Name: calculating elevations on a vertical curve
Uploaded: 2025-03-26T15:36:53.000Z
Duration: 1 min 23 s
Channel: JoVE

A vertical curve connects two grade lines, ensuring a smooth highway transition. The curve length, grades, P.V.I. location, and P.V.I. elevation are provided to calculate the curve&#8217;s elevations at specified stations.&#160;The P.V.C. and P.V.T.&#160;stations, marking the start and end of the curve, are calculated by subtracting and adding half the curve length to the P.V.I. station.Using the given grades, P.V.I. elevation, and half the curve length, the elevations at P.V.C. and P.V.T. are determined.For each station, the grade line elevation is computed by combining the grade and the horizontal distance from the P.V.C. or P.V.T.Next, the midpoint elevation of the long chord and the curve's midpoint elevation are determined to calculate the offset at P.V.I.This offset and the horizontal distance from the P.V.C. or P.V.T. are used to calculate tangent offsets for each station based on the curve length.Finally, the curve elevations at the stations are obtained by subtracting the tangent offsets from the grade line elevations.The computed elevations represent the vertical profile of the curve.

curva vertical: resolución de problemas

Las curvas verticales proporcionan la transici&#243;n entre dos pendientes de la calzada, lo que garantiza la seguridad, la comodidad y la funcionalidad. El c&#225;lculo de las elevaciones en estaciones definidas a lo largo de la curva implica varios pasos sistem&#225;ticos basados &#8203;&#8203;en la geometr&#237;a de la curva y los par&#225;metros de dise&#241;o proporcionados.
La curva vertical se define por su longitud, pendientes, ubicaci&#243;n del punto de intersecci&#243;n vertical (P.V.I.) y elevaci&#243;n del P.V.I. Las estaciones del punto de curvatura vertical (P.V.C.), donde comienza la curva, y el punto de tangencia vertical (P.V.T.), donde termina la curva, se determinan restando y sumando la mitad de la longitud de la curva a la estaci&#243;n del P.V.I. Las elevaciones en el P.V.C. y el P.V.T. se calculan utilizando las pendientes y la elevaci&#243;n del P.V.I.
La elevaci&#243;n de la l&#237;nea de pendiente se calcula para cada estaci&#243;n a lo largo de la curva utilizando la pendiente en el P.V.C. o el P.V.T. y la distancia horizontal a la estaci&#243;n. Este c&#225;lculo proporciona el perfil de elevaci&#243;n lineal antes de tener en cuenta la forma parab&#243;lica de la curva. La elevaci&#243;n en el punto medio de la cuerda larga y el punto medio de la curva se determinan para calcular el desplazamiento en el P.V.I. Este desplazamiento, derivado de la geometr&#237;a parab&#243;lica de la curva, representa la distancia vertical entre la l&#237;nea de nivel y la curva en el P.V.I.
Usando el desplazamiento del P.V.I. y la distancia horizontal desde el P.V.C. o P.V.T., se calculan los desplazamientos tangentes para cada estaci&#243;n. Estos desplazamientos reflejan la desviaci&#243;n de la l&#237;nea de nivel causada por la curvatura de la calzada. La elevaci&#243;n de la curva en cada estaci&#243;n se obtiene luego restando el desplazamiento tangente de la elevaci&#243;n de la l&#237;nea de nivel. Las elevaciones calculadas en estaciones definidas forman el perfil vertical de la curva, que es fundamental para dise&#241;ar transiciones suaves, garantizar un drenaje adecuado y mantener los est&#225;ndares de seguridad. Estos c&#225;lculos permiten a los ingenieros crear carreteras que equilibran la funcionalidad con la comodidad del conductor.

Curva vertical: resolución de problemas

Vertical curves provide the transition between two roadway grades, ensuring safety, comfort, and functionality. Calculating elevations at specific ...

Education

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JoVE Core

Civil Engineering

Ingeniería Civil

Unit 1

Unidad 1

Horizontal and Vertical Curves

Curvas horizontales y verticales

KEY TERMS AND CONCEPTS

TÉRMINOS Y CONCEPTOS CLAVE

Vertical Curve: Problem Solving

calculating elevations on a vertical curve

Vertical curves connect two roadway grades and help make the road safer, smoother, and more functional. To find the elevation at specific stations on the curve, engineers follow a set of steps based on the curve length, the grades, the Point of Vertical Intersection, or P.V.I., and the P.V.I. elevation.

The first step is to locate the Point of Vertical Curvature, or P.V.C., and the Point of Vertical Tangency, or P.V.T. The P.V.C. marks the start of the curve, and the P.V.T. marks the end. Their stations are found by subtracting and adding half the curve length from the P.V.I. station. The elevations at the P.V.C. and P.V.T. are then calculated from the grades and the P.V.I. elevation.

Next, the grade line elevation is found at each station along the curve. This uses the grade at the P.V.C. or P.V.T. and the horizontal distance to the station. The result gives the straight-line elevation profile before the parabolic curve shape is applied. Engineers then find the elevation at the midpoint of the long chord and the curve’s midpoint to determine the offset at the P.V.I.

That offset comes from the curve’s parabolic geometry. It is the vertical distance between the grade line and the actual curve at the P.V.I. Using the P.V.I. offset and the horizontal distance from the P.V.C. or P.V.T., tangent offsets are calculated for each station. These offsets show how far the roadway curve deviates from the grade line.

The final curve elevation at each station is found by subtracting the tangent offset from the grade line elevation. These station elevations form the vertical profile of the roadway. They are important for smooth transitions, proper drainage, and safety, while also helping the road remain comfortable for drivers.

Calculating Elevations on a Vertical Curve

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introduction to horizontal curves

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horizontal curve: problem solving

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introduction to vertical curves

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vertical curve: problem solving

Vertical curves connect two roadway grades and help make the road safer, smoother, and more functional. To find the elevation at specific stations on the curve, engineers follow a set of steps based on the curve length, the grades, the Point of Vertical Intersection, or P.V.I., and the P.V.I. elevation. The first step is to locate the Point of Vertical Curvature, or P.V.C., and the Point of Vertical Tangency, or P.V.T. The P.V.C. marks the start of the curve, and the P.V.T. marks the end.

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key terms and concepts

Learn how to calculate elevations on a vertical curve using P.V.C., P.V.T., P.V.I., grade line elevation, and tangent offsets in roadway design.

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JoVE Core Civil Engineering provides a foundational exploration of essential construction materials in civil engineering, focusing on bricks, stones, steel, wood, and concrete through easy-to-understand animated videos. This collection covers the properties, manufacturing processes, and practical applications of these materials. Additionally, the accompanied science-in-action videos demonstrate the research experiments performed in laboratories.

civil engineering

Calculating Elevations on a Vertical Curve

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