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CEE 320 Spring 2008 Geometric Design CEE 320 Anne Goodchild

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CEE 320 Spring 2008 Outline 1.Concepts 2.Vertical Alignment a.Fundamentals b.Crest Vertical Curves c.Sag Vertical Curves d.Examples 3.Horizontal Alignment a.Fundamentals b.Superelevation 4.Other Non-Testable Stuff

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CEE 320 Spring 2008 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

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CEE 320 Spring 2008 Stationing Horizontal Alignment Vertical Alignment

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From Perteet Engineering

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CEE 320 Spring 2008 Vertical Alignment

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CEE 320 Spring 2008 Vertical Alignment Objective: –Determine elevation to ensure Proper drainage Acceptable level of safety Primary challenge –Transition between two grades –Vertical curves G1G1 G2G2 G1G1 G2G2 Crest Vertical Curve Sag Vertical Curve

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CEE 320 Spring 2008 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

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CEE 320 Spring 2008 Vertical Curve Fundamentals G1G1 G2G2 PVI PVT PVC L L/2 δ x Choose Either: G 1, G 2 in decimal form, L in feet G 1, G 2 in percent, L in stations

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CEE 320 Spring 2008 Relationships Choose Either: G 1, G 2 in decimal form, L in feet G 1, G 2 in percent, L in stations

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CEE 320 Spring 2008 Example A 400 ft. equal tangent crest vertical curve has a PVC station of 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. G 1 =2.0% G 2 = - 4.5% PVI PVT PVC: STA EL 59 ft.

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G 1 =2.0% G 2 = -4.5% PVI PVT PVC: STA EL 59 ft.

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CEE 320 Spring 2008 Other Properties G1G1 G2G2 PVI PVT PVC x YmYm YfYf Y G 1, G 2 in percent L in feet

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CEE 320 Spring 2008 Other Properties K-Value (defines vertical curvature) –The number of horizontal feet needed for a 1% change in slope

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CEE 320 Spring 2008 Crest Vertical Curves G1G1 G2G2 PVI PVT PVC h2h2 h1h1 L SSD For SSD < LFor SSD > L Line of Sight

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CEE 320 Spring 2008 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 For SSD < LFor SSD > L

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CEE 320 Spring 2008 Crest Vertical Curves Assuming L > SSD…

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CEE 320 Spring 2008 Design Controls for Crest Vertical Curves from AASHTO’s A Policy on Geometric Design of Highways and Streets 2004

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CEE 320 Spring 2008 Design Controls for Crest Vertical Curves from AASHTO’s A Policy on Geometric Design of Highways and Streets 2004

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CEE 320 Spring 2008 Sag Vertical Curves G1G1 G2G2 PVI PVT PVC h 2 =0 h1h1 L Light Beam Distance (SSD) For SSD < LFor SSD > L headlight beam (diverging from LOS by β degrees)

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CEE 320 Spring 2008 Sag Vertical Curves Assumptions for design –h 1 = headlight height = 2.0 ft. –β = 1 degree Simplified Equations For SSD < L For SSD > L

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CEE 320 Spring 2008 Sag Vertical Curves Assuming L > SSD…

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CEE 320 Spring 2008 Design Controls for Sag Vertical Curves from AASHTO’s A Policy on Geometric Design of Highways and Streets 2004

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CEE 320 Spring 2008 Design Controls for Sag Vertical Curves from AASHTO’s A Policy on Geometric Design of Highways and Streets 2004

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CEE 320 Spring 2008 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?

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CEE 320 Spring 2008 Sag Vertical Curve Assume S

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CEE 320 Spring 2008 Sag Vertical Curves G1G1 G2G2 PVI PVT PVC h 2 =0 h1h1 L Light Beam Distance (S) diverging from horizontal plane of vehicle by β degrees Daytime sight distance unrestricted

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CEE 320 Spring 2008 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?

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CEE 320 Spring 2008 Crest Vertical Curve Assume S

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CEE 320 Spring 2008 Crest Vertical Curves G1G1 G2G2 PVI PVT PVC h2h2 h1h1 L SSD Line of Sight

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CEE 320 Spring 2008 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?

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CEE 320 Spring 2008 Horizontal Alignment

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CEE 320 Spring 2008 Horizontal Alignment Objective: –Geometry of directional transition to ensure: Safety Comfort Primary challenge –Transition between two directions –Horizontal curves Fundamentals –Circular curves –Superelevation Δ

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CEE 320 Spring 2008 Horizontal Curve Fundamentals R T PC PT PI M E R Δ Δ/2 L D = degree of curvature (angle subtended by a 100’ arc)

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CEE 320 Spring 2008 Horizontal Curve Fundamentals R T PC PT PI M E R Δ Δ/2 L

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CEE 320 Spring 2008 Example 4 A horizontal curve is designed with a 1500 ft. radius. The tangent length is 400 ft. and the PT station is What are the PI and PT stations?

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CEE 320 Spring 2008 Superelevation α α F cp F cn WpWp WnWn FfFf FfFf α FcFc W 1 ft e ≈ RvRv

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CEE 320 Spring 2008 Superelevation This is the minimum radius that provides for safe vehicle operation R v because it is to the vehicle’s path e = number of vertical feet of rise per 100 ft of horizontal distance = 100tan

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CEE 320 Spring 2008 Selection of e and f s Practical limits on superelevation (e) –Climate –Constructability –Adjacent land use Side friction factor (f s ) variations –Vehicle speed –Pavement texture –Tire condition Design values of f s are chosen somewhat below this maximum value so there is a margin of safety

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CEE 320 Spring 2008 Minimum Radius Tables

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CEE 320 Spring 2008 WSDOT Design Side Friction Factors from the 2005 WSDOT Design Manual, M For Open Highways and Ramps

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CEE 320 Spring 2008 WSDOT Design Side Friction Factors from the 2005 WSDOT Design Manual, M For Low-Speed Urban Managed Access Highways

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CEE 320 Spring 2008 Design Superelevation Rates - AASHTO from AASHTO’s A Policy on Geometric Design of Highways and Streets 2004

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CEE 320 Spring 2008 Design Superelevation Rates - WSDOT from the 2005 WSDOT Design Manual, M e max = 8%

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CEE 320 Spring 2008 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?

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CEE 320 Spring 2008 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? For the minimum curve radius we want the maximum superelevation. WSDOT max e = 0.10 For 70 mph, WSDOT f = 0.10

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CEE 320 Spring 2008 Stopping Sight Distance RvRv ΔsΔs Obstruction MsMs SSD (not L) Looking around a curve Measured along horizontal curve from the center of the traveled lane Need to clear back to M s (the middle of a line that has same arc length as SSD) Assumes curve exceeds required SSD

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CEE 320 Spring 2008 Stopping Sight Distance RvRv ΔsΔs Obstruction MsMs SSD (not L)

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CEE 320 Spring 2008 Example 6 A horizontal curve with a radius to the vehicle’s path of 2000 ft and a 60 mph design speed. Determine the distance that must be cleared from the inside edge of the inside lane to provide sufficient stopping sight distance.

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CEE 320 Spring 2008 Superelevation Transition from the 2001 Caltrans Highway Design Manual FYI – NOT TESTABLE

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CEE 320 Spring 2008 Spiral Curves No Spiral Spiral from AASHTO’s A Policy on Geometric Design of Highways and Streets 2004 FYI – NOT TESTABLE

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CEE 320 Spring 2008 No Spiral FYI – NOT TESTABLE

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CEE 320 Spring 2008 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

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CEE 320 Spring 2008 Operating vs. Design Speed 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 FYI – NOT TESTABLE

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