------- ---------- ---------- ---------- ----------

6.78 6.78 0.337 0 2016.78 16.78 2.065 2 326.78 26.78 5.260 5 1536.78 36.78 9.921 9 5546.78 46.78 16.049 16 256.78 56.78 23.644 23 3866.78 66.78 32.706 32 4276.78 76.78 43.234 43 1489.15 89.15 58.287 58 17

---------- ---------- ---------- ---------- ----------7.63 7.63 5.465 5 27

17.63 17.63 12.627 12 3727.63 27.63 19.789 19 4735.59 35.59 25.489 25 29

35.6 35.6 25.497 25 2933.56 33.56 24.036 24 223.56 23.56 16.874 16 52

3.56 3.56 2.550 2 32---------- ---------- ---------- ---------- ----------

89.15 89.15 58.287 58 1782.71 82.71 50.171 50 1072.71 72.71 38.772 38 4662.71 62.71 28.841 28 5052.71 52.71 20.376 20 2242.71 42.71 13.378 13 2232.71 32.71 7.847 7 5022.71 22.71 3.782 3 4612.71 12.71 1.185 1 11

2.70999999999998 2.71 0.054 0 3---------- ---------- ---------- ---------- ----------

A) ELEMENTOS DE CURVAS DE TRANSICIONGm= 1.43



𝐺𝑚= /( . )𝐼𝑜 𝐿 𝑐

Ls = 97.66 m


ENTONCES : 23.31


Rv = 91.19


DR= 9.81


Xm = 46.172


Dt = 24.367


De = 26.268



Ld= 2.620 m

HALLAMOS "θ" = β

α =


Ls=(0.04( ^3))/𝑉 𝑅

𝛽= /2 𝐿𝑠 ∗ 𝐺𝑚


𝐷𝑅= − (1−cos 𝑌𝑠 𝑅 〖𝐵 ) 〗






3.753


Td= 1.310 m


Ed= 0.021 m


Lt= ###m




ZZ'= ###m

PI= KM 0 752.54 -Tt 169.866

TS= KM 0 582.67 +Ls 97.66

SC= KM 0 680.33 +LD/2 1.3099

PM= KM 0 681.64 +LD/2 1.3099

CS= KM 0 682.95 +Ls 97.66

ST= KM 0 780.61


10.81 10.81 0.857 0 51

êd=

θ (β)


E = ( (𝑑 𝑅∗ 𝑆𝐸𝐶 )/2 𝑑−1)

Lt=Ld+2Ls

Tt=T+Xm+Dt

Et=Eb+De


30.81 30.81 6.962 6 5750.81 50.81 18.934 18 5670.81 70.81 36.772 36 4690.81 90.81 60.478 60 28

110.81 110.81 90.051 90 3130.81 130.81 125.492 125 29150.81 150.81 166.799 166 47170.81 170.81 213.973 213 58178.3 178.3 233.150 233 8

---------- ---------- ---------- ---------- ----------12.51 12.51 8.960 8 5732.51 32.51 23.284 23 1741.64 41.64 29.822 29 49

41.63 41.63 29.815 29 4830.76 30.76 22.030 22 110.76 10.76 7.706 7 42

---------- ---------- ---------- ---------- ----------

9.24000000000001 178.3 233.150 233 820 169.06 209.611 209 3620 149.06 162.950 162 5720 129.06 122.156 122 920 109.06 87.230 87 1320 89.06 58.170 58 1020 69.06 34.977 34 5820 49.06 17.652 17 3920 29.06 6.193 6 11

9.05999999999995 9.06 0.602 0 36---------- ---------- ---------- ---------- ----------




