geometric design (transportation engineering)
TRANSCRIPT
![Page 1: Geometric Design (Transportation Engineering)](https://reader034.vdocuments.mx/reader034/viewer/2022050812/5a6560cf7f8b9a931a8b4b69/html5/thumbnails/1.jpg)
CE
E 3
20W
inte
r 20
06
Geometric Design
CEE 320Steve Muench
![Page 2: Geometric Design (Transportation Engineering)](https://reader034.vdocuments.mx/reader034/viewer/2022050812/5a6560cf7f8b9a931a8b4b69/html5/thumbnails/2.jpg)
CE
E 3
20W
inte
r 20
06
Outline
1. Concepts2. Vertical Alignment
a. Fundamentalsb. Crest Vertical Curvesc. Sag Vertical Curvesd. Examples
3. Horizontal Alignmenta. Fundamentalsb. Superelevation
4. Other Non-Testable Stuff
![Page 3: Geometric Design (Transportation Engineering)](https://reader034.vdocuments.mx/reader034/viewer/2022050812/5a6560cf7f8b9a931a8b4b69/html5/thumbnails/3.jpg)
CE
E 3
20W
inte
r 20
06
Concepts
• Alignment is a 3D problem broken down into two 2D problems– Horizontal Alignment (plan view)– Vertical Alignment (profile view)
• Stationing– Along horizontal alignment– 12+00 = 1,200 ft.
Piilani Highway on Maui
![Page 4: Geometric Design (Transportation Engineering)](https://reader034.vdocuments.mx/reader034/viewer/2022050812/5a6560cf7f8b9a931a8b4b69/html5/thumbnails/4.jpg)
CE
E 3
20W
inte
r 20
06
Stationing
Horizontal Alignment
Vertical Alignment
![Page 5: Geometric Design (Transportation Engineering)](https://reader034.vdocuments.mx/reader034/viewer/2022050812/5a6560cf7f8b9a931a8b4b69/html5/thumbnails/5.jpg)
From Perteet Engineering
![Page 6: Geometric Design (Transportation Engineering)](https://reader034.vdocuments.mx/reader034/viewer/2022050812/5a6560cf7f8b9a931a8b4b69/html5/thumbnails/6.jpg)
CE
E 3
20W
inte
r 20
06
Vertical Alignment
![Page 7: Geometric Design (Transportation Engineering)](https://reader034.vdocuments.mx/reader034/viewer/2022050812/5a6560cf7f8b9a931a8b4b69/html5/thumbnails/7.jpg)
CE
E 3
20W
inte
r 20
06
Vertical Alignment
• Objective: – Determine elevation to ensure
• Proper drainage• Acceptable level of safety
• Primary challenge– Transition between two grades
– Vertical curves
G1 G2G1
G2
Crest Vertical Curve
Sag Vertical Curve
![Page 8: Geometric Design (Transportation Engineering)](https://reader034.vdocuments.mx/reader034/viewer/2022050812/5a6560cf7f8b9a931a8b4b69/html5/thumbnails/8.jpg)
CE
E 3
20W
inte
r 20
06
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
cbxaxy ++= 2
![Page 9: Geometric Design (Transportation Engineering)](https://reader034.vdocuments.mx/reader034/viewer/2022050812/5a6560cf7f8b9a931a8b4b69/html5/thumbnails/9.jpg)
CE
E 3
20W
inte
r 20
06
Vertical Curve Fundamentals
G1
G2
PVI
PVT
PVC
L
L/2
δ
cbxaxy ++= 2
x
Choose Either:• G1, G2 in decimal form, L in feet• G1, G2 in percent, L in stations
![Page 10: Geometric Design (Transportation Engineering)](https://reader034.vdocuments.mx/reader034/viewer/2022050812/5a6560cf7f8b9a931a8b4b69/html5/thumbnails/10.jpg)
CE
E 3
20W
inte
r 20
06
Relationships
Choose Either:• G1, G2 in decimal form, L in feet• G1, G2 in percent, L in stations
G1
G2
PVI
PVT
PVC
L
L/2
δ
x
1 and 0 :PVC At the Gbdx
dYx ===
cYx == and 0 :PVC At the
L
GGa
L
GGa
dx
Yd
22 :Anywhere 1212
2
2 −=⇒−==
![Page 11: Geometric Design (Transportation Engineering)](https://reader034.vdocuments.mx/reader034/viewer/2022050812/5a6560cf7f8b9a931a8b4b69/html5/thumbnails/11.jpg)
CE
E 3
20W
inte
r 20
06
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.
