Puente Colgante

Universidad Mayor de San Simn

Facultad de Ciencias y Tecnologia

Carrera: Ing. Civil

Hoja de CalculoDATOS :Longitud Total de Puente = 1430 m. Peso Espacifico del Acero = 7800 Kg/m3Numro de tramos = 4 vias Diametro del cable = 0.5 m.Pendolones Inclinados Seccin transversal del Cable es : 0.19635 m2Long. del Tramo Principal = 716 m. Volumen de 1 m de Cable = 0.19635 m3Long. de los Tramo Secundarios = 357 m. Peso de 1 m de Cable = 1531.53 Kg.

q = 1531.526 Kg/m1.- Catenaria del Tramo Principal

f = 71.6 f = 72 m.

Carga Lineal del Cable = 1531.526 Kg/mCarga Lineal del Cable = 1.532 Tn/m

180f = 72 m. n = 2.5 coef.de seguridada = 716 m.

Parabola Catenaria

T0 = 1363.101 Tn T0 = Tn

TA = 548.288 Tn

Hoja N 1 de

Materia: Estruc. EspecialesCalculado por: Grupo N 6Fecha de Entrega: 21/ 11 / 2005

= Kg/mm2

fl=

110

T 0=a2q8f

f=T 0q[cosh ( qa2T 01)]

T A=T 02+( qa2 )2 =QA T AMax=Qn T AT AMax A AMax

Universidad Mayor de San SimnFacultad de Ciencias y TecnologiaCarrera: Ing. Civil

Hoja de Calculo

Datos :

q = 1.53153 Tn/mT0 = 1363.10 Tn

2*T0/q = 1780.06 m.L = 735.464 m

((q*a)/(2*T0)) = 0.402

2.- Catenaria del Tramo Secundario.-

Hoja N de


L=2T 0q

senh ( qa2T 0 )

0.0 100.0 200.0 300.0 400.0 500.0 600.0 700.0 800.0

-80.000

-70.000

-60.000

-50.000

-40.000

-30.000

-20.000

-10.000

0.000

GRAFICA DE LA CATENARIA DEL TRAMO PRINCIPAL

Distancia (m.)

Altu

ra (m

)


Hoja de Calculo

Datos :

Longitud de los Tramo Secundarios = 357 m.

f = 35.7 m f = 36 m.

fa = 0 m d = 5 mf = 72 m

fb = 77 m fb = 78.201 m 1.201h = 77 mq = 1.532 Tn/m

H = 1267.477 Tn

H/q = 827.591 m

q/H = 0.0012 1/m

Hoja N de


fl=

110

H=ql2

h2( f a+f b2 f a f b)

H 'f '=ql '2

8cos = H

H '

y=Hq+Hqcosh ( q

Hx )

0 50 100 150 200 250 300 350 4000.0000

10.0000

20.0000

30.0000

40.0000

50.0000

60.0000

70.0000

80.0000

90.0000

GRAFICA DE LA CATENARIA DE TRAMO SECUNDARIO

Distancia (m.)

Altu

ra (m

.)


Hoja de Calculo

2.- Catenaria del Tramo Secundario.-

Datos :Carga de Rotura = 15536 Kg. q = 2.388 Kg/mCoeficiente de Seguridad = 3

La traccin del cable no debera exceder de :Seccin Total = 546.06 mm2.

TA = 5178.67 Kg. wA = 0.00437 Kg/m/mm2Calculo de la catenaria: tA = 9.48 Kg/mm2

1,- Adoptaremos una tensin arbitraria en el vertice de la catenaria:

Tv = 4500 Kg tv = 8.241 Kg/mm2 a = 800 m.d = 50 m.

h = 1884.42

0.42453 0.4277285661

0.026530.2122666667

xi = -283.18 m. xs = 516.8 m

ts = 8.553 Kg/mm2

Ts = 4670.305 Kg.

ts = 8.553 Kg/mm2 tv = 8.241 Kg/mm2tA = 9.48 Kg/mm2 tv = ?

tv = 9.138 Kg/mm2 Tv = 4990 Kg

Hoja N de


h=TVW A

dh=

ah=

dh=cosh ( a+xih )cosh ( x ih )

xi=h (arg senh(dh

senh2 ah(cosh ah1)2 )argtan ghcosh a

h1

senh ah )

senh2 ah(cosh ah1)2=argtan gh

cosh ah1

senh ah

=

tS=t vcosh ( xsh )xs=a+x i


Hoja de Calculo

Tv = 4990 Kg tv = 9.138 Kg/mm2 a = 800 m.d = 50 m.

h = 2089.54

0.38286 0.3852018402

0.023930.1914296102

xi = -270.28 m. xs = 529.7 m

ts = 9.43 Kg/mm2 ti = 9.21 Kg/mm2

Ts = 5151.025 Kg. Ti = 5031.63 Kg.

Con un coeficiente de seguridad de :

n = 3.02

L = 806.45 m.

Hoja N de


h=TVW A

dh=

ah=

dh=cosh ( a+xih )cosh ( x ih )

xi=h (arg senh(dh


h1

senh ah )

senh2 ah(cosh ah1)2=argtan gh

cosh ah1

senh ah

=

tS=t vcosh ( xsh )xs=a+x i

y=hcosh ( xh )

L=h (senh a+x ih senh x ih )

X (m.) Y (m.) X (m.) Y (m.)0 0.0000 0.0 0.000 0 01 0.0006 1.0 -0.413 1 0.0002392872 0.0024 2.0 -0.824 2 0.00095714813 0.0054 3.0 -1.234 3 0.00215358354 0.0097 4.0 -1.643 4 0.00382859345 0.0151 5.0 -2.051 5 0.00598217826 0.0217 6.0 -2.457 6 0.00861433847 0.0296 7.0 -2.862 7 0.01172507468 0.0387 8.0 -3.266 8 0.01531438759 0.0489 9.0 -3.669 9 0.01938227810 0.0604 10.0 -4.071 10 0.023928746911 0.0731 11.0 -4.471 11 0.028953795412 0.0870 12.0 -4.871 12 0.034457424513 0.1021 13.0 -5.269 13 0.040439635614 0.1184 14.0 -5.665 14 0.0469004315 0.1359 15.0 -6.061 15 0.053839809116 0.1547 16.0 -6.455 16 0.061257774617 0.1746 17.0 -6.849 17 0.069154328118 0.1958 18.0 -7.241 18 0.077529471619 0.2181 19.0 -7.631 19 0.086383206820 0.2417 20.0 -8.021 20 0.095715535821 0.2665 21.0 -8.409 21 0.105526460822 0.2924 22.0 -8.796 22 0.11581598423 0.3196 23.0 -9.182 23 0.126584107824 0.3480 24.0 -9.567 24 0.137830834625 0.3776 25.0 -9.951 25 0.14955616726 0.4084 26.0 -10.333 26 0.161760107727 0.4405 27.0 -10.714 27 0.174442659428 0.4737 28.0 -11.094 28 0.187603825229 0.5082 29.0 -11.473 29 0.201243607930 0.5438 30.0 -11.850 30 0.215362010831 0.5807 31.0 -12.227 31 0.229959037132 0.6187 32.0 -12.602 32 0.2450346933 0.6580 33.0 -12.976 33 0.260588973134 0.6985 34.0 -13.348 34 0.276621889935 0.7402 35.0 -13.720 35 0.293133444136 0.7831 36.0 -14.090 36 0.310123639537 0.8272 37.0 -14.459 37 0.3275924838 0.8726 38.0 -14.827 38 0.345539969539 0.9191 39.0 -15.194 39 0.363966112240 0.9668 40.0 -15.560 40 0.382870912241 1.0158 41.0 -15.924 41 0.40225437442 1.0660 42.0 -16.287 42 0.42211650243 1.1173 43.0 -16.649 43 0.442457300744 1.1699 44.0 -17.010 44 0.463276774745 1.2237 45.0 -17.369 45 0.484574928946 1.2787 46.0 -17.728 46 0.506351768147 1.3350 47.0 -18.085 47 0.528607297348 1.3924 48.0 -18.441 48 0.551341521749 1.4510 49.0 -18.796 49 0.574554446350 1.5109 50.0 -19.149 50 0.5982460765

51 0.622416417951 1.5719 51.0 -19.502 52 0.6470654758

0 50 100 150 200 250 300 350 4000

5

10

15

20

25

30

35

GRAFICO DE LA CATENARIA DEL TRAMO SECUNDARIO

Distancia (m.)