Ls = 65.10 m

HALLAMOS "θ" = β

Ls=(0.04( ^3))/𝑉 𝑅

𝛽= /2 𝐿𝑠 ∗ 𝐺𝑚

𝐺𝑚= /( . )𝐼𝑜 𝐿 𝑐


ENTONCES : 10.36


Rv = 64.25


DR= 2.94


Xm = 32.228


Dt = 1.021


De = 3.114



Ld= 25.005 m

23.878


Td= 12.687 m

α =


êd=


𝐷𝑅= − (1−cos 𝑌𝑠 𝑅 〖𝐵 ) 〗








Ed= 1.327 m


Lt= ###m




ZZ'= ###m

PI= KM 1 175.33 -Tt 54.081

TS= KM 1 121.25 +Ls 65.10

SC= KM 1 186.35 +LD/2 12.5025

PM= KM 1 198.86 +LD/2 12.5025

CS= KM 1 211.36 +Ls 65.10

ST= KM 1 276.46


6.25 6.25 0.286 0 1716.25 16.25 1.937 1 5626.25 26.25 5.053 5 336.25 36.25 9.637 9 3846.25 46.25 15.688 15 4156.25 56.25 23.205 23 1266.25 66.25 32.189 32 1176.25 76.25 42.640 42 38

θ (β)

E = ( (𝑑 𝑅∗ 𝑆𝐸𝐶 )/2 𝑑−1)

Lt=Ld+2Ls

Tt=T+Xm+Dt

Et=Eb+De


86.25 86.25 54.557 54 3396.25 96.25 67.941 67 56

106.25 106.25 82.792 82 47116.25 116.25 99.110 99 6118.86 118.86 103.611 103 36

---------- ---------- ---------- ---------- ----------7.3900000000001 7.39 5.293 5 1717.3900000000001 17.39 12.455 12 2727.3900000000001 27.39 19.617 19 3637.3900000000001 37.39 26.779 26 4639.3900000000001 39.39 28.211 28 12

39.3800000000001 39.38 28.204 28 1231.3800000000001 31.38 22.474 22 2821.3800000000001 21.38 15.312 15 1811.3800000000001 11.38 8.150 8 91.38000000000011 1.38 0.988 0 59---------- ---------- ---------- ---------- ----------

118.87 118.87 103.628 103 37110.25 110.25 89.144 89 8100.25 100.25 73.706 73 4290.25 90.25 59.735 59 4480.25 80.25 47.231 47 1370.25 70.25 36.193 36 1160.25 60.25 26.622 26 3750.25 50.25 18.518 18 3140.25 40.25 11.881 11 5230.25 30.25 6.711 6 4220.25 20.25 3.007 3 010.25 10.25 0.771 0 46

---------- ---------- ---------- ---------- ----------




Ls = 97.66 m

Ls=(0.04( ^3))/𝑉 𝑅

𝐺𝑚= /( . )𝐼𝑜 𝐿 𝑐


ENTONCES : 23.31


Rv = 91.19


DR= 9.81


Xm = 46.172


Dt = 7.538


De = 12.374



Ld= 45.255 m

64.823


HALLAMOS "θ" = β

α =


êd=

𝛽= /2 𝐿𝑠 ∗ 𝐺𝑚


𝐷𝑅= − (1−cos 𝑌𝑠 𝑅 〖𝐵 ) 〗







Td= 25.396 m


Ed= 7.381 m


Lt= ###m




ZZ'= ###m

PI= KM 1 271.54 -Tt 84.436

TS= KM 1 187.10 +Ls 97.66

SC= KM 1 284.76 +LD/2 22.6274

PM= KM 1 307.39 +LD/2 22.6274

CS= KM 1 330.01 +Ls 97.66

ST= KM 1 427.67


12.55 12.55 1.155 1 932.55 32.55 7.770 7 4652.55 52.55 20.252 20 1572.55 72.55 38.602 38 3692.55 92.55 62.818 62 49

θ (β)


E = ( (𝑑 𝑅∗ 𝑆𝐸𝐶 )/2 𝑑−1)

Lt=Ld+2Ls

Tt=T+Xm+Dt

Et=Eb+De


112.55 112.55 92.902 92 54132.55 132.55 128.852 128 51152.55 152.55 170.670 170 40172.55 172.55 218.355 218 21178.3 178.3 233.150 233 8

---------- ---------- ---------- ---------- ----------14.25 14.25 10.206 10 12

20 34.25 24.530 24 3120 54.25 38.854 38 51

8.70000000000005 62.95 45.085 45 5

62.95 62.95 45.085 45 551.6500000000001 51.65 36.992 36 5931.6500000000001 31.65 22.668 22 4011.6500000000001 11.65 8.344 8 20---------- ---------- ---------- ---------- ----------

