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FORMA ELIPTICA
Y
f = 56
unidades en metros
L = 106
DATOS CONOCIDOS
Longitud = 106 m
flecha = 56 m
X Y PARA AUTOCAD
a
b
X
Donde: a = 53
b = 56
Xo = 0
Yo = 0
a
PARABOLA
Y
X
(L/2 , f)
Reemplazando el punto conocido en la ecu
DATOS
Longitud = 70 m 4p = -0.
flecha = 25 m
Ecuacion de la parabola sera:
y = -0.
X Y PARA AUTOCAD
𝑦=4𝑝 ∗ 𝑥^
f
L
Punto conocido de la curva
el punto conocido en la ecuacion:
parabola sera:
x
2
𝑦=4𝑝 ∗ 𝑥^
CIRCULO
Z
r
Y
DATOS Estos datos nos dan 3 puntos para obtener 3 ecuacione
Longitud = 70 m
flecha = 25 m Nodo X Z
D E F
D
E
F
La ecuacion de la circunferencia sera: x^2 + z^2 + 0x +24z -1225 = 0
X Z PARA AUTOCAD
f
L
r
𝑥^2+𝑧^2+𝐷𝑥
Ecuacion general del circulo
X
os para obtener 3 ecuaciones
- ( x
**2
2 )
𝑥^2+𝑧^2+𝐷𝑥+𝐸𝑧+𝐹=
𝑥^2+𝑧^2+𝐷𝑥+𝐸𝑧+𝐹=
Longitud = 70 m
- 11 54.78 11,54,78,
- 12 54.55 12,54,55,
- 13 54.29 13,54,29,
- 14 54.01 14,54,01,
- 15 53.71 15,53,71,
- 16 53.39 16,53,39,
- 17 53.04 17,53,04,
- 18 52.67 18,52,67,
- 19 52.28 19,52,28,
- 20 51.86 20,51,86,
- 21 51.42 21,51,42,
- 22 50.95 22,50,95,
- 23 50.45 23,50,45,
- 24 49.93 24,49,93,
- 25 49.38 25,49,38,
- 26 48.80 26,48,8,
- 27 48.19 27,48,19,
- 28 47.55 28,47,55,
- 29 46.87 29,46,87,
- 30 46.17 30,46,17,
- 31 45.42 31,45,42,
- 32 44.64 32,44,64,
- 33 43.82 33,43,82,
- 34 42.96 34,42,96,
- 35 42.05 35,42,05,
- 36 41.10 36,41,1,
- 37 40.10 37,40,1,
- 38 39.04 38,39,04,
- 39 37.92 39,37,92,
- 40 36.74 40,36,74,
- 41 35.49 41,35,49,
- 42 34.16 42,34,16,
- 43 32.74 43,32,74,
- 44 31.22 44,31,22,
- 45 29.58 45,29,58,
- 46 27.81 46,27,81,
- 47 25.88 47,25,88,
- 48 23.74 48,23,74,
- 49 21.34 49,21,34,
- 50 18.57 50,18,57,
- 51 15.24 51,15,24,
- 52 10.83 52,10,83,
- 53 0.00 53,0,
- 54 Err:
- 55 Err:
- 20 -8.16 20,-8.163,
- 21 -9.00 21,-9,
- 22 -9.88 22,-9.878,
- 23 -10.80 23,-10.796,
- 24 -11.76 24,-11.755,
- 25 -12.76 25,-12.755,
- 26 -13.80 26,-13.796,
- 27 -14.88 27,-14.878,
- 28 -16.00 28,-16,
- 29 -17.16 29,-17.163,
- 30 -18.37 30,-18.367,
- 31 -19.61 31,-19.612,
- 32 -20.90 32,-20.898,
- 33 -22.22 33,-22.224,
- 34 -23.59 34,-23.592,
- 35 -25.00 35,-25,
- 36 -26.45 36,-26.449,
- 37 -27.94 37,-27.939,
- 38 -29.47 38,-29.469,
- 39 -31.04 39,-31.041,
- 40 -32.65 40,-32.653,
- 41 -34.31 41,-34.306,
- 42 -36.00 42,-36,
- 43 -37.74 43,-37.735,
- 44 -39.51 44,-39.51,
- 45 -41.33 45,-41.327,
- 46 -43.18 46,-43.184,
- 46.5 -44.1346.5,-44.128,
- 48 -47.02 48,-47.02,
- 49 -49.00 49,-49,
- 50 -51.02 50,-51.02,