G1=2.0%
G2= - 4.5%
PVI
PVT
PVC: STA 100+00EL 59 ft.
![Page 12: Geometric Design (Transportation Engineering)](https://reader034.vdocuments.mx/reader034/viewer/2022050812/5a6560cf7f8b9a931a8b4b69/html5/thumbnails/12.jpg)
G1=2.0%
G2= -4.5%
PVI
PVT
PVC: STA 100+00EL 59 ft.
![Page 13: Geometric Design (Transportation Engineering)](https://reader034.vdocuments.mx/reader034/viewer/2022050812/5a6560cf7f8b9a931a8b4b69/html5/thumbnails/13.jpg)
CE
E 3
20W
inte
r 20
06
Other Properties
G1
G2
PVI
PVTPVC
x
Ym
Yf
Y
2
200x
L
AY =
800
ALYm =
200
ALY f =
21 GGA −=
•G1, G2 in percent•L in feet
![Page 14: Geometric Design (Transportation Engineering)](https://reader034.vdocuments.mx/reader034/viewer/2022050812/5a6560cf7f8b9a931a8b4b69/html5/thumbnails/14.jpg)
CE
E 3
20W
inte
r 20
06
Other Properties
• K-Value (defines vertical curvature)– The number of horizontal feet needed for a 1%
change in slope
A
LK =
1./ GKxptlowhigh =⇒
![Page 15: Geometric Design (Transportation Engineering)](https://reader034.vdocuments.mx/reader034/viewer/2022050812/5a6560cf7f8b9a931a8b4b69/html5/thumbnails/15.jpg)
CE
E 3
20W
inte
r 20
06
Crest Vertical Curves
G1G2
PVI
PVTPVC
h2h1
L
SSD
( )( )221
2
22100 hh
SSDAL
+= ( ) ( )
A
hhSSDL
2
212002
+−=
For SSD < L For SSD > L
Line of Sight
![Page 16: Geometric Design (Transportation Engineering)](https://reader034.vdocuments.mx/reader034/viewer/2022050812/5a6560cf7f8b9a931a8b4b69/html5/thumbnails/16.jpg)
CE
E 3
20W
inte
r 20
06
Crest Vertical Curves
• Assumptions for design– h1 = driver’s eye height = 3.5 ft.
– h2 = tail light height = 2.0 ft.
• Simplified Equations
( )2158
2SSDAL = ( )
ASSDL
21582 −=
For SSD < L For SSD > L
![Page 17: Geometric Design (Transportation Engineering)](https://reader034.vdocuments.mx/reader034/viewer/2022050812/5a6560cf7f8b9a931a8b4b69/html5/thumbnails/17.jpg)
CE
E 3
20W
inte
r 20
06
Crest Vertical Curves
• Assuming L > SSD…
2158
2SSDK =
![Page 18: Geometric Design (Transportation Engineering)](https://reader034.vdocuments.mx/reader034/viewer/2022050812/5a6560cf7f8b9a931a8b4b69/html5/thumbnails/18.jpg)
CE
E 3
20W
inte
r 20
06
Design Controls for Crest Vertical Curves
from AASHTO’s A Policy on Geometric Design of Highways and Streets 2001
![Page 19: Geometric Design (Transportation Engineering)](https://reader034.vdocuments.mx/reader034/viewer/2022050812/5a6560cf7f8b9a931a8b4b69/html5/thumbnails/19.jpg)
CE
E 3
20W
inte
r 20
06
Design Controls for Crest Vertical Curves
fro
m A
AS
HT
O’s
A P
olic
y o
n G
eo
me
tric
De
sig
n o
f H
igh
wa
ys a
nd
Str
ee
ts 2
00
1
![Page 20: Geometric Design (Transportation Engineering)](https://reader034.vdocuments.mx/reader034/viewer/2022050812/5a6560cf7f8b9a931a8b4b69/html5/thumbnails/20.jpg)
CE
E 3
20W
inte
r 20
06
Sag Vertical Curves
G1 G2
PVI
PVTPVC
h2=0h1
L
Light Beam Distance (SSD)
( )( )βtan200 1
2
Sh
SSDAL
+= ( ) ( )( )
A
SSDhSSDL
βtan2002 1 +−=
For SSD < L For SSD > L
headlight beam (diverging from LOS by β degrees)
![Page 21: Geometric Design (Transportation Engineering)](https://reader034.vdocuments.mx/reader034/viewer/2022050812/5a6560cf7f8b9a931a8b4b69/html5/thumbnails/21.jpg)
CE
E 3
20W
inte
r 20
06
Sag Vertical Curves
• Assumptions for design– h1 = headlight height = 2.0 ft.