178.3 178.3 233.150 233 8169.95 169.95 211.824 211 49149.95 149.95 164.902 164 54129.95 129.95 123.847 123 50109.95 109.95 88.659 88 3989.95 89.95 59.338 59 2069.95 69.95 35.885 35 5349.95 49.95 18.298 18 1729.95 29.95 6.578 6 34

9.95000000000005 9.95 0.726 0 43---------- ---------- ---------- ---------- ----------




Ls = 78.13 m

HALLAMOS "θ" = β

Ls=(0.04( ^3))/𝑉 𝑅

𝛽= /2 𝐿𝑠 ∗ 𝐺𝑚

𝐺𝑚= /( . )𝐼𝑜 𝐿 𝑐


ENTONCES : 14.92


Rv = 76.01


DR= 5.07


Xm = 38.237


Dt = 3.335


De = 6.072



Ld= 19.977 m

22.892


Td= 10.124 m

α =


êd=


𝐷𝑅= − (1−cos 𝑌𝑠 𝑅 〖𝐵 ) 〗








Ed= 1.015 m


Lt= ###m




ZZ'= ###m

PI= KM 1 420.92 -Tt 74.436

TS= KM 1 346.48 +Ls 78.13

SC= KM 1 424.61 +LD/2 9.9887

PM= KM 1 434.60 +LD/2 9.9887

CS= KM 1 444.59 +Ls 78.13

ST= KM 1 522.71


8.72000000000003 8.72 0.558 0 3328.72 28.72 6.049 6 248.72 48.72 17.408 17 2468.72 68.72 34.634 34 3888.72 88.72 57.727 57 43

108.72 108.72 86.687 86 41128.72 128.72 121.514 121 30142.64 142.64 149.216 149 12

θ (β)

E = ( (𝑑 𝑅∗ 𝑆𝐸𝐶 )/2 𝑑−1)

Lt=Ld+2Ls

Tt=T+Xm+Dt

Et=Eb+De


---------- ---------- ---------- ---------- ----------6.07999999999993 6.08 4.354 4 2116.0799999999999 16.08 11.516 11 3026.0799999999999 26.08 18.678 18 4036.0799999999999 36.08 25.840 25 50

42.24 42.24 30.252 30 15

42.25 42.25 30.259 30 1538.4100000000001 38.41 27.509 27 3028.4100000000001 28.41 20.347 20 2018.4100000000001 18.41 13.185 13 118.41000000000008 8.41 6.023 6 1---------- ---------- ---------- ---------- ----------

142.64 142.64 149.216 149 12141.05 141.05 145.908 145 54121.05 121.05 107.464 107 27101.05 101.05 74.887 74 5381.05 81.05 48.177 48 1061.05 61.05 27.334 27 2041.05 41.05 12.358 12 2121.05 21.05 3.250 3 14

1.04999999999995 1.05 0.008 0 0---------- ---------- ---------- ---------- ----------




Ls = 97.66 m


ENTONCES : 23.31


HALLAMOS "θ" = β

α =

Ls=(0.04( ^3))/𝑉 𝑅

𝛽= /2 𝐿𝑠 ∗ 𝐺𝑚

𝑅𝑣= (1−0.04444 ^2)𝐿𝑠 ∗ ∗𝐵

𝐺𝑚= /( . )𝐼𝑜 𝐿 𝑐

Rv = 91.19


DR= 9.81


Xm = 46.172


Dt = 4.754


De = 10.904



Ld= 61.567 m

88.188


Td= 38.755 m


Ed= 15.695 m



êd=


𝐷𝑅= − (1−cos 𝑌𝑠 𝑅 〖𝐵 ) 〗







E = ( (𝑑 𝑅∗ 𝑆𝐸𝐶 )/2 𝑑−1)

Lt= ###m




ZZ'= ###m

PI= KM 1 516.38 -Tt 70.303

TS= KM 1 446.08 +Ls 97.66

SC= KM 1 543.73 +LD/2 30.7835

PM= KM 1 574.52 +LD/2 30.7835

CS= KM 1 605.30 +Ls 97.66

ST= KM 1 702.96


7.98000000000002 7.98 0.467 0 2827.98 27.98 5.742 5 4447.98 47.98 16.883 16 5267.98 67.98 33.892 33 5387.98 87.98 56.768 56 46

