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- 2. CEE320 Winter2006 Esquema 1. Conceptos 2. Alineamiento Vertical a. Fundamentos b. CV Convexas c. CV Cóncavas d. Ejemplos 3. Alineamiento Horizontal a. Fundamentos b. Peralte 4. Otros
- 3. CEE320 Winter2006 Conceptos • El alineamiento en un problema en 3D representado en dos problemas 2D – Alineamiento Horizontal (planta) – Alineamiento Vertical (perfil) • Progresivas – A lo largo del alineamiento horizontal – 12+300 = 12300 m
- 7. CEE320 Winter2006 Alineamiento Vertical • Objetivo: – Determinar cotas para asegurar • drenaje • aceptable nivel de seguridad • Primer desafío – Transición entre dos pendientes – Curvas verticales G1 G2 G1 G2 CV Convexa CV Cóncava
- 8. CEE320 Winter2006 Fundamentos Curva Vertical • Función parabólica – Tasa constante de cambio de pendiente – Implica tangentes iguales (proyectadas sobre la horizontal) • y es la cota de rasante, x las progresivas desde el comienzo de la curva cbxaxy ++= 2
- 9. CEE320 Winter2006 Fundamentos Curva Vertical G1 G2 PVI PVT PVC L L/2 δ cbxaxy ++= 2 x Choose Either: • G1, G2 in decimal form, L in feet • G1, G2 in percent, L in stations
- 10. CEE320 Winter2006 Relaciones Choose Either: • G1, G2 in decimal form, L in feet • G1, G2 in percent, L in stations G1 G2 PVI PVT PVC L L/2 δ x 1and0:PVCAt the Gb dx dY x === cYx == and0:PVCAt the L GG a L GG a dx Yd 2 2:Anywhere 1212 2 2 − =⇒ − ==
- 11. CEE320 Winter2006 Otras Propiedades • El Valor-K defines la curvatura vertical – Es la longitud horizontal necesaria para un cambio de pendiente de 1%. En el sistema métrico la unidad es m/%. A L K = 1./ GKxptlowhigh =⇒
- 12. CEE320 Winter2006 Curvas Verticales Convexas G1 G2 PVI PVTPVC h2 h1 L SSD ( ) ( )2 21 2 22100 hh SSDA L + = ( ) ( ) A hh SSDL 2 21200 2 + −= DVD < L DVD > L Line of Sight
- 13. CEE320 Winter2006 Curvas Verticales Convexas • Suposiciones – h1 = altura ojo conductor ≈ 1.1 m – h2 = altura luz trasera ≈ 0.6 m • Ecuaciones Simplificadas ( ) 2158 2 SSDA L = ( ) A SSDL 2158 2 −= DVD < L DVD > L
- 14. CEE320 Winter2006 Controles Diseño Curva Vertical Convexa from AASHTO’s A Policy on Geometric Design of Highways and Streets 2001
- 15. CEE320 Winter2006 Controles Diseño Curva Vertical Convexa fromAASHTO’sAPolicyonGeometricDesignofHighwaysandStreets2001
- 16. CEE320 Winter2006 Curvas Verticales Cóncavas G1 G2 PVI PVTPVC h2=0h1 L Distancia Iluminación Faros (DVD) ( ) ( )βtan200 1 2 Sh SSDA L + = ( ) ( )( ) A SSDh SSDL βtan200 2 1 + −= DVD < L DVD > L Rayo luz faros (divergencia β grados)
- 17. CEE320 Winter2006 Curvas Verticales Cóncavas • Suposiciones – h1 = altura faros delanteros ≈ 0.6 m – β = 1 grado • Ecuaciones Simplificadas ( ) ( )SSD SSDA L 5.3400 2 + = ( ) ( ) + −= A SSD SSDL 5.3400 2 DVD < L DVD > L
- 18. CEE320 Winter2006 Controles Diseño Curvas Verticales Cóncavas from AASHTO’s A Policy on Geometric Design of Highways and Streets 2001
- 19. CEE320 Winter2006 Controles Diseño Curvas Verticales Cóncavas fromAASHTO’sAPolicyonGeometricDesignofHighwaysandStreets2001
- 21. CEE320 Winter2006 Alineamiento Horizontal • Objetivo: – Geometry of directional transition to ensure: • Safety • Comfort • Primary challenge – Transition between two directions – Horizontal curves • Fundamentals – Circular curves – Superelevation Δ
- 22. CEE320 Winter2006 Fundamentos de Curva Horizontal R T PC PT PI M E R Δ Δ/2Δ/2 Δ/2 RR D π π 000,18 180 100 = = 2 tan ∆ = RT D RL ∆ =∆= 100 180 π L
- 23. CEE320 Winter2006 Fundamentos de Curva Horizontal − ∆ = 1 2cos 1 RE ∆ −= 2 cos1RM R T PC PT PI M E R Δ Δ/2Δ/2 Δ/2 L
- 24. CEE320 Winter2006 Peralte cpfp FFW =+ αααα cossincossin 22 vv s gR WV gR WV WfW = ++ α α Fcp Fcn Wp Wn Ff Ff α Fc W 1 ft e ≈ Rv
- 25. CEE320 Winter2006 Peralte αααα cossincossin 22 vv s gR WV gR WV WfW = ++ ( )αα tan1tan 2 s v s f gR V f −=+ ( )ef gR V fe s v s −=+ 1 2 ( )efg V R s v + = 2
