# COMPARATIVE STUDY OF STRENGTH OF FIGURE OF FOUR BRACED QUADRILATERAL USING A MINOR TRIANGULATION SCHEME, A RESEARCH PROJECT TOPIC ON QUANTITY SURVEYING

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#### COMPARATIVE STUDY OF STRENGTH OF FIGURE OF FOUR BRACED QUADRILATERAL USING A MINOR TRIANGULATION SCHEME, A RESEARCH PROJECT TOPIC ON QUANTITY SURVEYING

CHAPTER ONE

1.0 INTRODUCTION

1.1 Background of study

Triangulation is one of the methods of fixing accurate controls on the earth surface. It is based on the trigonometric proposition that if one side and two angles of a triangle are known, the remaining sides can be computed. A triangulation system consists of a series of overlapping triangles in which an occasional side called a baseline is measured and remaining sides are calculated from the angles measured at the vertices of the triangles, vertices being the control points are called triangulation stations (Chandra, 2012).

When all sides of a triangulation are measured it is known as the triliteration system.

However, the angular measurement define the shape of the triangulation system better than wholly linear measurements and so it is preferred that a number of angles are included in trilateration system.

A combined triangulation and trilateration system in which all the angles and all the sides are measured, represents the strongest network for creating horizontal control and   it is called triangulation.

Because, at one time, it was easier to measure angles than it was for distance, triangulation was the preferred method of establishing the position of control points.

Many countries used triangulation as the basis of their national mapping system. The procedure was generally to establish primary triangulation networks, with triangles having sides ranging from 30 to 50 km in length. The primary trigonometric points were fixed at the corners of these triangles and the sum of the measured angles was correct to ± 3″. These points were usually established on the tops of mountains to afford long, uninterrupted sight lines.

The process of measuring the angles of a chain network of triangles of the earth is called triangulation. (Agor, 2010).

1.1.1 Objective of triangulation surveys

The main objective of any triangulation or trilateration surveys is to provide a number of stations whose relative and absolute positions, horizontal as well as vertical, are accurately established. More detailed location or engineering survey is then carried out from these stations.

The triangulation surveys therefore are carried out for the following reasons:

(i)     To create accurate control for plane and geodetic surveys of large areas, by terrestrial methods,

(ii)    To establish precise control for photogrammetric surveys of large areas,

(iii)    To support in the determination of the size and shape of the earth by making observations for latitude, longitude and gravity, and

(iv) To determine accurate locations of points in engineering works such as:

(a) Fitting centre line and abutments of long bridges over large rivers.

(b) Fitting centre line, terminal points, and shafts for extended tunnels.

(c) Transferring the control points across wide sea channels, large water bodies, etc.

(d) Detection of crustal activities, etc.

(e) Finding the direction of the movement of clouds.

1.1.2 Strength of Figures

The strength of figure is a thing to be considered in establishing a triangulation system to maintain the computations within a desired degree of precision. It plays also an important role in deciding the layout of triangulation system. The strength of figure is a function of:

Angles change more rapidly than those of large angles. This suggests that smaller angles less than 30° should not be used in the computation of triangulation. If, due to unavoidable circumstances, angles less than 30° are used, then it must be ensured that this is not opposite the side whose length is required to be computed for carrying forward the triangulation series.

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