Geometric Design by oddt1s8q

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									              Geometric Design
Spring 2008
CEE 320




                                       CEE 320
                                 Anne Goodchild
              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
Spring 2008
CEE 320
              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.
Spring 2008
CEE 320




                                                      Piilani Highway on Maui
              Stationing
                           Horizontal Alignment




                              Vertical Alignment
Spring 2008
CEE 320
From Perteet Engineering
              Vertical Alignment
Spring 2008
CEE 320
              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
                                                  G1                 G2
Spring 2008




                   Crest Vertical Curve
CEE 320
              Vertical Curve Fundamentals

              • Parabolic function
                – Constant rate of change of slope
                – Implies equal curve tangents


                             y  ax  bx  c
                                     2



              • y is the roadway elevation x stations
                (or feet) from the beginning of the curve
Spring 2008
CEE 320
              Vertical Curve Fundamentals

                                     PVI
                            G1             δ
               PVC                             G2
                                                         PVT
                      L/2


                                      L
                            x



                      y  ax  bx  c
                                 2

                                                    Choose Either:
Spring 2008




                                                    • G1, G2 in decimal form, L in feet
CEE 320




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

              Relationships                                • G1, G2 in percent, L in stations




               At the PVC : x  0 and Y  c
                                                 dY
               At the PVC : x  0 and                b  G1
                                                 dx

                          d 2Y        G2  G1     G2  G1
               Anywhere :    2
                                2a          a
                          dx             L          2L
                                            PVI
                                       G1         δ
                          PVC                         G2
                                                                PVT
                                 L/2
Spring 2008
CEE 320




                                             L
                                       x
              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



              PVC: STA 100+00
                      EL 59 ft.
Spring 2008
CEE 320
                    PVI


                          PVT

PVC: STA 100+00
        EL 59 ft.
                                                      •G1, G2 in percent
              Other Properties                        •L in feet


               G1           x

                                                                       PVT
               PVC

                                   Y
                                           Ym         G2

                                       PVI                        Yf
              A  G1  G2

                   A 2               AL              AL
              Y      x         Ym             Yf 
                 200L                800             200
Spring 2008
CEE 320
              Other Properties

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


                                     L
                                  K
                                     A

                         high / low pt.  x  K G1
Spring 2008
CEE 320
              Crest Vertical Curves
                                                  SSD

                                                        PVI
                                  Line of Sight


                                       PVC                             PVT          G2
              G1

                                                                 h2
                             h1

                                                         L
                         For SSD < L                                  For SSD > L

              L
                             ASSD 
                                          2

                                                        L  2SSD 
                                                                             
                                                                     200 h1  h2         
                                                                                         2


                                                 
Spring 2008




                                                  2
                   100        2h1  2h2                                   A
CEE 320
              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
                     ASSD 
                               2
                                            L  2SSD 
                                                         2158
                  L
                      2158                                A
Spring 2008
CEE 320
              Crest Vertical Curves

              • Assuming L > SSD…

                                    2
                                SSD
                             K
                                2158
Spring 2008
CEE 320
              Design Controls for Crest Vertical Curves
Spring 2008
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




from AASHTO’s A Policy on Geometric Design of Highways and Streets 2004
              Sag Vertical Curves
                                      Light Beam Distance (SSD)


               G1
                               headlight beam (diverging from LOS by β degrees)          G2


                               PVC                                           PVT

                          h1                       PVI
                                                                                  h2=0



                                                     L
                     For SSD < L                                           For SSD > L

                    ASSD                                   200h1  SSD tan  
                                  2
              L                                L  2SSD 
                 200h1  S tan  
Spring 2008




                                                                       A
CEE 320
              Sag Vertical Curves

              • Assumptions for design
                – h1 = headlight height = 2.0 ft.
                – β = 1 degree


              • Simplified Equations
                 For SSD < L                        For SSD > L

                    ASSD                          400  3.5SSD 
                             2
              L                      L  2SSD                  
                 400  3.5SSD                            A       
Spring 2008
CEE 320
              Sag Vertical Curves

              • Assuming L > SSD…

                                    2
                                SSD
                         K
                            400  3.5SSD
Spring 2008
CEE 320
              Design Controls for Sag Vertical Curves
Spring 2008
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




from AASHTO’s A Policy on Geometric Design of Highways and Streets 2004
              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?
Spring 2008
CEE 320
              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?
Spring 2008
CEE 320
              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?
Spring 2008
CEE 320
              Horizontal
              Alignment
Spring 2008
CEE 320
              Horizontal Alignment

              • Objective:
                – Geometry of directional transition to ensure:
                   • Safety
                   • Comfort
              • Primary challenge                       Δ
                – Transition between two directions
                – Horizontal curves
              • Fundamentals
                – Circular curves
                – Superelevation
Spring 2008
CEE 320
              Horizontal Curve Fundamentals
                                            PI
                                     T             Δ
                                             E
                        
              T  R tan              L
                                             M
                        2     PC                   Δ/2       PT