– β = 1 degree
• Simplified Equations
( )( )SSD
SSDAL
5.3400
2
+= ( ) ( )
+−=
A
SSDSSDL
5.34002
For SSD < L For SSD > L
![Page 22: Geometric Design (Transportation Engineering)](https://reader034.vdocuments.mx/reader034/viewer/2022050812/5a6560cf7f8b9a931a8b4b69/html5/thumbnails/22.jpg)
CE
E 3
20W
inte
r 20
06
Sag Vertical Curves
• Assuming L > SSD…
SSD
SSDK
5.3400
2
+=
![Page 23: Geometric Design (Transportation Engineering)](https://reader034.vdocuments.mx/reader034/viewer/2022050812/5a6560cf7f8b9a931a8b4b69/html5/thumbnails/23.jpg)
CE
E 3
20W
inte
r 20
06
Design Controls for Sag Vertical Curves
from AASHTO’s A Policy on Geometric Design of Highways and Streets 2001
![Page 24: Geometric Design (Transportation Engineering)](https://reader034.vdocuments.mx/reader034/viewer/2022050812/5a6560cf7f8b9a931a8b4b69/html5/thumbnails/24.jpg)
CE
E 3
20W
inte
r 20
06
Design Controls for Sag Vertical Curves
fro
m A
AS
HT
O’s
A P
olic
y o
n G
eo
me
tric
De
sig
n o
f H
igh
wa
ys a
nd
Str
ee
ts 2
00
1
![Page 25: Geometric Design (Transportation Engineering)](https://reader034.vdocuments.mx/reader034/viewer/2022050812/5a6560cf7f8b9a931a8b4b69/html5/thumbnails/25.jpg)
CE
E 3
20W
inte
r 20
06
Example 1
A car is traveling at 30 mph in the country at night on a wet road through a 150 ft. long sag vertical curve. The entering grade is -2.4 percent and the exiting grade is 4.0 percent. A tree has fallen across the road at approximately the PVT. Assuming the driver cannot see the tree until it is lit by her headlights, is it reasonable to expect the driver to be able to stop before hitting the tree?
![Page 26: Geometric Design (Transportation Engineering)](https://reader034.vdocuments.mx/reader034/viewer/2022050812/5a6560cf7f8b9a931a8b4b69/html5/thumbnails/26.jpg)
CE
E 3
20W
inte
r 20
06
Example 2
Similar to Example 1 but for a crest curve.
A car is traveling at 30 mph in the country at night on a wet road through a 150 ft. long crest vertical curve. The entering grade is 3.0 percent and the exiting grade is -3.4 percent. A tree has fallen across the road at approximately the PVT. Is it reasonable to expect the driver to be able to stop before hitting the tree?
![Page 27: Geometric Design (Transportation Engineering)](https://reader034.vdocuments.mx/reader034/viewer/2022050812/5a6560cf7f8b9a931a8b4b69/html5/thumbnails/27.jpg)
CE
E 3
20W
inte
r 20
06
Example 3
A roadway is being designed using a 45 mph design speed. One section of the roadway must go up and over a small hill with an entering grade of 3.2 percent and an exiting grade of -2.0 percent. How long must the vertical curve be?
