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Handout 10

The document describes elements of horizontal curves used in transportation design. It defines simple, compound, reverse, and spiral curves. Key elements of a simple curve are defined as the point of curvature (PC), point of tangency (PT), intersection angle, vertex, tangent distance, chord distance, external distance, and middle ordinate. Formulas are provided to calculate these elements based on the radius and intersection angle. Example problems demonstrate calculating values for simple curves given information like stationing, radii, and intersection angles.

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Daniel Cañones
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128 views1 page

Handout 10

The document describes elements of horizontal curves used in transportation design. It defines simple, compound, reverse, and spiral curves. Key elements of a simple curve are defined as the point of curvature (PC), point of tangency (PT), intersection angle, vertex, tangent distance, chord distance, external distance, and middle ordinate. Formulas are provided to calculate these elements based on the radius and intersection angle. Example problems demonstrate calculating values for simple curves given information like stationing, radii, and intersection angles.

Uploaded by

Daniel Cañones
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as PDF, TXT or read online on Scribd
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HORIZONTAL CURVE

1. Simple Curve
2. Compound Curve
3. Reverse Curve
4. Spiral Curve

ELEMENTS OF SIMPLE CURVE

• Simple Curve – a circular arc extending from one tangent to the next.
• Point of Curvature (PC) – point where the curve leaves the back tangent (first tangent).
• Point of Tangency (PT) – point where the curve joins the forward tangent (second tangent).
• Intersection Angle (I) – angle of intersection of tangents.
• Vertex or Point of Intersection (V or PI) – intersection of back tangent and forward tangent.
• Tangent Distance/Line (T) – distance from vertex to the PC or PT.
• Chord Distance (C) / Long Chord – Line connecting PC and PT.
• External Distance (E) – distance form the vertex to the curve.
• Middle Ordinate (M) – line joining the middle of the curve and the middle of the chord.

FORMULAS:

T = R tan (I/2)

C = 2R Sin(I/2)

M = R [1 – Cos (I/2)]

E = R [Sec (I/2) – 1]

D = 1145.916/R

L = RI (π/180°)

L = I (20/D)

Deflection Angle = Central Angle /2

ILLUSTRATIVE PROBLEMS:

1. A simple curve connects two tangents AB and BC with bearing N 84° E and S 65° E, respectively. If the
stationing of the vertex is 4+362 and the stationing of PC is 4+285, determine the following:
a.) Radius of the curve
b.) The external distance
c.) The middle ordinate
d.) Chord Distance
e.) The length of the curve

2. A simple curve has a central angle of 38 degrees and a degree of curve of 5 degrees. Find the following:
a.) The external distance
b.) The middle ordinate
c.) If the stationing of the PC is at 11+025, compute the stationing of a point on the curve which intersects with
the line making a deflection angle of 6 degrees with the tangent passing through the PC.

3. It is required to layout a simple curve by deflection angles. The curve is to connect two tangents with an
intersection angle of 32° and a radius of 240 m. If the transit is set up at the P.C. which is at station 5+767.2,
what is the stationing of the P.T.

4. A 5° curve intersects a property line CD, at point D. The back tangent intersects the property line at point C
which is 105.720 m from the PC which is at station 0+612.690. The angle that the property line CD makes with
the back tangent is 110°50’.
a) Determine the distance CD.
b) Determine the stationing at CD.

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