                          100
               L     R 
                  180       D        R                   R

                     180               Δ/2 Δ/2
                 100     
              D        18,000
Spring 2008




                              R
CEE 320




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


                    1          
                    cos  2  1
              E  R            
                                       R                   R

                                             Δ/2 Δ/2
                          
              M  R1  cos 
Spring 2008




                          2
CEE 320
              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?
Spring 2008
CEE 320
              Superelevation                    W p  F f  Fcp

              Rv


                       ≈
                      Fc



                                                                e
                                    W                    1 ft




                       α

                                      WV 2        WV 2
               W sin   f s W cos       sin   
                                                   gR cos
Spring 2008




                             
CEE 320




                                      gRv           v
              Superelevation

                                     WV 2        WV 2
              W sin   f s W cos 
                                          sin   
                                                  gR cos
                                     gRv           v

                                                   V2
                                     tan   f s      1  f s tan  
                                                   gRv
                                                  V2
                                         e  fs      1  f s e
                                                  gRv

                                                      V2
                                             Rv 
                                                  g  f s  e
Spring 2008
CEE 320
              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
Spring 2008
CEE 320
              Side Friction Factor
Spring 2008
CEE 320




                        from AASHTO’s A Policy on Geometric Design of Highways and Streets 2004
              Minimum Radius Tables
Spring 2008
CEE 320
              WSDOT Design Side Friction Factors
                         For Open Highways and Ramps




                                                       from the 2005 WSDOT Design Manual, M 22-01
Spring 2008
CEE 320
              WSDOT Design Side Friction Factors
                    For Low-Speed Urban Managed Access Highways




                                                                  from the 2005 WSDOT Design Manual, M 22-01
Spring 2008
CEE 320
              Design Superelevation Rates - AASHTO
Spring 2008
CEE 320




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


                                        emax = 8%
Spring 2008
CEE 320




                                  from the 2005 WSDOT Design Manual, M 22-01
              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?
Spring 2008
CEE 320
               Stopping Sight Distance
                                                 SSD
                                100 s
              SSD      Rv  s 
                    180            D
                     180 SSD                         Ms
                s 
                        Rv
                                 90SSD 
                                  R 
                M s  Rv 1  cos
                                              Obstruction
                                         
                                    v                   Rv

                       Rv    Rv  M s 
                         cos           
                                1
                SSD           R        
                                                  Δs
Spring 2008




                      90               
CEE 320




                                    v
                                            FYI – NOT TESTABLE


              Supplemental Stuff

              • Cross section
              • Superelevation Transition
                – Runoff
                – Tangent runout
              • Spiral curves
              • Extra width for curves
Spring 2008
CEE 320
                              FYI – NOT TESTABLE


              Cross Section
Spring 2008
CEE 320
                                              FYI – NOT TESTABLE


              Superelevation Transition
Spring 2008
CEE 320




                                 from the 2001 Caltrans Highway Design Manual
                                                               FYI – NOT TESTABLE


              Superelevation Transition
Spring 2008
CEE 320




                       from AASHTO’s A Policy on Geometric Design of Highways and Streets 2001
CEE 320
Spring 2008




                                                                Superelevation Runoff/Runout
                                                                                               FYI – NOT TESTABLE




from AASHTO’s A Policy on Geometric Design of Highways and Streets 2004
                                             FYI – NOT TESTABLE


              Superelevation Runoff - WSDOT
Spring 2008
CEE 320




                                from the 2005 WSDOT Design Manual, M 22-01
                                                               FYI – NOT TESTABLE


              Spiral Curves


                                                             No Spiral




                                                             Spiral
Spring 2008
CEE 320




                       from AASHTO’s A Policy on Geometric Design of Highways and Streets 2004
                          FYI – NOT TESTABLE


              No Spiral
Spring 2008
CEE 320
                                                 FYI – NOT TESTABLE


              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
Spring 2008
CEE 320
                                                               FYI – NOT TESTABLE


              Desirable Spiral Lengths
Spring 2008
CEE 320




                       from AASHTO’s A Policy on Geometric Design of Highways and Streets 2004
                                                        FYI – NOT TESTABLE


              Operating vs. Design Speed

                                               85th Percentile Speed
                                               vs. Inferred Design Speed for
                                               138 Rural Two-Lane Highway
                                               Horizontal Curves




                       85th Percentile Speed
              vs. Inferred Design Speed for
                   Rural Two-Lane Highway
               Limited Sight Distance Crest
                             Vertical Curves
Spring 2008
CEE 320
              Primary References

              • Mannering, F.L.; Kilareski, W.P. and Washburn, S.S. (2005).
                Principles of Highway Engineering and Traffic Analysis, Third
                Edition. Chapter 3

              • American Association of State Highway and Transportation
                Officials (AASHTO). (2001). A Policy on Geometric Design of
                Highways and Streets, Fourth Edition. Washington, D.C.
Spring 2008
CEE 320

								
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