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2. Linear methods of setting out curves

The chapter discusses methods for setting out simple circular curves, including linear methods like ordinates from the long chord, successive bisections of arcs, offsets from tangents, and chords produced. It also covers angular methods like Rankine's method of tangential angles and the two theodolite method. Additionally, compound and reverse curves, their elements, and procedures for setting them out, alongside transition curves and the concept of super-elevation, are explored.

Sections

Linear methods of setting out curves

This section covers the linear methods used to set out simple circular curves in construction, focusing on four key techniques.

1 Section Overview

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1.1 By ordinates from the long chord

This section describes the method of setting out curves by ordinates from the long chord, emphasizing the calculations and steps involved.

1.2 By successive bisections of arcs

This section discusses the linear methods of setting out circular curves, particularly the method of successive bisections of arcs.

1.3 By offsets from the tangents

This section discusses methods for setting out circular curves using offset measurements from tangents.

1.3.1 By radial offsets

This section explains linear methods of setting out simple circular curves using radial offsets, focusing on calculations and procedures.

1.3.2 By offsets perpendicular to the tangents

This section discusses the method of setting out curves using offsets that are perpendicular to the tangents, explaining both exact and approximate approaches.

1.4 By offsets from chords produced

This section details the method of setting out curves using offsets from chords produced, highlighting the steps, formulas, and significance in practical applications.

Angular methods of setting out curves

Angular methods provide techniques for setting out circular curves using instruments and calculating angular measurements.

2 Section Overview

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2.1 Rankine’s method of tangential angles

Rankine's method of tangential angles involves setting out curves using tangential or deflection angles calculated through theodolite measurements.

2.2 Two theodolites method

The Two Theodolites Method is an angular method used in civil engineering for setting out curves where distance measurement by tape is difficult.

Compound Curves

This section introduces compound curves, which consist of two circular arcs of different radii that are tangential to three straight lines.

2.4 Section Overview

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2.4.1 Elements of a compound curve

This section explores the key elements and characteristics of compound curves in geometry, emphasizing their structure and calculation methods.

2.4.2 Setting out the compound curve

This section discusses how to set out compound curves using various methods, including deflection angles and chainages.

Reverse Curves

This section discusses reverse curves, including their definition, applications, and the challenges they present in road and railway design.

2.5 Section Overview

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2.5.1 Elements of a reverse curve

This section details the key elements and calculations involved in designing reverse curves, including definitions and geometric relationships pertinent to their construction.

Transition Curves

Transition curves are non-circular curves designed to provide a smooth change from straight to curved path, essential for vehicle comfort and safety.

2.6 Section Overview

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2.6.1 Super-elevation or Cant

Super-elevation, or cant, refers to the elevation of the outer edge of a curve in road construction to counteract centrifugal force acting on vehicles.

Learning Objectives

  • Various linear and angular methods exist for setting out curves.

  • Compound curves involve two circular arcs with different radii meeting at a common point.

  • Super-elevation is necessary to counteract centrifugal forces acting on vehicles in curves.

Key Concepts

Linear Methods

Methods for setting out curves that use linear measurements such as chains or tapes.

Angular Methods

Techniques for setting out curves that involve the use of angles measured with a theodolite.

Compound Curve

A curve made up of two circular arcs with different radii that meet at a common point.

Super-elevation

The raising of the outer edge of a road curve to counteract centrifugal force on vehicles.

Practice Exercises

Total Questions

2

Estimated Time

4 min

Passing Score

70%

Instructions

  • Read each question carefully
  • You can use hints if you need help
  • Complete all questions before submitting

1 more question available

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