107.98 107.98 85.510 85 30127.98 127.98 120.120 120 7147.98 147.98 160.597 160 35167.98 167.98 206.942 206 56178.3 178.3 233.150 233 8

---------- ---------- ---------- ---------- ----------9.68000000000006 9.68 6.933 6 5529.6800000000001 29.68 21.257 21 15

θ (β)

Lt=Ld+2Ls

Tt=T+Xm+Dt

Et=Eb+De


49.6800000000001 49.68 35.581 35 3469.6800000000001 69.68 49.905 49 5451.1000000000001 71.1 50.922 50 55

71.1099999999999 71.11 50.929 50 5552.53 52.53 37.622 37 3732.53 32.53 23.298 23 1712.53 12.53 8.974 8 58

---------- ---------- ---------- ---------- ----------

178.3 178.3 233.150 233 8170.83 170.83 214.023 214 1150.83 150.83 166.843 166 50130.83 130.83 125.530 125 31110.83 110.83 90.084 90 5

90.8299999999999 90.83 60.505 60 3070.8299999999999 70.83 36.793 36 4750.8299999999999 50.83 18.948 18 5630.8299999999999 30.83 6.971 6 58---------- ---------- ---------- ---------- ----------




Ls = 97.66 m


ENTONCES : 23.31


Rv = 91.19

HALLAMOS "θ" = β

α =

Ls=(0.04( ^3))/𝑉 𝑅

𝛽= /2 𝐿𝑠 ∗ 𝐺𝑚


𝐺𝑚= /( . )𝐼𝑜 𝐿 𝑐


DR= 9.81


Xm = 46.172


Dt = 2.501


De = 10.126



Ld= 77.691 m

111.285


Td= 58.511 m


Ed= 30.877 m


Lt= ###m



êd=

𝐷𝑅= − (1−cos 𝑌𝑠 𝑅 〖𝐵 ) 〗







E = ( (𝑑 𝑅∗ 𝑆𝐸𝐶 )/2 𝑑−1)

Lt=Ld+2Ls

Tt=T+Xm+Dt



ZZ'= ###m

PI= KM 1 582.27 -Tt 58.868

TS= KM 1 523.40 +Ls 97.66

SC= KM 1 621.06 +LD/2 38.8457

PM= KM 1 659.90 +LD/2 38.8457

CS= KM 1 698.75 +Ls 97.66

ST= KM 1 796.41


6.13000000000011 6.13 0.276 0 1626.1300000000001 26.13 5.007 5 046.1300000000001 46.13 15.606 15 3666.1300000000001 66.13 32.072 32 486.1300000000001 86.13 54.405 54 24

106.13 106.13 82.605 82 36126.13 126.13 116.673 116 40146.13 146.13 156.607 156 36166.13 166.13 202.408 202 24178.3 178.3 233.150 233 8

---------- ---------- ---------- ---------- ----------7.82999999999993 7.83 5.608 5 3627.8299999999999 27.83 19.932 19 5547.8299999999999 47.83 34.256 34 1567.8299999999999 67.83 48.580 48 3479.1599999999999 79.16 56.694 56 41

79.1700000000001 79.17 56.701 56 42

θ (β)

Tt=T+Xm+Dt

Et=Eb+De


70.5 70.5 50.492 50 2950.5 50.5 36.168 36 1030.5 30.5 21.844 21 5010.5 10.5 7.520 7 31

---------- ---------- ---------- ---------- ----------

178.3 178.3 233.150 233 8168.8 168.8 208.967 208 58148.8 148.8 162.382 162 22128.8 128.8 121.665 121 39108.8 108.8 86.814 86 4888.8 88.8 57.831 57 4968.8 68.8 34.714 34 4248.8 48.8 17.465 17 2728.8 28.8 6.083 6 4

8.79999999999995 8.8 0.568 0 34---------- ---------- ---------- ---------- ----------

CURVA N°1

PUNTO DE INTERSECCION DATOS :PUNTO DE TANGENCIAPRINCIPIO DE CURVA R = 80 metros

EXTERNA Io = 114 ° 49 58 "TANGENTERADIO

LONG. DE CIRCF.


m.m.m.

