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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

Piilani Highway on Maui

Horizontal Alignment

Introduction

Vertical Alignment

Introduction

From Perteet Engineering

- Sight Distances
- Superelevation
- Horizontal Alignment
- Vertical Alignment

Sag Vertical Curve

G1

G2

G2

G1

Crest Vertical Curve

- Objective:
- Determine elevation to ensure
- Proper drainage
- Acceptable level of safety

- Determine elevation to ensure
- Primary challenge
- Transition between two grades
- Vertical curves

- 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

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

- Choose Either:
- G1, G2 in decimal form, L in feet
- G1, G2 in percent, L in stations

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

- 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

- Assumptions for design
- h1 = driver’s eye height = 3.5 ft.
- h2 = tail light height = 2.0 ft.

- Simplified Equations

- Assuming L > SSD…

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

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

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

- Assuming L > SSD…

- Assumptions for design
- h1 = headlight height = 2.0 ft.
- β = 1 degree

- Simplified Equations

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

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

- Objective:
- Geometry of directional transition to ensure:
- Safety
- Comfort

- Geometry of directional transition to ensure:
- 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

- Practical limits on superelevation (e)
- Climate
- Constructability
- Adjacent land use

- Side friction factor (fs) variations
- Vehicle speed
- Pavement texture
- Tire condition

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

For Open Highways and Ramps

from the 2005 WSDOT Design Manual, M 22-01

For Low-Speed Urban Managed Access Highways

from the 2005 WSDOT Design Manual, M 22-01

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

emax = 8%

from the 2005 WSDOT Design Manual, M 22-01

- 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

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

Maximum degree of curve/min radius:

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

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

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

- 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?

- 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

from the 2001 Caltrans Highway Design Manual

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

No Spiral

Spiral

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

- Involve complex geometry
- Require more surveying
- Are somewhat empirical
- If used, superelevation transition should occur entirely within spiral

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