DISEÑO CURVAS HORIZONTALES CIRCULARES

DATOS DE DISEÑO

DATOS SIMBOLOGÍA VALOR UNIDADES

Velocidad Proyecto Vp 70 km/hRadio Calculado Rmin 113.40 m

Gradiente máximo i% 14Peralte e% 10

Radio Mínimo Rmin 115 m

Radio de diseño Rdis 210 m

Punto de Intersección PI 0 + 415 85 km+m,cmAngulo de Deflexión

α90°00'00'' grados,min, seg

90 grados

1.5707963267949 rad

ELEMENTOS DE LA CURVA CIRCULAR

ELEMENTOS FÓRMULA VALOR UNIDADES

Tangente 210.00 mCuerda C= 2.R.sen(α/2) 296.98 mFlecha f= R.(1-cos(α/2)) 61.51 mExternal E= R(sec(α/2)-1 ) 47.63 mLongitud de la Curva 329.87 m

ABCISAS DE LA CURVA CIRCULAR

ABSCISAS FÓRMULA VALOR UNIDADES

Abs. Punto de Comienzo Abs.Pc= abs.PI -T 0 + 205 85 km+m,cm

Abs. Punto de Termino Abs.Pt=abs.Pc + L 0 + 535 72 km+m,cm

Abs. Centro de la Curva Abs.Cc=abs.Pc +Lc/2 0 + 370 79 km+m,cm

T= R.tan(α/2)

Lc= (π.R.α)/180°

REPLANTEO DE CURVAS CIRCULARES HORIZONTALES MÉTODO DE COORDENADAS POLARES

KM 415.85 PUNTO ABSCISA CUERDA

ABS PC=ABS PI-T 205.85 CUERDA CUERDA ACMGRAD

ABS PT=ABS PC+LC 535.72PC 0+ 205.85

0+ 210 4.15 4.15 0.566

ABS CC= ABSPC +LC/2 370.790+ 220 10.00 14.15 1.3640+ 230 10.00 24.15 1.364

CC 0+ 240 10.00 34.15 1.3640+ 250 10.00 44.15 1.3640+ 260 10.00 54.15 1.3640+ 270 10.00 64.15 1.3640+ 280 10.00 74.15 1.3640+ 290 10.00 84.15 1.3640+ 300 10.00 94.15 1.3640+ 310 10.00 104.15 1.3640+ 320 10.00 114.15 1.3640+ 330 10.00 124.15 1.3640+ 340 10.00 134.15 1.3640+ 350 10.00 144.15 1.3640+ 360 10.00 154.15 1.3640+ 370 10.00 164.15 1.364

CC 0+ 370.79 0.79 164.94 0.108164.94

329.87

∆ 𝛾/2=(90∗𝐶)/(𝜋∗𝑅)

REPLANTEO DE CURVAS CIRCULARES HORIZONTALES REPLANTEO DE CURVAS CIRCULARES HORIZONTALES MÉTODO DE COORDENADAS POLARES MÉTODO DE COORDENADAS POLARES

PUNTO ABSCISA CUERDACUERDA CUERDA ACM

G,M,SS GRAD G,M,SSPC 0+ 535.72

0º33'58'' 0º33'58'' 0+ 530 5.72 5.72 0.780 0º46'49''1º21'51'' 1º55'49'' 0+ 520 10.00 15.72 1.364 1º21'51''1º21'51'' 3º17'40'' 0+ 510 10.00 25.72 1.364 1º21'51''1º21'51'' 4º39'31'' 0+ 500 10.00 35.72 1.364 1º21'51''1º21'51'' 6º01'22'' 0+ 490 10.00 45.72 1.364 1º21'51''1º21'51'' 7º23'13'' 0+ 480 10.00 55.72 1.364 1º21'51''1º21'51'' 8º45'04'' 0+ 470 10.00 65.72 1.364 1º21'51''1º21'51'' 10º06'55'' 0+ 460 10.00 75.72 1.364 1º21'51''1º21'51'' 11º28'46'' 0+ 450 10.00 85.72 1.364 1º21'51''1º21'51'' 12º50'37'' 0+ 440 10.00 95.72 1.364 1º21'51''1º21'51'' 14º12'28'' 0+ 430 10.00 105.72 1.364 1º21'51''1º21'51'' 15º34'19'' 0+ 420 10.00 115.72 1.364 1º21'51''1º21'51'' 16º56'10'' 0+ 410 10.00 125.72 1.364 1º21'51''1º21'51'' 18º18'01'' 0+ 400 10.00 135.72 1.364 1º21'51''1º21'51'' 19º39'53'' 0+ 390 10.00 145.72 1.364 1º21'51''1º21'51'' 21º01'44'' 0+ 380 10.00 155.72 1.364 1º21'51''1º21'51'' 22º23'35'' CC 0+ 370.79 9.21 164.93 1.256 1º15'23''0º06'27'' 22º30'03''