CURVA N°3

0 '

60 metros38 ° 17 31 "


20.83 m.40.10 m.3.51 m.

CURVA6

metros° 41 39 "


m.m.m.

2L = 12.2262

0 '

0 '


b3.20

DEFLEXIONPARCIALES ACUMULADO

M S NORMAL G M S- - - - - -

59 11.6 2.987 2 59 11.634 51.6 6.568 6 34 3.134 51.6 10.15 10 8 54.734 51.6 13.73 13 43 46.234 51.6 17.31 17 18 37.834 51.6 20.89 20 53 29.334 51.6 24.47 24 28 20.934 51.6 28.05 28 3 12.434 51.6 31.63 31 38 4.034 51.6 35.22 35 12 55.534 51.6 38.80 38 47 47.138 52.4 67.44 67 26 39.534 51.6 71.03 71 1 31.034 51.6 74.61 74 36 22.634 51.6 78.19 78 11 14.134 51.6 81.77 81 46 5.728 57.1 83.25 83 15 2.815 2.8

25 50 3.8



52 12.5 4.8701 4 52 12.59 43.1 7.1620 7 9 43.19 43.1 7.1620 7 9 43.19 43.1 7.1620 7 9 43.1


9 43.1 7.1620 7 9 43.19 43.1 7.1620 7 9 43.19 43.1 7.1620 7 9 43.19 43.1 7.1620 7 9 43.19 43.1 7.1620 7 9 43.1

54 5.3 5.9015 5 54 5.34 2.6

0 0 9.1



21 16.1 4.354 4 21 16.146 28.7 9.129 9 7 44.946 28.7 13.90 13 54 13.646 28.7 18.68 18 40 42.328 4.5 19.15 19 8 46.88 46.8

0 0 1.3



7 47.2 3.130 3 7 47.29 43.1 10.292 10 17 30.39 43.1 17.45 17 27 13.49 43.1 24.62 24 36 56.59 43.1 31.78 31 46 39.6

45 3.8 37.53 37 31 43.431 43.4

0 0 3.6



32 27.2 3.541 3 32 27.243 46.5 9.270 9 16 13.6

43 46.5 15.00 15 0 0.143 46.5 20.73 20 43 46.643 46.5 26.46 26 27 33.143 46.5 32.19 32 11 19.67 22.8 33.31 33 18 42.4

18 42.4

0 0 15.6



41 21.4 6.689 6 41 21.49 43.1 13.851 13 51 4.59 43.1 21.01 21 0 47.6

50 3.6 25.85 25 50 51.250 51.2

0 0 1.7



43 33.7 1.726 1 43 33.79 43.1 7.162 7 9 43.1

24 26.2 5.407 5 24 26.217 43.1

0 0 12.4

ANGULOS X (m) Y (m)M S- - - -

6 24.81 66.4063496 35.3883816 7.91 71.4501671 44.0156525 51.01 75.3790287 53.2044435 34.11 78.1316257 62.8113745 17.21 79.6650049 72.6865255 0.32 79.9552382 82.67579

4 43.42 78.9977969 92.6233214 26.52 76.8076213 102.37395 2.41 75.6032191 106.1563

25 3.12 67.4093781 36.918965 55.91 63.97382 31.96511

56 12.81 57.4859383 24.3639846 29.71 50.1010077 17.6310336 46.61 41.9342677 11.8713227 3.51 33.1131574 7.17473817 20.41 23.7753274 3.6145717 37.30 14.0664913 1.246373

57 54.20 4.13815238 0.107099- - - -


44 25.02 6.77 0.583 51.22 16.31 3.48

23 17.42 24.84 8.6542 43.62 31.82 15.772 9.82 36.83 24.394 2.59 37.10 25.064 2.59 37.10 25.06

46 29.15 32.68 16.9327 2.95 25.95 9.567 36.75 17.61 4.09

48 10.55 8.18 0.85- - - -


42 32.25 9.08492246 0.69178715 29.72 18.798038 3.020768 46.82 19.6789228 3.3189638 46.82 19.6789228 3.318963

