Explanation Given: The initial grade is − 3.5 % , and final grade of the curve is + 6.5 % . The station of the PVCis 115 + 00 and is at elevation 750 ft . Formula used: The formula to calculate the distance between the stations is given by D 1 = L 2 ....... (I) Here, D 1 is the distance between the station of point of tangent intersection, and the station of the initial point of vertical curve and L is the distance of the vertical curve. The formula to calculate the stationing of the point of tangent intersection ( PVI ) is given by S P V I = S P V C + D 1 100 ft ....... (II) Here, S P V C is the station of the Initial Point of Vertical Curve ( PVC ), and Station of Point of Vertical Intersection ( PVI ). The formula to calculate the elevation of PVI is given by. E P V I = E P V C + ( G i × N i ) ....... (III) Here, E P V C is the elevation of the beginning of the vertical curve, E P V I is the elevation of the point of intersection of the tangents, G i is the initial grade of the curve and N i is the number of stations in between PVC and PVI. The formula to calculate the stationing of the final point of vertical curve ( PVT ) is given by S P V T = S P V I + D 2 100 ft ....... (IV) Here, S P V T is the station of the final point of vertical curve ( PVT ), D 2 is the distance between the station of point of tangent intersection and the station of the final point of vertical curve. The formula to calculate the elevation of PVT is given by. E P V T = E P V I + ( G f × N 2 ) ....... (III) Here, E P V T is the elevation of the end of the vertical curve, E P V I is the elevation of the point of intersection of the tangents, G f is the final grade of the curve and N 2 is the number of stations in between PVTand PVI. The formula to calculate the elevation of high point is given by y = a x 2 + b x + c ....... (V) Here, x is the distance from the beginning of the vertical curve in station or feet, c is the elevation of PVC, y is the roadway elevation at a distance x from the beginning of the vertical curve in station. Differentiate equation (X). d y d x = 2 a x + b ....... (VI) The formula to calculate the value of the coefficient b is given by b = G 1 ....... (VII) The formula to calculate the coefficient is given by a = G f − G i 2 L ....... (VIII) Here, a is the coefficient, L is the length of the curve in ft , and A is the absolute value of difference in grade. The formula to calculate the stationing of low point from the PVC is given by S low point = S P V C + x ....... (IX) Here, S low point is the station of the low point, and S P V C is the station of the PVC. Calculation: Substitute 1400 ft for L in equation (I). D 1 = 1400 ft 2 = 700 ft Substitute 115 + 00 for S P V C , and 700 ft for D in equation (II). S P V I = 115 + 00 + 700 ft 100 ft = 122 + 00 Substitute 750 ft for E P V C , − 3

PRIN.OF HIGHWAY ENGINEERING&TRAFFIC ANA.

7th Edition

ISBN: 9781119610526

Author: Mannering

Publisher: WILEY

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Chapter 3, Problem 20P

To determine

The elevation and stationing of the low pointPVI, and PVT.

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Chapter 3, Problem 19P

Chapter 3, Problem 21P

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PRIN.OF HIGHWAY ENGINEERING&TRAFFIC ANA.

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