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Given the following spiral curve data: R= 220m; V= 80km/h; Δ = 28° 08’RT; PI@ 1+286.441; Two-Lane Road: Determine the value of each key spiral and horizontal curve component (Ls, X, Y, q, P, LT, ST, Lc, Δs, θs) using the charts provided, and determine the chainage of the T.S., S.C., C.S., and S.T.

Given the following spiral curve data: R= 220m; V= 80km/h; Δ = 28° 08’RT; PI@ 1+286.441; Two-Lane Road: Determine the value of each key spiral and horizontal curve component (Ls, X, Y, q, P, LT, ST, Lc, Δs, θs) using the charts provided, and determine the chainage of the T.S., S.C., C.S., and S.T.

Structural Analysis
Structural Analysis
6th Edition
ISBN:9781337630931
Author:KASSIMALI, Aslam.
Publisher:KASSIMALI, Aslam.
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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  1. Given the following spiral curve data: R= 220m; V= 80km/h; Δ = 28° 08’RT; PI@ 1+286.441; Two-Lane Road: Determine the value of each key spiral and horizontal curve component (Ls, X, Y, q, P, LT, ST, Lc, Δs, θs) using the charts provided, and determine the chainage of the T.S., S.C., C.S., and S.T.
    1. Note: Lc from table 11.9 represents the long chord of the spiral (not used in these calculations).
    2. Note: Although minimum radius is suggested to be 250m, we will continue to use a radius of 220m for this assignment.

PLEASE USE THE GIVEN TABLES FOR VALUES.

THANKS

Table 11.7 (continued) 90 100 110 120 130 140 Table 11.9 FUNCTIONS OF THE STANDARD SPIRAL FOR A = 125 m AIR L X P LT L. e, ST A, A 2 3 & 4 A A R 2 3 & 4 2 3 & 4 2 3 & 4 2 3 & 4 2 3 & 4 (m) e Meters Deg. Min. Sec. Deg. Min. Sec. Lane Lane Lane Lane Lane Lane Lane Lane Lane Lane Lane Lane 115 1.0870 135.870 131.204 26.095 67.152 6.606 92.293 46.851 88.183 133.774 33 50 48.3 11 05 05.8 10 38 52.4 14 55.1 1.0417 130.208 126.428 23.057 1.0000 125.000 121.911 0.9615 120.192 117.649 0.8929 111.607 109.847 NC NC NC NC NC 700 700 RC 700 700 120 64.471 5.825 44.658 128.513 31 20 08.3 500 500 125 20.464 61.983 5.162 84.451 42.685 123.617 28 9 31 44.3 NC NC 600 0.024 625 500 0.028 560 450 0.030 450 450 0.034 495 400 0.043 400 330 0.050 345 300 0.056 330 0.060 325 300 0.060 325 NC RC 600 600 0.021 600 625 560 130 18.240 59.671 4.595 81.044 40.898 119.055 26 29 11.7 8 48 46.1 NC RC 480 480 RC 500 0.022 500 500 0.025 S00 140 50 16.5 7 36 19 53 39.7 6 37 17 29 07.0 5 49 15 29 19.3 5 09 48 55.9 4 36 14.661 55.509 3.686 75.034 37.755 110.821 22 08.5 RC 390 400 0.025 400 400 0.023 450 450 0.027 450 495 150 0.8333 104.167 102.918 11.953 51.875 3.001 69.888 35.126 103.610 28.8 0.023 300 350 0.027 340 340 0.031 350 350 0.035 350 350 0.039 400 400 160 0.7813 97.656 96.751 9.868 48.677 2.475 65.425 32.844 97.253 25.8 0.033 