Explanation Given: The initial grade is − 3 % . The final grade is + 1 % The design speed is 60 mi / h . The elevation of PVI is 732 ft . The PVI is at station 250 + 50 . Formula used: The expression for the minimum length of the curve is given by, L m = K ( | G 1 − G 2 | ) ...... (I) Here, G 1 is the initial grade of the curve, G 2 is the final grade of the curve, L m is the minimum length of the vertical curve, and K is the horizontal distance required to effect 1 % change in the vertical curve. The distance between the initial point of the vertical curve and the point of tangent intersection is given by, D 1 = L m 2 ......... (II) Here, D 1 is distance between the initial point of the vertical curve and the point of tangent intersection. The expression for the station at the initial point of the vertical curve is given by, Station of P V C = Station of P V I − D I 100 ft ........ (III) Here, station of P V C is the station at the initial point of the vertical curve, and Station of P V I is the distance between the station points of tangent intersection. The expression to determine the elevation of P V I is given by, Elevation of P V I = Elevation of P V C + ( G 1 × N i ) Elevation of P V C = Elevation of P V I − ( G 1 × N i ) ........ (IV) Here, G i is the initial grade of the curve, N i is the number of station between PVC and PVI, Elevation of PVC is the elevation of the beginning of the curve and Elevation of PVI is the elevation of point of intersection of tangents. The expression to determine the distance from the point of the vertical curve (PVC) to the high point on the curve is given as, x hl = K ( | G 1 | ) ........ (V) Here, x hl is the distance from the point of the vertical curve (PVC) to the high point on the curve. The equation of vertical curve is given by, y = a x 2 + b x + c ........ (VI) Here, y is the roadway elevation at distance x from the beginning of the vertical curve in stations or feet, x is the distance from the beginning of the vertical curve, a and b are the coefficients and c is the elevations of the P V C . The coefficient b is given by, b = G 1 The coefficient a is given by, a = ( G 2 − G 1 ) 2 ( L 100 ) ........ (VII) The expression for the station at low point of the vertical curve is given by, Station of low point = Station of P V C + x hl ........ (VIII) Here, Station of low point is the station at low point of the vertical curve. Calculation: Refer table 3.3 "Design controls for sag vertical curves based on stopping sight distance" For the design speed 60 mi / h , the value of K is, K = 136 ft Substitute − 3

PRIN.OF HIGHWAY ENGINEERING&TRAFFIC ANA.

7th Edition

ISBN: 9781119610526

Author: Mannering

Publisher: WILEY

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Chapter 3, Problem 24P

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PRIN.OF HIGHWAY ENGINEERING&TRAFFIC ANA.

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The station and elevation of the lowest point on the curve.

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