Altu

ra (m

.)

52 1.6342 52.0 -19.853 53 0.672193255953 1.6977 53.0 -20.203 54 0.69779976454 1.7624 54.0 -20.552 55 0.72388500655 1.8283 55.0 -20.899 56 0.750448987856 1.8954 56.0 -21.246 57 0.777491715557 1.9637 57.0 -21.591 58 0.805013195358 2.0332 58.0 -21.935 59 0.833013433659 2.1040 59.0 -22.278 60 0.861492436660 2.1759 60.0 -22.620 61 0.89045021161 2.2491 61.0 -22.960 62 0.919886763462 2.3235 62.0 -23.300 63 0.949802100563 2.3991 63.0 -23.638 64 0.980196229164 2.4759 64.0 -23.975 65 1.011069156365 2.5539 65.0 -24.311 66 1.042420889166 2.6331 66.0 -24.645 67 1.074251434767 2.7136 67.0 -24.979 68 1.106560800468 2.7952 68.0 -25.311 69 1.139348993569 2.8781 69.0 -25.642 70 1.172616021670 2.9622 70.0 -25.972 71 1.206361892371 3.0475 71.0 -26.300 72 1.240586613472 3.1340 72.0 -26.628 73 1.275290192673 3.2217 73.0 -26.954 74 1.310472637974 3.3106 74.0 -27.279 75 1.346133957575 3.4007 75.0 -27.603 76 1.382274159376 3.4921 76.0 -27.926 77 1.418893251877 3.5847 77.0 -28.248 78 1.455991243378 3.6785 78.0 -28.568 79 1.493568142379 3.7734 79.0 -28.887 80 1.531623957480 3.8697 80.0 -29.205 81 1.570158697381 3.9671 81.0 -29.522 82 1.609172370982 4.0657 82.0 -29.838 83 1.648664987183 4.1656 83.0 -30.152 84 1.688636554984 4.2666 84.0 -30.466 85 1.729087083585 4.3689 85.0 -30.778 86 1.770016582186 4.4724 86.0 -31.089 87 1.811425060287 4.5771 87.0 -31.399 88 1.853312527288 4.6831 88.0 -31.707 89 1.895678992789 4.7902 89.0 -32.015 90 1.938524466390 4.8985 90.0 -32.321 91 1.981848958191 5.0081 91.0 -32.626 92 2.025652477792 5.1189 92.0 -32.930 93 2.069935035493 5.2309 93.0 -33.233 94 2.114696641194 5.3441 94.0 -33.534 95 2.159937305295 5.4586 95.0 -33.835 96 2.205657038196 5.5742 96.0 -34.134 97 2.251855850297 5.6911 97.0 -34.432 98 2.29853375298 5.8092 98.0 -34.729 99 2.345690754399 5.9285 99.0 -35.025 100 2.3933268679

100 6.0490 100.0 -35.319 101 2.4414421037101 6.1707 101.0 -35.612 102 2.4900364727102 6.2937 102.0 -35.905 103 2.539109986103 6.4178 103.0 -36.196 104 2.5886626549

105 2.6386944907104 6.5432 104.0 -36.486 106 2.6892055049

105 6.6698 105.0 -36.774 107 2.7401957091106 6.7977 106.0 -37.062 108 2.7916651149107 6.9267 107.0 -37.348 109 2.8436137341108 7.0570 108.0 -37.633 110 2.8960415786109 7.1884 109.0 -37.917 111 2.9489486605110 7.3211 110.0 -38.200 112 3.0023349917111 7.4551 111.0 -38.482 113 3.0562005847112 7.5902 112.0 -38.762 114 3.1105454517113 7.7266 113.0 -39.042 115 3.1653696051114 7.8641 114.0 -39.320 116 3.2206730575115 8.0029 115.0 -39.597 117 3.2764558216116 8.1429 116.0 -39.873 118 3.3327179101117 8.2842 117.0 -40.147 119 3.389459336118 8.4266 118.0 -40.421 120 3.4466801123119 8.5703 119.0 -40.693 121 3.5043802519120 8.7152 120.0 -40.964 122 3.5625597682121 8.8613 121.0 -41.234 123 3.6212186745122 9.0087 122.0 -41.503 124 3.6803569842123 9.1572 123.0 -41.771 125 3.7399747109124 9.3070 124.0 -42.038 126 3.8000718682125 9.4580 125.0 -42.303 127 3.8606484698126 9.6102 126.0 -42.567 128 3.9217045297127 9.7637 127.0 -42.830 129 3.9832400619128 9.9184 128.0 -43.092 130 4.0452550803129 10.0743 129.0 -43.353 131 4.1077495993130 10.2314 130.0 -43.612 132 4.1707236332131 10.3897 131.0 -43.871 133 4.2341771963132 10.5493 132.0 -44.128 134 4.2981103032133 10.7101 133.0 -44.384 135 4.3625229686134 10.8721 134.0 -44.639 136 4.4274152071135 11.0353 135.0 -44.893 137 4.4927870337136 11.1998 136.0 -45.145 138 4.5586384634137 11.3655 137.0 -45.397 139 4.6249695111138 11.5324 138.0 -45.647 140 4.6917801922139 11.7005 139.0 -45.896 141 4.7590705219140 11.8699 140.0 -46.144 142 4.8268405156141 12.0405 141.0 -46.391 143 4.8950901888142 12.2123 142.0 -46.637 144 4.9638195572143 12.3853 143.0 -46.881 145 5.0330286365144 12.5596 144.0 -47.125 146 5.1027174426145 12.7351 145.0 -47.367 147 5.1728859914146 12.9118 146.0 -47.608 148 5.243534299147 13.0897 147.0 -47.848 149 5.3146623816148 13.2689 148.0 -48.086 150 5.3862702555149 13.4493 149.0 -48.324 151 5.458357937150 13.6309 150.0 -48.560 152 5.5309254427151 13.8138 151.0 -48.796 153 5.6039727892152 13.9979 152.0 -49.030 154 5.6774999932153 14.1832 153.0 -49.263 155 5.7515070716154 14.3697 154.0 -49.494 156 5.8259940413155 14.5575 155.0 -49.725 157 5.9009609194156 14.7465 156.0 -49.955 158 5.9764077231

159 6.0523344696157 14.9367 157.0 -50.183 160 6.1287411763

158 15.1282 158.0 -50.410 161 6.2056278607159 15.3209 159.0 -50.636 162 6.2829945404160 15.5148 160.0 -50.861 163 6.3608412332161 15.7100 161.0 -51.085 164 6.4391679569162 15.9064 162.0 -51.307 165 6.5179747294163 16.1040 163.0 -51.529 166 6.5972615688164 16.3028 164.0 -51.749 167 6.6770284932165 16.5029 165.0 -51.968 168 6.7572755208166 16.7042 166.0 -52.186 169 6.8380026702167 16.9068 167.0 -52.403 170 6.9192099597168 17.1105 168.0 -52.619 171 7.000897408169 17.3156 169.0 -52.833 172 7.0830650337170 17.5218 170.0 -53.047 173 7.1657128558171 17.7293 171.0 -53.259 174 7.248840893172 17.9380 172.0 -53.470 175 7.3324491646173 18.1479 173.0 -53.680 176 7.4165376895174 18.3591 174.0 -53.889 177 7.5011064871175 18.5715 175.0 -54.096 178 7.5861555767176 18.7852 176.0 -54.303 179 7.6716849779177 19.0001 177.0 -54.508 180 7.7576947101178 19.2162 178.0 -54.712 181 7.8441847932179 19.4336 179.0 -54.915 182 7.9311552469180 19.6522 180.0 -55.117 183 8.0186060911181 19.8720 181.0 -55.318 184 8.1065373458182 20.0931 182.0 -55.518 185 8.1949490313183 20.3154 183.0 -55.716 186 8.2838411677184 20.5389 184.0 -55.913 187 8.3732137754185 20.7637 185.0 -56.109 188 8.4630668749186 20.9898 186.0 -56.305 189 8.5534004868187 21.2170 187.0 -56.498 190 8.6442146317188 21.4455 188.0 -56.691 191 8.7355093305189 21.6753 189.0 -56.883 192 8.827284604190 21.9063 190.0 -57.073 193 8.9195404732191 22.1385 191.0 -57.262 194 9.0122769594192 22.3719 192.0 -57.451 195 9.1054940838193 22.6067 193.0 -57.638 196 9.1991918676194 22.8426 194.0 -57.824 197 9.2933703324195 23.0798 195.0 -58.008 198 9.3880294997196 23.3182 196.0 -58.192 199 9.4831693912197 23.5579 197.0 -58.374 200 9.5787900287198 23.7988 198.0 -58.556 201 9.6748914341199 24.0410 199.0 -58.736 202 9.7714736294200 24.2844 200.0 -58.915 203 9.8685366367201 24.5290 201.0 -59.093 204 9.9660804783202 24.7749 202.0 -59.269 205 10.0641051764203 25.0220 203.0 -59.445 206 10.1626107537204 25.2704 204.0 -59.620 207 10.2615972325205 25.5201 205.0 -59.793 208 10.3610646356206 25.7709 206.0 -59.965 209 10.4610129858207 26.0230 207.0 -60.136 210 10.5614423059208 26.2764 208.0 -60.306 211 10.662352619209 26.5310 209.0 -60.475 212 10.7637439482

