CEE 320 Spring 2008 Geometric Design CEE 320
- Slides: 55
CEE 320 Spring 2008 Geometric Design CEE 320 Anne Goodchild
Outline 1. Concepts 2. Vertical Alignment a. b. c. d. Fundamentals Crest Vertical Curves Sag Vertical Curves Examples 3. Horizontal Alignment a. Fundamentals b. Superelevation CEE 320 Spring 2008 4. Other Non-Testable Stuff
Concepts • Alignment is a 3 D problem broken down into two 2 D problems – Horizontal Alignment (plan view) – Vertical Alignment (profile view) • Stationing CEE 320 Spring 2008 – Along horizontal alignment – 12+00 = 1, 200 ft. Piilani Highway on Maui
Stationing Horizontal Alignment CEE 320 Spring 2008 Vertical Alignment
From Perteet Engineering
CEE 320 Spring 2008 Vertical Alignment
Vertical Alignment • Objective: – Determine elevation to ensure • Proper drainage • Acceptable level of safety • Primary challenge – Transition between two grades – Vertical curves Sag Vertical Curve CEE 320 Spring 2008 G 1 G 2 Crest Vertical Curve G 1 G 2
Vertical Curve Fundamentals • Parabolic function – Constant rate of change of slope – Implies equal curve tangents CEE 320 Spring 2008 • y is the roadway elevation x stations (or feet) from the beginning of the curve
Vertical Curve Fundamentals G 1 PVC PVI δ G 2 PVT L/2 L CEE 320 Spring 2008 x Choose Either: • G 1, G 2 in decimal form, L in feet • G 1, G 2 in percent, L in stations
Choose Either: CEE 320 Spring 2008 Relationships • G 1, G 2 in decimal form, L in feet • G 1, G 2 in percent, L in stations
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. PVI % 2. 0 = G 1 CEE 320 Spring 2008 PVC: STA 100+00 EL 59 ft. PVT G= 2 4. 5 %
PVI % 2. 0 G 1= PVC: STA 100+00 EL 59 ft. PVT G= 2 4. 5 %
• G 1, G 2 in percent • L in feet Other Properties G 1 x PVT PVC Y Ym CEE 320 Spring 2008 PVI G 2 Yf
Other Properties • K-Value (defines vertical curvature) CEE 320 Spring 2008 – The number of horizontal feet needed for a 1% change in slope
Crest Vertical Curves SSD PVI Line of Sight PVC G 1 PVT h 2 h 1 L CEE 320 Spring 2008 For SSD < L For SSD > L G 2
Crest Vertical Curves • Assumptions for design – h 1 = driver’s eye height = 3. 5 ft. – h 2 = tail light height = 2. 0 ft. • Simplified Equations CEE 320 Spring 2008 For SSD < L For SSD > L
Crest Vertical Curves CEE 320 Spring 2008 • Assuming L > SSD…
CEE 320 Spring 2008 Design Controls for Crest Vertical Curves from AASHTO’s A Policy on Geometric Design of Highways and Streets 2004
from AASHTO’s A Policy on Geometric Design of Highways and Streets 2004 CEE 320 Spring 2008 Design Controls for Crest Vertical Curves
Sag Vertical Curves Light Beam Distance (SSD) G 1 headlight beam (diverging from LOS by β degrees) PVT PVC h 1 CEE 320 Spring 2008 For SSD < L G 2 PVI L h 2=0 For SSD > L
Sag Vertical Curves • Assumptions for design – h 1 = headlight height = 2. 0 ft. – β = 1 degree • Simplified Equations CEE 320 Spring 2008 For SSD < L For SSD > L
Sag Vertical Curves CEE 320 Spring 2008 • Assuming L > SSD…
CEE 320 Spring 2008 Design Controls for Sag Vertical Curves from AASHTO’s A Policy on Geometric Design of Highways and Streets 2004
from AASHTO’s A Policy on Geometric Design of Highways and Streets 2004 CEE 320 Spring 2008 Design Controls for Sag Vertical Curves
Example 1 CEE 320 Spring 2008 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?
Example 2 Similar to Example 1 but for a crest curve. CEE 320 Spring 2008 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?
Example 3 CEE 320 Spring 2008 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?
