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

Principles Of Highway Engineering And Traffic Analysis

7th Edition

ISBN: 9781119493969

Author: Mannering, Fred L., WASHBURN, Scott S.

Publisher: Wiley,

See similar textbooks

Question

Chapter 3, Problem 24P

To determine

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

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 3, Problem 23P

Chapter 3, Problem 25P

Students have asked these similar questions

a. Ultimate Bearing Capacity (qult)b. Allowable Bearing Capacity (qall)c. Allowable Load (Qa)d. Maximum applied contact pressuree. Minimum applied contact pressuref. Draw the contact pressure diagramg. Is the footing size appropriate and why

Handwritten answers only please. Thank you!

handwritten answers only please. Thank you!

Chapter 3 Solutions

Principles Of Highway Engineering And Traffic Analysis

Ch. 3 - Prob. 1P Ch. 3 - Prob. 2P Ch. 3 - Prob. 3P Ch. 3 - Prob. 4P Ch. 3 - Prob. 5P Ch. 3 - Prob. 6P Ch. 3 - Prob. 7P Ch. 3 - Prob. 8P Ch. 3 - Prob. 9P Ch. 3 - Prob. 10P

Ch. 3 - Prob. 11P Ch. 3 - Prob. 12P Ch. 3 - Prob. 13P Ch. 3 - Prob. 14P Ch. 3 - Prob. 15P Ch. 3 - Prob. 16P Ch. 3 - Prob. 17P Ch. 3 - Prob. 18P Ch. 3 - Prob. 19P Ch. 3 - Prob. 20P Ch. 3 - Prob. 21P Ch. 3 - Prob. 22P Ch. 3 - Prob. 23P Ch. 3 - Prob. 24P Ch. 3 - Prob. 25P Ch. 3 - Prob. 26P Ch. 3 - Prob. 27P Ch. 3 - Prob. 28P Ch. 3 - Prob. 29P Ch. 3 - Prob. 30P Ch. 3 - Prob. 31P Ch. 3 - Prob. 32P Ch. 3 - Prob. 33P Ch. 3 - Prob. 34P Ch. 3 - Prob. 35P Ch. 3 - Prob. 36P Ch. 3 - Prob. 37P Ch. 3 - Prob. 38P Ch. 3 - Prob. 39P Ch. 3 - Prob. 40P Ch. 3 - Prob. 41P Ch. 3 - Prob. 42P Ch. 3 - Prob. 43P Ch. 3 - Prob. 44P Ch. 3 - Prob. 45P Ch. 3 - Prob. 46P Ch. 3 - Prob. 47P Ch. 3 - Prob. 48P Ch. 3 - Prob. 49P Ch. 3 - Prob. 50P Ch. 3 - Prob. 51P Ch. 3 - Prob. 52P Ch. 3 - Prob. 53P Ch. 3 - Prob. 54P Ch. 3 - Prob. 55P Ch. 3 - Prob. 56P Ch. 3 - Prob. 57P Ch. 3 - Prob. 58P Ch. 3 - Prob. 59P Ch. 3 - Prob. 60P Ch. 3 - Prob. 61P Ch. 3 - Prob. 62P Ch. 3 - Prob. 63P Ch. 3 - Prob. 64P Ch. 3 - Prob. 65P Ch. 3 - Prob. 66P Ch. 3 - Prob. 67P

Knowledge Booster

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

Solution Summary: The author describes the station and elevation of the lowest point on the curve.

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

Want to see the full answer?

Chapter 3 Solutions