213 10.8656163166210 26.7869 210.0 -60.642 214 10.9679697477

211 27.0440 211.0 -60.809 215 11.0708042648212 27.3023 212.0 -60.974 216 11.1741198915213 27.5619 213.0 -61.138 217 11.2779166515214 27.8228 214.0 -61.301 218 11.3821945686215 28.0849 215.0 -61.463 219 11.4869536666216 28.3482 216.0 -61.624 220 11.5921939695217 28.6128 217.0 -61.784 221 11.6979155015218 28.8787 218.0 -61.942 222 11.8041182867219 29.1458 219.0 -62.100 223 11.9108023495220 29.4141 220.0 -62.256 224 12.0179677142221 29.6837 221.0 -62.411 225 12.1256144056222 29.9546 222.0 -62.565 226 12.2337424481223 30.2267 223.0 -62.718 227 12.3423518666224 30.5000 224.0 -62.870 228 12.4514426859225 30.7746 225.0 -63.020 229 12.5610149311226 31.0505 226.0 -63.170 230 12.6710686272227 31.3276 227.0 -63.318 231 12.7816037994228 31.6060 228.0 -63.465 232 12.892620473229 31.8856 229.0 -63.611 233 13.0041186735230 32.1665 230.0 -63.756 234 13.1160984265231 32.4486 231.0 -63.900 235 13.2285597575232 32.7320 232.0 -64.042 236 13.3415026923233 33.0166 233.0 -64.184 237 13.4549272568234 33.3025 234.0 -64.324 238 13.5688334769235 33.5897 235.0 -64.463 239 13.6832213788236 33.8781 236.0 -64.601 240 13.7980909886237 34.1678 237.0 -64.738 241 13.9134423327238 34.4587 238.0 -64.874 242 14.0292754375239 34.7509 239.0 -65.009 243 14.1455903294240 35.0444 240.0 -65.142 244 14.2623870353241 35.3391 241.0 -65.275 245 14.3796655817242 35.6351 242.0 -65.406 246 14.4974259955243 35.9323 243.0 -65.536 247 14.6156683038244 36.2308 244.0 -65.665 248 14.7343925336245 36.5305 245.0 -65.793 249 14.8535987121246 36.8315 246.0 -65.920 250 14.9732868666247 37.1338 247.0 -66.045 251 15.0934570245248 37.4374 248.0 -66.170 252 15.2141092133249 37.7422 249.0 -66.293 253 15.3352434607250 38.0482 250.0 -66.415 254 15.4568597944251 38.3556 251.0 -66.536 255 15.5789582423252 38.6641 252.0 -66.656 256 15.7015388323253 38.9740 253.0 -66.775 257 15.8246015925254 39.2851 254.0 -66.893 258 15.9481465512255 39.5975 255.0 -67.009 259 16.0721737365256 39.9112 256.0 -67.125 260 16.1966831769257 40.2261 257.0 -67.239 261 16.3216749009258 40.5423 258.0 -67.352 262 16.4471489371259 40.8597 259.0 -67.464 263 16.5731053143260 41.1785 260.0 -67.575 264 16.6995440614261 41.4985 261.0 -67.685 265 16.8264652072

266 16.9538687809262 41.8197 262.0 -67.794 267 17.0817548116263 42.1422 263.0 -67.901 268 17.2101233287

264 42.4660 264.0 -68.008 269 17.3389743614265 42.7911 265.0 -68.113 270 17.4683079394266 43.1175 266.0 -68.217 271 17.5981240923267 43.4451 267.0 -68.320 272 17.7284228497268 43.7740 268.0 -68.422 273 17.8592042416269 44.1041 269.0 -68.522 274 17.9904682978270 44.4355 270.0 -68.622 275 18.1222150485271 44.7682 271.0 -68.721 276 18.2544445238272 45.1022 272.0 -68.818 277 18.3871567541273 45.4375 273.0 -68.914 278 18.5203517696274 45.7740 274.0 -69.009 279 18.6540296009275 46.1118 275.0 -69.103 280 18.7881902787276 46.4509 276.0 -69.196 281 18.9228338336277 46.7912 277.0 -69.288 282 19.0579602965278 47.1329 278.0 -69.378 283 19.1935696984279 47.4758 279.0 -69.468 284 19.3296620702280 47.8200 280.0 -69.556 285 19.4662374432281 48.1654 281.0 -69.643 286 19.6032958487282 48.5122 282.0 -69.729 287 19.740837318283 48.8602 283.0 -69.814 288 19.8788618826284 49.2095 284.0 -69.898 289 20.0173695742285 49.5601 285.0 -69.981 290 20.1563604244286 49.9119 286.0 -70.062 291 20.2958344652287 50.2651 287.0 -70.143 292 20.4357917284288 50.6195 288.0 -70.222 293 20.5762322462289 50.9752 289.0 -70.300 294 20.7171560506290 51.3322 290.0 -70.377 295 20.8585631739291 51.6904 291.0 -70.453 296 21.0004536486292 52.0500 292.0 -70.528 297 21.1428275071293 52.4108 293.0 -70.601 298 21.2856847821294 52.7730 294.0 -70.674 299 21.4290255062295 53.1364 295.0 -70.745 300 21.5728497123296 53.5011 296.0 -70.816 301 21.7171574334297 53.8671 297.0 -70.885 302 21.8619487024298 54.2343 298.0 -70.953 303 22.0072235526299 54.6029 299.0 -71.020 304 22.1529820172300 54.9727 300.0 -71.086 305 22.2992241296301 55.3439 301.0 -71.150 306 22.4459499233302 55.7163 302.0 -71.214 307 22.5931594318303 56.0900 303.0 -71.276 308 22.740852689304 56.4650 304.0 -71.337 309 22.8890297287305 56.8413 305.0 -71.397 310 23.0376905847306 57.2189 306.0 -71.457 311 23.1868352912307 57.5978 307.0 -71.514 312 23.3364638822308 57.9779 308.0 -71.571 313 23.4865763921309 58.3594 309.0 -71.627 314 23.6371728553310 58.7421 310.0 -71.681 315 23.7882533061311 59.1262 311.0 -71.735 316 23.9398177793312 59.5115 312.0 -71.787 317 24.0918663096313 59.8982 313.0 -71.838 318 24.2443989317314 60.2861 314.0 -71.888 319 24.3974156806315 60.6753 315.0 -71.937 320 24.5509165914316 61.0659 316.0 -71.985 321 24.7049016991317 61.4577 317.0 -72.031 322 24.8593710392318 61.8508 318.0 -72.077 323 25.0143246469