![Page 28: Geometric Design (Transportation Engineering)](https://reader034.vdocuments.mx/reader034/viewer/2022050812/5a6560cf7f8b9a931a8b4b69/html5/thumbnails/28.jpg)
CE
E 3
20W
inte
r 20
06
Horizontal Alignment
![Page 29: Geometric Design (Transportation Engineering)](https://reader034.vdocuments.mx/reader034/viewer/2022050812/5a6560cf7f8b9a931a8b4b69/html5/thumbnails/29.jpg)
CE
E 3
20W
inte
r 20
06
Horizontal Alignment
• Objective: – Geometry of directional transition to ensure:
• Safety• Comfort
• Primary challenge– Transition between two directions– Horizontal curves
• Fundamentals– Circular curves– Superelevation
Δ
![Page 30: Geometric Design (Transportation Engineering)](https://reader034.vdocuments.mx/reader034/viewer/2022050812/5a6560cf7f8b9a931a8b4b69/html5/thumbnails/30.jpg)
CE
E 3
20W
inte
r 20
06
Horizontal Curve Fundamentals
R
T
PC PT
PI
M
E
R
Δ
Δ/2Δ/2
Δ/2
RRD
ππ 000,18
180100
=
=
2tan
∆= RT
DRL
∆=∆= 100
180
π
L
![Page 31: Geometric Design (Transportation Engineering)](https://reader034.vdocuments.mx/reader034/viewer/2022050812/5a6560cf7f8b9a931a8b4b69/html5/thumbnails/31.jpg)
CE
E 3
20W
inte
r 20
06
Horizontal Curve Fundamentals
−
∆= 1
2cos
1RE
∆−=
2cos1RM
R
T
PC PT
PI
M
E
R
Δ
Δ/2Δ/2
Δ/2L
![Page 32: Geometric Design (Transportation Engineering)](https://reader034.vdocuments.mx/reader034/viewer/2022050812/5a6560cf7f8b9a931a8b4b69/html5/thumbnails/32.jpg)
CE
E 3
20W
inte
r 20
06
Example 4
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?
![Page 33: Geometric Design (Transportation Engineering)](https://reader034.vdocuments.mx/reader034/viewer/2022050812/5a6560cf7f8b9a931a8b4b69/html5/thumbnails/33.jpg)
CE
E 3
20W
inte
r 20
06
Superelevation cpfp FFW =+
αααα cossincossin22
vvs gR
WV
gR
WVWfW =
++
α
α
Fcp
Fcn
Wp
Wn F f
F f
α
Fc
W 1 fte
≈Rv
![Page 34: Geometric Design (Transportation Engineering)](https://reader034.vdocuments.mx/reader034/viewer/2022050812/5a6560cf7f8b9a931a8b4b69/html5/thumbnails/34.jpg)
CE
E 3
20W
inte
r 20
06
Superelevation
αααα cossincossin22
vvs gR
WV
gR
WVWfW =
++
( )αα tan1tan2
sv
s fgR
Vf −=+
( )efgR
Vfe s
vs −=+ 1
2
( )efg
VR
sv +
=2
![Page 35: Geometric Design (Transportation Engineering)](https://reader034.vdocuments.mx/reader034/viewer/2022050812/5a6560cf7f8b9a931a8b4b69/html5/thumbnails/35.jpg)
CE
E 3
20W
inte
r 20
06
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
![Page 36: Geometric Design (Transportation Engineering)](https://reader034.vdocuments.mx/reader034/viewer/2022050812/5a6560cf7f8b9a931a8b4b69/html5/thumbnails/36.jpg)
CE
E 3
20W
inte
r 20
06
Side Friction Factor
from AASHTO’s A Policy on Geometric Design of Highways and Streets 2004
New Graph
![Page 37: Geometric Design (Transportation Engineering)](https://reader034.vdocuments.mx/reader034/viewer/2022050812/5a6560cf7f8b9a931a8b4b69/html5/thumbnails/37.jpg)
CE
E 3
20W
inte
r 20
06
Minimum Radius Tables
New Table
![Page 38: Geometric Design (Transportation Engineering)](https://reader034.vdocuments.mx/reader034/viewer/2022050812/5a6560cf7f8b9a931a8b4b69/html5/thumbnails/38.jpg)