29 6.46 10.9188177 1.001869- - - -


15 34.43 4.36131212 0.23847435 0.63 14.0628885 2.55356954 26.83 22.8901025 7.19690231 43.45 24.3663697 8.27808331 43.45 24.3663697 8.27808349 33.86 17.4256299 3.99517530 7.66 7.97617299 0.803308

- - - -


4 54.33 6.16427675 0.38143832 27.29 15.8990881 2.5951590 0.25 25.000053 6.69876

19 2.98 27.4639007 8.21801618 21.73 27.4555437 8.2125249 51.50 21.2607764 4.745394

42 18.54 11.846274 1.42360914 45.58 1.95949807 0.038411

- - - -


22 42.83 9.2553581 1.085550 51.21 17.4391305 4.00171250 51.21 17.4391305 4.00171259 33.39 16.2647509 3.45608340 7.19 6.71800945 0.568181

- - - -


27 7.45 2.40854219 0.07257917 43.07 9.87677888 1.2385617 43.07 9.87677888 1.2385648 52.48 7.5052497 0.710418

- - - -

β = 0.31

Coordenadas PolaresXs= 48.37Ys= 4.94

ZONA ESPIRAL

θ (β)HALLAMOS INCREMENTO O DESPLAZAMIENTO DE LA TANGENTE

α

XmHALLAMOS INCREMENTO DE EXTERNA

Ym


𝑋𝑠= cos ( )𝑅𝑣∗ 𝑎Y = sen ( )𝑠 𝑅𝑣∗ 𝑎

𝜃=( 𝐿𝑠〖〖〗 _𝑎𝑐𝑢𝑚𝑢𝑙𝑎𝑑𝑜 〗 ^2 180)/(2∗ 𝑅∗ 〖〗𝐿𝑠 _ )𝑡𝑜𝑡𝑎𝑙∗𝜋

∝= /3𝛽

𝑋𝑚= 〖〗𝐿𝑠 _( .)𝑎𝑐𝑢𝑚 ∗𝑐𝑜𝑠∝

Y =𝑚 〖〗𝐿𝑠 _( .)𝑎𝑐𝑢𝑚 ∗𝑠𝑒𝑛∝

Xm Ym α

Xm Ym α G M ------------------------------ ----- -----

6.78 0.01 0.112 0 616.78 0.20 0.688 0 4126.77 0.82 1.753 1 4536.72 2.12 3.307 3 1846.58 4.36 5.350 5 2056.24 7.79 7.881 7 5265.57 12.63 10.902 10 5474.36 19.11 14.411 14 2484.07 29.65 19.429 19 25

------------------------------ ----- -----7.618 0.364 2.732 2 43

17.488 1.935 6.313 6 1827.084 4.724 9.894 9 5334.428 7.787 12.745 12 44

34.437 7.791 12.748 12 4432.584 6.937 12.018 12 123.221 3.444 8.437 8 26

3.559 0.079 1.275 1 16------------------------------ ----- -----

84.07 29.65 19.429 19 2579.21 23.80 16.724 16 4370.87 16.26 12.924 12 5561.83 10.47 9.614 9 3652.34 6.23 6.792 6 4742.58 3.32 4.459 4 2732.68 1.49 2.616 2 3622.70 0.50 1.261 1 1512.71 0.09 0.395 0 232.71 0.00 0.018 0 1

------------------------------ ----- -----

β = 1.22


ZONA ESPIRAL


α


Ym



𝜃=( 〖〖〗𝐿𝑠 _𝑎𝑐𝑢𝑚𝑢𝑙𝑎𝑑𝑜 〗 ^2 180)/(2∗ 𝑅∗ 〖〗𝐿𝑠 _ )𝑡𝑜𝑡𝑎𝑙∗𝜋

∝= /3𝛽



Xm Ym αα G M

------------------------------ ----- -----10.81 0.05 0.286 0 17

30.78 1.25 2.321 2 1950.50 5.59 6.311 6 1869.20 15.03 12.257 12 1585.25 31.30 20.159 20 995.95 55.43 30.017 30 197.47 87.24 41.831 41 4985.20 124.43 55.600 55 3554.70 161.82 71.324 71 1937.93 174.22 77.717 77 42

------------------------------ ----- -----12.459 0.976 4.480 4 2831.623 6.515 11.642 11 3839.785 10.594 14.911 14 54

