Highway Engineering * Transition curves are used to connect

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Geometric Design

• Highway Engineering

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Geometric Design

• Geometric Design for transportation facilities
  includes the design of geometric cross section,
  horizontal alignment, vertical alignment,
  intersections, and various design details.

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goals of geometric design

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

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FUNDAMENTALS OF GEOMETRIC DESIGN

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

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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.

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Two-lane highway cross section, curbed.
Two-lane highway cross section, with ditches.
Two-lane highway cross section, curbed.
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Divided highway cross section, depressed median,
with ditches.
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Divided highway cross section, raised median,
curbed.
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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.

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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.

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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.
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Vertical Curves

• Vertical tangents with different grades are
  joined by vertical curves.

Symmetrical Vertical Curve
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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
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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.
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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,
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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?

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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.

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Stopping sight distance diagram for crest
vertical curve.
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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.

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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
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• 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.

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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.

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Stopping sight distance diagram for sag vertical
curve.
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SAG VERTICAL CURVES

• For sag vertical curves, the formula is

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• 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.

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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.

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• 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

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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.

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Horizontal alignments with and without transition
curves.
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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.

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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).

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ELEMENTS OF A HORIZONTAL CURVE
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• 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.

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Transition Curves

• Transition curves are used to connect tangents to
  circular curves.

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

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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.

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(No Transcript)
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• A commonly used mixed-unit version of the
  equation is
• where V is in km/h and R is in meters.
  Alternatively,

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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.

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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

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Three Basic Ways of Resolving Crossing Conflicts

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

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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,

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General types of at-grade Intersections
Unchannelized T
Unchannelized Y
Flared T
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3-leg intersections Y with turning roadways
Unchannelized
Channelized
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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.

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DIAMOND INTERCHANGE
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CLOVERLEAF INTERCHANGE
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Partial cloverleaf
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TRumpet
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FULL DIRECTIONAL
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DIRECTIONAL-Y
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ON-RAMP (entrance to highway)
ON-RAMP (entrance to highway)
OFF-RAMP (exit to highway)
OFF-RAMP (exit to highway)
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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.

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• Cloverleaf Interchange
• Employ loop ramps, in which vehicles turn left by
  turning 270 degrees to the right.

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• Partial Cloverleaf Interchange (Parclo)
• Involves various combinations of diamond and loop
  ramps.

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• Trumpet Interchange