22º30'03''

∆ 𝛾/2=(90∗𝐶)/(𝜋∗𝑅)∆ 𝛾/2 𝐴𝐶𝑈𝑀 ∆ 𝛾/2=(90∗𝐶)/(𝜋∗𝑅)∆ 𝛾/2 𝐴𝐶𝑈𝑀

REPLANTEO DE CURVAS CIRCULARES HORIZONTALES MÉTODO DE COORDENADAS POLARES

0º46'49''2º08'40''3º30'31''4º52'22''6º14'13''7º36'04''8º57'55''

10º19'46''11º41'37''13º03'28''14º25'19''15º47'10''17º09'01''18º30'52''19º52'44''21º14'35''22º29'58''

∆ 𝛾/2 𝐴𝐶𝑈𝑀

r 210b alfa alfa rad alf acum

4.15 1.13227373799663 1.13227373799663 0.019761904761905 0.01976190476190510.00 2.72837045300392 3.86064419100055 0.047619047619048 0.06738095238095210.00 2.72837045300392 6.58901464400447 0.047619047619048 0.11510.00 2.72837045300392 9.31738509700839 0.047619047619048 0.16261904761904810.00 2.72837045300392 12.0457555500123 0.047619047619048 0.21023809523809510.00 2.72837045300392 14.7741260030162 0.047619047619048 0.25785714285714310.00 2.72837045300392 17.5024964560202 0.047619047619048 0.30547619047619110.00 2.72837045300392 20.2308669090241 0.047619047619048 0.35309523809523810.00 2.72837045300392 22.959237362028 0.047619047619048 0.40071428571428610.00 2.72837045300392 25.6876078150319 0.047619047619048 0.44833333333333310.00 2.72837045300392 28.4159782680358 0.047619047619048 0.49595238095238110.00 2.72837045300392 31.1443487210397 0.047619047619048 0.54357142857142910.00 2.72837045300392 33.8727191740437 0.047619047619048 0.59119047619047610.00 2.72837045300392 36.6010896270476 0.047619047619048 0.63880952380952410.00 2.72837045300392 39.3294600800515 0.047619047619048 0.68642857142857210.00 2.72837045300392 42.0578305330554 0.047619047619048 0.73404761904761910.00 2.72837045300392 44.7862009860593 0.047619047619048 0.781666666666667

0.79 0.215541265787315 45.0017422518467 0.003761904761905 0.78542857142857245.0017422518467 0.785428571428571

b alfa alfa rad alf acum9.21 2.51282918721661 2.51282918721661 0.043857142857143 0.043857142857143

10.00 2.72837045300392 5.24119964022053 0.047619047619048 0.0914761904761910.00 2.72837045300392 7.96957009322445 0.047619047619048 0.13909523809523810.00 2.72837045300392 10.6979405462284 0.047619047619048 0.18671428571428610.00 2.72837045300392 13.4263109992323 0.047619047619048 0.23433333333333310.00 2.72837045300392 16.1546814522362 0.047619047619048 0.28195238095238110.00 2.72837045300392 18.8830519052401 0.047619047619048 0.32957142857142910.00 2.72837045300392 21.6114223582441 0.047619047619048 0.37719047619047610.00 2.72837045300392 24.339792811248 0.047619047619048 0.42480952380952410.00 2.72837045300392 27.0681632642519 0.047619047619048 0.47242857142857110.00 2.72837045300392 29.7965337172558 0.047619047619048 0.52004761904761910.00 2.72837045300392 32.5249041702597 0.047619047619048 0.56766666666666710.00 2.72837045300392 35.2532746232636 0.047619047619048 0.61528571428571410.00 2.72837045300392 37.9816450762676 0.047619047619048 0.66290476190476210.00 2.72837045300392 40.7100155292715 0.047619047619048 0.7105238095238110.00 2.72837045300392 43.4383859822754 0.047619047619048 0.758142857142858