300 300 0.046 330 170 0.7353 91.912 91.242 8.239 45.844 2.065 61.511 30.852 300 0.047 285 0.029 270 275 300 300 0.037 0.041 300 340 91.614 34.9 0.033 240 180 0.6944 86.086 86.302 6.948 43.319 1.741 58.048 29.096 86.581 13 10.5 240 0.042 0.044 0.047 200 225 0,038 250 250 0.042 275 275 285 0.051 300 330 190 0.6579 82.237 81.853 5.913 41.054 1.481 54.960 27.535 82.066 12 23 58.3 4 07 53.5 0.037 225 225 240 240 0.046 250 260 0.051 250 275 0.055 300 300 325 200 11 I| 26.1 3 43 10 09 00.7 3 22 9 14 54.3 3 04 8 27 42.1 2 49 7 46 7 09 24 34.1 0.6250 78.125 77.828 5.072 39.013 1.270 52.188 26.137 77.993 44.4 0.039 200 200 225 225 0.049 230 250 0.053 250 270 0.057 300 325 210 0.5952 74.405 74.172 4.384 37.163 1.097 49.685 24.876 74.301 57.0 260 0.060 275 275 250 0.060 275 275 0.042 200 200 0.051 225 250 Minimum R= 1000 220 0.5682 0.5435 0.5208 0.056 250 71.023 70.838 3.814 35.481 0.954 47.413 23.733 70.941 55.6 0.045 185 185 0.049 200 220 0.054 225 235 0.059 250 230 67.935 67.787 3.339 33.94 0.835 45.342 22.692 67.869 12.1 0.048 175 185 0.057 0.060 25 0 250 240 65.104 64,984 2.940 32.532 0.735 43.455 21.739 65.051 16.5 2 35 24.0 0.053 200 200 220 220 Minimum R = 800 250 0.5000 62.500 62.402 2.601 31.234 0.651 41.701 20.864 62.457 7 43.1 2 23 13.2 0.052 160 175 0.057 200 200 0.060 220 220 Minimum R- 650 280 1 54 1 39 4 22 16.8 27 1 17 I 13 I 01 0 55 0.4464 55.804 55.748 1.852 27.983 0.463 0.377. 34,736 0.310 37.222 18.619 55.779 10.8 Minimum R = 525 0.060 200 200 Minimum R- 420 0.057 160 165 300 0.4167 52.083 52.044 1.506 26.035 17.374 52.066 4 58 24.9 27.9 - 0.059 160 160 320 0.3906 48.828 48.800 1.241 24.409 32.562 16.285 48.815 25.3 0.060 160 160 340 0.3676 45.956 45.935 1.035 22.974 0.259 30.645 15.325 45.947 3 52 19.8 26.4 350 0.3571 44.643 44.625 0.949 22.318 0.237 3 39 14.6 3 05 59.6 Minimum R - 340 29.768 14.887 44.635 04.7 380 0.185 0.159 0.3289 41.118 41.106 0.741 20.557 27.416 13.710 41.113 59.8 400 0.3125 39.063 39.063 0.636 19.530 26.045 2 47 51.5 13.024 39.058 57.1 420 0.2976 37.202 37.195 0.549 18.600 0.137 24.804 12.403 37.195 2 32 15.2 2 0 50 45.0 450 0.2778 34.722 34,717 0.446 17.360 0.112 23.150 11.576 34.720 37.7 0 44 12.5 475 0.2632 32.895 32.891 0.380 16.447 0.095 21.931 10.966 32.893 I 59 59 02.1 0 39 40.7 500 0.2500 31.250 31.247 0.325 15,624 0.081 20.834 19.842 10.418 31.249 47 25.8 0 35 48.6 525 0.2381 29.762 29.760 0.281 14.881 0.070 0.061 9.921 29.761 37 26.5 1 28 47.1 0 29 1 21 13.9 0 27 0 32 20.8 550 0.2273 28.409 28.407 0.245 14.204 18.940 9.470 28.408 1 35.7 575 0.2174 27.174 27.172 0.214 13.587 0054 18.116 9.058 27.173 04.6 Source: Metric Curve Tables, Table IV, Roads and Transportation Association of Canada (RTAC). *Short radius (i.e., < 150 m) may require a correction to A/3 to determine the precise value of 0.
