CEE 320 Spring 2008 Geometric Design CEE 320

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CEE 320 Spring 2008 Geometric Design CEE 320 Anne Goodchild

CEE 320 Spring 2008 Geometric Design CEE 320 Anne Goodchild

Outline 1. Concepts 2. Vertical Alignment a. b. c. d. Fundamentals Crest Vertical Curves

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

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

Stationing Horizontal Alignment CEE 320 Spring 2008 Vertical Alignment

From Perteet Engineering

From Perteet Engineering

CEE 320 Spring 2008 Vertical Alignment

CEE 320 Spring 2008 Vertical Alignment

Vertical Alignment • Objective: – Determine elevation to ensure • Proper drainage • Acceptable

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 –

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

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

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

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=

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, 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

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

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

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…

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

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

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

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 =

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…

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

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

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

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

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

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

CEE 320 Spring 2008 Horizontal Alignment

Horizontal Alignment • Objective: – Geometry of directional transition to ensure: • Safety •

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

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

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

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

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

CEE 320 Spring 2008 Superelevation

Selection of e and fs • Practical limits on superelevation (e) – Climate –

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

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

CEE 320 Spring 2008 Minimum Radius Tables

WSDOT Design Side Friction Factors from the 2005 WSDOT Design Manual, M 22 -01

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

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

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

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

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

Stopping Sight Distance SSD Ms Obstruction Rv CEE 320 Spring 2008 Δs

FYI – NOT TESTABLE Supplemental Stuff • Cross section • Superelevation Transition – Runoff

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 Cross Section

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

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

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

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

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

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 CEE 320 Spring 2008 No Spiral

FYI – NOT TESTABLE Spiral Curves CEE 320 Spring 2008 • • • WSDOT

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

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

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.

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.