HIGHWAY AND
RAILROAD
ENGINEERING:
LESSON 4.2
CE408
ENGR. ALYZZA ELAINE B. OJEDA
ENGR. HAROLD LOYD M. ILUSTRISIMO
GEOMETRIC DESIGN
FOR HIGHWAY AND
RAILWAYS
HIGHWAY AND RAILWAY
ENGINEERING
Topics Outline
1.
2.
3.
4.
Spiral Curves
Super Elevation
Earthwork
Sight Distance
SPIRAL CURVES
SPIRAL CURVES
Spirals are used to overcome the abrupt change in curvature
and super elevation that occurs between tangent and circular
curve. The spiral curve is used to gradually change the
curvature and super elevation of the road, thus
called transition curve.
Elements of Spiral Curve
TS = Tangent to spiral
SC = Spiral to curve
CS = Curve to spiral
ST = Spiral to tangent
LT = Long tangent
ST = Short tangent
R = Radius of simple curve
Ts = Spiral tangent distance
Tc = Circular curve tangent
SPIRAL CURVES
SPIRAL CURVES
Xc = Offset distance (right
angle distance) from tangent
to SC
Elements of Spiral Curve
L = Length of spiral
from TS to any point along
the spiral
Ls = Length of spiral
PI = Point of intersection
I = Angle of intersection
Ic = Angle of intersection of
the simple curve
p = Length of throw or the
distance from tangent that
the circular curve has been
offset
X = Offset distance (right
angle distance) from tangent
to any point on the spiral
SPIRAL CURVES
SPIRAL CURVES
D = Degree of spiral curve at any
point
Dc = Degree of simple curve
Elements of Spiral Curve
Y = Distance along tangent
to any point on the spiral
Yc = Distance along tangent
from TS to point at right
angle to SC
Es = External distance of the
simple curve
θ = Spiral angle from
tangent to any point on the
spiral
θs = Spiral angle from
tangent to SC
i = Deflection angle
from TS to any point on the
spiral, it is proportional to
the square of its distance
is = Deflection angle
from TS to SC
SPIRAL CURVES
Formulas for Spiral Curves
SPIRAL CURVES
Distance along tangent to any
point on the spiral:
Offset distance from tangent to
any point on the spiral:
SPIRAL CURVES
Formulas for Spiral Curves
Length of throw:
SPIRAL CURVES
Spiral angle from tangent to any
point on the spiral (in radian):
SPIRAL CURVES
Formulas for Spiral Curves
SPIRAL CURVES
Deflection angle from TS to any
point on the spiral:
This angle is proportional to the
square of its distance
Tangent distance:
SPIRAL CURVES
Formulas for Spiral Curves
Angle of intersection of simple
curve:
SPIRAL CURVES
External distance::
Degree of spiral curve:
Questions?
SUPERELEVATION
SUPERELEVATION
BANKING CURVES
SUPERELEVATION
SUPERELEVATION
BANKING CURVES
SUPERELEVATION
SUPERELEVATION
EXAMPLE: A roadway is designed to have a maximum
speed of 75 kilometers per hour. One of its
horizontal curves is designed to be simple circular
having a radius of 195 meters. What
should be the angle the roadway makes with the
horizontal so that the vehicles will not
overturn? The coefficient of side friction is set at 0.15.
Given:
v = 75 kph = 20.83 m/s
Rv = 195 meters
fs = 0.15
Required:
The angle the roadway makes with the horizontal
SUPERELEVATION
SUPERELEVATION
Questions?
CROSS SECTION OF TYPHICAL HIGHWAY
EARTHWORKS
The cross section of a typical highway has latitude of
variables to consider such as:
1.
2.
3.
4.
The volume of traffic.
Character of the traffic.
Speed of the traffic.
Characteristics of motor vehicles and of the driver
CROSS SECTION OF TYPHICAL HIGHWAY
A cross section design generally offers the expected level of service
for safety and a recent study showed that:
1. A 7.20 meters wide pavement has l8% less accident
compared with pavement narrower than 5.50 m. wide.
EARTHWORKS
2. A 7.20 meters wide pavement has 4% fewer accidents
than the 6.00 meters wide roadway.
3.
Accident records showed no difference between the 6.60 meters
and the 7.20 meters wide pavement.
4.
