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Circular Curves Homework Help

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Circular Curves

Circular curves are used to join intersecting straight lines. Circular curves are assumed to be concave. An angle point is called the point of intersection or PI station and change in alignment is defined by a deflection angle, Δ.

Types of circular curves

The types of circular curves are, simple curve, compound curve, Broken back curves, and reverse curves.

Circular curves in civil engineering

The most common type of horizontal curve used to connect the intersecting tangents sections of highways or railroads is circular curves. Normally two methods of defining circular curves are used in most countries. First, it is generally used in rail road works. It defines the degree of curves as the central angle subtended by the chord of 100 ft (30.48m) in length. Secondly, it is used in the highways work. It defines the degree of curve as the central angle subtended by an arc of 100 ft (30.48m) in length.

  • Pc = point of curvature, beginning of curve.
  • PI= point of intersection of tangents.
  • PT = point of tangency, end of curve.
  • R = radius of curve, ft (m)
  • D = degree of curve
  • I = deflection angle between tangents at PI, also central angle of curve.
  • T = tangent distance, distance from PI to PC or PT, ft(m)
  • L = length of curve from PC to PT measured on 100ft (30.48m) chord for chord definition, on arc for arc definition, ft(m).
  • C = length of long chord from the PC to PT, ft (m).
  • E = external distance, distance from PI to midpoint of the curve.

Radius of circular curve

The distance from the centre of the curve to any point on the circular curve is called radius of the curve.

Direction of the circular curve

The direction of the circular curves is defined as the direction the curve tends, as stationing along the curve increases. The direction of circular curve can be expressed as left, right, north, east, south, west, free text.

The central angle of a circular curve

The angle at the centre of radius of a circular arc included between the radii, passing through the beginning and ending of the arc is called the central angle of a circular curve.

Long chord length

The straight line distances that connecting the beginning of the curve and the end of the curve is called the long chord length.

Degree of curvature

The degree of curvature is defined as the angle subtended by an arc, whose length is 100ft.


  • What is circular curve?
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