Unformatted text preview: VERTICAL ALIGNMENT
NOTES AND ASSIGNMENT #2 BACKGROUND
Created by John Caruano Created by John Caruano Vertical Alignment Vertical Alignment Introduction MWK Text pages 4749 Specifies the elevation of points on a roadway. Elevation of roadway points determined by the need to provide:
– Acceptable level of driver safety – Driver comfort – Proper drainage (rainfall runoff) Primary Goals of Vertical Primary Goals of Vertical Alignment
1. Provide a smooth transition between vertical tangents (grades)
PVC = Point of Vertical Curvature PVI = Point of Vertical Intersection PVT = Point of Vertical Tangency *Note: In practice, vast majority of vertical curves are arranged such that half of the curve length is positioned before the PVI and half after. This type of curve is said to be equaltangent vertical curves. Primary Goals of Vertical Primary Goals of Vertical Alignment
1. Grade lines are used to: (a) Minimize cut and fill (b) Balance cut and fill values (c) Maintain adequate drainage (d) Not exceed maximum slopes (e) Meet fixed elevations Types of Curves: Types of Curves: Crest Vertical Curve – Negative change in grade – Stopping Sight Distance
Driver eye height 3.5 ft Object height 2 ft Sag Vertical Curve – Positive change in grade – Headlamp sight distance Diagrams Diagrams Crest Vertical Curve Crest Vertical Curve Sag Vertical Curve Sag Vertical Curve Elevation along a curve… Elevation along a curve…
To find elevation along a vertical curve at a specific location, a parabolic equation is used: y = ax^2 + bx + c Parabolic Relationship Parabolic Relationship Diagram Parabolic Relationship Parabolic Relationship Derivation @ x = 0, y = a(0)^2 + b(0) + c y = c @ x = 0, y = PVCELEV. THEREFORE c = PVCELEV. Parabolic Relationship Parabolic Relationship Derivation (cont.) dy/dx = 2ax + b @ x = 0, dy/dx = 2a(0) + b dy/dx = b @ x = 0, dy/dx = g1 THEREFORE b = g1 Parabolic Relationship Parabolic Relationship Derivation (cont.) d^2y/dx^2 = 2a @ x = 0, d^2y/dx^2 = (g2 – g1)/L THEREFORE 2a = (g2 – g1)/L a = (g2 – g1)/2L Parabolic Relationship Parabolic Relationship Derivation (cont.) y = [(g2 – g1)/2L]x^2 + (g1)x + PVCELEV. Refer to examples 3.1 & 3.2 in MKW text. ASSIGNMENT #2 ASSIGNMENT #2 The purpose of this assignment is to develop a profile view of the alignment created in CAD Assignment #1 using AutoCAD, Microsoft Excel, and a contour map.
– Create grid – Determine existing ground elevations from contour map (approximation) – Draw finished grade tangent lines – Calculate and create vertical curves Assignment #2 Submission Assignment #2 Submission Includes: The EXCEL spreadsheet to calculate finished grade tangent lines and curve elevations (electronically). The completed profile drawing with labels for existing and finished grades and the vertical curve data. (see manual on ANGEL for further detail) THE SCALE FACTOR THE SCALE FACTOR EXPLAINED When creating the grid, use a horizontal offset distance of 500’ to create the vertical gridlines. All distances along the horizontal direction are in true units. (e.g. 500’ = 500’) Create the horizontal gridlines, use a vertical spacing of 500’, but label the spacing as 100’. Therefore, the vertical measurements will be exaggerated by a factor of 5. For example, if you construct a vertical line that is 5’ then you would need to draw it 25’ long in the AutoCAD environment. Typically on all construction drawings exaggerate the vertical scale by a factor of either 5 or 10 so that changes in the vertical profile can be observed. Example Finished Product Example Finished Product ...
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 Spring '02
 Petrucha
 vertical curve, sag vertical curve, Crest Vertical Curve Crest Vertical Curve, Relationship Parabolic Relationship

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