39.776 10.589 14.908 14 5430.008 5.841 11.015 11 010.728 0.723 3.853 3 51

------------------------------ ----- -----

37.93 174.22 77.717 77 4258.18 158.73 69.870 69 5286.95 121.07 54.317 54 1997.82 84.19 40.719 40 4395.32 53.00 29.077 29 484.01 29.57 19.390 19 2367.64 13.96 11.659 11 3948.80 5.03 5.884 5 5329.04 1.05 2.064 2 39.06 0.03 0.201 0 12

------------------------------ ----- -----

β = 0.54






Xm Ym αα G M

------------------------------ ----- -----6.25 0.01 0.095 0 5

16.25 0.18 0.646 0 3826.24 0.77 1.684 1 4136.19 2.03 3.212 3 1246.06 4.22 5.229 5 1355.74 7.57 7.735 7 4465.09 12.33 10.730 10 4373.92 18.72 14.213 14 12

81.94 26.92 18.186 18 1188.83 37.06 22.647 22 3894.16 49.22 27.597 27 3597.45 63.38 33.037 33 297.91 67.39 34.537 34 32

------------------------------ ----- -----7.379 0.341 2.646 2 38

17.253 1.883 6.227 6 1326.858 4.643 9.808 9 4836.044 8.580 13.389 13 2337.818 9.503 14.106 14 6

37.809 9.498 14.102 14 630.581 6.076 11.237 11 1421.126 2.840 7.656 7 3911.342 0.808 4.075 4 41.380 0.012 0.494 0 29

------------------------------ ----- -----

97.91 67.40 34.543 34 3295.75 54.65 29.715 29 4291.17 41.68 24.569 24 3484.85 30.74 19.912 19 5477.24 21.77 15.744 15 4468.70 14.68 12.064 12 359.53 9.29 8.874 8 5249.96 5.40 6.173 6 1040.15 2.78 3.960 3 5730.23 1.18 2.237 2 1420.25 0.35 1.002 1 010.25 0.05 0.257 0 15

------------------------------ ----- -----

β = 1.22


ZONA ESPIRAL


α


Ym




∝= /3𝛽



Xm Ym αα G M

------------------------------ ----- -----12.55 0.08 0.385 0 2332.52 1.47 2.590 2 3552.19 6.18 6.751 6 4570.73 16.16 12.867 12 5286.44 33.08 20.939 20 56

96.51 57.91 30.967 30 5897.02 90.32 42.951 42 5783.33 127.78 56.890 56 5351.07 164.82 72.785 72 4737.93 174.22 77.717 77 42

------------------------------ ----- -----14.175 1.266 5.103 5 633.213 7.220 12.265 12 1550.187 17.700 19.427 19 2556.652 23.515 22.542 22 32

56.652 23.515 22.542 22 3248.136 16.102 18.496 18 2930.831 6.180 11.334 11 2011.609 0.847 4.172 4 10

------------------------------ ----- -----

37.93 174.22 77.717 77 4256.43 160.31 70.608 70 3686.08 122.78 54.967 54 5897.65 85.74 41.282 41 1695.65 54.23 29.553 29 3384.64 30.44 19.779 19 4668.43 14.50 11.962 11 5749.67 5.31 6.099 6 529.93 1.15 2.193 2 119.95 0.04 0.242 0 14

------------------------------ ----- -----

β = 0.78


ZONA ESPIRAL


α


Ym




∝= /3𝛽



Xm Ym αα G M

------------------------------ ----- -----8.72 0.03 0.186 0 11

28.70 1.01 2.016 2 048.47 4.93 5.803 5 4867.33 13.75 11.545 11 3283.76 29.24 19.242 19 1495.18 52.53 28.896 28 5397.87 83.60 40.505 40 3092.18 108.85 49.739 49 44

------------------------------ ----- -----6.074 0.231 2.177 2 10

15.972 1.611 5.758 5 4525.621 4.214 9.339 9 2034.869 7.999 12.920 12 5540.305 10.895 15.126 15 7

40.313 10.900 15.130 15 736.951 9.045 13.755 13 4527.817 4.992 10.174 10 1018.248 2.109 6.593 6 358.395 0.442 3.012 3 0