- 51 -53.08 51,-53.082,
- 52 -55.18 52,-55.184,
- 53 -57.33 53,-57.327,
- 54 -59.51 54,-59.51,
- 55 -61.74 55,-61.735,
- 56 -64.00 56,-64,
- 57 -66.31 57,-66.306,
- 58 -68.65 58,-68.653,
- 59 -71.04 59,-71.041,
- 60 -73.47 60,-73.469,
- 61 -75.94 61,-75.939,
- 62 -78.45 62,-78.449,
- 63 -81.00 63,-81,
- 64 -83.59 64,-83.592,
- 65 -86.22 65,-86.224,
- 66 -88.90 66,-88.898,
- 67 -91.61 67,-91.612,
- 68 -94.37 68,-94.367,
- 69 -97.16 69,-97.163,
- 70 -100.00 70,-100,
- 71 -102.8871,-102.878,
- 72 -105.8072,-105.796,
- 73 -108.7673,-108.755,
- 74 -111.7674,-111.755,
- 75 -114.8075,-114.796,
- 76 -117.8876,-117.878,
- 77 -121.00 77,-121,
- 78 -124.1678,-124.163,
- 79 -127.3779,-127.367,
- 80 -130.6180,-130.612,
- 81 -133.9081,-133.898,
- 82 -137.2282,-137.224,
- 83 -140.5983,-140.592,
- 84 -144.00 84,-144,
- 85 -147.4585,-147.449,
- 86 -150.9486,-150.939,
- 87 -154.4787,-154.469,
- 88 -158.0488,-158.041,
- 89 -161.6589,-161.653,
- 90 -165.3190,-165.306,
- 91 -169.00 91,-169,
- 92 -172.7492,-172.735,
- 93 -176.51 93,-176.51,
- 94 -180.3394,-180.327,
- 95 -184.1895,-184.184,
- 96 -188.0896,-188.082,
- 97 -192.02 97,-192.02,
- 98 -196.00 98,-196,
- 99 -200.02 99,-200.02,
- 100 -204.08100,-204.082,
- 101 -208.18101,-208.184,
- 102 -212.33102,-212.327,
- 103 -216.51103,-216.51,
- 104 -220.74104,-220.735,
- 105 -225.00 105,-225,
- 106 -229.31106,-229.306,
- 107 -233.65107,-233.653,
- 108 -238.04108,-238.041,
- 109 -242.47109,-242.469,
- 110 -246.94110,-246.939,
- 111 -251.45111,-251.449,
- 112 -256.00 112,-256,
- 113 -260.59113,-260.592,
- 114 -265.22114,-265.224,
- 115 -269.90115,-269.898,
- 116 -274.61116,-274.612,
- 117 -279.37117,-279.367,
- 118 -284.16118,-284.163,
- 119 -289.00 119,-289,
- 120 -293.88120,-293.878,
- 121 -298.80121,-298.796,
- 122 -303.76122,-303.755,
- 123 -308.76123,-308.755,
- 124 -313.80124,-313.796,
- 125 -318.88125,-318.878,
- 126 -324.00 126,-324,
- 127 -329.16127,-329.163,
- 128 -334.37128,-334.367,
- 129 -339.61129,-339.612,
- 130 -344.90130,-344.898,
- 131 -350.22131,-350.224,
- 132 -355.59132,-355.592,
- 133 -361.00 133,-361,
- 134 -366.45134,-366.449,
- 135 -371.94135,-371.939,
- 136 -377.47136,-377.469,
- 137 -383.04137,-383.041,
- 138 -388.65138,-388.653,
- 139 -394.31139,-394.306,
- 140 -400.00 140,-400,
- 141 -405.74141,-405.735,
- 142 -411.51142,-411.51,
- 143 -417.33143,-417.327,
- 144 -423.18144,-423.184,
- 145 -429.08145,-429.082,
- 146 -435.02146,-435.02,
- 147 -441.00 147,-441,
- 148 -447.02148,-447.02,