319 62.2452 319.0 -72.121 324 25.1697625578320 62.6410 320.0 -72.165 325 25.3256848073321 63.0380 321.0 -72.207 326 25.4820914314322 63.4363 322.0 -72.248 327 25.6389824657323 63.8359 323.0 -72.288 328 25.7963579462324 64.2369 324.0 -72.327 329 25.954217909325 64.6391 325.0 -72.364 330 26.1125623902326 65.0426 326.0 -72.401 331 26.2713914261327 65.4474 327.0 -72.436 332 26.430705053328 65.8536 328.0 -72.470 333 26.5905033075329 66.2610 329.0 -72.504 334 26.7507862261330 66.6698 330.0 -72.536 335 26.9115538456331 67.0798 331.0 -72.566 336 27.0728062027332 67.4912 332.0 -72.596 337 27.2345433344333 67.9038 333.0 -72.625 338 27.3967652778334 68.3178 334.0 -72.652 339 27.55947207335 68.7331 335.0 -72.679 340 27.7226637482336 69.1497 336.0 -72.704 341 27.8863403499337 69.5676 337.0 -72.728 342 28.0505019126338 69.9868 338.0 -72.751 343 28.2151484737339 70.4073 339.0 -72.773 344 28.3802800711340 70.8291 340.0 -72.794 345 28.5458967425341 71.2523 341.0 -72.814 346 28.711998526342 71.6767 342.0 -72.832 347 28.8785854594343 72.1025 343.0 -72.850 348 29.0456575811344 72.5296 344.0 -72.866 349 29.2132149292345 72.9580 345.0 -72.881 350 29.3812575421346 73.3877 346.0 -72.895 351 29.5497854584347 73.8187 347.0 -72.908 352 29.7187987165348 74.2511 348.0 -72.920 353 29.8882973553349 74.6847 349.0 -72.931 354 30.0582814135350 75.1197 350.0 -72.940 355 30.2287509301351 75.5560 351.0 -72.948 356 30.3997059442352 75.9936 352.0 -72.956 357 30.5711464948353 76.4325 353.0 -72.962354 76.8728 354.0 -72.967355 77.3144 355.0 -72.971356 77.7572 356.0 -72.974357 78.2015 357.0 -72.975

358.0 -72.976359.0 -72.975360.0 -72.974361.0 -72.971362.0 -72.967363.0 -72.962364.0 -72.956365.0 -72.948366.0 -72.940367.0 -72.931368.0 -72.920369.0 -72.908370.0 -72.895371.0 -72.881372.0 -72.866373.0 -72.850

374.0 -72.832375.0 -72.814376.0 -72.794377.0 -72.773378.0 -72.751379.0 -72.728380.0 -72.704381.0 -72.679382.0 -72.652383.0 -72.625384.0 -72.596385.0 -72.566386.0 -72.536387.0 -72.504388.0 -72.470389.0 -72.436390.0 -72.401391.0 -72.364392.0 -72.327393.0 -72.288394.0 -72.248395.0 -72.207396.0 -72.165397.0 -72.121398.0 -72.077399.0 -72.031400.0 -71.985401.0 -71.937402.0 -71.888403.0 -71.838404.0 -71.787405.0 -71.735406.0 -71.681407.0 -71.627408.0 -71.571409.0 -71.514410.0 -71.457411.0 -71.397412.0 -71.337413.0 -71.276414.0 -71.214415.0 -71.150416.0 -71.086417.0 -71.020418.0 -70.953419.0 -70.885420.0 -70.816421.0 -70.745422.0 -70.674423.0 -70.601424.0 -70.528425.0 -70.453426.0 -70.377427.0 -70.300428.0 -70.222

429.0 -70.143430.0 -70.062431.0 -69.981432.0 -69.898433.0 -69.814434.0 -69.729435.0 -69.643436.0 -69.556437.0 -69.468438.0 -69.378439.0 -69.288440.0 -69.196441.0 -69.103442.0 -69.009443.0 -68.914444.0 -68.818445.0 -68.721446.0 -68.622447.0 -68.522448.0 -68.422449.0 -68.320450.0 -68.217451.0 -68.113452.0 -68.008453.0 -67.901454.0 -67.794455.0 -67.685456.0 -67.575457.0 -67.464458.0 -67.352459.0 -67.239460.0 -67.125461.0 -67.009462.0 -66.893463.0 -66.775464.0 -66.656465.0 -66.536466.0 -66.415467.0 -66.293468.0 -66.170469.0 -66.045470.0 -65.920471.0 -65.793472.0 -65.665473.0 -65.536474.0 -65.406475.0 -65.275476.0 -65.142477.0 -65.009478.0 -64.874479.0 -64.738480.0 -64.601481.0 -64.463482.0 -64.324483.0 -64.184

484.0 -64.042485.0 -63.900486.0 -63.756487.0 -63.611488.0 -63.465489.0 -63.318490.0 -63.170491.0 -63.020492.0 -62.870493.0 -62.718494.0 -62.565495.0 -62.411496.0 -62.256497.0 -62.100498.0 -61.942499.0 -61.784500.0 -61.624501.0 -61.463502.0 -61.301503.0 -61.138504.0 -60.974505.0 -60.809506.0 -60.642507.0 -60.475508.0 -60.306509.0 -60.136510.0 -59.965511.0 -59.793512.0 -59.620513.0 -59.445514.0 -59.269515.0 -59.093516.0 -58.915517.0 -58.736518.0 -58.556519.0 -58.374520.0 -58.192521.0 -58.008522.0 -57.824523.0 -57.638524.0 -57.451525.0 -57.262526.0 -57.073527.0 -56.883528.0 -56.691529.0 -56.498530.0 -56.305531.0 -56.109532.0 -55.913533.0 -55.716534.0 -55.518535.0 -55.318536.0 -55.117537.0 -54.915538.0 -54.712

539.0 -54.508540.0 -54.303541.0 -54.096542.0 -53.889543.0 -53.680544.0 -53.470545.0 -53.259546.0 -53.047547.0 -52.833548.0 -52.619549.0 -52.403550.0 -52.186551.0 -51.968552.0 -51.749553.0 -51.529554.0 -51.307555.0 -51.085556.0 -50.861557.0 -50.636558.0 -50.410559.0 -50.183560.0 -49.955561.0 -49.725562.0 -49.494563.0 -49.263564.0 -49.030565.0 -48.796566.0 -48.560567.0 -48.324568.0 -48.086569.0 -47.848570.0 -47.608571.0 -47.367572.0 -47.125573.0 -46.881574.0 -46.637575.0 -46.391576.0 -46.144577.0 -45.896578.0 -45.647579.0 -45.397580.0 -45.145581.0 -44.893582.0 -44.639583.0 -44.384584.0 -44.128585.0 -43.871586.0 -43.612587.0 -43.353588.0 -43.092589.0 -42.830590.0 -42.567591.0 -42.303592.0 -42.038593.0 -41.771

594.0 -41.503595.0 -41.234596.0 -40.964597.0 -40.693598.0 -40.421599.0 -40.147600.0 -39.873601.0 -39.597602.0 -39.320603.0 -39.042604.0 -38.762605.0 -38.482606.0 -38.200607.0 -37.917608.0 -37.633609.0 -37.348610.0 -37.062611.0 -36.774612.0 -36.486613.0 -36.196614.0 -35.905615.0 -35.612616.0 -35.319617.0 -35.025618.0 -34.729619.0 -34.432620.0 -34.134621.0 -33.835622.0 -33.534623.0 -33.233624.0 -32.930625.0 -32.626626.0 -32.321627.0 -32.015628.0 -31.707629.0 -31.399630.0 -31.089631.0 -30.778632.0 -30.466633.0 -30.152634.0 -29.838635.0 -29.522636.0 -29.205637.0 -28.887638.0 -28.568639.0 -28.248640.0 -27.926641.0 -27.603642.0 -27.279643.0 -26.954644.0 -26.628645.0 -26.300646.0 -25.972647.0 -25.642648.0 -25.311

649.0 -24.979650.0 -24.645651.0 -24.311652.0 -23.975653.0 -23.638654.0 -23.300655.0 -22.960656.0 -22.620657.0 -22.278658.0 -21.935659.0 -21.591660.0 -21.246661.0 -20.899662.0 -20.552663.0 -20.203664.0 -19.853665.0 -19.502666.0 -19.149667.0 -18.796668.0 -18.441669.0 -18.085670.0 -17.728671.0 -17.369672.0 -17.010673.0 -16.649674.0 -16.287675.0 -15.924676.0 -15.560677.0 -15.194678.0 -14.827679.0 -14.459680.0 -14.090681.0 -13.720682.0 -13.348683.0 -12.976684.0 -12.602685.0 -12.227686.0 -11.850687.0 -11.473688.0 -11.094689.0 -10.714690.0 -10.333691.0 -9.951692.0 -9.567693.0 -9.182694.0 -8.796695.0 -8.409696.0 -8.021697.0 -7.631698.0 -7.241699.0 -6.849700.0 -6.455701.0 -6.061702.0 -5.665703.0 -5.269

704.0 -4.871705.0 -4.471706.0 -4.071707.0 -3.669708.0 -3.266709.0 -2.862710.0 -2.457711.0 -2.051712.0 -1.643713.0 -1.234714.0 -0.824715.0 -0.413716.0 0.000

0 50 100 150 200 250 300 350 4000

5

10

15

20

25

30

35


Distancia (m.)

