Answer Happy

HW Assignment 8: Fundamentals of Horizontal Curve Design Problem 1. Given: External Distance (E) = 71 ft, Middle Ordinate Distance (M) = 59 ft: STA PC = 130+00, calculate the following design elements of horizontal curve a) Radius (R) b) Central Angle (A) c) Length of Tangent (T) d) Curve Length (L) e) Cord Length (C) 1) Degree of Curve (D) g) Stations of the Pl and PT Problem 2. You are designing a horizontal curve for a two-lane highway with 12-ft lanes. The design speed for this curve is 65 mi/h and the maximum superelevation that can be applied is 7%. The PI of the curve is at station 250 + 50. If the central angle of the curve is 38 degrees, determine the radius of the curve, as well as stationing of the PC and PT. Problem 3. A two-lane road has 12-ft lanes. You are asked to design a horizontal curve for this road. The applicable highway design guidelines require the superelevation not to exceed 8%. Due to the cost associated with excavation and vegetation clearing, it was determined that a maximum of 34 ft can be cleared from the centerline of the road toward the inside lane (ie toward the center of the curve) to provide for stopping sight distance. Considering these parameters, determine the maximum possible design speed for this curve. Problem 4. A section of a two-lane highway has 12-ft lanes and a design speed of 75 mi/h. The section contains a vertical curve and a horizontal curve. The vertical curve connects a-2.5% grade and a +1.5% grade. The PVT of this vertical curve is at station 36 + 50. The PC of the horizontal curve is located 294 ft before the PVC of the vertical curve. The horizontal curve has superelevation of 8% and central angle of 38 degrees. If the vertical and horizontal curves are designed to meet the minimum required lengths for the given design speed, calculate the stations of the PC and PT. (Hint for Problem 4: In this problem we have both combined) vertical and horizontal curve on the same roadway section. This kind of design problem usually can be split into two 2. dimensional problems; vertical alignment and horizontal alignment. They are solved separately, with consideration of design speed that is common for both vertical and horizontal alignment.) 1
Design Control Tables: Table 3.2 Design Controls for Crest Vertical Curves Based on Stopping Sight Distance Design Speed Stopping Sight Distance Rate of Vertical Curvature, K (mi/h) (ft) Calculated Design 15 80 3.0 3 20 115 6.1 7 25 155 11.1 12 30 200 18.5 19 35 250 29.0 29 40 305 43.1 44 45 360 60.1 61 50 425 83.7 84 55 495 113.5 114 60 570 150.6 151 65 645 192.8 193 70 730 246.9 247 75 820 311.6 312 80 910 383.7 384 Table 3.3 Design Controls for Sag Vertical Curves Based on Stopping Sight Distance Design Stopping Sight Speed Distance Rate of Vertical Curvature, K (mi/h) (ft) Calculated Design 15 80 9.4 10 20 115 16.5 17 25 155 25.5 26 30 200 36.4 37 35 250 49.0 50 40 305 63.4 64 45 360 78.1 79 50 425 95.7 96 55 495 114.9 115 60 570 135.7 136 65 645 156.5 157 70 730 180.3 181 75 820 205.6 206 80 910 231.0 231