Transcribed Image Text:Table 11.7 (continued) 90 100 110 120 130 140 Table 11.9 FUNCTIONS OF THE STANDARD SPIRAL FOR A = 125 m AIR L X P LT L. e, ST A, A 2 3 & 4 A A R 2 3 & 4 2 3 & 4 2 3 & 4 2 3 & 4 2 3 & 4 (m) e Meters Deg. Min. Sec. Deg. Min. Sec. Lane Lane Lane Lane Lane Lane Lane Lane Lane Lane Lane Lane 115 1.0870 135.870 131.204 26.095 67.152 6.606 92.293 46.851 88.183 133.774 33 50 48.3 11 05 05.8 10 38 52.4 14 55.1 1.0417 130.208 126.428 23.057 1.0000 125.000 121.911 0.9615 120.192 117.649 0.8929 111.607 109.847 NC NC NC NC NC 700 700 RC 700 700 120 64.471 5.825 44.658 128.513 31 20 08.3 500 500 125 20.464 61.983 5.162 84.451 42.685 123.617 28 9 31 44.3 NC NC 600 0.024 625 500 0.028 560 450 0.030 450 450 0.034 495 400 0.043 400 330 0.050 345 300 0.056 330 0.060 325 300 0.060 325 NC RC 600 600 0.021 600 625 560 130 18.240 59.671 4.595 81.044 40.898 119.055 26 29 11.7 8 48 46.1 NC RC 480 480 RC 500 0.022 500 500 0.025 S00 140 50 16.5 7 36 19 53 39.7 6 37 17 29 07.0 5 49 15 29 19.3 5 09 48 55.9 4 36 14.661 55.509 3.686 75.034 37.755 110.821 22 08.5 RC 390 400 0.025 400 400 0.023 450 450 0.027 450 495 150 0.8333 104.167 102.918 11.953 51.875 3.001 69.888 35.126 103.610 28.8 0.023 300 350 0.027 340 340 0.031 350 350 0.035 350 350 0.039 400 400 160 0.7813 97.656 96.751 9.868 48.677 2.475 65.425 32.844 97.253 25.8 0.033 300 300 0.046 330 170 0.7353 91.912 91.242 8.239 45.844 2.065 61.511 30.852 300 0.047 285 0.029 270 275 300 300 0.037 0.041 300 340 91.614 34.9 0.033 240 180 0.6944 86.086 86.302 6.948 43.319 1.741 58.048 29.096 86.581 13 10.5 240 0.042 0.044 0.047 200 225 0,038 250 250 0.042 275 275 285 0.051 300 330 190 0.6579 82.237 81.853 5.913 41.054 1.481 54.960 27.535 82.066 12 23 58.3 4 07 53.5 0.037 225 225 240 240 0.046 250 260 0.051 250 275 0.055 300 300 325 200 11 I| 26.1 3 43 10 09 00.7 3 22 9 14 54.3 3 04 8 27 42.1 2 49 7 46 7 09 24 34.1 0.6250 78.125 77.828 5.072 39.013 1.270 52.188 26.137 77.993 44.4 0.039 200 200 225 225 0.049 230 250 0.053 250 270 0.057 300 325 210 0.5952 74.405 74.172 4.384 37.163 1.097 49.685 24.876 74.301 57.0 260 0.060 275 275 250 0.060 275 275 0.042 200 200 0.051 225 250 Minimum R= 1000 220 0.5682 0.5435 0.5208 0.056 250 71.023 70.838 3.814 35.481 0.954 47.413 23.733 70.941 55.6 0.045 185 185 0.049 200 220 0.054 225 235 0.059 250 230 67.935 67.787 3.339 33.94 0.835 45.342 22.692 67.869 12.1 0.048 175 185 0.057 0.060 25 0 250 240 65.104 64,984 2.940 32.532 0.735 43.455 21.739 65.051 16.5 2 35 24.0 0.053 200 200 220 220 Minimum R = 800 250 0.5000 62.500 62.402 2.601 31.234 0.651 41.701 20.864 62.457 7 43.1 2 23 13.2 0.052 160 175 0.057 200 200 0.060 220 220 Minimum R- 650 280 1 54 1 39 4 22 16.8 27 1 17 I 13 I 01 0 55 0.4464 55.804 55.748 1.852 27.983 0.463 0.377. 