[6] horizontal alignment - sharifsharif.edu/~asamimi/site_files/course/rproject/4.pdf · horizontal...
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Highway Design Project
Horizontal Alignment
Highway Design Project
Amir Amir SamimiSamimi
Civil Engineering DepartmentSharif University of Technology
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Horizontal Alignment
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Curve Types
1. Simple curves with spirals
. S p e cu ves w t sp a s2. Broken Back – two curves same direction (avoid) 3. Compound curves: multiple curves connected directly
together (use with caution) go from large radii to smaller radii and have R(large) < 1.5 R(small)
4. Reverse curves – two curves, opposite direction (require separation typically for superelevation attainment)
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Types of Circular Curves
Si l C
Simple Curve Compound Curves Broken-Back Curves
B k B k C h ld b id d if
Reverse CurvesBroken-Back Curves should be avoided if possible. It is better to replace the Curves with a larger radius circular curve.
A tangent should be placed between reverse Curves.
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Typical Configurations of Curves
Spirals are typically placed
Spirals are typically placed between tangents and circular curves to provide a transition from a normal crown section to a superelevated one.
Spirals are typically used at intersections to increase the room for large trucks to make turning movements.
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Horizontal Alignment
Objective:
Objective: Geometry of directional transition to ensure: Safety Comfort
Primary challenge Transition between two directions
H i t l
Δ
Horizontal curves Fundamentals Circular curves Superelevation
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Horizontal Alignment
1. Tangents
. a ge ts2. Curves3. Transitions
Curves require superelevation Retard sliding, g, Allow more uniform speed, Allow use of smaller radii curves (less land)
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Horizontal Curve Fundamentals
2tan
RT
RL
100
RRD
000,18
180100
DRL
180
D = degree of curvature (Delta / L = D / 100)
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Horizontal Curve Fundamentals
11RE
12cos
RE
2cos1RM
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Example
A horizontal curve is designed with a 1500 ft. radius. The
A horizontal curve is designed with a 1500 ft. radius. The tangent length is 400 ft. and the PT station is 20+00. What are the PI and PT stations?
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Superelevation
cpfp FFW ≈Rv
Fc
W 1 fte
cossincossin22
vvs gR
WVgR
WVWfW
α
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Superelevation
cossincossin22 WVWVWfW
cossincossinvv
s gRgRWfW
tan1tan2
sv
s fgRVf
fVf 12
efgR
fe sv
s 1
efgVR
sv
2
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Radius Calculation
Rmin related to max. f and max. e allowed
Rmin related to max. f and max. e allowed Rmin use max e and max f and design speed f is a function of speed, roadway surface, weather condition,
tire condition, and based on comfort AASHTO: 0.5 @ 20 mph with new tires and wet pavement to
0.35 @ 60 mph f decreases as speed increases (less tire/pavement contact)
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Selection of e and fs
Practical limits on superelevation (e)
Practical limits on superelevation (e) Climate Constructability Adjacent land use
Side friction factor (fs) variations Vehicle speed Pavement texture Tire condition
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Maximum e
Controlled by 4 factors:
Co t o ed by acto s: Climate conditions (amount of ice and snow) Terrain (flat, rolling, mountainous) Frequency of slow moving vehicles who might be influenced by
high superelevation rates Highest in common use = 10%, 12% with no ice and snow on low
volume gravel surfaced roadsvolume gravel-surfaced roads 8% is logical maximum to minimized slipping by stopped vehicles
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Side Friction Factor
from AASHTO’s A Policy on Geometric Design of Highways and Streets 2004
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Minimum Radius Tables
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WSDOT Design Side Friction FactorsFor Open Highways and Ramps
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WSDOT Design Side Friction FactorsFor Low-Speed Urban Managed Access Highways
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Design Superelevation Rates - AASHTO
from AASHTO’s A Policy on Geometric Design of Highways and Streets 2004
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Design Superelevation Rates - WSDOT
emax = 8%
from the 2005 WSDOT Design Manual, M 22-01
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Radius Calculation (Example)
Assume a maximum e of 8% and design speed of 60 mph, what
Assume a maximum e of 8% and design speed of 60 mph, what is the minimum radius?
