Geometric Design Session 02-06

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Geometric Design Session 02-06. Matakuliah : S0753 – Teknik Jalan Raya Tahun : 2009. Contents. Concepts Vertical Alignment Fundamentals Crest Vertical Curves Sag Vertical Curves Examples Horizontal Alignment Fundamentals Superelevation.

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### Geometric DesignSession 02-06

Matakuliah : S0753 – Teknik Jalan Raya

Tahun : 2009

### Contents

Concepts

Vertical Alignment

Fundamentals

Crest Vertical Curves

Sag Vertical Curves

Examples

Horizontal Alignment

Fundamentals

Superelevation

Alignment is a 3D problem broken down into two 2D problems

Horizontal Alignment (plan view)

Vertical Alignment (profile view)

Stationing

Along horizontal alignment

Introduction

Piilani Highway on Maui

Horizontal AlignmentStationing

Introduction

Vertical Alignment

Introduction

From Perteet Engineering

Geometric Design Elements
• Sight Distances
• Superelevation
• Horizontal Alignment
• Vertical Alignment
Sag Vertical Curve

G1

G2

G2

G1

Crest Vertical Curve

Vertical Alignment
• Objective:
• Determine elevation to ensure
• Proper drainage
• Acceptable level of safety
• Primary challenge
• Vertical curves
Vertical Curve Fundamentals
• Parabolic function
• Constant rate of change of slope
• Implies equal curve tangents
• y is the roadway elevation x stations (or feet) from the beginning of the curve
Vertical Curve Fundamentals

PVI

G1

δ

PVC

G2

PVT

L/2

L

x

• Choose Either:
• G1, G2 in decimal form, L in feet
• G1, G2 in percent, L in stations
Relationships
• Choose Either:
• G1, G2 in decimal form, L in feet
• G1, G2 in percent, L in stations
Example

A 400 ft. equal tangent crest vertical curve has a PVC station of 100+00 at 59 ft. elevation. The initial grade is 2.0 percent and the final grade is -4.5 percent. Determine the elevation and stationing of PVI, PVT, and the high point of the curve.

PVI

PVT

G1=2.0%

G2= - 4.5%

PVC: STA 100+00

EL 59 ft.

PVI

PVT

G1=2.0%

PVC: STA 100+00

EL 59 ft.

G2= -4.5%

G1, G2 in percent
• L in feet
Other Properties

G1

x

PVT

PVC

Y

Ym

G2

PVI

Yf

Other Properties
• K-Value (defines vertical curvature)
• The number of horizontal feet needed for a 1% change in slope
Crest Vertical Curves

SSD

PVI

Line of Sight

PVC

PVT

G2

G1

h2

h1

L

For SSD < L

For SSD > L

For SSD < L

For SSD > L

Crest Vertical Curves
• Assumptions for design
• h1 = driver’s eye height = 3.5 ft.
• h2 = tail light height = 2.0 ft.
• Simplified Equations
• Assuming L > SSD…
Design Controls for Crest Vertical Curves

from AASHTO’s A Policy on Geometric Design of Highways and Streets 2001

Design Controls for Crest Vertical Curves

from AASHTO’s A Policy on Geometric Design of Highways and Streets 2001

Sag Vertical Curves

Light Beam Distance (SSD)

G1

headlight beam (diverging from LOS by β degrees)

G2

PVT

PVC

h1

PVI

h2=0

L

For SSD < L

For SSD > L

For SSD < L

For SSD > L

Sag Vertical Curves
• Assuming L > SSD…
• Assumptions for design
• h1 = headlight height = 2.0 ft.
• β = 1 degree
• Simplified Equations
Design Controls for Sag Vertical Curves

from AASHTO’s A Policy on Geometric Design of Highways and Streets 2001

Design Controls for Sag Vertical Curves

from AASHTO’s A Policy on Geometric Design of Highways and Streets 2001

Horizontal Alignment
• Objective:
• Geometry of directional transition to ensure:
• Safety
• Comfort
• Primary challenge
• Transition between two directions
• Horizontal curves
• Fundamentals
• Circular curves
• Superelevation