34,736 0.310 37.222 18.619 55.779 10.8 Minimum R = 525 0.060 200 200 Minimum R- 420 0.057 160 165 300 0.4167 52.083 52.044 1.506 26.035 17.374 52.066 4 58 24.9 27.9 - 0.059 160 160 320 0.3906 48.828 48.800 1.241 24.409 32.562 16.285 48.815 25.3 0.060 160 160 340 0.3676 45.956 45.935 1.035 22.974 0.259 30.645 15.325 45.947 3 52 19.8 26.4 350 0.3571 44.643 44.625 0.949 22.318 0.237 3 39 14.6 3 05 59.6 Minimum R - 340 29.768 14.887 44.635 04.7 380 0.185 0.159 0.3289 41.118 41.106 0.741 20.557 27.416 13.710 41.113 59.8 400 0.3125 39.063 39.063 0.636 19.530 26.045 2 47 51.5 13.024 39.058 57.1 420 0.2976 37.202 37.195 0.549 18.600 0.137 24.804 12.403 37.195 2 32 15.2 2 0 50 45.0 450 0.2778 34.722 34,717 0.446 17.360 0.112 23.150 11.576 34.720 37.7 0 44 12.5 475 0.2632 32.895 32.891 0.380 16.447 0.095 21.931 10.966 32.893 I 59 59 02.1 0 39 40.7 500 0.2500 31.250 31.247 0.325 15,624 0.081 20.834 19.842 10.418 31.249 47 25.8 0 35 48.6 525 0.2381 29.762 29.760 0.281 14.881 0.070 0.061 9.921 29.761 37 26.5 1 28 47.1 0 29 1 21 13.9 0 27 0 32 20.8 550 0.2273 28.409 28.407 0.245 14.204 18.940 9.470 28.408 1 35.7 575 0.2174 27.174 27.172 0.214 13.587 0054 18.116 9.058 27.173 04.6 Source: Metric Curve Tables, Table IV, Roads and Transportation Association of Canada (RTAC). *Short radius (i.e., < 150 m) may require a correction to A/3 to determine the precise value of 0.
Table 11.7 SPIRAL CURVE LENGTHS AND SUPERELEVATION RATES (METRIC)* Design Speed km/h 40 50 60 70 80 A A A A Radius 2 3 & 4 3 & 4 2 3 & 4 2 3 & 4 2 3 & 4 m Lane Lane Lane Lane Lane Lane Lane Lane Lane Lane 7000 NC NC NC NC NC S000 NC NC NC NC NC 4000 NC NC NC NC NC 3000 NC NC NC NC 2000 NC NC NC RC 275 275 RC 300 300 1500 NC NC RC 225 225 RC 250 250 0.024 250 250 225 1200 NC NC RC 200 200 0.028 0.032 0.034 0.036 0.039 0.042 0.046 0.023 225 225 225 1000 NC RC 170 170 0.021 175 175 0.027 200 200 200 200 900 NC RC 150 150 0.023 175 175 0.029 180 180 200 200 800 NC RC 150 150 0.025 160 160 0.031 175 175 175 175 700 NC 0.021 140 140 0.027 150 150 0.034 175 175 175 175 600 NC 120 120 0.024 125 125 0.030 140 140 0.037 150 150 175 175 500 RC 100 100 0.027 120 120 0.034 125 125 0.041 140 150 150 160 400 0.023 90 90 0.031 100 100 0.038 115 120 0.045 125 135 0.051 135 150 0.034 100 0.037 0.054 0.057 0.060 0.060 350 0.025 90 90 100 0.041 110 115 0.048 120 125 125 140 0.028 0.031 300 80 80 90 100 0.044 100 110 0.051 120 125 125 135 250 75 80 0.040 85 90 0.048 90 100 0.055 110 120 125 125 220 0.034 70 80 0.043 80 90 0.050 90 100 0.057 110 110 125 125 06 90 200 0.036 70 75 0.045 75 0.052 85 100 0.059 110 110 Minimum R = 250 180 0.038 60 75 0.047 70 0.054 85 95 0.060 110 110 160 0.040 60 75 0.049 70 85 0.056 85 90 Minimum R = 190 140 0.043 60 70 0.052 65 80 0.059 85 90 120 0.048 60 65 0.055 65 75 0.060 85 90 100 0.049 50 65 0.058 65 70 Minimum R 130 90 0.051 50 60 0.060 65 70 80 0.054 50 60 0.060 65 70 70 0.058 50 60 Minimum R= 90 60 0.059 S0 60 50 60 0.059 Minimum R = 55 Source: Roads and Transportation Association of Canada (RTAC). *Dmas- 0.06 e is superelevation. A is spiral parameter in meters. NC is normal cross section. RC is remove adverse crown and superelevate at normal rate. Spiral length, L= A + radius. Spiral parameters are minimum and higher values should be used where possible. Spirals are desirable but not essential above the heavy line. For 6-lane pavement: above the dashed line use 4-lane values; below the dashed line use 4-lane values x 1.15. A divided road having a median less than 7 m may be treated as a single pavement.
