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Geometric Design. CEE 320 Steve Muench. Outline. Concepts Vertical Alignment Fundamentals Crest Vertical Curves Sag Vertical Curves Examples Horizontal Alignment Fundamentals Superelevation Other Non-Testable Stuff. Alignment is a 3D problem broken down into two 2D problems

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Geometric Design


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    1. Geometric Design CEE 320Steve Muench

    2. Outline • Concepts • Vertical Alignment • Fundamentals • Crest Vertical Curves • Sag Vertical Curves • Examples • Horizontal Alignment • Fundamentals • Superelevation • Other Non-Testable Stuff

    3. 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. Concepts Piilani Highway on Maui

    4. Stationing Horizontal Alignment Vertical Alignment

    5. From Perteet Engineering

    6. Vertical Alignment

    7. Vertical Alignment • Objective: • Determine elevation to ensure • Proper drainage • Acceptable level of safety • Primary challenge • Transition between two grades • Vertical curves Sag Vertical Curve G1 G2 G2 G1 Crest Vertical Curve

    8. 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

    9. Vertical Curve Fundamentals PVI G1 δ PVC G2 PVT L/2 L x • Choose Either: • G1, G2 in decimal form, L in feet • G1, G2 in percent, L in stations

    10. Choose Either: • G1, G2 in decimal form, L in feet • G1, G2 in percent, L in stations Relationships

    11. 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 PVT G1=2.0% G2= - 4.5% PVC: STA 100+00 EL 59 ft.

    12. PVI PVT G1=2.0% PVC: STA 100+00 EL 59 ft. G2= -4.5%

    13. G1, G2 in percent • L in feet Other Properties G1 x PVT PVC Y Ym G2 PVI Yf

    14. Other Properties • K-Value (defines vertical curvature) • The number of horizontal feet needed for a 1% change in slope

    15. Crest Vertical Curves SSD PVI Line of Sight PVC PVT G2 G1 h2 h1 L For SSD < L For SSD > L

    16. Crest Vertical Curves • Assumptions for design • h1 = driver’s eye height = 3.5 ft. • h2 = tail light height = 2.0 ft. • Simplified Equations For SSD < L For SSD > L

    17. Crest Vertical Curves • Assuming L > SSD…

    18. Design Controls for Crest Vertical Curves from AASHTO’s A Policy on Geometric Design of Highways and Streets 2001

    19. Design Controls for Crest Vertical Curves from AASHTO’s A Policy on Geometric Design of Highways and Streets 2001

    20. Sag Vertical Curves Light Beam Distance (SSD) G1 headlight beam (diverging from LOS by β degrees) G2 PVT PVC h1 PVI h2=0 L For SSD < L For SSD > L

    21. Sag Vertical Curves • Assumptions for design • h1 = headlight height = 2.0 ft. • β = 1 degree • Simplified Equations For SSD < L For SSD > L

    22. Sag Vertical Curves • Assuming L > SSD…

    23. Design Controls for Sag Vertical Curves from AASHTO’s A Policy on Geometric Design of Highways and Streets 2001

    24. Design Controls for Sag Vertical Curves from AASHTO’s A Policy on Geometric Design of Highways and Streets 2001

    25. 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?

    26. 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?

    27. 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?

    28. Horizontal Alignment

    29. Horizontal Alignment • Objective: • Geometry of directional transition to ensure: • Safety • Comfort • Primary challenge • Transition between two directions • Horizontal curves • Fundamentals • Circular curves • Superelevation Δ

    30. Horizontal Curve Fundamentals PI T Δ E M L Δ/2 PT PC R R Δ/2 Δ/2

    31. Horizontal Curve Fundamentals PI T Δ E M L Δ/2 PT PC R R Δ/2 Δ/2

    32. 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?

    33. Superelevation Rv ≈ Fc α Fcn Fcp α e W 1 ft Wn Ff Wp Ff α

    34. Superelevation

    35. 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

    36. New Graph Side Friction Factor from AASHTO’s A Policy on Geometric Design of Highways and Streets 2004

    37. New Table Minimum Radius Tables

    38. New Table WSDOT Design Side Friction Factors For Open Highways and Ramps from the 2005 WSDOT Design Manual, M 22-01

    39. New Graph WSDOT Design Side Friction Factors For Low-Speed Urban Managed Access Highways from the 2005 WSDOT Design Manual, M 22-01

    40. New Graph Design Superelevation Rates - AASHTO from AASHTO’s A Policy on Geometric Design of Highways and Streets 2004

    41. New Graph Design Superelevation Rates - WSDOT emax = 8% from the 2005 WSDOT Design Manual, M 22-01

    42. 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?

    43. Stopping Sight Distance SSD Ms Obstruction Rv Δs

    44. FYI – NOT TESTABLE Supplemental Stuff • Cross section • Superelevation Transition • Runoff • Tangent runout • Spiral curves • Extra width for curves

    45. FYI – NOT TESTABLE Cross Section

    46. FYI – NOT TESTABLE Superelevation Transition from the 2001 Caltrans Highway Design Manual

    47. FYI – NOT TESTABLE Superelevation Transition from AASHTO’s A Policy on Geometric Design of Highways and Streets 2001

    48. FYI – NOT TESTABLE Superelevation Runoff/Runout from AASHTO’s A Policy on Geometric Design of Highways and Streets 2001

    49. FYI – NOT TESTABLE New Graph Superelevation Runoff - WSDOT from the 2005 WSDOT Design Manual, M 22-01

    50. FYI – NOT TESTABLE Spiral Curves No Spiral Spiral from AASHTO’s A Policy on Geometric Design of Highways and Streets 2001