Altu

ra (m

.)

Universidad Mayor de San Simn

Facultad de Ciencias y Tecnologia

Carrera: Ing. Civil

Hoja de CalculoDATOS :Longitud Total de Puente = 1430 m. Peso Espacifico del Acero = 7800 Kg/m3Numro de tramos = 4 vias Diametro del cable = 0.3 m.Pendolones Inclinados Seccin transversal del Cable es : 0.07069 m2Long. del Tramo Principal = 716 m. Volumen de 1 m de Cable = 0.07069 m3Long. de los Tramo Secundarios = 357 m. Peso de 1 m de Cable = 551.35 Kg.

q = 551.35 Kg/m1.- Catenaria del Tramo Principal

f = 89.5 f = 72 m.

Carga Lineal del Cable = 551.350 Kg/m 180Carga Lineal del Cable = 0.551 Tn/m n = 3 coef.de seguridad

Q = 12723.45 Tn.f = 72 m.a = 716 m.

Catenaria

g = 197383.125u = 39697.1648

Hoja N 1 de 8


= Kg/mm2

fl=18

f=T 0q[cosh ( qa2T 01)]

=QA

= qa2T 0

ec . 1

f=T 0q [cosh ( )1 ] ec . 2

=197383 .125T 0

ec . 1

72=T 0

551 .35 [cosh ( )1 ] ec . 2

T 0=39697 .1648[cosh ( )1 ]

ec . 2


Hoja de CalculoResolviendo las dos ecuaciones, como simultaneas, por aproximaciones sucesivas se obtiene:

T0 = 497195.22 Kg 7.60 Kg/mm2 Ok!0.39699

La tensin en el cable es :

T = 536892.38 Kg.T = 536.89 Tn Tmax = 4241.15 Tn Ok!

x z0 0

100 34.84200 58.12 L = 735 m.300 70.13400 71.02500 60.80600 39.33700 6.37716 0.00

Hoja N 2 de 8


=

L=2T 0q

senh ( qa2T 0 )

T=T 0cosh ( )

=TS=

y=T 0q [cosh ( q2T 0 (2xa ))cosh ( qa2T 0 )] Catenaria

0 100 200 300 400 500 600 700 800-80.0000

-70.0000

-60.0000

-50.0000

-40.0000

-30.0000

-20.0000

-10.0000

0.0000

10.0000

GRAFICA DE LA CATENARIA DEL TRAMO PRINCIPAL

Catenaria

Distancia (m .)

Altu

ra (m

.)


Hoja de Calculo2.- Catenaria del Tramo Secundario.-

Datos :12723.45 Tn. q = 551.350 Kg/m

Coeficiente de Seguridad = 3 Seccin Total = 0.070686 m2La traccin del cable no debera exceder de : Long. del Tramo Secundario = 357 m.

Tmax = 4241.15 Tn ta max = 60 Kg/mm2Calculo de la catenaria:

1.- Adoptaremos una tensin arbitraria en el vertice de la catenaria:f = 72 m.

Tv = 492989.90 Kg tv = 6.974 Kg/mm2 a = 357 m.d = 80 m.

h = 894.15

0.40191848220.39926

0.19963063680.08947

Hoja N 3 de 8


Carga de Rotura (Q) =

h=T Vq

dh=

ah= senh2 ah(cosh ah1)2=

argtan ghcosh a

h1

senh ah

=


Hoja de Calculo2.-Calculamos la distancia " xi" cituado a la derecha del punto A

Haciendo operaciones tenemos :

xi = 18.937 m.

3.-Conocido la abscisa xi del apoyo inferior A, podemos calcular la abscisa xs del apoyo superior B:

xs = 375.94 m.y, por consiguiente, los valores de la tensin en ambos apoyos sern, respectivamente :

TA = 493100.467 Kg. TA = 493.10 Tn.

TB = 537208.43 Kg. TB = 537.21 Tn.T = 536892.38

Tmax = 4241.15 Tnta max = 60 Kg/mm2

Tv max = 3892053.9 Kg. Tv max = 3892.05 Tn.f = 72 m.

Tv = 3892053.90 Kg tv = 55.061 Kg/mm2 a = 357 m.d = 80 m.q = 551.350 Kg/m

h = 7059.14

0.05057811550.05057

0.0252863630.01133

Hoja N 4 de 8


dh=cosh ( a+xih )cosh ( xih )

xi=h (arg senh(dh


h1

senh ah )

xs=a+x i

En el pto . A . .. . . .. . . .. . . T i=T v cosh ( xih )En el pto . B . . . .. . . .. . . .. T S=T v cosh ( x Sh )Si:T B . . . .. . . .. . . .. .T vTmax . .. . . .. . . .. .?

h=T Vq

dh=

ah= senh2 ah(cosh ah1)2=

argtan ghcosh a

h1

senh ah

=


Hoja de CalculoCalculamos la distancia " xi" cituado a la derecha del punto A

Haciendo operaciones tenemos :

xi = 1390.267 m.

Conocido la abscisa xi del apoyo inferior A, podemos calcular la abscisa xs del apoyo superior B:

xs = 1747.27 m.y, por consiguiente, los valores de la tensin en ambos apoyos sern, respectivamente :

TA = 3967779.88 Kg. TA = 3967.78 Tn.

TB = 4011887.84 Kg. TB = 4011.89 Tn.

Tmax = 4241.15 Tnta max = 60 Kg/mm2

Con un coeficiente de seguridad de :

L = 366.56 m. x y0 894.151333098

50 895.549671064100 899.749058601150 906.762630318200 916.612322868250 929.32894356300 944.952266721350 963.531158097357 966.371250623

Hoja N 5 de 8


y=hcosh ( xh )

L=h (senh a+x ih senh x ih )

dh=cosh ( a+xih )cosh ( xih )

xi=h (arg senh(dh


h1

senh ah )

xs=a+x i

En el pto . A . .. . . .. . . .. . . T i=T v cosh ( xih )En el pto . B . . . .. . . .. . . .. T S=T v cosh ( x Sh )


Hoja de Calculo

Tabla N 3 Hoja N 6 de 8


0 50 100 150 200 250 300 350 400840

860

880

900

920

940

960

980

GRAFICA DE LA CTENARIA DE TRAMO SECUNDARIO

Catenaria

Distancia (m.)

Altu

ra R

elat

iva

(m)

0 50 100 150 200 250 300 350 400497195.2

497195.2

497195.3

497195.3

497195.4

497195.4


Catenaria

Distancia (m)

Altu

ra R

elat

iva

(m)


Hoja de CalculoEn este caso las expresiones que describen el comportamiento del cable son bastante mas complejas que enel cable simetrico.

Existen dos alternativas de enfoque al problema presentado:- Suponer que la componente horizontal de la tensin en el extremo superior es la misma que la que proviene

del tramo central. Con esta hiptesis se asume que la torre de sustentacin no soportr ninguna fuerza horizontal por concepto de cargas gravitacinales.

- Suponer que la tensin en la parte superior del cable es la misma que la tensin en el tramo central del cable. Con esta hiptesis se asume que el cable est colocado sobre rodillos libres de rozamiento coloca-dos en las torres de sustentacin,y que las torres pueden resistir fuerzas horizontales de pequea magnitud.

La situacin real se ubic en algn punto intermedio entre las dos hiptesis, por lo que, es conveniente que se diseen los puentes de modo que los resultados obtenidos con las dos hiptesis sean similares.

Asumiendo como vlida la primera hiptesis para el problema propuesto, la componente horizontal de la tensin en la parte superior del cable es igual a la componente horizontal en el tramo central, por lo que, tomando la informacin anterior, se tiene: H = 497195.22 kg.

Las expresiones que describen el comportamiento del cable asimtrico son:

DATOS :Seccin del cable = 0.07069 m2 E = 2000000 Kg/cm2

q = 551.350 Kg/m E = 2.000E+010 Kg/m2z = 80 m.x = 357 m.

0.19794

0.41878

368.13 m.