Transcribed Image Text:Table 11.7 SPIRAL CURVE LENGTHS AND SUPERELEVATION RATES (METRIC)* Design Speed km/h 40 50 60 70 80 A A A A Radius 2 3 & 4 3 & 4 2 3 & 4 2 3 & 4 2 3 & 4 m Lane Lane Lane Lane Lane Lane Lane Lane Lane Lane 7000 NC NC NC NC NC S000 NC NC NC NC NC 4000 NC NC NC NC NC 3000 NC NC NC NC 2000 NC NC NC RC 275 275 RC 300 300 1500 NC NC RC 225 225 RC 250 250 0.024 250 250 225 1200 NC NC RC 200 200 0.028 0.032 0.034 0.036 0.039 0.042 0.046 0.023 225 225 225 1000 NC RC 170 170 0.021 175 175 0.027 200 200 200 200 900 NC RC 150 150 0.023 175 175 0.029 180 180 200 200 800 NC RC 150 150 0.025 160 160 0.031 175 175 175 175 700 NC 0.021 140 140 0.027 150 150 0.034 175 175 175 175 600 NC 120 120 0.024 125 125 0.030 140 140 0.037 150 150 175 175 500 RC 100 100 0.027 120 120 0.034 125 125 0.041 140 150 150 160 400 0.023 90 90 0.031 100 100 0.038 115 120 0.045 125 135 0.051 135 150 0.034 100 0.037 0.054 0.057 0.060 0.060 350 0.025 90 90 100 0.041 110 115 0.048 120 125 125 140 0.028 0.031 300 80 80 90 100 0.044 100 110 0.051 120 125 125 135 250 75 80 0.040 85 90 0.048 90 100 0.055 110 120 125 125 220 0.034 70 80 0.043 80 90 0.050 90 100 0.057 110 110 125 125 06 90 200 0.036 70 75 0.045 75 0.052 85 100 0.059 110 110 Minimum R = 250 180 0.038 60 75 0.047 70 0.054 85 95 0.060 110 110 160 0.040 60 75 0.049 70 85 0.056 85 90 Minimum R = 190 140 0.043 60 70 0.052 65 80 0.059 85 90 120 0.048 60 65 0.055 65 75 0.060 85 90 100 0.049 50 65 0.058 65 70 Minimum R 130 90 0.051 50 60 0.060 65 70 80 0.054 50 60 0.060 65 70 70 0.058 50 60 Minimum R= 90 60 0.059 S0 60 50 60 0.059 Minimum R = 55 Source: Roads and Transportation Association of Canada (RTAC). *Dmas- 0.06 e is superelevation. A is spiral parameter in meters. NC is normal cross section. RC is remove adverse crown and superelevate at normal rate. Spiral length, L= A + radius. Spiral parameters are minimum and higher values should be used where possible. Spirals are desirable but not essential above the heavy line. For 6-lane pavement: above the dashed line use 4-lane values; below the dashed line use 4-lane values x 1.15. A divided road having a median less than 7 m may be treated as a single pavement.
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