Environmental Design + Construction April 2011 by Derrick Teal

By Derrick Teal

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Given R and I, find T: T = R × tan 1/2I. Given R and C, find D: Sin D = 1/2C/R. D = arcsin of sin D. Given C and D, find R: R = 1/2C/sin D. Given I, D, and C, find T: T = (C × tan 1/2I)/2sinD. Given I, T, and C, find D: Sin D = (C × tan 1/2I)/2T. If 100-foot chords are used: Sin D = 50/R; R = 50/sin D. Sin D = (50 × tan 1/2I)/T; T = (50 × tan 1/2I)/sin D. Remember that the number of chords in the length of a curve is N = 1/2l/D. If D is not evenly divisible into 1/2I, there will be a subchord, as mentioned above.

Given R and I, find T: T = R × tan 1/2I. Given R and C, find D: Sin D = 1/2C/R. D = arcsin of sin D. Given C and D, find R: R = 1/2C/sin D. Given I, D, and C, find T: T = (C × tan 1/2I)/2sinD. Given I, T, and C, find D: Sin D = (C × tan 1/2I)/2T. If 100-foot chords are used: Sin D = 50/R; R = 50/sin D. Sin D = (50 × tan 1/2I)/T; T = (50 × tan 1/2I)/sin D. Remember that the number of chords in the length of a curve is N = 1/2l/D. If D is not evenly divisible into 1/2I, there will be a subchord, as mentioned above.

The pier centers will lie on the bridge centerline. The piers stand at Stations 12 + 95 and 13 + 40. Station 13 + 85 is on the streamside face of the opposite wing abutment. Establish a baseline on each stream bank, one at Station 12 + 25 and one at Station 14 + 10. Set points 8, 9, 10, 11, 12, 13, 14, and 15 on the baselines, with the points at the ends of lines intersecting on the pier centers. Choose some standard of angle that gives you an easy computation, for instance, 45°. Because pier 1 stands at Stations 12 + 95, 70 feet from the 62 Construction Surveying & Layout  baseline at Station 12 + 25, point 14 lies on the baseline 70 feet from the centerline.

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