For the 6.00 m., 6.60 m. and,7.20 meters wide pavement with
2.70 to 3.00 m. wide shoulder, recorded accident decreases by
30% compared to 0 to .60 m. wide shoulder. And 20% compared
with a .90 to 1.20 meters wide shoulder.
EARTHWORKS
CROSS SECTION OF TYPHICAL HIGHWAY
FIGURE 2-1 CROSS SECTION OF TYPICAL TWO LANE HIGHWAYS
FIGURE 2-2 MULTI-LANE HIGHWAYS AND FREEWAYS (HALF SECTION))
EARTHWORKS
CROSS SECTION OF TYPHICAL HIGHWAY
FIGURE 2-3
DIVIDED
HIGHWAYS
EARTHWORKS
CROSS SECTION OF TYPHICAL HIGHWAY
FIGURE 2-4
UNDIVIDED
HIGHWAYS
EARTHWORKS
CROSS SECTION METHOD
The method of plotting the existing cross section
perpendicular to a particular line for the purpose of
obtaining quantities such as volumes. The procedure
involves staking the centerline then elevations are
obtained at strategic points on the right angle to the
centerline at intervals of full or half stations. Crosssectional data is needed in estimating the amount of
cut or fill needed for a given strip of roadway.
Station Notes
EARTHWORKS
VOLUME APPROXIMATION METHODS IN
EARTHWORKS
VOLUME APPROXIMATION METHODS IN
EARTHWORKS
Example: The cross section notes shown below are for
a ground excavation.
EARTHWORKS
Sta. 25+100
Sta. 25+150
What is the volume of excavation between the two
stations using.
a. Find x
b. Find y
c. End Area Method
d. Prismoidal Formula
(0,x)
(-9.8,2.4)
(7.4,1.2)
(0,0)
(-5,0)
7.4x
6
-12 -9.8x
(5,0)
Questions?
SIGHT DISTANCE
SIGHT DISTANCE
• distance at which a driver of a vehicle can see an
object of specified height on the road ahead, assuming
adequate sight and visual acuity and clear atmospheric
conditions.
SIGHT DISTANCE
STOPPING SIGHT DISTANCE
SIGHT DISTANCE ON HORIZONTAL CURVES
SIGHT DISTANCE
STOPPING SIGHT DISTANCE ON VERTICAL CURVES (SUMMIT)
Maximum Speed (for summit and sag curves)
Standard values in road design:
For stopping sight distance (SSD)
For passing sight distance (PSD)
SIGHT DISTANCE
STOPPING SIGHT DISTANCE ON VERTICAL CURVES (SAG)
SIGHT DISTANCE
Types of Sight Distances
SIGHT DISTANCE
1. Stopping or absolute minimum sight distance (SSD)
Minimum sight distance available on a highway at any spot
should be of sufficient length to stop a vehicle traveling at design
speed, safely without collision with any other obstruction.
It depends on
a. Feature of road ahead
b. Height of driver’s eye above the road surface (1.2m)
c. Height of the object above the road surface (0.15m)
Criteria for measurement
a. Height of driver’s eye above road surface (H)
b. Height of object above road surface (h)
SIGHT DISTANCE
SIGHT DISTANCE
Factors affecting SSD
• Total reaction time of driver
• Speed of vehicle
• Efficiency of brakes
• Frictional resistance between road and tire
• Gradient of road
SIGHT DISTANCE
Total reaction time of driver:
SIGHT DISTANCE
• It is the time taken from the instant the object is visible to the
driver to the instant the brake is effectively applied.
• It is divided into types
(a) Perception time
It is the time from the instant the object comes on the line
of sight of the driver to the instant he realizes that the vehicle
needs to be stopped.
(b) Brake reaction time.
The brake reaction also depends on several factor including
the skill of the driver, the type of the problems and various other
environment factor. Total reaction time of driver can be calculated
by “PIEV” theory.
PIEV Theory: P-perception, I-intellection, E-Emotion, V-Volition
SIGHT DISTANCE
SIGHT DISTANCE
Analysis of SSD
• The stopping sight distance is the sum of lag distance
and the braking distance
1. Lag Distance
- The distance the vehicle travelled during the
reaction time
- If “V” is the design speed in m/s, ‘t’ is the total
reaction time of the driver in seconds
lag distance = v ∙ t
- If “V” is in kph,
lag distance = 0.278 v ∙ t
- AASHTO recommended reaction time is 2.5 seconds
SIGHT DISTANCE
SIGHT DISTANCE
SIGHT DISTANCE
2. Breaking Distance
SIGHT DISTANCE
The stopping sight distance
SIGHT DISTANCE
SIGHT DISTANCE
• Using typical units for velocity (kph) and considering the
braking action of the driver, the stopping sight distance
may also be written as
Braking Action
- Based on the driver’s
ability to decelerate the
vehicle while staying
within the travel lane and
maintaining steering
control during the braking
maneuver. A deceleration
rate of 3.4 m/s2 is
comfortable for 90% of
the drivers.
