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Geometric Design

- Highway Engineering

Geometric Design

- Geometric Design for transportation facilities

includes the design of geometric cross section,

horizontal alignment, vertical alignment,

intersections, and various design details.

goals of geometric design

- maximize the comfort
- safety,
- economy of facilities
- while maximizing their environmental impacts

FUNDAMENTALS OF GEOMETRIC DESIGN

- geometric cross section
- vertical alignment
- horizontal alignment
- super elevation
- intersections
- various design details.

GEOMETRIC CROSS SECTION

- The primary consideration in the design of cross

sections is drainage. - Highway cross sections consist of traveled way,

shoulders (or parking lanes), and drainage

channels. - Shoulders are intended primarily as a safety

feature. - Shoulders provide
- accommodation of stopped vehicles
- emergency use,
- and lateral support of the pavement.
- Shoulders may be either paved or unpaved.
- Drainage channels may consist of ditches (usually

grassed swales) or of paved shoulders with berms

of curbs and gutters.

Two-lane highway cross section, curbed.

Two-lane highway cross section, with ditches.

Two-lane highway cross section, curbed.

Divided highway cross section, depressed median,

with ditches.

Divided highway cross section, raised median,

curbed.

Geometric cross section cont..

- Standard lane widths are normally 3.6 m (12 ft),

although narrower lanes are common on older

roadways, and may still be provided in cases

where the standard lane width is not economical.

Shoulders or parking lanes for heavily traveled

roads are normally 2.4 to 3.6 m (8 to 12 ft) in

width narrower shoulders are sometimes used on

lightly traveled road.

VERTICAL ALIGNMENT

- The vertical alignment of a transportation

facility consists of - tangent grades (straight line in the vertical

plane) - vertical curves. Vertical alignment is documented

by the profile.

TANGENT GRADES

Tangent grades are designated according to their

slopes or grades. Maximum grades vary depending

on the type of facility, and usually do not

constitute an absolute standard. The effect of a

steep grade is to slow down the heavier vehicles

(which typically have the lowest power/weight

ratios) and increase operating costs.

Vertical Curves

- Vertical tangents with different grades are

joined by vertical curves.

Symmetrical Vertical Curve

VERTICAL CURVES CONT

Vertical curves are normally parabolas centered

about the point of intersection (P.I.) of the

vertical tangents they join. Vertical curves are

thus of the form

where y elevation of a point on the curve

yo elevation of the beginning of the

vertical curve (BVC) g1 grade

just prior to the curve x horizontal distance

from the BVC to the point on the curve r rate

of change of grade

VERTICAL CURVES CONT

The rate of change of grade, in turn, is given by

where g2 is the grade just beyond the end of the

vertical curve (EVC) and L is the length of the

curve. Vertical curves are classified as sags

where g2 gt g1 and crests otherwise. Not that r

(and hence the term rx2 /2) will be positive for

sags and negative for crests. If grades are in

percent, horizontal distance must be in

stations If grades are dimensionless ratios,

horizontal distances must be in meters.

VERTICAL CURVES CONT

The grade of any point in the vertical curve is a

linear function of the distance from the BVC to

the point. That is,

PROBLEM

- A 2.5 grade is connected to a 1.0 grade by

means of a 180-m vertical curve. The P.I. station

is 100 00 and the P.I elevation is 100.0 m

above sea level. What are the station and

elevation of the lowest point on the vertical

curve?

VERTICAL CURVES CONT

- Design standards for vertical curves establish

their minimum lengths for specific circumstances - based on sight distance,
- on comfort standards involving vertical

acceleration, - or appearance criteria.
- In most cases, sight distance or appearance

standards will govern for highways. - the equations used to calculate minimum lengths

of vertical curves based on sight distance depend

on whether the sight distance is greater than or

less than the vertical curve length.

Stopping sight distance diagram for crest

vertical curve.

CREST VERTICAL CURVES

- For crest vertical curves, the minimum length

depends on the sight distance, the height of the

drivers eye, and the height of the object to be

seen over the crest of the curve.

CREST VERTICAL CURVES

When SL

When SL

where S sight distance (from Table) L

vertical curve length A absolute value of the

algebraic difference in grades, in percent,

g1-g2 h1 height of eye h2 height of

object

- For stopping sight distance, the height of object

is normally taken to be 150mm. for passing sight

distance, the height of object used by AASHTO is

1300 mm. Height of eye is assumed to be 1070 mm.

SAG VERTICAL CURVES

- For sag vertical curves, stopping sight distance

is based on the distance illuminated by the

headlights at night. - Design standards are based on an assumed

headlight height of 600 mm and an upward

divergence of the headlight beam of 1. - As in the case of crest vertical curves, the

formulas for minimum length of vertical curve

depend on whether the length of the curve is

greater or less than the sight distance.

Stopping sight distance diagram for sag vertical

curve.