506967.39 Kg. T = 506967.4 Kg.5.12

497325.496 Kg. T' = 497325.5 Kg

214352.8 Kg S = 214352.8 Kg

11382.5 Kg S = 11382.5 KgHoja N 7 de 8


= qx2H

=

=senh1[ (z x)senh( ) ]+=L=2H

qsenh( )cosh( )=

T=Hcosh ( )=T '=q

2[Lcoth( ) z ]=

cot angh( )=

S=Hsenh ( )=S '= q

2 [ zcoth ( )L ]=


Hoja de Calculo

369.59 m.

82.7 m.

0.13 m. 0.575 m.

Para equilibrar totalmente a las tensiones en el cable se requiere de una fuerza de 497195,22 Kg (T), que debe ser provista por el anclaje.La deflexin que se produce en el extremo del voladizo debido al alargamiento del cable es aproximadamente:

x y0 497195.2

50 497195.2100 497195.2150 497195.2200 497195.3250 497195.3300 497195.3350 497195.3357 497195.3

Tabla N 3

Hoja N 8 de 8


Z =

hxhy cosh

X=(Hq )Ln [ T +T '+qLT+T 'qL ]=Z=( S+S 'T+T ' )L=L=(HL2X ) 1EA=

Tabla N 11 Iteracin 2 Iteracin 2 Iteracin 4 Iteracin

T0 estimado 50000 1593.19 0.00 #NUM! 3.95 123.89 ### #NUM!T0 calculado 1593.19 0.00 #NUM! #NUM!

1 Iteracin 2 Iteracin 2 Iteracin 4 Iteracin 5 Iteracin 6 IteracinT0 estimado 50000 98406.81 182550.72 303437.68 425721.22 488653.48 3.95 2.01 1.08 0.65 0.46 0.40T0 calculado 1593.19 14262.89 61663.76 181154.14 362788.96 480036.69

q/(2*T0)= 0.0005544598x z z0 0 0.00001 0.407 -0.40692 0.813 -0.81263 1.217 -1.21714 1.620 -1.62045 2.023 -2.02266 2.423 -2.42357 2.823 -2.82328 3.222 -3.22189 3.619 -3.6191

10 4.015 -4.015211 4.410 -4.410212 4.804 -4.804013 5.197 -5.196514 5.588 -5.587915 5.978 -5.978116 6.367 -6.367117 6.755 -6.754918 7.142 -7.141619 7.527 -7.527020 7.911 -7.911221 8.294 -8.294322 8.676 -8.676223 9.057 -9.056924 9.436 -9.436425 9.815 -9.814726 10.192 -10.191827 10.568 -10.567728 10.942 -10.942529 11.316 -11.316130 11.688 -11.688531 12.060 -12.059732 12.430 -12.429733 12.799 -12.798534 13.166 -13.166235 13.533 -13.532736 13.898 -13.898037 14.262 -14.2621

38 14.625 -14.625039 14.987 -14.986840 15.347 -15.347441 15.707 -15.706842 16.065 -16.065043 16.422 -16.422044 16.778 -16.777945 17.133 -17.132646 17.486 -17.486147 17.838 -17.838448 18.190 -18.189649 18.540 -18.539650 18.888 -18.888451 19.236 -19.236152 19.583 -19.582553 19.928 -19.927854 20.272 -20.271955 20.615 -20.614956 20.957 -20.956757 21.297 -21.297358 21.637 -21.636759 21.975 -21.975060 22.312 -22.312061 22.648 -22.648062 22.983 -22.982763 23.316 -23.316364 23.649 -23.648765 23.980 -23.980066 24.310 -24.310067 24.639 -24.638968 24.967 -24.966769 25.293 -25.293370 25.619 -25.618771 25.943 -25.942972 26.266 -26.266073 26.588 -26.587974 26.909 -26.908675 27.228 -27.228276 27.547 -27.546677 27.864 -27.863978 28.180 -28.180079 28.495 -28.494980 28.809 -28.808781 29.121 -29.121382 29.433 -29.432783 29.743 -29.743084 30.052 -30.052185 30.360 -30.360186 30.667 -30.666987 30.973 -30.972588 31.277 -31.277089 31.580 -31.580390 31.883 -31.882591 32.184 -32.1835

92 32.483 -32.483493 32.782 -32.782194 33.080 -33.079695 33.376 -33.376096 33.671 -33.671297 33.965 -33.965298 34.258 -34.258299 34.550 -34.5499

100 34.841 -34.8405101 35.130 -35.1299102 35.418 -35.4182103 35.705 -35.7054104 35.991 -35.9914105 36.276 -36.2762106 36.560 -36.5599107 36.842 -36.8424108 37.124 -37.1237109 37.404 -37.4040110 37.683 -37.6830111 37.961 -37.9609112 38.238 -38.2377113 38.513 -38.5133114 38.788 -38.7878115 39.061 -39.0611116 39.333 -39.3333117 39.604 -39.6043118 39.874 -39.8742119 40.143 -40.1429120 40.410 -40.4105121 40.677 -40.6769122 40.942 -40.9422123 41.206 -41.2063124 41.469 -41.4693125 41.731 -41.7311126 41.992 -41.9918127 42.251 -42.2513128 42.510 -42.5097129 42.767 -42.7670130 43.023 -43.0231131 43.278 -43.2781132 43.532 -43.5319133 43.785 -43.7846134 44.036 -44.0361135 44.286 -44.2865136 44.536 -44.5357137 44.784 -44.7838138 45.031 -45.0308139 45.277 -45.2766140 45.521 -45.5213141 45.765 -45.7648142 46.007 -46.0072143 46.248 -46.2485144 46.489 -46.4886145 46.728 -46.7275

146 46.965 -46.9654147 47.202 -47.2021148 47.438 -47.4376149 47.672 -47.6720150 47.905 -47.9053151 48.137 -48.1374152 48.368 -48.3684153 48.598 -48.5983154 48.827 -48.8270155 49.055 -49.0546156 49.281 -49.2811157 49.506 -49.5064158 49.731 -49.7305159 49.954 -49.9536160 50.175 -50.1755161 50.396 -50.3963162 50.616 -50.6159163 50.834 -50.8344164 51.052 -51.0517165 51.268 -51.2680166 51.483 -51.4831167 51.697 -51.6970168 51.910 -51.9098169 52.122 -52.1215170 52.332 -52.3321171 52.542 -52.5415172 52.750 -52.7498173 52.957 -52.9570174 53.163 -53.1630175 53.368 -53.3679176 53.572 -53.5716177 53.774 -53.7743178 53.976 -53.9758179 54.176 -54.1761180 54.375 -54.3754181 54.573 -54.5735182 54.770 -54.7705183 54.966 -54.9663184 55.161 -55.1610185 55.355 -55.3546186 55.547 -55.5471187 55.738 -55.7384188 55.929 -55.9286 x y189 56.118 -56.1177 0 894.1513331190 56.306 -56.3056 1 894.15189229191 56.492 -56.4924 2 894.15356986192 56.678 -56.6781 3 894.15636581193 56.863 -56.8627 4 894.16028014194 57.046 -57.0461 5 894.16531287195 57.228 -57.2284 6 894.17146399196 57.410 -57.4096 7 894.17873352197 57.590 -57.5896 8 894.18712146198 57.769 -57.7686 9 894.19662783199 57.946 -57.9464 10 894.20725263

200 58.123 -58.1230 11 894.21899588201 58.299 -58.2986 12 894.23185759202 58.473 -58.4730 13 894.24583778203 58.646 -58.6463 14 894.26093647204 58.818 -58.8184 15 894.27715368205 58.989 -58.9895 16 894.29448942206 59.159 -59.1594 17 894.31294372207 59.328 -59.3282 18 894.3325166208 59.496 -59.4959 19 894.35320809209 59.662 -59.6624 20 894.37501821210 59.828 -59.8278 21 894.39794699211 59.992 -59.9921 22 894.42199445212 60.155 -60.1553 23 894.44716063213 60.317 -60.3173 24 894.47344556214 60.478 -60.4783 25 894.50084928215 60.638 -60.6381 26 894.52937181216 60.797 -60.7968 27 894.55901319217 60.954 -60.9543 28 894.58977346218 61.111 -61.1107 29 894.62165266219 61.266 -61.2661 30 894.65465082220 61.420 -61.4202 31 894.688768221 61.573 -61.5733 32 894.72400422222 61.725 -61.7253 33 894.76035954223 61.876 -61.8761 34 894.797834224 62.026 -62.0258 35 894.83642765225 62.174 -62.1744 36 894.87614054226 62.322 -62.3218 37 894.91697271227 62.468 -62.4682 38 894.95892422228 62.613 -62.6134 39 895.00199511229 62.757 -62.7575 40 895.04618545230 62.900 -62.9005 41 895.09149529231 63.042 -63.0423 42 895.13792468232 63.183 -63.1831 43 895.18547369233 63.323 -63.3227 44 895.23414237234 63.461 -63.4612 45 895.28393078235 63.599 -63.5986 46 895.33483898236 63.735 -63.7348 47 895.38686705237 63.870 -63.8700 48 895.44001504238 64.004 -64.0040 49 895.49428302239 64.137 -64.1369 50 895.54967106240 64.269 -64.2687 51 895.60617923241 64.399 -64.3993 52 895.6638076242 64.529 -64.5289 53 895.72255624243 64.657 -64.6573 54 895.78242522244 64.785 -64.7846 55 895.84341462245 64.911 -64.9108 56 895.90552452246 65.036 -65.0359 57 895.96875499247 65.160 -65.1599 58 896.03310611248 65.283 -65.2827 59 896.09857797249 65.404 -65.4044 60 896.16517063250 65.525 -65.5250 61 896.2328842251 65.645 -65.6445 62 896.30171875252 65.763 -65.7629 63 896.37167437253 65.880 -65.8802 64 896.44275115

