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Fundamentos del alineamiento de autopistas
Norman W. GarrickLecture 11.1
Street and Highway Design
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Ejemplos de alineamientos
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Blue Ridge Parkway
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Trinity CollegePaseo inferior
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Storrs HeightsDiseño vernáculo
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Una entrada en Willington, CTProbable alineamiento de ingeniería
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Dónde utilizar diferentes tipos de alineaciónContexto urbanoGeneralmente no se aplica la alineación curvilíneaEn la alineación horizontal tangente contexto urbano son generalmente un mejor ajuste
Rural (mayor velocidad) contextoCurvilínea alineación son un buen ajuste. Herramientas de diseño geométrico son generalmente aplicables.
Contexto informalDiseño vernáculo se puede utilizar con buenos resultados.Diseño geométrico también puede estar de acuerdo pero con mucho cuidado para asegurarse de que la alineación ajustan estrechamente el terreno y que es recomendable viajar de baja velocidad.
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Diseño geométrico de carreterasLos aspectos de ingeniería de diseño de alineación generalmente se conoce como diseño geométrico
Alineación de carretera es en realidad un problema tridimensional
Diseño & construcción es difícil en 3D para diseño de carretera se trata normalmente como tres problemas 2-D: Alineación Horizontal, alineación vertical, transversal
Esto a menudo crean una situación disfuncional cuando el diseñador se olvida que las tres dimensiones deben trabajar juntos como una alineación - el Blue Ridge Parkway y la Trinidad inferior largo camino muestra cómo las tres dimensiones pueden ser coordinadas con buen efecto global
Storrs Heights y la entrada de Willington ilustran una alineación más naturalista
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Austin, TXDiscontinuous Alignment
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Near Cincinnati, OH
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Dónde utilizar diferentes tipos de alineación
Contexto urbanoGeneralmente no se aplica la alineación curvilíneaEn la alineación horizontal tangente contexto urbano son generalmente un mejor ajuste
Rural (mayor velocidad) contextoCurvilínea alineación son un buen ajuste. Herramientas de diseño geométrico son generalmente aplicables.
Contexto informalDiseño vernáculo se puede utilizar con buenos resultados.Diseño geométrico también puede estar de acuerdo pero con mucho cuidado para asegurarse de que la alineación ajustan estrechamente el terreno y que es recomendable viajar de baja velocidad.
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Componentes del alineamiento
Alineamiento horizontal
Alineamiento vertical
Sección transversal
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Alineación horizontal
Hoy nos centramos enComponentes del alineamiento horizontalPropiedades de una curva circular simplePropiedades de una curva espiral
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Alineamiento horizontal
Rectas Curvas
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Rectas & Curvas
Recta
Curva
Recta a Curva Circular
Recta a Curva Espiral a Curva Circular
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Diseño de Curva Horizontal SimpleR = Radius of Circular CurveBC = Beginning of Curve (or PC = Point of Curvature)EC = End of Curve (or PT = Point of Tangency)PI = Point of IntersectionT = Tangent Length
(T = PI – BC = EC - PI)L = Length of Curvature
(L = EC – BC)M = Middle OrdinateE = External DistanceC = Chord LengthΔ = Deflection Angle
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Properties of Circular CurvesGrado de Curvatura• Tradicionalmente, la “agudeza” de la curvatura se define por el radio (R) o
el grado de curvatura (D)• En diseño vial se usa la definición de ARC• Grado de curvatura = ángulo subtendido por un arco de 100 pies de
longitud, o de 100 m de longitud en el sistema métrico, con valores numéricos diferentes relacionados.
Definición según el diseño vial
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Grado de CurvaturaEcuación para D
Degree of curvature = angle subtended by an arc of length 100 feet
By simple ratio: D/360 = 100/2πR
Therefore
R = 5730 / D
(Degree of curvature is not used with metric units because D is defined in terms of feet.)
Sí se puede; FJS.
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Length of Curve
By simple ratio: D/ Δ = ?
D/ Δ = 100/L
L = 100 Δ / D
Therefore
L = 100 Δ / DOr (from R = 5730 / D, substitute for D = 5730/R)
L = Δ R / 57.30
(note: D is not Δ – the two are often confused )
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Properties of Circular Curves
Other Useful Formulas…
Tangent: T = R tan(Δ/2)
Chord: C = 2R sin(Δ/2)
Mid Ordinate: M = R – R cos(Δ/2)
External Distance: E = R sec(Δ/2) - R
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Spiral CurveA transition curve is sometimes used in horizontal alignment design
It is used to provide a gradual transition between tangent sections and circular curve sections. Different types of transition curve may be used but the most common is the Euler Spiral
Properties of Euler Spiral(reference: Surveying: Principles and Applications, Kavanagh and Bird, Prentice Hall]
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Sin Espiral
Con Espiral
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Degree of Curvature of a spiral at any point is proportional to its length at that point
The spiral curve is defined by ‘k’ the rate of increase in degree of curvature per station (100 ft)
In other words,
k = 100 D/ Ls
Características de la Espiral de Euler = Clotoide = Transición de Barnett
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As with circular curve the central angle is also important for spiralRecall for circular curve
Δc = Lc D / 100
But for spiral
Δs = Ls D / 200
Central (or Deflection) Angle of Euler Spiral
The total deflection angle for a spiral/circular curve system is
Δ = Δc + 2 Δs
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Length of Euler Spiral
Note: The total length of curve (circular plus spirals) is longer than the original circular curve by one spiral leg
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Example Calculation – Spiral and Circular Curve
The central angle for a curve is 24 degrees - the radius of the circular curve selected for the location is 1000 ft.
Determine the length of the curve (with no spiral)
L = 100 Δ / D or L = Δ R / 57.30 = 24*1000/57.30 = 418.8 ft
R = 5730 / D >> D = 5.73 degree
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Example Calculation – Spiral and Circular Curve
The central angle for a curve is 24 degrees - the radius of the circular curve selected for the location is 1000 ft
If a spiral with central angle of 4 degrees is to be used instead of the simple circular curve, determine the
i) length of each spiral leg, ii) k for the spiral, iii) total length of curve
Δs = 4 degrees
Δs = Ls D / 200 >> 4 = Ls * 5.73/200 >> Ls = 139.6 ft
k = 100 D/ Ls = 100 * 5.73/ 139.76 = 4.1 degree/100 feet
Total Length of curve = length with no spiral + Ls = 418.8+139.76 = 558.4 feet