Name: setting out a horizontal curve
Uploaded: 2025-03-26T15:36:39.000Z
Duration: 1 min 3 s
Channel: JoVE

A horizontal curve has a radius of 400 meters, and the angle of intersection is 30 degrees, the station of point of curvature is 0 + 150 meters.The objective is to determine the stations of the point of intersection, point of tangency, and midpoint of the curve, as well as to calculate the length of the long chord.To identify the stations, the tangent distance and length of the curve are first calculated using the radius, and intersection angle of the curve.The station of the point of intersection is given by adding the length of the tangent to the station at the point of curvature.The station of the point of tangency is calculated by adding the length of the curve to the station at the point of curvature.Lastly, the station of the midpoint is found by adding half the curve's length to the station of the point of curvature.&#160;Then, the length of the long chord is obtained by the corresponding expression.

curva orizzontale: risoluzione di problemi

Una curva orizzontale &#232; caratterizzata da un suo raggio, da un 'angolo di intersezione e da una progressiva dei punti chiave. In questo caso, il raggio &#232; di 400 metri e l'angolo di intersezione &#232; di 30 gradi, con la progressiva del punto di curvatura (P.C.) a 0 + 150 metri. L'obiettivo &#232; determinare i valori della progressiva nel punto di intersezione (P.I.), nel punto di tangenza (P.T.) e nel punto medio della curva, nonch&#233; la lunghezza della corda lunga.
Il processo inizia con il calcolo della distanza della tangente (T) e della lunghezza della curva (L). La distanza della tangente dipende dal raggio e dalla tangente di met&#224; dell'angolo di intersezione. La lunghezza della curva dipende dal raggio e dall'angolo di intersezione convertiti in radianti.
La progressiva del P.I. si calcola sommando la distanza tangente alla progressiva di P.C. mentre la progressiva di P.T. si determina sommando la lunghezza della curva alla progressiva di P.C. La progressiva del punto medio della curva viene calcolata aggiungendo met&#224; della lunghezza della curva alla progressiva di P.C.
La lunghezza della corda lunga, che attraversa la curva tra P.C. e P.T., viene ricavata utilizzando relazioni trigonometriche che coinvolgono il raggio e l'angolo di intersezione. Questi calcoli assicurano una progressiva precisa e l'integrit&#224; del progetto nella definizione di semplici curve orizzontali.

Curva Orizzontale: Risoluzione di Problemi

A horizontal curve is characterized by its radius, intersection angle, and stationing of key points. In this case, the radius is 400 meters, and the angle ...

Education

Didattica

JoVE Core

Civil Engineering

Ingegneria Civile

Unit 1

Unità 1

Horizontal and Vertical Curves

Curve orizzontali e verticali

KEY TERMS AND CONCEPTS

TERMINI E CONCETTI CHIAVE

Horizontal Curve: Problem Solving

setting out a horizontal curve

A horizontal curve is set out by using its radius, intersection angle, and stationing of key points. In this example, the radius is 400 meters, the intersection angle is 30 degrees, and the station of the point of curvature, or P.C., is 0 + 150 meters. The goal is to find the station values for the point of intersection, or P.I., the point of tangency, or P.T., and the midpoint of the curve. The length of the long chord is also needed.

The first step is to calculate the tangent distance, T, and the curve length, L. Tangent distance depends on the radius and the tangent of half the intersection angle. Curve length depends on the radius and the intersection angle written in radians. These values are used to place the curve correctly in station form.

Next, the station of the P.I. is found by adding the tangent distance to the station of the P.C. The station of the P.T. is found by adding the curve length to the station of the P.C. The station of the midpoint of the curve is the P.C. station plus half of the curve length. The long chord, which stretches directly from the P.C. to the P.T., is found with trigonometric relationships that use the radius and the intersection angle. These calculations support accurate design and setting out of simple horizontal curves.

Setting Out a Horizontal Curve

introduction to horizontal curves

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degree of curvature and radius of curvature

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Curvature Measures in Civil Engineering Curves

Degree of curvature and radius of curvature help describe how sharply a curve bends in civil engineering. The degree of curvature measures the steepness of the bend. The radius of curvature shows how tight or smooth the curve is. The degree of curvature can be found by the chord basis or the arc basis. In the chord basis method, the degree is the central angle subtended by a chord of 30.48 meters. In the arc basis method, it is the central angle subtended by an arc of length 30.48 meters. <br...

curve equations

Curve Measurements and Arc Length

Curve measurements describe the key parts of a curved line. The main values are tangent distance, chord length, middle ordinate, and total arc length. These measurements help explain a curve’s shape and size using its radius and central angle. Tangent distance, or T, is the straight-line distance from the point where two tangents meet to the start or end of the curve. It depends on the curve radius, R, and the central angle, I. These two values work together to set the curve’s layout. Chord...

horizontal curve: problem solving

A horizontal curve is set out by using its radius, intersection angle, and stationing of key points. In this example, the radius is 400 meters, the intersection angle is 30 degrees, and the station of the point of curvature, or P.C., is 0 + 150 meters. The goal is to find the station values for the point of intersection, or P.I., the point of tangency, or P.T., and the midpoint of the curve. The length of the long chord is also needed. The first step is to calculate the tangent distance, T,...

field procedure for staking out curves

Surveying Curve Layout with Deflection Angles

Surveying curve layout with deflection angles turns a designed curve into stakes placed in the field. In construction, this step helps keep structures aligned along a curved path. Surveyors use calculated positions so the physical markers match the plan. The process starts by finding the curve’s geometric values. These include the radius, central angle, and tangent distances. Surveyors also identify the Point of Curvature (PC), the Point of Tangency (PT), and the midpoint of the curve. These...

introduction to vertical curves

Designing Smooth Road Grade Transitions

Vertical curves are parabolic transitions that connect different grades on highways and railroads. They help create a smooth alignment between the back tangent and the forward tangent. The back tangent is the first grade, and the forward tangent is the next grade. These curves may be symmetrical or nonsymmetrical. In a symmetrical vertical curve, the tangent lengths are equal. In a nonsymmetrical curve, the tangent lengths are different. The main points used to describe the curve are the Point...

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.

elevation of intermediate points on vertical curves

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Finding High and Low Points on Vertical Curves

Vertical curves help roadways move smoothly from one grade to another. Engineers use them to connect changing slopes and keep the road profile safe and even. To design these curves, they calculate intermediate elevations and find the highest or lowest point on the curve. Intermediate elevations on a vertical curve are found with the tangent offset method. This method uses the starting elevation, the grades at each end, and the curve shape. It gives the elevation of any point along the curve by...

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design example: setting a curve using design data

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Plotting a Horizontal Curve from Field Data

Plotting a horizontal curve from field data starts with careful geometric design. The curve in this example has a radius of 200 meters and an intersection angle of 20 degrees. Engineers use the method of perpendicular offsets from the long chord to place the curve on the ground. The long chord is the straight line between the two ends of the curve. Here, its length is calculated as 69.46 meters. To improve accuracy, 3-meter intervals are marked along the chord. Offset distances at each point...

key terms and concepts

Find the P.I., P.T., midpoint, and long chord for a horizontal curve using radius, intersection angle, and stationing from the point of curvature.

Setting Out a Horizontal Curve | JoVE K12

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civil engineering

Setting Out a Horizontal Curve

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