254 65.996 -65.9963 65 896.51494917255 66.111 -66.1113 66 896.58826852256 66.225 -66.2252 67 896.6627093257 66.338 -66.3380 68 896.73827161258 66.450 -66.4497 69 896.81495552259 66.560 -66.5603 70 896.89276115260 66.670 -66.6697 71 896.97168859261 66.778 -66.7781 72 897.05173793262 66.885 -66.8853 73 897.13290928263 66.991 -66.9914 74 897.21520274264 67.096 -67.0964 75 897.29861841265 67.200 -67.2002 76 897.38315639266 67.303 -67.3030 77 897.4688168267 67.405 -67.4046 78 897.55559973268 67.505 -67.5051 79 897.6435053269 67.605 -67.6046 80 897.73253362270 67.703 -67.7029 81 897.8226848271 67.800 -67.8000 82 897.91395894272 67.896 -67.8961 83 898.00635618273 67.991 -67.9911 84 898.09987661274 68.085 -68.0849 85 898.19452036275 68.178 -68.1776 86 898.29028755276 68.269 -68.2692 87 898.38717829277 68.360 -68.3597 88 898.48519271278 68.449 -68.4491 89 898.58433093279 68.537 -68.5374 90 898.68459307280 68.625 -68.6246 91 898.78597927281 68.711 -68.7106 92 898.88848964282 68.796 -68.7955 93 898.99212431283 68.879 -68.8794 94 899.09688342284 68.962 -68.9621 95 899.20276709285 69.044 -69.0437 96 899.30977546286 69.124 -69.1242 97 899.41790866287 69.204 -69.2035 98 899.52716682288 69.282 -69.2818 99 899.63755009289 69.359 -69.3589 100 899.7490586290 69.435 -69.4350 101 899.86169249291 69.510 -69.5099 102 899.9754519292 69.584 -69.5837 103 900.09033698293 69.656 -69.6564 104 900.20634786294 69.728 -69.7280 105 900.3234847295 69.798 -69.7985 106 900.44174763296 69.868 -69.8678 107 900.56113681297 69.936 -69.9361 108 900.68165239298 70.003 -70.0032 109 900.80329452299 70.069 -70.0692 110 900.92606334300 70.134 -70.1342 111 901.04995902301 70.198 -70.1980 112 901.1749817302 70.261 -70.2607 113 901.30113155303 70.322 -70.3222 114 901.42840872304 70.383 -70.3827 115 901.55681337305 70.442 -70.4421 116 901.68634566306 70.500 -70.5003 117 901.81700576307 70.557 -70.5575 118 901.94879382

308 70.613 -70.6135 119 902.08171002309 70.668 -70.6684 120 902.21575451310 70.722 -70.7222 121 902.35092747311 70.775 -70.7749 122 902.48722906312 70.827 -70.8265 123 902.62465946313 70.877 -70.8770 124 902.76321884314 70.926 -70.9264 125 902.90290736315 70.975 -70.9746 126 903.04372522316 71.022 -71.0218 127 903.18567257317 71.068 -71.0678 128 903.3287496318 71.113 -71.1127 129 903.47295649319 71.157 -71.1565 130 903.61829342320 71.199 -71.1992 131 903.76476057321 71.241 -71.2408 132 903.91235812322 71.281 -71.2813 133 904.06108626323 71.321 -71.3207 134 904.21094517324 71.359 -71.3590 135 904.36193505325 71.396 -71.3961 136 904.51405607326 71.432 -71.4322 137 904.66730844327 71.467 -71.4671 138 904.82169234328 71.501 -71.5009 139 904.97720796329 71.534 -71.5337 140 905.1338555330 71.565 -71.5653 141 905.29163516331 71.596 -71.5958 142 905.45054713332 71.625 -71.6252 143 905.61059161333 71.653 -71.6534 144 905.77176881334 71.681 -71.6806 145 905.93407892335 71.707 -71.7067 146 906.09752214336 71.732 -71.7316 147 906.26209869337 71.755 -71.7555 148 906.42780876338 71.778 -71.7782 149 906.59465257339 71.800 -71.7998 150 906.76263032340 71.820 -71.8203 151 906.93174222 tabla N3341 71.840 -71.8398 152 907.10198849 x342 71.858 -71.8581 153 907.27336933 0343 71.875 -71.8752 154 907.44588497 1344 71.891 -71.8913 155 907.61953561 2345 71.906 -71.9063 156 907.79432148 3346 71.920 -71.9202 157 907.97024279 4347 71.933 -71.9329 158 908.14729977 5348 71.945 -71.9446 159 908.32549263 6349 71.955 -71.9551 160 908.50482159 7350 71.965 -71.9645 161 908.68528689 8351 71.973 -71.9728 162 908.86688875 9352 71.980 -71.9800 163 909.04962739 10353 71.986 -71.9861 164 909.23350305 11354 71.991 -71.9911 165 909.41851595 12355 71.995 -71.9950 166 909.60466632 13356 71.998 -71.9978 167 909.7919544 14357 71.999 -71.9994 168 909.98038042 15358 72.000 -72.0000 169 910.16994462 16359 71.999 -71.9994 170 910.36064724 17360 71.998 -71.9978 171 910.55248851 18361 71.995 -71.9950 172 910.74546867 19

362 71.991 -71.9911 173 910.93958796 20363 71.986 -71.9861 174 911.13484664 21364 71.980 -71.9800 175 911.33124493 22365 71.973 -71.9728 176 911.52878309 23366 71.965 -71.9645 177 911.72746137 24367 71.955 -71.9551 178 911.92728001 25368 71.945 -71.9446 179 912.12823926 26369 71.933 -71.9329 180 912.33033938 27370 71.920 -71.9202 181 912.53358061 28371 71.906 -71.9063 182 912.73796321 29372 71.891 -71.8913 183 912.94348744 30373 71.875 -71.8752 184 913.15015356 31374 71.858 -71.8581 185 913.35796181 32375 71.840 -71.8398 186 913.56691247 33376 71.820 -71.8203 187 913.77700579 34377 71.800 -71.7998 188 913.98824204 35378 71.778 -71.7782 189 914.20062148 36379 71.755 -71.7555 190 914.41414437 37380 71.732 -71.7316 191 914.62881099 38381 71.707 -71.7067 192 914.8446216 39382 71.681 -71.6806 193 915.06157647 40383 71.653 -71.6534 194 915.27967587 41384 71.625 -71.6252 195 915.49892008 42385 71.596 -71.5958 196 915.71930937 43386 71.565 -71.5653 197 915.94084402 44387 71.534 -71.5337 198 916.1635243 45388 71.501 -71.5009 199 916.38735049 46389 71.467 -71.4671 200 916.61232287 47390 71.432 -71.4322 201 916.83844172 48391 71.396 -71.3961 202 917.06570733 49392 71.359 -71.3590 203 917.29411998 50393 71.321 -71.3207 204 917.52367995 51394 71.281 -71.2813 205 917.75438754 52395 71.241 -71.2408 206 917.98624302 53396 71.199 -71.1992 207 918.2192467 54397 71.157 -71.1565 208 918.45339886 55398 71.113 -71.1127 209 918.6886998 56399 71.068 -71.0678 210 918.92514981 57400 71.022 -71.0218 211 919.16274918 58401 70.975 -70.9746 212 919.40149821 59402 70.926 -70.9264 213 919.64139721 60403 70.877 -70.8770 214 919.88244646 61404 70.827 -70.8265 215 920.12464628 62405 70.775 -70.7749 216 920.36799697 63406 70.722 -70.7222 217 920.61249882 64407 70.668 -70.6684 218 920.85815215 65408 70.613 -70.6135 219 921.10495727 66409 70.557 -70.5575 220 921.35291447 67410 70.500 -70.5003 221 921.60202408 68411 70.442 -70.4421 222 921.8522864 69412 70.383 -70.3827 223 922.10370175 70413 70.322 -70.3222 224 922.35627044 71414 70.261 -70.2607 225 922.60999278 72415 70.198 -70.1980 226 922.86486911 73416 70.134 -70.1342 227 923.12089972 74