Table 3.4 Design Controls for Crest Vertical Curves Based on Passing Sight Distance Design Speed (mi/h) Stopping Sight Distance (ft) Rate of Vertical Curvature, K 44 15 20 25 30 35 40 45 50 55 60 65 70 75 80 350 400 450 500 550 600 700 800 900 1000 1100 1200 1300 1400 57 72 89 108 129 175 229 289 357 432 514 604 700
0.27 Table 3.5 Minimum Radius Using Limiting Values of e and f. Design Limiting Total Calculated Rounded Design Limiting Total speed Maximum values (e/100 + radius, radius, Calculated Rounded speed Maximum values (e/100+ radius radius, (mi/h) (%) off. Ᏹ R. (ft) R. (ft) (mi/h) (%) off, R. (f) R. (f) 10 4.0 0.38 0.42 15.9 16 10 10.0 0.38 0.48 15 13.9 0.32 14 4.0 0.36 41.7 42 15 10.0 0.32 0.42 35.7 20 36 4.0 0.27 0.32 86.0 86 20 10.0 0.37 72 25 72.1 4.0 0.23 0.27 154.3 154 25 10.0 0.23 0.33 126.3 126 30 4.0 0.20 0.24 250.0 250 30 10.0 0.20 0.30 200.0 200 35 4.0 0.18 0.22 371.2 371 35 10.0 0.18 0.28 291.7 292 40 4,0 0.16 0.20 533.3 533 40 10.0 0.16 0.26 410.3 410 45 4.0 0.15 0.19 710.5 711 45 10.0 0.15 0.25 540.0 540 50 4.0 0.14 0.18 925.9 926 50 10.0 0.14 0.24 6944 694 S5 4.0 0.13 0.17 1186.3 1190 55 10.0 0.13 0.23 876.8 877 60 4.0 0.12 0.16 1500.0 1500 60 10.0 0.12 0.22 1090.9 1090 65 10.0 0.11 0.21 13413 10 1340 6.0 0.38 0.44 15.2 15 70 10.0 0.10 0.20 1633.3 IS 1630 6.0 0.32 0.38 39.5 39 75 10.0 0.09 0.19 1973.7 1970 20 6.0 0.27 0.33 80.8 81 80 10.0 0.08 0.18 2370.4 2370 25 6.0 0.23 0.29 143.7 144 30 6.0 0.20 0.26 230.8 231 10 12.0 0.38 0.50 35 13.3 13 6.0 0.18 0.24 340.3 340 15 12.0 0.32 0.44 34.1 34 40 6.0 0.16 0.22 484.8 485 20 12.0 0.27 0.39 68.4 68 45 6.0 0.15 0.21 642.9 643 25 12.0 0.23 0.35 119.0 119 50 6.0 0.14 0.20 833.3 833 30 12.0 0.20 0.32 187.5 188 SS 6.0 0.13 0.19 1061.4 1060 35 12.0 0.18 0.30 60 2722 272 6.0 0.12 0.18 1333.3 1330 40 12.0 0.16 0.28 381.0 381 65 6.0 0.11 0.17 1656.9 1660 45 12.0 0.15 0.27 500.0 70 500 6.0 0.10 0.16 2041.7 2040 50 0.14 0.26 75 641.0 0.09 2500.0 2500 55 12.0 0.13 0.25 80 806.7 807 6.0 0.08 0.14 3047.6 3050 60 12.0 0.12 0.24 1000.0 1000 65 12.0 0.11 0.23 1224.6 10 1220 8.0 0.38 0.46 14.5 14 70 12.0 0.10 0.22 1484.8 1480 IS 0.32 0.40 37.5 38 75 12.0 0.09 0.21 1785.7 1790 20 8.0 0.27 0.35 76.2 76 80 12.0 0.08 0.20 21333 25 2130 8,0 0.23 0.31 134.4 134 30 8.0 0.20 2143 214 35 0.18 314.1 314 40 8.0 0.16 0.24 444 45 8.0 0.15 0.23 587.0 587 SO 8.0 0.14 0.22 757.6 758 SS 8.0 0.13 0.21 960.3 960 60 8.0 0.12 0.20 1200.0 1200 65 8.0 0.11 0.19 1482.5 1480 70 8.0 0.10 0.18 1814,8 1810 75 8.0 0.09 0.17 2205.9 2210 80 8.0 0.08 0.16 2666.7 2670 Note: In recognition of safety considerations, use of ema = 4.0% should be limited to urban conditions Source: American Association of State Highway and Transportation Officials, A Policy on Geometric Design of Highways and Streets, 6 Edition, Washington, DC, 2011. Used by permission. 120 641 6.0 0.15 8.0 8.0 0.28 0.26