SIGHT DISTANCE
SIGHT DISTANCE
Example : A vehicle is travelling at 35 kilometers per hour. Its
driver is about to hit a 2-meter high wall 30 meters away if he
did not react accordingly. Assuming the coefficient of friction
between the road and tires is 0.35 and the driver steps on the
brakes 2 seconds after seeing the obstruction, will he hit the
wall? The road is perfectly horizontal.
Given:
v = 35 kph = 9.72 m/s
t = 2 seconds
f = 0.35
G=0
Required:
If SSD > 30, will the vehicle hit the wall?
SIGHT DISTANCE
SSD and Crest Vertical Curve
SIGHT DISTANCE
Figure shows SSD and
crest vertical curve
(Image taken from
ascelibrary.com)
The equations used in designing a crest vertical curve are as follows:
Assuming SSD < L:
Assuming SSD > L
where,
Lm = minimum length of crest curve, in meters
S = stopping sight distance, in meters
H1 = driver’s eye level above roadway surface,
in meters
H2 = height of obstruction above roadway
surface, in meters
A = absolute value of the difference in grades,
SIGHT DISTANCE
SSD and Sag Vertical Curve
SIGHT DISTANCE
Figure shows SSD and
sag vertical curve
(Image taken from
ascelibrary.com)
The equations used in designing a sag vertical curve are as follows:
Assuming SSD < L:
Assuming SSD > L
where, Lm = minimum length of sag curve, in
meters
S = stopping sight distance, in meters
H = height of headlight above roadway, in meters
α = inclined angle of headlight beam, in degrees
A = absolute value of the difference in grades, in
percentage
SIGHT DISTANCE
EXAMPLE 1:
SIGHT DISTANCE
Determine the length of the vertical curve with a stopping
sight distance of 230 meters. Its initial and final grades are
+1.75% and -2.05% respectively. The driver’s eye level
above the roadway surface is 150 centimeters and the
height of obstruction is 100 centimeters.
SIGHT DISTANCE
SIGHT DISTANCE
EXAMPLE 2:
A vertical curve is to be designed with a stopping sight
distance of 310 m. Its initial and final grades are -3.2%
and +2.1% respectively. The average height of the
headlights of the vehicles that will pass through this road
is 60 centimeters and α is set at 1°. Determine the length
of the curve.
SIGHT DISTANCE
SIGHT DISTANCE
2. Safe overtaking (OSD) or passing sight distance (PSD)
- The minimum distance open to the vision of the
driver of a vehicle intending to overtake slow vehicle
ahead with safety against the traffic of opposite direction
is known as the minimum overtaking sight distance (OSD)
or the safe passing sight distance
- In limited 2-lane or 2-way highways, vehicles may
overtake slower moving vehicles, and the passing
maneuver must be accomplished on a lane used by
opposing traffic
SIGHT DISTANCE
SIGHT DISTANCE
SIGHT DISTANCE
SIGHT DISTANCE
These values are determined using the AASHTO Policy on geometric
design of highways and streets.
SIGHT DISTANCE
SIGHT DISTANCE
For Rural Areas, the guideline considers the terrain in which road is
being constructed. Table below shows the recommended values
SIGHT DISTANCE
SIGHT DISTANCE
3. Safe sight distance for entering an intersection,
Intersection Sight Distance
- Driver entering an uncontrolled intersection (particularly
unsignalized intersection) has sufficient visibility to
enable him to take control of his vehicle and to avoid
collision with another vehicle.
- The corner sight distance available in intersection
quadrants that allows a driver approaching an
intersection to observe the actions of vehicles on the
crossing leg(s)
- Evaluations involve establishing the needed sight triangle
in each quadrant by determining the legs of the triangle
on the two crossing roadways
- Clear sight triangle must be free of sight obstructions
such as buildings, parked or turning vehicles, trees,
hedges, fences, retaining walls, and the actual ground
line.
Questions?
LECTURE 4.2
THANK YOU