fmax = 0.12 (from Green Book)
.)120080(15
60)(15
22
min
feVR
Rmin = 1200 feet
)12.008.0(15)(15 fe
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Radius Calculation (Example)
Assume a maximum e of 4%
ssu e a a u e o %
fmax = 0.12 (from Green Book)
.)12.004.0(15
60)(15
22
min
feVR
Rmin = 1500 feet
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Stopping Sight Distance
svRSSD 180 SSD
Obstruction
Ms v
s RSSD
180
180
SSDRM 90cos1
Rv
Δs
v
vs RRM
cos1
v
svv
RMRRSSD 1cos
90
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Sight Distance Example
A horizontal curve with R = 800 ft is part of a 2-lane highway
A horizontal curve with R 800 ft is part of a 2 lane highway with a posted speed limit of 35 mph. What is the minimum distance that a large billboard can be placed from the centerline of the inside lane of the curve without reducing required SSD? Assume p/r =2.5 sec and a = 11.2 ft/sec2
VSS 412
Ga
VVtSSD
2.3230
47.1
feetmphmph 2460
2.322.1130
)35(sec)5.2)(35(47.12
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Sight Distance Example
Now estimate the minimum distance that the billboard can be
Now estimate the minimum distance that the billboard can be placed :
f tCOSR
RSSDRm
vv
439)246(65.281
90cos1
in radians not degrees
feetCOSR 43.9)800(
)(1
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Horizontal Curve Example
Deflection angle of a 4º curve is 55º25’, PC at station 238 +
e ect o a g e o a cu ve s 55 5 , C at stat o 3844.75. Find length of curve, T, and station of PT. D = 4º = 55º25’ = 55.417º
. ftRRR
D 4.143258.5729180100
ftftRL 4.1385360
)417.55)(4.1432(2360
2
ftRT 3.7522417.55tan4.1432
2tan
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Horizontal Curve Example
Stationing goes around horizontal curve.
Stat o g goes a ou d o o ta cu ve. What is station of PT?
PC = 238 + 44.75 L = 1385.42 ft = 13 + 85.42 Station at PT = (238 + 44.75) + (13 + 85.42) = 252 + 30.17
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Superelevation Transition
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Superelevation Transition
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Superelevation Runoff/Runout
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Superelevation Runoff - WSDOT
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Purpose of Transition Curves
Provides path for vehicle to move from straight to a circular
Provides path for vehicle to move from straight to a circular curve
Improved appearance of curve to driver Allows introduction of superelevation and pavement widening
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Characteristics of Transition Curve
Should have constant rate of change of radius of curvature
Should have constant rate of change of radius of curvature Transition should be equal to zero at start of straight and equal
to radius of curvature at circular curve Allows passengers to adjust to change in rate of curvature
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Types of Transition Curve
Clothoid
C ot o d Most commonly used Will be examined in more detail
Lemniscate Used for large deflection
angles on high speed roads
Cubic Parabola Cubic Parabola Unsuitable for large
deflection angles
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Geometry of Clothoid
K = Lp.R
p. Lp = Length of plan transition R = Radius of circular curve K = constant
Coordinates can be represented by x = l l5/40(RL )2 x = l – l5/40(RLp)2 - … y = l3/6RLp – l7/336(RLp)3 +…
x and y are measured along the tangent and at right angles from the tangent respectively.
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Shift of Curve for Transition
To accommodate the transition curve the circular curve is
To accommodate the transition curve the circular curve is normally shifted inwards towards the centre of the curve.
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Shift of Curve for Transition
The shift can be calculated by:
The shift can be calculated by: Shift = S =Lp2/24R Lp is the length of transition If S <0.25m then the transition
is usually ignored or not required
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Terminology
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Tangent Length
When a transition curve is used :
W e a t a s t o cu ve s used :
Tangent Length = (R +S) tan (/2)
The distance from the IP to the TS = (R+S) tan (/2) + Lp/2
The circular arc length from SC – CS is reduced by Lp: Arc = R* - Lp
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Transition Length
Radial Acceleration Method:
Radial Acceleration Method: Lp = V3/46.73Ra Lp = length of plan transition V = design speed (km/hr) R = radius of circular curve a = radial acceleration
a varies with design speed and design authority.g p g y Typical values:
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Transition Length
Rate of Rotation of Pavement Method:
Rate of Rotation of Pavement Method: Most calculations for plan transition are done in conjunction with
the superelevation development length (Le). Usually relies on design speed and rate of rotation of pavement:
Lp = Le – 0.4V
Le = (e1 - e2) V / 0.09 Rotations of 2.5%/sec – this is most common, where e1 = 0
Le = (e1 - e2) V / 0.126 Rotation rates of 3.5%/sec
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Tables