- 149 -453.08149,-453.082,
- 150 -459.18150,-459.184,
- 151 -465.33151,-465.327,
- 152 -471.51152,-471.51,
- 153 -477.74153,-477.735,
- 154 -484.00 154,-484,
- 155 -490.31155,-490.306,
- 156 -496.65156,-496.653,
- 157 -503.04157,-503.041,
- 158 -509.47158,-509.469,
- 159 -515.94159,-515.939,
- 160 -522.45160,-522.449,
- 161 -529.00 161,-529,
- 162 -535.59162,-535.592,
- 163 -542.22163,-542.224,
- 164 -548.90164,-548.898,
- 165 -555.61165,-555.612,
- 166 -562.37166,-562.367,
- 167 -569.16167,-569.163,
- 168 -576.00 168,-576,
- 169 -582.88169,-582.878,
- 170 -589.80170,-589.796,
- 171 -596.76171,-596.755,
- 172 -603.76172,-603.755,
- 173 -610.80173,-610.796,
- 174 -617.88174,-617.878,
- 175 -625.00 175,-625,
- 176 -632.16176,-632.163,
- 177 -639.37177,-639.367,
- 178 -646.61178,-646.612,
- 179 -653.90179,-653.898,
- 180 -661.22180,-661.224,
- 181 -668.59181,-668.592,
- 182 -676.00 182,-676,
- 183 -683.45183,-683.449,
- 184 -690.94184,-690.939,
- 185 -698.47185,-698.469,
- 186 -706.04186,-706.041,
- 187 -713.65187,-713.653,
- 188 -721.31188,-721.306,
- 189 -729.00 189,-729,
- 190 -736.74190,-736.735,
- 191 -744.51191,-744.51,
- 192 -752.33192,-752.327,
- 193 -760.18193,-760.184,
- 194 -768.08194,-768.082,
- 195 -776.02195,-776.02,
- 196 -784.00 196,-784,
- 197 -792.02197,-792.02,
- 198 -800.08198,-800.082,
- 199 -808.18199,-808.184,
- 200 -816.33200,-816.327,
- 201 -824.51201,-824.51,
- 202 -832.74202,-832.735,
- 203 -841.00 203,-841,
- 204 -849.31204,-849.306,
- 205 -857.65205,-857.653,
- 206 -866.04206,-866.041,
- 207 -874.47207,-874.469,
- 208 -882.94208,-882.939,
- 209 -891.45209,-891.449,
- 210 -900.00 210,-900,
- 211 -908.59211,-908.592,
- 212 -917.22212,-917.224,
- 213 -925.90213,-925.898,
- 214 -934.61214,-934.612,
- 215 -943.37215,-943.367,
- 216 -952.16216,-952.163,
- 217 -961.00 217,-961,
- 218 -969.88218,-969.878,
- 219 -978.80219,-978.796,
- 220 -987.76220,-987.755,
- 221 -996.76221,-996.755,
- 222 -1005.80222,-1005.796,
- 223 -1014.88223,-1014.878,
- 224 -1024.00 224,-1024,
- 225 -1033.16225,-1033.163,
- 226 -1042.37226,-1042.367,
- 227 -1051.61227,-1051.612,
- 228 -1060.90228,-1060.898,
- 229 -1070.22229,-1070.224,
- 230 -1079.59230,-1079.592,
- 231 -1089.00 231,-1089,
- 232 -1098.45232,-1098.449,
- 233 -1107.94233,-1107.939,
- 234 -1117.47234,-1117.469,
- 235 -1127.04235,-1127.041,
- 236 -1136.65236,-1136.653,
- 237 -1146.31237,-1146.306,
- 238 -1156.00 238,-1156,
- 239 -1165.74239,-1165.735,
- 240 -1175.51240,-1175.51,