CE
E 3
20W
inte
r 20
06
WSDOT Design Side Friction Factors
from
the
20
05 W
SD
OT
Des
ign
Man
ual,
M 2
2-01
New Table
For Open Highways and Ramps
![Page 39: Geometric Design (Transportation Engineering)](https://reader034.vdocuments.mx/reader034/viewer/2022050812/5a6560cf7f8b9a931a8b4b69/html5/thumbnails/39.jpg)
CE
E 3
20W
inte
r 20
06
WSDOT Design Side Friction Factors
from
the
20
05 W
SD
OT
Des
ign
Man
ual,
M 2
2-01
For Low-Speed Urban Managed Access Highways
New Graph
![Page 40: Geometric Design (Transportation Engineering)](https://reader034.vdocuments.mx/reader034/viewer/2022050812/5a6560cf7f8b9a931a8b4b69/html5/thumbnails/40.jpg)
CE
E 3
20W
inte
r 20
06
Design Superelevation Rates - AASHTO
from AASHTO’s A Policy on Geometric Design of Highways and Streets 2004
New Graph
![Page 41: Geometric Design (Transportation Engineering)](https://reader034.vdocuments.mx/reader034/viewer/2022050812/5a6560cf7f8b9a931a8b4b69/html5/thumbnails/41.jpg)
CE
E 3
20W
inte
r 20
06
Design Superelevation Rates - WSDOT
from the 2005 WSDOT Design Manual, M 22-01
emax = 8%
New Graph
![Page 42: Geometric Design (Transportation Engineering)](https://reader034.vdocuments.mx/reader034/viewer/2022050812/5a6560cf7f8b9a931a8b4b69/html5/thumbnails/42.jpg)
CE
E 3
20W
inte
r 20
06
Example 5
A section of SR 522 is being designed as a high-speed divided highway. The design speed is 70 mph. Using WSDOT standards, what is the minimum curve radius (as measured to the traveled vehicle path) for safe vehicle operation?
![Page 43: Geometric Design (Transportation Engineering)](https://reader034.vdocuments.mx/reader034/viewer/2022050812/5a6560cf7f8b9a931a8b4b69/html5/thumbnails/43.jpg)
CE
E 3
20W
inte
r 20
06
Stopping Sight Distance
Rv
Δs
Obstruction
Ms( )v
s R
SSD
π180=∆
DRSSD s
sv
∆=∆= 100
180
π SSD
−=
vvs R
SSDRM
π90
cos1
−= −
v
svv
R
MRRSSD 1cos
90
π
![Page 44: Geometric Design (Transportation Engineering)](https://reader034.vdocuments.mx/reader034/viewer/2022050812/5a6560cf7f8b9a931a8b4b69/html5/thumbnails/44.jpg)
CE
E 3
20W
inte
r 20
06
Supplemental Stuff
• Cross section• Superelevation Transition
– Runoff
– Tangent runout
• Spiral curves• Extra width for curves
FYI – NOT TESTABLE
![Page 45: Geometric Design (Transportation Engineering)](https://reader034.vdocuments.mx/reader034/viewer/2022050812/5a6560cf7f8b9a931a8b4b69/html5/thumbnails/45.jpg)
CE
E 3
20W
inte
r 20
06
Cross Section
FYI – NOT TESTABLE
![Page 46: Geometric Design (Transportation Engineering)](https://reader034.vdocuments.mx/reader034/viewer/2022050812/5a6560cf7f8b9a931a8b4b69/html5/thumbnails/46.jpg)
CE
E 3
20W
inte
r 20
06
Superelevation Transition
from the 2001 Caltrans Highway Design Manual
FYI – NOT TESTABLE
![Page 47: Geometric Design (Transportation Engineering)](https://reader034.vdocuments.mx/reader034/viewer/2022050812/5a6560cf7f8b9a931a8b4b69/html5/thumbnails/47.jpg)
CE
E 3
20W
inte
r 20
06