- 26. CEE320 Winter2006 Selección de e y fs • Límites prácticos de peralte (e) – Clima – Constructibilidad – Uso del suelo adyacente • Variaciones de Factor de fricción lateral (fs) – Velocidad vehículo – Textura pavimento – Condición neumático
- 27. CEE320 Winter2006 Factor Fricción Lateral from AASHTO’s A Policy on Geometric Design of Highways and Streets 2004
- 28. CEE320 Winter2006 Tablas de Radio Mínimo
- 29. CEE320 Winter2006 Factores Fricción Lateral WSDOT fromthe2005WSDOTDesignManual,M22-01 Para caminos y ramas
- 30. CEE320 Winter2006 Factores de Peralte WSDOT fromthe2005WSDOTDesignManual,M22-01 For Low-Speed Urban Managed Access Highways
- 31. CEE320 Winter2006 Peralte de Diseño - AASHTO from AASHTO’s A Policy on Geometric Design of Highways and Streets 2004
- 32. CEE320 Winter2006 Peralte de Diseño - WSDOT from the 2005 WSDOT Design Manual, M 22-01 emax = 8%
- 33. CEE320 Winter2006 Distancia Visual Detención Rv Δs Obstruction Ms( ) v s R SSD π 180 =∆ D RSSD s sv ∆ =∆= 100 180 π SSD −= v vs R SSD RM π 90 cos1 − = − v svv R MRR SSD 1 cos 90 π
- 34. CEE320 Winter2006 Suplementos • Sección transversal • Transición del peralte – Desarrollo – Tangente extendida • Curvas espirales • Sobreancho
- 36. CEE320 Winter2006 Transición Peralte from the 2001 Caltrans Highway Design Manual
- 37. CEE320 Winter2006 Transición Peralte from AASHTO’s A Policy on Geometric Design of Highways and Streets 2001
- 39. CEE320 Winter2006 Desarrollo Peralte - WSDOT from the 2005 WSDOT Design Manual, M 22-01
- 40. CEE320 Winter2006 Curvas Espirales Sin Espiral Espiral from AASHTO’s A Policy on Geometric Design of Highways and Streets 2001
- 42. CEE320 Winter2006 Curvas Espirales • WSDOT no usa curvas espirales • Involucra geometría compleja • Requiere más relevamiento • Son algo empíricas • Si se usan, la transición del peralte debe realizarse en toda la espiral PARA DISCUTIR
- 43. CEE320 Winter2006 Longitudes Espirales Deseables from AASHTO’s A Policy on Geometric Design of Highways and Streets 2001
- 44. CEE320 Winter2006 Velocidades de Operación y Directriz Velocidad 85º Percentil vs. Velocidad Directriz Inferida según 138 Curvas Horizontales de CR2C Velocidad 85º Percentil vs. Velocidad Directriz Inferida con DVD limitada por Curva Vertical Convexa
- 45. CEE320 Winter2006 Referencias • 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.
Notas del editor
- Therefore, roads will almost always be a bit longer than their stationing because of the vertical alignment Draw in stationing on each of these curves and explain it
- Typical set of road plans – one page only
- G is in percent, x is in feet G is in decimal, x is in stations
- Minimum lengths are about 100 to 300 ft. Another way to get min length is 3 x (design speed in mph)
- What can you do if you need a shorter sag vertical curve than calculated? Provide fixed-source street lighting Minimum lengths are about 100 to 300 ft. Another way to get min length is 3 x design speed in mph
- Trinity Road between Sonoma and Napa valleys
- D = degree of curvature (angle subtended by a 100’ arc)
- Divide both sides by Wcos(α) Assume fse is small and can be neglected – it is the normal component of centripetal acceleration
- The maximum side friction factor is the point at which the tires begin to skid Design values of fs are chosen somewhat below this maximum value so there is a margin of safety
- There is a different curve for each superelevation rate, this one is for 8%
- Basically it’s figuring out L and M from the normal equations
- Can also rotate about inside/outside axis
- Ease driver into the curve Think of how the steering wheel works, it’s a change from zero angle to the angle of the turn in a finite amount of time This can result in lane wander Often make lanes bigger in turns to accommodate for this
- I-90 past North Bend looking east
- According to NCHRP Report