- 241 -1185.33241,-1185.327,
- 242 -1195.18242,-1195.184,
- 243 -1205.08243,-1205.082,
- 244 -1215.02244,-1215.02,
- 245 -1225.00 245,-1225,
- 246 -1235.02246,-1235.02,
- 247 -1245.08247,-1245.082,
- 248 -1255.18248,-1255.184,
- 249 -1265.33249,-1265.327,
- 250 -1275.51250,-1275.51,
- 251 -1285.74251,-1285.735,
- 252 -1296.00 252,-1296,
- 253 -1306.31253,-1306.306,
- 254 -1316.65254,-1316.653,
- 255 -1327.04255,-1327.041,
- 256 -1337.47256,-1337.469,
- 257 -1347.94257,-1347.939,
- 258 -1358.45258,-1358.449,
- 259 -1369.00 259,-1369,
- 260 -1379.59260,-1379.592,
- 261 -1390.22261,-1390.224,
- 262 -1400.90262,-1400.898,
- 263 -1411.61263,-1411.612,
- 264 -1422.37264,-1422.367,
- 265 -1433.16265,-1433.163,
- 266 -1444.00 266,-1444,
- 267 -1454.88267,-1454.878,
- 268 -1465.80268,-1465.796,
- 269 -1476.76269,-1476.755,
- 270 -1487.76270,-1487.755,
- 271 -1498.80271,-1498.796,
- 272 -1509.88272,-1509.878,
- 273 -1521.00 273,-1521,
- 274 -1532.16274,-1532.163,
- 275 -1543.37275,-1543.367,
- 276 -1554.61276,-1554.612,
- 277 -1565.90277,-1565.898,
- 278 -1577.22278,-1577.224,
- 279 -1588.59279,-1588.592,
- 280 -1600.00 280,-1600,
- 281 -1611.45281,-1611.449,
- 282 -1622.94282,-1622.939,
- 283 -1634.47283,-1634.469,
- 284 -1646.04284,-1646.041,
- 285 -1657.65285,-1657.653,
- 286 -1669.31286,-1669.306,
- 287 -1681.00 287,-1681,
- 288 -1692.74288,-1692.735,
- 289 -1704.51289,-1704.51,
- 290 -1716.33290,-1716.327,
- 291 -1728.18291,-1728.184,
- 292 -1740.08292,-1740.082,
- 293 -1752.02293,-1752.02,
- 294 -1764.00 294,-1764,
- 295 -1776.02295,-1776.02,
- 296 -1788.08296,-1788.082,
- 297 -1800.18297,-1800.184,
- 298 -1812.33298,-1812.327,
- 299 -1824.51299,-1824.51,
- 300 -1836.74300,-1836.735,
- 301 -1849.00 301,-1849,
- 302 -1861.31302,-1861.306,
- 303 -1873.65303,-1873.653,
- 304 -1886.04304,-1886.041,
- 305 -1898.47305,-1898.469,
- 306 -1910.94306,-1910.939,
- 307 -1923.45307,-1923.449,
- 308 -1936.00 308,-1936,
- 309 -1948.59309,-1948.592,
- 310 -1961.22310,-1961.224,
- 311 -1973.90311,-1973.898,
- 312 -1986.61312,-1986.612,
- 313 -1999.37313,-1999.367,
- 314 -2012.16314,-2012.163,
- 315 -2025.00 315,-2025,
- 21 18.46 21,18.463,
- 28 12.19 28,12.187,
- 35 0.00 35,0,
- 6 24.51 6,24.51,
- 7 24.33 7,24.332,
- 8 24.13 8,24.125,
- 9 23.89 9,23.889,
- 10 23.62 10,23.623,
- 11 23.33 11,23.327,
- 12 23.00 12,23,
- 13 22.64 13,22.641,
- 14 22.25 14,22.249,
- 15 21.82 15,21.823,
- 16 21.36 16,21.362,
- 17 20.86 17,20.863,
- 18 20.33 18,20.326,