------------------------------ ----- -----

92.18 108.85 49.739 49 4493.21 105.86 48.636 48 3898.15 70.85 35.821 35 4991.61 42.65 24.962 24 5777.89 22.42 16.059 16 360.28 9.67 9.111 9 640.94 2.95 4.119 4 721.05 0.40 1.083 1 41.05 0.00 0.003 0 0

------------------------------ ----- -----

β = 1.22

Coordenadas Polares

Xs= 83.74Ys= 36.09





Xm Ym αα G M

------------------------------ ----- -----7.98 0.02 0.156 0 9

27.96 0.93 1.914 1 5447.75 4.71 5.628 5 3766.66 13.32 11.297 11 1783.23 28.53 18.923 18 5594.89 51.53 28.503 28 3097.98 82.33 40.040 40 287.95 119.00 53.532 53 3160.25 156.80 68.981 68 5837.93 174.22 77.717 77 42

------------------------------ ----- -----9.656 0.585 3.466 3 27

29.004 5.443 10.628 10 37

46.548 14.936 17.790 17 4761.198 28.475 24.952 24 5762.103 29.569 25.461 25 27

62.109 29.577 25.464 25 2748.836 16.635 18.811 18 4831.641 6.523 11.649 11 3812.479 0.979 4.487 4 29

------------------------------ ----- -----

37.93 174.22 77.717 77 4254.65 161.85 71.341 71 2085.18 124.47 55.614 55 3697.46 87.28 41.843 41 5095.95 55.46 30.028 30 185.26 31.32 20.168 20 1069.21 15.05 12.264 12 1550.52 5.59 6.316 6 1830.80 1.25 2.324 2 19

------------------------------ ----- -----

β = 1.22



ZONA ESPIRAL


α


Ym



∝= /3𝛽



Xm Ym αα G M

------------------------------ ----- -----6.13 0.01 0.092 0 5

26.12 0.76 1.669 1 4045.94 4.18 5.202 5 1264.98 12.27 10.691 10 4181.85 26.81 18.135 18 894.11 49.06 27.535 27 3298.17 79.19 38.891 38 5389.56 115.47 52.202 52 1263.66 153.45 67.469 67 2837.93 174.22 77.717 77 42

------------------------------ ----- -----7.818 0.383 2.804 2 48

27.272 4.792 9.966 9 5745.031 13.877 17.128 17 759.990 27.074 24.290 24 1766.860 36.071 28.347 28 20

66.866 36.080 28.351 28 21

61.723 29.105 25.246 25 1447.212 15.417 18.084 18 529.766 5.744 10.922 10 5510.470 0.688 3.760 3 45

------------------------------ ----- -----

37.93 174.22 77.717 77 4258.69 158.27 69.656 69 3987.19 120.58 54.127 54 797.86 83.74 40.555 40 3395.22 52.64 28.938 28 5683.82 29.32 19.277 19 1667.40 13.80 11.571 11 3448.55 4.95 5.822 5 4928.78 1.02 2.028 2 18.80 0.03 0.189 0 11

------------------------------ ----- -----

CURVA N°4

DATOS :

R = 40 metrosIo = 75 ° 3 34 "


T = 30.73 m.Lc = 52.40 m.E = 10.44 m.

CURVA N°4

DATOS :

R = 40 metrosIo = 28 ° 35 51 "


T = 10.19 m.Lc = 19.96 m.E = 1.28 m.

0 '

0 '

ZONA ESPIRAL ZONA CIRCULAR𝜃=( 〖〖〗𝐿𝑠 _𝑎𝑐𝑢𝑚𝑢𝑙𝑎𝑑𝑜 〗 ^2 180)/(2∗ 𝑅∗ 〖〗𝐿𝑠 _ )𝑡𝑜𝑡𝑎𝑙∗𝜋

∝= /3𝛽



𝑋𝑚=𝑅∗𝑠𝑒𝑛𝜃

Y =2𝑚 𝑅 〖〗𝑠𝑒𝑛 ^2 /2𝜃

∝= /2𝜃

𝜃= 〖〗𝐿𝑠 _( .)𝑎𝑐𝑢𝑚 ∗𝐺𝑚

CURVAS HORIZONTALES

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