5.72 1.56062789911824 44.9990138813936 0.027238095238095 0.78538095238095344.9990138813936 0.785380952380952

185-45-alfa 185-45-alfa rad sen sen rad x y133.867726 2.33643258543 2.33643258543 0.90537996 0.01976062 5.75598635 4.15054032131.139356 2.28881353781 4.62524612324 0.4015624 0.04760105 18.7745001 14.1714535128.410985 2.24119449019 6.86644061343 0.4015624 0.04760105 30.7524162 24.2570275125.682615 2.19357544257 9.06001605601 0.4015624 0.04760105 41.8580995 34.4542505122.954244 2.14595639495 11.205972451 0.4015624 0.04760105 52.2288232 44.8121875120.225874 2.09833734734 13.3043097983 0.4015624 0.04760105 61.9779737 55.3829522117.497504 2.05071829972 15.355028098 0.4015624 0.04760105 71.200384 66.2228054114.769133 2.0030992521 17.3581273501 0.4015624 0.04760105 79.9763442 77.3934292112.040763 1.95548020448 19.3136075546 0.4015624 0.04760105 88.3746663 88.9634425109.312392 1.90786115686 21.2214687114 0.4015624 0.04760105 96.4550587 101.010241106.584022 1.86024210924 23.0817108207 0.4015624 0.04760105 104.269997 113.622273103.855651 1.81262306162 24.8943338823 0.4015624 0.04760105 111.866218 126.901899101.127281 1.765004014 26.65933789631 0.4015624 0.04760105 119.285937 140.96905198.3989104 1.71738496638 28.3767228627 0.4015624 0.04760105 126.567856 155.9659695.6705399 1.66976591876 30.0464887815 0.4015624 0.04760105 133.748018 172.06339892.9421695 1.62214687114 31.6686356526 0.4015624 0.04760105 140.860548 189.469

90.213799 1.57452782353 33.2431634761 0.4015624 0.04760105 147.938322 208.43859189.9982577 1.57076591876 34.8139293949 0.2138762 0.0037619 148.496939 210.01277289.9982577 1.57076591876 0.85181748 0.70712828 148.496939

185-45-alfa 185-45-alfa rad sen sen rad x y132.487171 2.31233734734 2.31233734734 0.58814515 0.04384308 12.4853415 9.21590954

129.7588 2.26471829972 4.57705564705 0.4015624 0.04760105 24.9539896 19.2637624127.03043 2.2170992521 6.79415489915 0.4015624 0.04760105 36.4716596 29.3998494

124.302059 2.16948020448 8.96363510363 0.4015624 0.04760105 47.1899389 39.6720942121.573689 2.12186115686 11.0854962605 0.4015624 0.04760105 57.2332466 50.1309761118.845319 2.07424210924 13.1597383697 0.4015624 0.04760105 66.705008 60.8305602116.116948 2.02662306162 15.1863614313 0.4015624 0.04760105 75.6922625 71.8296778113.388578 1.979004014 17.1653654453 0.4015624 0.04760105 84.2691577 83.1933135110.660207 1.93138496638 19.0967504117 0.4015624 0.04760105 92.4996376 94.9942729107.931837 1.88376591876 20.9805163305 0.4015624 0.04760105 100.439543 107.315227105.203466 1.83614687114 22.8166632016 0.4015624 0.04760105 108.138279 120.251263102.475096 1.78852782353 24.6051910252 0.4015624 0.04760105 115.640156 133.91311599.7467254 1.74090877591 26.3460998011 0.4015624 0.04760105 122.985496 148.43132497.0183549 1.69328972829 28.0393895294 0.4015624 0.04760105 130.211558 163.9616794.2899845 1.64567068067 29.68506021 0.4015624 0.04760105 137.353326 180.692373