Superelevation Transition
from AASHTO’s A Policy on Geometric Design of Highways and Streets 2001
FYI – NOT TESTABLE
![Page 48: Geometric Design (Transportation Engineering)](https://reader034.vdocuments.mx/reader034/viewer/2022050812/5a6560cf7f8b9a931a8b4b69/html5/thumbnails/48.jpg)
CE
E 3
20W
inte
r 20
06
Superelevation Runoff/Runout
from
AA
SH
TO
’s A
Pol
icy
on G
eom
etric
Des
ign
of
Hig
hway
s an
d S
tree
ts 2
001
FYI – NOT TESTABLE
![Page 49: Geometric Design (Transportation Engineering)](https://reader034.vdocuments.mx/reader034/viewer/2022050812/5a6560cf7f8b9a931a8b4b69/html5/thumbnails/49.jpg)
CE
E 3
20W
inte
r 20
06
Superelevation Runoff - WSDOT
from the 2005 WSDOT Design Manual, M 22-01
FYI – NOT TESTABLENew Graph
![Page 50: Geometric Design (Transportation Engineering)](https://reader034.vdocuments.mx/reader034/viewer/2022050812/5a6560cf7f8b9a931a8b4b69/html5/thumbnails/50.jpg)
CE
E 3
20W
inte
r 20
06
Spiral Curves
No Spiral
Spiral
from AASHTO’s A Policy on Geometric Design of Highways and Streets 2001
FYI – NOT TESTABLE
![Page 51: Geometric Design (Transportation Engineering)](https://reader034.vdocuments.mx/reader034/viewer/2022050812/5a6560cf7f8b9a931a8b4b69/html5/thumbnails/51.jpg)
CE
E 3
20W
inte
r 20
06
No Spiral
FYI – NOT TESTABLE
![Page 52: Geometric Design (Transportation Engineering)](https://reader034.vdocuments.mx/reader034/viewer/2022050812/5a6560cf7f8b9a931a8b4b69/html5/thumbnails/52.jpg)
CE
E 3
20W
inte
r 20
06
Spiral Curves
• WSDOT no longer uses spiral curves• Involve complex geometry
• Require more surveying• Are somewhat empirical• If used, superelevation transition should
occur entirely within spiral
FYI – NOT TESTABLE
![Page 53: Geometric Design (Transportation Engineering)](https://reader034.vdocuments.mx/reader034/viewer/2022050812/5a6560cf7f8b9a931a8b4b69/html5/thumbnails/53.jpg)
CE
E 3
20W
inte
r 20
06
Desirable Spiral Lengths
from AASHTO’s A Policy on Geometric Design of Highways and Streets 2001
FYI – NOT TESTABLE
![Page 54: Geometric Design (Transportation Engineering)](https://reader034.vdocuments.mx/reader034/viewer/2022050812/5a6560cf7f8b9a931a8b4b69/html5/thumbnails/54.jpg)
CE
E 3
20W
inte
r 20
06
Operating vs. Design Speed
85th Percentile Speed vs. Inferred Design Speed for 138 Rural Two-Lane Highway Horizontal Curves
85th Percentile Speed vs. Inferred Design Speed for
Rural Two-Lane Highway Limited Sight Distance Crest
Vertical Curves
FYI – NOT TESTABLE
![Page 55: Geometric Design (Transportation Engineering)](https://reader034.vdocuments.mx/reader034/viewer/2022050812/5a6560cf7f8b9a931a8b4b69/html5/thumbnails/55.jpg)
CE
E 3
20W
inte
r 20
06
Primary References
• Mannering, F.L.; Kilareski, W.P. and Washburn, S.S. (2005). Principles of Highway Engineering and Traffic Analysis, Third Edition. Chapter 3
• American Association of State Highway and Transportation Officials (AASHTO). (2001). A Policy on Geometric Design of Highways and Streets, Fourth Edition. Washington, D.C.