CEE 320 Spring 2008 Horizontal Alignment
Horizontal Alignment • Objective: – Geometry of directional transition to ensure: • Safety • Comfort • Primary challenge – Transition between two directions – Horizontal curves • Fundamentals CEE 320 Spring 2008 – Circular curves – Superelevation Δ
Horizontal Curve Fundamentals PI T Δ E M PC L Δ/2 R R Δ/2 CEE 320 Spring 2008 PT
Horizontal Curve Fundamentals PI T Δ E M PC L Δ/2 R R Δ/2 CEE 320 Spring 2008 PT
Example 4 CEE 320 Spring 2008 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?
Superelevation ≈ Rv Fc α F cn F cp α W Ff CEE 320 Spring 2008 α e Wn Wp Ff 1 ft
CEE 320 Spring 2008 Superelevation
Selection of e and fs • Practical limits on superelevation (e) – Climate – Constructability – Adjacent land use • Side friction factor (fs) variations CEE 320 Spring 2008 – Vehicle speed – Pavement texture – Tire condition
CEE 320 Spring 2008 Side Friction Factor from AASHTO’s A Policy on Geometric Design of Highways and Streets 2004
CEE 320 Spring 2008 Minimum Radius Tables
WSDOT Design Side Friction Factors from the 2005 WSDOT Design Manual, M 22 -01 CEE 320 Spring 2008 For Open Highways and Ramps
WSDOT Design Side Friction Factors from the 2005 WSDOT Design Manual, M 22 -01 CEE 320 Spring 2008 For Low-Speed Urban Managed Access Highways
CEE 320 Spring 2008 Design Superelevation Rates - AASHTO from AASHTO’s A Policy on Geometric Design of Highways and Streets 2004
Design Superelevation Rates - WSDOT CEE 320 Spring 2008 emax = 8% from the 2005 WSDOT Design Manual, M 22 -01
Example 5 CEE 320 Spring 2008 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?
Stopping Sight Distance SSD Ms Obstruction Rv CEE 320 Spring 2008 Δs
FYI – NOT TESTABLE Supplemental Stuff • Cross section • Superelevation Transition – Runoff – Tangent runout CEE 320 Spring 2008 • Spiral curves • Extra width for curves
FYI – NOT TESTABLE CEE 320 Spring 2008 Cross Section
FYI – NOT TESTABLE CEE 320 Spring 2008 Superelevation Transition from the 2001 Caltrans Highway Design Manual
FYI – NOT TESTABLE CEE 320 Spring 2008 Superelevation Transition from AASHTO’s A Policy on Geometric Design of Highways and Streets 2001
Superelevation Runoff/Runout from AASHTO’s A Policy on Geometric Design of Highways and Streets 2004 CEE 320 Spring 2008 FYI – NOT TESTABLE
FYI – NOT TESTABLE CEE 320 Spring 2008 Superelevation Runoff - WSDOT from the 2005 WSDOT Design Manual, M 22 -01
FYI – NOT TESTABLE Spiral Curves No Spiral CEE 320 Spring 2008 Spiral from AASHTO’s A Policy on Geometric Design of Highways and Streets 2004
FYI – NOT TESTABLE CEE 320 Spring 2008 No Spiral
FYI – NOT TESTABLE Spiral Curves CEE 320 Spring 2008 • • • 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 CEE 320 Spring 2008 Desirable Spiral Lengths from AASHTO’s A Policy on Geometric Design of Highways and Streets 2004
FYI – NOT TESTABLE Operating vs. Design Speed CEE 320 Spring 2008 85 th Percentile Speed vs. Inferred Design Speed for 138 Rural Two-Lane Highway Horizontal Curves 85 th Percentile Speed vs. Inferred Design Speed for Rural Two-Lane Highway Limited Sight Distance Crest Vertical Curves
Primary References • Mannering, F. L. ; Kilareski, W. P. and Washburn, S. S. (2005). Principles of Highway Engineering and Traffic Analysis, Third Edition. Chapter 3 CEE 320 Spring 2008 • American Association of State Highway and Transportation Officials (AASHTO). (2001). A Policy on Geometric Design of Highways and Streets, Fourth Edition. Washington, D. C.
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