SAG VERTICAL CURVES

- For sag vertical curves, the formula is

- Design charts of tables are used to determine

minimum length of vertical curve to provide

stopping sight distance for both crest and sag

vertical curves, and passing sight distance on

crests. These may be found in the AASHTO Policy

on Geometric Design of Highways and Streets.

Vertical CURVE limited to provide clearances

- Finally, vertical curve lengths may be limited by

the need to provide clearances over or under

objects such as overpasses or drainage

structures.

- VERTICAL CURVES PASSING OVER OBJECTS(e.g.

Overpass) - SAG CURVE Minimum Lengths
- CREST CURVE Maximum Lengths
- VERTICAL CURVES PASSING UNDER OBJECTS(e.g.

Drainage - SAG CURVE Maximum Lengths
- CREST CURVE Minimum Lengths

HORIZONTAL ALIGNMENT

- Horizontal alignment for linear transportation

facilities such as highways and railways consists

of horizontal tangents, circular curves, and

possibly transition curves. In the case of

highways, transition curves are not always used.

Horizontal alignments with and without transition

curves.

HORIZONTAL TANGENTS

- Horizontal tangents are described in terms of

their lengths (as expressed in the stationing of

the job) and their directions. Directions may be

either expressed as bearings or as azimuths and

are always defined in the direction of increasing

station. Azimuths are expressed as angles turned

clockwise from due north bearings are expressed

as angles turned either clockwise or

counterclockwise from either north or south.

CIRCULAR CURVES

- Horizontal curves are normally circular. Figure

in the next slide illustrates several of their

important features. Horizontal curves are also

described by radius, central angle (which is

EQUAL to the deflection angle between the

tangents), length, semitangent distance, middle

ordinate, external distance, and chord. The curve

begins at the tangent-to-curve point (TC) and

ends at the curve-to-tangent point (CT).

ELEMENTS OF A HORIZONTAL CURVE

- Design standards for horizontal curves establish

their minimum radii and, in some cases, their

minimum lengths. Minimum radius of horizontal

curve is most commonly established by the

relationship between design speed, maximum rate

of superelevation, and curve radius. In other

cases, minimum radii or curve lengths for

highways may be established by the need to

provide stopping sight distance or by appearance

standards.

Transition Curves

- Transition curves are used to connect tangents to

circular curves.

- tangent to spiral point (TS),
- spiral to curve point (SC),
- curve to spiral point (CS),
- spiral to tangent point (ST).

SUPERELEVATION

- The purpose of superelevation or banking of

curves is to counteract the centripetal

acceleration produced as a vehicle rounds a

curve. The term itself comes from railroad

practice, where the top of the rail is the

profile grade.

(No Transcript)

- A commonly used mixed-unit version of the

equation is - where V is in km/h and R is in meters.

Alternatively,

Example

- Compute the minimum radius of a circular curve

for a highway designed for 110 km/h. The maximum

superelevation rate is 12. Value of f(from

AASHTO table) is 0.11.

INTERSECTIONS INTERCHANGES

- Geometric Design of transportation facilities

must provide for the resolution of traffic

conflicts. - In general, these conflicts may be classified as
- Merging conflicts
- Occurs when vehicles enter a traffic stream
- Diverging conflicts
- Occurs when vehicles leave the traffic stream
- Weaving conflicts
- Occurs by merging then diverging
- Crossing conflicts
- Occurs when they cross paths directly

Three Basic Ways of Resolving Crossing Conflicts

- Time-sharing Solutions
- Space-sharing Solutions
- Grade separation Solutions

At-grade intersections

- Except for freeways, all highways have

intersections at grade, so that the intersection

area is a part of every connecting road or

street. - In this area, crossing and turning movements

occur. - Some intersection are channelized to minimize

traffic accidents, speed control, prevention of

prohibited turns, refuge may be provided for

pedestrians,

General types of at-grade Intersections

Unchannelized T

Unchannelized Y

Flared T

3-leg intersections Y with turning roadways

Unchannelized

Channelized

INTERCHANGES

- Are classified according to the way they handle

left-turning traffic. - INTERCHANGE CONFIGURATION
- - are selected on the basis of structural cost,

right-of-way costs, and ability to serve traffic.

DIAMOND INTERCHANGE

CLOVERLEAF INTERCHANGE

Partial cloverleaf

TRumpet

FULL DIRECTIONAL

DIRECTIONAL-Y

ON-RAMP (entrance to highway)

ON-RAMP (entrance to highway)

OFF-RAMP (exit to highway)

OFF-RAMP (exit to highway)

General Classes of Freeway Interchanges

- Diamond Interchange
- Employ diamond ramps which connect to the cross

road by means of an at grade intersection. - Left turns are accomplished by having vehicles

turn left across traffic on the cross road.

- Cloverleaf Interchange
- Employ loop ramps, in which vehicles turn left by

turning 270 degrees to the right.

- Partial Cloverleaf Interchange (Parclo)
- Involves various combinations of diamond and loop

ramps.

- Trumpet Interchange

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