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2. Solution

This chapter focuses on the geometry and calculations involved in setting out circular curves, tangent lengths, and vertical curves in civil engineering. It emphasizes various methods for calculating angles, lengths, and offsets, as well as practical examples illustrating these concepts. The chapter also covers the transition curves and compound curves critical in roadway design and alignment.

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Sections

  • 1

    Solution:

    Learning

  • 1.1

    Chainage Of Apex V

    This section details the calculations necessary for determining chainage and related measurements in road alignment, specifically focusing on the apex of a circular curve.

    Learning Practice

  • 1.2

    Deflection Angle D

    This section explains the concept of the deflection angle in road design, detailing how to calculate various key parameters such as tangent lengths, the length of curves, and chainages.

    Learning Practice

  • 1.3

    Radius R

    This section provides fundamental calculations related to circular curves in surveying, including the methods to determine the radius, lengths of tangents, and other crucial parameters.

    Learning Practice

  • 1.4

    Peg Interval

    This section discusses the calculation of peg intervals in survey measurements, particularly in relation to setting out circular curves.

    Learning Practice

  • 2

    Example 2.10:

    Learning

  • 2.1

    Tabulate The Data Needed

    Learning

  • 2.2

    Chainage Of Pi

    This section covers the calculations and methodologies used to determine the chainage of points of intersection (PI) in circular curves.

    Learning Practice

  • 3

    Example 2.11:

    This section provides a comprehensive approach to setting out a circular curve, including calculations of chainage, tangent lengths, and offsets.

    Learning Practice

  • 3.1

    Tabulate The Necessary Data

    Learning

  • 4

    Example 2.12:

    Learning

  • 4.1

    Two Tangents Intersect

    This section focuses on the calculations and principles related to the intersection of two tangents and the layout of circular curves.

    Learning Practice

  • 5

    Example 2.13:

    This section outlines the calculations necessary to set out a simple circular curve connecting two straights based on given parameters.

    Learning Practice

  • 5.1

    Two Straights Intersect

    This section covers the principles of calculating intersections between two straight lines and the design of curves connecting them.

    Learning Practice

  • 6

    Example 2.14:

    This section focuses on calculating key data for setting out a compound curve using specified parameters such as radius, deflection angle, and chainages.

    Learning Practice

  • 6.1

    A Right Hand Compound Curve

    This section details the calculations and methods for setting out right-hand compound curves in highway engineering.

    Learning Practice

  • 7

    Example 2.15:

    Learning

  • 7.1

    Two Straights Ac And Bc

    This section focuses on calculating parameters for setting up circular curves that connect two straight paths, emphasizing concepts like chainage, deflection angles, and tangential lengths.

    Learning Practice

  • 8

    Example 2.16:

    This section covers the calculation of chainages related to circular curves involving two intersecting straights.

    Learning Practice

  • 8.1

    Two Straights Ba And Ac

    This section covers the calculation of various parameters for connecting two straight lines using circular curves.

    Learning Practice

  • 9

    Example 2.17:

    Learning

  • 9.1

    Two Straights Ac And Cb

    This section delves into the calculations and processes involved in setting out circular curves between two straights, focusing on determining chainages, tangent lengths, and curve lengths.

    Learning Practice

  • 10

    Example 2.18:

    Learning

  • 10.1

    Two Parallel Railway Lines

    This section focuses on calculating parameters for setting circular curves between two parallel railway lines.

    Learning Practice

  • 11

    Example 2.19:

    Learning

  • 11.1

    Two Parallel Lines

    This section discusses the calculations involved in setting out circular curves connecting two parallel lines, emphasizing tangent lengths, chainages, and deflection angles.

    Learning Practice

  • 12

    Example 2.20:

    Learning

  • 12.1

    A Reverse Curve Acb

    This section covers the calculations and principles involved in setting out a reverse curve in road design, including tangent lengths, chainages, and curve lengths.

    Learning Practice

  • 13

    Example 2.21:

    Learning

  • 13.1

    A Reverse Curve

    This section discusses reverse curves in road and railway design, focusing on the calculations needed to set out curves accurately.

    Learning Practice

  • 14

    Example 2.22:

    This section covers the calculations necessary for setting out a transition curve with key parameters such as lengths and offsets.

    Learning Practice

  • 14.1

    A Transition Curve Of The Cubic Parabola Type

    This section covers the mathematical principles and applications of cubic parabola transition curves in road and railway construction, emphasizing their importance in managing changes in curvature.

    Learning Practice

  • 15

    Example 2.23:

    Learning

  • 15.1

    A Compound Curve Ab And Bc

    This section explains the principles of calculating and setting out compound curves in surveying, detailing examples and formulas for practical application.

    Learning Practice

  • 16

    Example 2.24:

    Learning

  • 16.1

    Length Of Vertical Curve

    This section explores the calculations and methodologies involved in determining the length of vertical curves, crucial for effective road design.

    Learning Practice

  • 17

    Example 2.25:

    Learning

  • 17.1

    Length Of Vertical Curve

    This section delves into the calculations and concepts essential for determining the length of vertical curves in roadway design.

    Learning Practice

  • 18

    Example 2.26:

    This section provides calculations for the reduced levels (RL) of various stations on a vertical curve connecting two grades, detailing the necessary formulas, the chainage of relevant points, and the derived elevations.

    Learning Practice

  • 18.1

    Calculate The Rl Of Various Stations

    This section outlines the methodology for calculating the Reduced Level (RL) at various stations by employing geometric principles involved in road design and surveying.

    Learning Practice

  • 19

    Example 2.27:

    Learning

  • 19.1

    A 1% Grade Meets A +2.0% Grade

    This section covers the calculations and methodology involved in designing curves in highway engineering, focusing on vertical and horizontal alignment transitioning between different gradients.

    Learning Practice

  • 20

    Example 2.28:

    Learning

  • 20.1

    Two Straights Ab And Bc

    This section discusses the calculation and setting out of circular curves connecting two straight lines, with practical examples illustrating the concepts.

    Learning Practice

References

2d.pdf

Class Notes

Memorization

What we have learnt

  • Understanding the geometric...
  • The calculations necessary ...
  • How to execute practical ex...

Final Test

Revision Tests