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 Design Session 02-06

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Geometric design session 02 06

Geometric DesignSession 02-06

Matakuliah: S0753 – Teknik Jalan Raya

Tahun: 2009


Contents

Contents

Concepts

Vertical Alignment

Fundamentals

Crest Vertical Curves

Sag Vertical Curves

Examples

Horizontal Alignment

Fundamentals

Superelevation


Introduction

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


Stationing

Horizontal Alignment

Stationing

Introduction

Vertical Alignment


Geometric design session 02 06

Introduction

From Perteet Engineering


Geometric design elements

Geometric Design Elements

  • Sight Distances

  • Superelevation

  • Horizontal Alignment

  • Vertical 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

    • Transition between two grades

    • Vertical curves


Vertical curve fundamentals

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 fundamentals1

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

Relationships

  • Choose Either:

  • G1, G2 in decimal form, L in feet

  • G1, G2 in percent, L in stations


Example

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.


Geometric design session 02 06

PVI

PVT

G1=2.0%

PVC: STA 100+00

EL 59 ft.

G2= -4.5%


Other properties

  • G1, G2 in percent

  • L in feet

Other Properties

G1

x

PVT

PVC

Y

Ym

G2

PVI

Yf


Other properties1

Other Properties

  • K-Value (defines vertical curvature)

    • The number of horizontal feet needed for a 1% change in slope


Crest vertical curves

Crest Vertical Curves

SSD

PVI

Line of Sight

PVC

PVT

G2

G1

h2

h1

L

For SSD < L

For SSD > L


Crest vertical curves1

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

Design Controls for Crest Vertical Curves

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


Design controls for crest vertical curves1

Design Controls for Crest Vertical Curves

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


Sag vertical curves

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


Sag vertical curves1

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

Design Controls for Sag Vertical Curves

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


Design controls for sag vertical curves1

Design Controls for Sag Vertical Curves

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


Horizontal alignment

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

Horizontal Curve Fundamentals

PI

T

Δ

E

M

L

Δ/2

PT

PC

R

R

Δ/2

Δ/2


Horizontal curve fundamentals1

Horizontal Curve Fundamentals

PI

T

Δ

E

M

L

Δ/2

PT

PC

R

R

Δ/2

Δ/2


Superelevation

Superelevation

Rv

Fc

α

Fcn

Fcp

α

e

W

1 ft

Wn

Ff

Wp

Ff

α


Superelevation1

Superelevation


Selection of e and f s

Selection of e and fs

  • Practical limits on superelevation (e)

    • Climate

    • Constructability

    • Adjacent land use

  • Side friction factor (fs) variations

    • Vehicle speed

    • Pavement texture

    • Tire condition


Side friction factor

Side Friction Factor

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


Minimum radius tables

Minimum Radius Tables


Wsdot design side friction factors

WSDOT Design Side Friction Factors

For Open Highways and Ramps

from the 2005 WSDOT Design Manual, M 22-01


Wsdot design side friction factors1

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

Design Superelevation Rates - AASHTO

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


Design superelevation rates wsdot

Design Superelevation Rates - WSDOT

emax = 8%

from the 2005 WSDOT Design Manual, M 22-01


Circular curve geometrics

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 geometrics1

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

Maximum degree of curve/min radius:

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

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


Horizontal sight distance

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 alignment1

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 geometrics2

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

Stopping Sight Distance

SSD

Ms

Obstruction

Rv

Δs


Cross section

Cross Section


Superelevation transition

Superelevation Transition

from the 2001 Caltrans Highway Design Manual


Superelevation transition1

Superelevation Transition

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


Spiral curves

Spiral Curves

No Spiral

Spiral

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


Spiral curves1

Spiral Curves

  • Involve complex geometry

  • Require more surveying

  • Are somewhat empirical

  • If used, superelevation transition should occur entirely within spiral


Desirable spiral lengths

Desirable Spiral Lengths

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


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