417 70.069 -70.0692 228 923.37808495 75418 70.003 -70.0032 229 923.63642511 76419 69.936 -69.9361 230 923.89592053 77420 69.868 -69.8678 231 924.15657153 78421 69.798 -69.7985 232 924.41837844 79422 69.728 -69.7280 233 924.68134159 80423 69.656 -69.6564 234 924.9454613 81424 69.584 -69.5837 235 925.21073791 82425 69.510 -69.5099 236 925.47717175 83426 69.435 -69.4350 237 925.74476314 84427 69.359 -69.3589 238 926.01351243 85428 69.282 -69.2818 239 926.28341996 86429 69.204 -69.2035 240 926.55448605 87430 69.124 -69.1242 241 926.82671105 88431 69.044 -69.0437 242 927.10009529 89432 68.962 -68.9621 243 927.37463913 90433 68.879 -68.8794 244 927.6503429 91434 68.796 -68.7955 245 927.92720696 92435 68.711 -68.7106 246 928.20523163 93436 68.625 -68.6246 247 928.48441728 94437 68.537 -68.5374 248 928.76476425 95438 68.449 -68.4491 249 929.04627289 96439 68.360 -68.3597 250 929.32894356 97440 68.269 -68.2692 251 929.61277661 98441 68.178 -68.1776 252 929.89777238 99442 68.085 -68.0849 253 930.18393125 100443 67.991 -67.9911 254 930.47125357 101444 67.896 -67.8961 255 930.75973969 102445 67.800 -67.8000 256 931.04938998 103446 67.703 -67.7029 257 931.3402048 104447 67.605 -67.6046 258 931.63218452 105448 67.505 -67.5051 259 931.92532949 106449 67.405 -67.4046 260 932.21964009 107450 67.303 -67.3030 261 932.51511668 108451 67.200 -67.2002 262 932.81175964 109452 67.096 -67.0964 263 933.10956933 110453 66.991 -66.9914 264 933.40854613 111454 66.885 -66.8853 265 933.70869041 112455 66.778 -66.7781 266 934.01000254 113456 66.670 -66.6697 267 934.31248291 114457 66.560 -66.5603 268 934.61613189 115458 66.450 -66.4497 269 934.92094986 116459 66.338 -66.3380 270 935.2269372 117460 66.225 -66.2252 271 935.5340943 118461 66.111 -66.1113 272 935.84242154 119462 65.996 -65.9963 273 936.1519193 120463 65.880 -65.8802 274 936.46258798 121464 65.763 -65.7629 275 936.77442795 122465 65.645 -65.6445 276 937.08743962 123466 65.525 -65.5250 277 937.40162337 124467 65.404 -65.4044 278 937.71697959 125468 65.283 -65.2827 279 938.03350869 126469 65.160 -65.1599 280 938.35121105 127470 65.036 -65.0359 281 938.67008707 128471 64.911 -64.9108 282 938.99013715 129

472 64.785 -64.7846 283 939.3113617 130473 64.657 -64.6573 284 939.63376111 131474 64.529 -64.5289 285 939.95733579 132475 64.399 -64.3993 286 940.28208614 133476 64.269 -64.2687 287 940.60801256 134477 64.137 -64.1369 288 940.93511548 135478 64.004 -64.0040 289 941.26339529 136479 63.870 -63.8700 290 941.5928524 137480 63.735 -63.7348 291 941.92348723 138481 63.599 -63.5986 292 942.25530019 139482 63.461 -63.4612 293 942.5882917 140483 63.323 -63.3227 294 942.92246217 141484 63.183 -63.1831 295 943.25781202 142485 63.042 -63.0423 296 943.59434167 143486 62.900 -62.9005 297 943.93205155 144487 62.757 -62.7575 298 944.27094206 145488 62.613 -62.6134 299 944.61101365 146489 62.468 -62.4682 300 944.95226672 147490 62.322 -62.3218 301 945.29470172 148491 62.174 -62.1744 302 945.63831906 149492 62.026 -62.0258 303 945.98311918 150493 61.876 -61.8761 304 946.32910251 151494 61.725 -61.7253 305 946.67626948 152495 61.573 -61.5733 306 947.02462052 153496 61.420 -61.4202 307 947.37415608 154497 61.266 -61.2661 308 947.72487659 155498 61.111 -61.1107 309 948.07678248 156499 60.954 -60.9543 310 948.4298742 157500 60.797 -60.7968 311 948.78415219 158501 60.638 -60.6381 312 949.13961689 159502 60.478 -60.4783 313 949.49626875 160503 60.317 -60.3173 314 949.85410821 161504 60.155 -60.1553 315 950.21313573 162505 59.992 -59.9921 316 950.57335174 163506 59.828 -59.8278 317 950.9347567 164507 59.662 -59.6624 318 951.29735106 165508 59.496 -59.4959 319 951.66113528 166509 59.328 -59.3282 320 952.02610981 167510 59.159 -59.1594 321 952.39227511 168511 58.989 -58.9895 322 952.75963164 169512 58.818 -58.8184 323 953.12817984 170513 58.646 -58.6463 324 953.4979202 171514 58.473 -58.4730 325 953.86885316 172515 58.299 -58.2986 326 954.24097919 173516 58.123 -58.1230 327 954.61429876 174517 57.946 -57.9464 328 954.98881233 175518 57.769 -57.7686 329 955.36452038 176519 57.590 -57.5896 330 955.74142337 177520 57.410 -57.4096 331 956.11952178 178521 57.228 -57.2284 332 956.49881607 179522 57.046 -57.0461 333 956.87930672 180523 56.863 -56.8627 334 957.26099421 181524 56.678 -56.6781 335 957.64387902 182525 56.492 -56.4924 336 958.02796162 183526 56.306 -56.3056 337 958.41324249 184

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2

4

6

8

10

12


Distancia (m.)

Altu

ra (m

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497195.3497195.3497195.3497195.3497195.3497195.3497195.3497195.3

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0 50 100 150 200 250 300 350 4000

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8

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12


Distancia (m.)

Altu

ra (m

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Existen dos alternativas de enfoque al problema presentado:

Suponer que la componente horizontal de la tensin en el extremo superior es la misma que la que proviene del tramo central. Con esta hiptesis se asume que la torre de sustentacin no soportr ninguna fuerza horizontal por concepto de cargas gravitacinales.Suponer que la tensin en la parte superior del cable es la misma que la tensin en el tramo central del cable. Con esta hiptesis se asume que el cable est colocado sobre rodillos libres de rozamiento colocados en las torres de sustentacin, y que las torres pueden resistir fuerzas horizontales de pequea magnitud.


Asumiendo como vlida la primera hiptesis para el problema propuesto, la componente horizontal de la tensin en la parte superior del cable es igual a la componente horizontal en el tramo central, por lo que, tomando la informacin del ejemplo 1, se tiene:

Existen dos alternativas de enfoque al problema presentado:




Suponer que la tensin en la parte superior del cable es la misma que la tensin en el tramo central del cable. Con esta hiptesis se asume que el cable est colocado sobre rodillos libres de rozamiento colocados en las torres de sustentacin, y que las torres pueden resistir fuerzas horizontales de pequea magnitud.

Suponer que la tensin en la parte superior del cable es la misma que la tensin en el tramo central del cable. Con esta hiptesis se asume que el cable est colocado sobre rodillos libres de rozamiento colocados en las torres de sustentacin, y que las torres pueden resistir fuerzas horizontales de pequea magnitud.

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