91.561614 1.59805163305 31.2831118431 0.4015624 0.04760105 144.444215 198.85380490.0009861 1.57081353781 32.8539253809 0.9999483 0.02723473 148.489868 209.99277190.0009861 1.57081353781 0.85038508 0.70709461 148.489868

4.15054032 4.15054032 -4.1505403210.0075654 14.1581058 -10.020913210.0075654 24.1656712 -10.085573910.0075654 34.1732366 -10.19722310.0075654 44.1808021 -10.35793710.0075654 54.1883675 -10.570764710.0075654 64.195933 -10.839853210.0075654 74.2034984 -11.170623810.0075654 84.2110639 -11.570013310.0075654 94.2186293 -12.046798410.0075654 104.226195 -12.612031710.0075654 114.23376 -13.279626810.0075654 124.241326 -14.067151410.0075654 134.248891 -14.996909410.0075654 144.256456 -16.097437510.0075654 154.264022 -17.405602610.0075654 164.271587 -18.96959020.79000373 165.061591 -1.57418124165.061591 -210.012772

9.21590954 9.21590954 -9.2159095410.0075654 19.223475 -10.047852810.0075654 29.2310404 -10.13608710.0075654 39.2386059 -10.272244810.0075654 49.2461713 -10.458881910.0075654 59.2537367 -10.699584110.0075654 69.2613022 -10.999117610.0075654 79.2688676 -11.363635710.0075654 89.2764331 -11.800959410.0075654 99.2839985 -12.320954210.0075654 109.291564 -12.936035910.0075654 119.299129 -13.661852110.0075654 129.306695 -14.518209110.0075654 139.31426 -15.530345410.0075654 149.321826 -16.730703110.0075654 159.329391 -18.1614315

5.721415 165.050806 -11.1389673165.050806 -209.992771

DISEÑO CURVAS HORIZONTALES CIRCULARES

DATOS DE DISEÑO

DATOS SIMBOLOGÍA VALOR UNIDADES

Velocidad Proyecto Vp 60 km/hRadio Mínimo Rmin 115 mRadio Recomendado Rdis 210 mPeralte Máximo 10 %

Punto de Intersección PI km+m,cm

Angulo de Deflexión αgrados,min, seg

100.93 grados1.76 rad

ELEMENTOS DE LA CURVA CIRCULAR

ELEMENTOS FÓRMULA VALOR UNIDADES

Tangente 254.42 mCuerda C= 2.R.sen(α/2) 323.91 mFlecha f= R.(1-cos(α/2)) 76.32 mExternal E= R(sec(α/2)-1 ) 119.89 mLongitud de la Curva 369.91 m

ABCISAS DE LA CURVA CIRCULAR

ABSCISAS FÓRMULA VALOR UNIDADES

Abs. Punto de Comienzo Abs.Pc= abs.PI -T 0 + 132 32 km+m,cm

Abs. Punto de Termino Abs.Pt=abs.Pc + L 0 + 224 47 km+m,cm

Abs. Centro de la Curva Abs.Cc=abs.Pc +Lc/2 0 + 178 39 km+m,cm

T= R.tan(α/2)

Lc= (π.R.α)/180°

388.70

134.28504.20319.24

REPLANTEO DE CURVAS CIRCULARES HORIZONTALES MÉTODO DE LAS TANGENTES

Abscisa

grad

Pc 0+132 32

0+140 5.72 2.7298 5.72 0.14

0+150 15.72 7.5044 15.67 1.03

0+160 25.72 12.2791 25.52 2.75

0+170 35.72 17.0537 35.19 5.28

Cc 0+178 39 44.96 21.4655 43.91 8.32

Pt 0+224 47

0+220 4.20 2.0041 4.20 0.07

0+210 14.20 6.7787 14.16 0.84

Longitud de Cuerda

ɭ= π.R.ϒ/180° (m)

Ánguloϒ= (ɭ.180°)/π.R

XX=R.senϒ

(m)

YY= R.(1-cosϒ)

(m)

00

00

00

00

00

00

0+200 24.20 11.5534 24.03 2.43

0+190 34.20 16.3280 33.74 4.84

0+180 44.20 21.1027 43.20 8.05

Cc 0+178 39 -95.04 -45.3796 -85.41 35.71

00

00

00

Pc 134.28 140

Cc 319.24 310

Pt 504.20 500