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Geometric Design Session 02-06

Geometric Design Session 02-06. Matakuliah : S0753 – Teknik Jalan Raya Tahun : 2009. Contents. Concepts Vertical Alignment Fundamentals Crest Vertical Curves Sag Vertical Curves Examples Horizontal Alignment Fundamentals Superelevation.

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Geometric Design Session 02-06

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  1. Geometric DesignSession 02-06 Matakuliah : S0753 – Teknik Jalan Raya Tahun : 2009

  2. Contents Concepts Vertical Alignment Fundamentals Crest Vertical Curves Sag Vertical Curves Examples Horizontal Alignment Fundamentals Superelevation

  3. Alignment is a 3D problem broken down into two 2D problems Horizontal Alignment (plan view) Vertical Alignment (profile view) Stationing Along horizontal alignment Introduction Piilani Highway on Maui

  4. Horizontal Alignment Stationing Introduction Vertical Alignment

  5. Introduction From Perteet Engineering

  6. Geometric Design Elements • Sight Distances • Superelevation • Horizontal Alignment • Vertical Alignment

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

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

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

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

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

  19. 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

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

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

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

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

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

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

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

  27. Superelevation

  28. 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

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

  30. Minimum Radius Tables

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

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

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

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

  35. Circular Curve Geometrics • PC = Point of Curvature • PT = Point of Tangency • PI = Point of Intercept • 100/D = L/Δ, so, • L = 100 (Δ /D) where: • L = arc length(measured in Stations (1 Sta = 100 ft) • Δ = internal angle (deflection angle) • D = 5729.58/R • M = middle ordinate m=R [1 – cos(Δ /2) ] M - is maximum distance from curve to long chord

  36. Circular Curve Geometrics Degree of curvature: D = central angle which subtends an arc of 100 feet D=5729.58/R where R – radius of curve For R=1000 ft. D = 5.73 degrees Maximum degree of curve/min radius: Dmax = 85,660 (e + f)/V2 or Rmin = V2/[15 (e + f)]

  37. Horizontal Sight Distance 1) Sight line is a chord of the circular curve 2) Applicable Minimum Stopping Sight Distance (MSSD) measured along centerline of inside lane Criterion: no obstruction within middle ordinate Assume: driver eye height = 3.5 ft object height = 2.0 ft. Note: results in line of sight obstruction height at middle ordinate of 2.75 ft

  38. Horizontal Alignment • Basic controlling expression: e + f = V2/15R • Example: • A horizontal curve has the following characteristics: Δ = 45˚, L = 1200 ft, e = 0.06 ft/ft. What coefficient of side friction would be required by a vehicle traveling at 70 mph?

  39. Circular Curve Geometrics • PC = Point of Curvature • PT = Point of Tangency • PI = Point of Intercept • 100/D = L/Δ, so, • L = 100 (Δ /D) where: • L = arc length(measured in Stations (1 Sta = 100 ft) • Δ = internal angle (deflection angle) • D = 5729.58/R • M = middle ordinate m=R [1 – cos(Δ /2) ] M - is maximum distance from curve to long chord

  40. Stopping Sight Distance SSD Ms Obstruction Rv Δs

  41. Cross Section

  42. Superelevation Transition from the 2001 Caltrans Highway Design Manual

  43. Superelevation Transition from AASHTO’s A Policy on Geometric Design of Highways and Streets 2001

  44. Spiral Curves No Spiral Spiral from AASHTO’s A Policy on Geometric Design of Highways and Streets 2001

  45. Spiral Curves • Involve complex geometry • Require more surveying • Are somewhat empirical • If used, superelevation transition should occur entirely within spiral

  46. Desirable Spiral Lengths from AASHTO’s A Policy on Geometric Design of Highways and Streets 2001

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