Δ

Horizontal Curve Fundamentals

PI

T

Δ

E

M

L

Δ/2

PT

PC

R

R

Δ/2

Δ/2

Horizontal Curve Fundamentals

PI

T

Δ

E

M

L

Δ/2

PT

PC

R

R

Δ/2

Δ/2

Superelevation

Rv

Fc

α

Fcn

Fcp

α

e

W

1 ft

Wn

Ff

Wp

Ff

α

Selection of e and fs
• Practical limits on superelevation (e)
• Climate
• Constructability
• Side friction factor (fs) variations
• Vehicle speed
• Pavement texture
• Tire condition
Side Friction Factor

from AASHTO’s A Policy on Geometric Design of Highways and Streets 2004

WSDOT Design Side Friction Factors

For Open Highways and Ramps

from the 2005 WSDOT Design Manual, M 22-01

WSDOT Design Side Friction Factors

For Low-Speed Urban Managed Access Highways

from the 2005 WSDOT Design Manual, M 22-01

Design Superelevation Rates - AASHTO

from AASHTO’s A Policy on Geometric Design of Highways and Streets 2004

Design Superelevation Rates - WSDOT

emax = 8%

from the 2005 WSDOT Design Manual, M 22-01

Circular Curve Geometrics
• PC = Point of Curvature
• PT = Point of Tangency
• PI = Point of Intercept
• 100/D = L/Δ, so,
• L = 100 (Δ /D) where:
• L = arc length(measured in Stations (1 Sta = 100 ft)
• Δ = internal angle (deflection angle)
• D = 5729.58/R
• M = middle ordinate m=R [1 – cos(Δ /2) ]

M - is maximum distance from curve to long chord

Circular Curve Geometrics

Degree of curvature: D = central angle which subtends an arc of 100 feet

D=5729.58/R where R – radius of curve

For R=1000 ft. D = 5.73 degrees

Dmax = 85,660 (e + f)/V2 or

Rmin = V2/[15 (e + f)]

Horizontal Sight Distance

1) Sight line is a chord of the circular curve

2) Applicable Minimum Stopping Sight Distance (MSSD) measured along centerline of inside lane

Criterion: no obstruction

within middle ordinate

Assume:

driver eye height = 3.5 ft

object height = 2.0 ft.

Note: results in line of sight obstruction height at middle ordinate of 2.75 ft

Horizontal Alignment
• Basic controlling expression:

e + f = V2/15R

• Example:
• A horizontal curve has the following characteristics: Δ = 45˚, L = 1200 ft, e = 0.06 ft/ft. What coefficient of side friction would be required by a vehicle traveling at 70 mph?
Circular Curve Geometrics
• PC = Point of Curvature
• PT = Point of Tangency
• PI = Point of Intercept
• 100/D = L/Δ, so,
• L = 100 (Δ /D) where:
• L = arc length(measured in Stations (1 Sta = 100 ft)
• Δ = internal angle (deflection angle)
• D = 5729.58/R
• M = middle ordinate m=R [1 – cos(Δ /2) ]

M - is maximum distance from curve to long chord

Stopping Sight Distance

SSD

Ms

Obstruction

Rv

Δs

Superelevation Transition

from the 2001 Caltrans Highway Design Manual

Superelevation Transition

from AASHTO’s A Policy on Geometric Design of Highways and Streets 2001

Spiral Curves

No Spiral

Spiral

from AASHTO’s A Policy on Geometric Design of Highways and Streets 2001

Spiral Curves
• Involve complex geometry
• Require more surveying
• Are somewhat empirical
• If used, superelevation transition should occur entirely within spiral
Desirable Spiral Lengths

from AASHTO’s A Policy on Geometric Design of Highways and Streets 2001