# Geometric Design Session 02-06 - PowerPoint PPT Presentation

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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 Design Session 02-06

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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 Alignment

### Stationing

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

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

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

PI

T

Δ

E

M

L

Δ/2

PT

PC

R

R

Δ/2

Δ/2

PI

T

Δ

E

M

L

Δ/2

PT

PC

R

R

Δ/2

Δ/2

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

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