### Example Problem: Determining the Length of a Vertical Curve#### Problem Statement:An incoming grade of +3.00% meets an existing grade of -1.50% at a PVI having station 18+00 & elevation 120.00'. A perpendicular street crosses at station 19+50.00 & elevation 117.00'. What is the length of the vertical curve required to match elevations at the intersection?#### Solution Options:- A. 155.85'- B. 600.00'- C. 577.49'- D. 639.51'#### Analysis:To solve this problem, we need to apply principles of vertical curve design, ensuring that the provided grades and stationing intersect correctly at the given elevations. The primary goal is to calculate the length of vertical curve necessary for smooth transition between the incoming and existing grades at the given elevational intersection.---This problem involves calculating geometric relationships between grades, heights, and distances on a roadway's vertical curve. Understanding of vertical curves and their properties is essential for the solution.Graphical or diagrammatic representations depicting the grades, PVI (Point of Vertical Intersection), and significant points along the vertical curve would help visualize and solve the problem accurately. However, for this textual representation, thorough knowledge of the mathematics and physics governing these principles is necessary. Refer to your textbooks or class notes on vertical curves in highway design to correctly determine the appropriate length of the required curve. Also, use specific formulae and methods (such as the equation \( L = \dfrac{\Delta H}{(G1 - G2)} \), where \( L \) is the curve length, \( \Delta H \) is the elevation difference, \( G1 \) and \( G2 \) are the incoming and existing grades respectively) as part of the calculation process.

Incoming grade, Existing grade, PVI stationElevation of PVI, Station of street, Elevation of street,…

18. An incoming grade of +3.00% meets an existing grade of -1.50% at a PVI having station 18+00 & elevation 120.00'. A perpendicular street crosses at station 19+50.00 & elevation 117.00. What is the length of vertical curve required to match elevations at the intersection? A. 155.85' B. 600.00' C. 577.49' D. 639.51'

18. An incoming grade of +3.00% meets an existing grade of -1.50% at a PVI having station 18+00 & elevation 120.00'. A perpendicular street crosses at station 19+50.00 & elevation 117.00. What is the length of vertical curve required to match elevations at the intersection? A. 155.85' B. 600.00' C. 577.49' D. 639.51'

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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Concept explainers

Drainage of Pavements

Pavement Drainage holds ample significance, as it prevents the accumulation of water or any liquid on the surface of pavements and ensures proper drainage system. With proper design and gradual slopes provided, the water gets easily removed from the surface into the drains, which are essential during heavy rains and unusual weather conditions keeping it less prone to accidents and increasing the durability of the pavement structure.

Question

### Example Problem: Determining the Length of a Vertical Curve

#### Problem Statement:
An incoming grade of +3.00% meets an existing grade of -1.50% at a PVI having station 18+00 & elevation 120.00'. A perpendicular street crosses at station 19+50.00 & elevation 117.00'. What is the length of the vertical curve required to match elevations at the intersection?

#### Solution Options:
- A. 155.85'
- B. 600.00'
- C. 577.49'
- D. 639.51'

#### Analysis:
To solve this problem, we need to apply principles of vertical curve design, ensuring that the provided grades and stationing intersect correctly at the given elevations. The primary goal is to calculate the length of vertical curve necessary for smooth transition between the incoming and existing grades at the given elevational intersection.

---
This problem involves calculating geometric relationships between grades, heights, and distances on a roadway's vertical curve. Understanding of vertical curves and their properties is essential for the solution.

Graphical or diagrammatic representations depicting the grades, PVI (Point of Vertical Intersection), and significant points along the vertical curve would help visualize and solve the problem accurately. However, for this textual representation, thorough knowledge of the mathematics and physics governing these principles is necessary.

Refer to your textbooks or class notes on vertical curves in highway design to correctly determine the appropriate length of the required curve. Also, use specific formulae and methods (such as the equation \( L = \dfrac{\Delta H}{(G1 - G2)} \), where \( L \) is the curve length, \( \Delta H \) is the elevation difference, \( G1 \) and \( G2 \) are the incoming and existing grades respectively) as part of the calculation process.

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