- 19 19.75 19,19.749,
- 20 19.13 20,19.129,
- 21 18.46 21,18.463,
- 22 17.75 22,17.749,
- 23 16.98 23,16.983,
- 24 16.16 24,16.16,
- 25 15.28 25,15.276,
- 26 14.33 26,14.325,
- 27 13.30 27,13.298,
- 28 12.19 28,12.187,
- 29 10.98 29,10.978,
- 30 9.66 30,9.656,
- 31 8.20 31,8.199,
- 32 6.57 32,6.574,
- 33 4.73 33,4.733,
- 34 2.60 34,2.595,
- 35 0.00 35,0,
- 36 -3.46 36,-3.456,
- 37 -12.00 37,-12,
- 38 Err:502 Err:
- 39 Err:502 Err:
- 40 Err:502 Err:
- 41 Err:502 Err:
- 42 Err:502 Err:
- 43 Err:502 Err:
- 44 Err:502 Err:
- 45 Err:502 Err:
- 46 Err:502 Err:
- 47 Err:502 Err:
- 48 Err:502 Err:
- 49 Err:502 Err:
- 50 Err:502 Err:
- 51 Err:502 Err:
- 52 Err:502 Err:
- 53 Err:502 Err:
- 54 Err:502 Err:
- 55 Err:502 Err:
- 56 Err:502 Err:
- 57 Err:502 Err:
- 58 Err:502 Err:
- 59 Err:502 Err:
- 60 Err:502 Err:
- 61 Err:502 Err:
- 62 Err:502 Err:
- 63 Err:502 Err:
- 64 Err:502 Err:
- 65 Err:502 Err:
- 66 Err:502 Err:
- 67 Err:502 Err:
- 68 Err:502 Err:
- 69 Err:502 Err:
- 70 Err:502 Err:
- 71 Err:502 Err:
- 72 Err:502 Err:
- 73 Err:502 Err:
- 74 Err:502 Err:
- 74.5 Err:502 Err:
- 76 Err:502 Err:
- 77 Err:502 Err:
- 78 Err:502 Err:
- 79 Err:502 Err:
- 80 Err:502 Err:
- x = L/2 = flecha = 25 m
- y = f = -
- Probar un "a"=27.8891459 y= -25.
- error = 0.
- 0 0.00 0,0, X Y PARA AUTOCAD
- 7 -0.88 7,-0.883,
- 14 -3.59 14,-3.588,
- 21 -8.29 21,-8.287,
- 28 -15.28 28,-15.277,
- 35 -25.00 35,-25,
- 6 -0.65 6,-0.648,
- 7 -0.88 7,-0.883,
- 8 -1.16 8,-1.155,
- 9 -1.47 9,-1.465,
- 10 -1.81 10,-1.812,
- 11 -2.20 11,-2.198,
- 12 -2.62 12,-2.622,
- 13 -3.09 13,-3.085,
- 14 -3.59 14,-3.588,
- 15 -4.13 15,-4.132,
- 16 -4.72 16,-4.717,
- 17 -5.34 17,-5.344,
- 18 -6.01 18,-6.013,
- 19 -6.73 19,-6.726,
- 20 -7.48 20,-7.484,
- 21 -8.29 21,-8.287,
- 22 -9.14 22,-9.137,
- 23 -10.03 23,-10.034,
- 24 -10.98 24,-10.98,
- 25 -11.98 25,-11.976,
- 26 -13.02 26,-13.023,
- 27 -14.12 27,-14.123,
- 28 -15.28 28,-15.277,
- 29 -16.49 29,-16.486,
- 30 -17.75 30,-17.752,
- 31 -19.08 31,-19.078,
- 32 -20.46 32,-20.463,
- 33 -21.91 33,-21.911,
- 34 -23.42 34,-23.422,
- 35 -25.00 35,-25,
- 36 -26.65 36,-26.646,
- 37 -28.36 37,-28.361,
- 38 -30.15 38,-30.15,
- 39 -32.01 39,-32.012,
- 40 -33.95 40,-33.952,
- 41 -35.97 41,-35.971,
- 42 -38.07 42,-38.073,
- 43 -40.26 43,-40.259,
- 44 -42.53 44,-42.533,
- 45 -44.90 45,-44.897,
- 46 -47.36 46,-47.355,
- 47 -49.91 47,-49.91,
- 48 -52.56 48,-52.56,
- 49 -55.32 49,-55.323,
- 50 -58.19 50,-58.188,
- 51 -61.16 51,-61.164,
- 52 -64.25 52,-64.254,
