• Home
  • Download PDF
  • Order CD-ROM
  • Order in Print
TRIANGULATION - 14070_358
Chain of Quadrilaterals - 14070_360

Engineering Aid 1 - Advanced Structural engineering guide book
Page Navigation
  332    333    334    335    336  337  338    339    340    341    342  
Figure 15-15.-Chain of single triangles. high-order triangulation network to establish control across the United States. TYPES OF TRIANGULATION NETWORKS In  triangulation  there  are  three  types  of  triangulation networks  (or  nets).  They  are  the  chain  of  single triangles, chain of polygons, and chain of quadri- laterals. Chain of Single Triangles The simplest triangulation system is the chain of single  triangles  shown  in  figure  15-15.  Suppose  AB is the  base  line  and  measures  780.00  feet  in  length. Suppose, also, that angle A (that is, the observed angle BAC)  measures 98°54´ and that angle  ABC measures 32°42´. (In actual practice you will use more precise values than these; we are using rough values to simplify the  explanation.)  Subtracting  the  sum  of  these  two angles from 180°, we get 48°24´ for angle  ACB. Next, solve for sides BC and AC by using the law of  sines  as  follows: Now that you know how to find the length of BC, you can proceed in the same manner to determine the lengths of  BD and CD. Knowing the length of  CD, you can proceed in the same manner to determine the lengths of CE and DE, knowing  the  length  of  DE, you  can determine the lengths of DF and EF, and so on. You should use this method only when locating inaccessible points, not when a side of the triangle is to be used to extend  control. In comparison with the other systems about to be described,   the   chain   of   single   triangles   has   two disadvantages. In the first place, it can be used to cover only a relatively narrow area. In the second place, it provides  no  means  for  cross-checking  computed distances using computations made by a different route. In figure 15-15, for example, the only way to compute the length of BC is by solving the triangle ABC, the only way to compute the length of  CD is  by  solving  the triangle  BCD  (using  the  length  of  BC  previously computed);  and  so  on.  In  the  systems  about  to  be described, a distance maybe computed by solving more than one series of triangles. Chain  of  Polygons Technically  speaking,  of  course,  a  triangle  is  a polygon; and therefore a chain of single triangles could be called a chain of polygons. However, in reference to triangulation figures, the term chain of polygons refers to a system in which a number of adjacent triangles are combined  to  forma  polygon,  as  shown  in  figure  15-16. Within each polygon the common vertex of the triangles that compose it is an observed  triangulation station (which is not the case in the chain of quadrilaterals described  later). You can see how the length of any line shown can be computed by two different routes. Assume that  AB is the base line, and you wish to determine the length of line  EF.  You  can  compute  this  length  by  solving Figure 15-16.—Chain of polygons. 15-25







Western Governors University

Privacy Statement
Press Release
Contact

© Copyright Integrated Publishing, Inc.. All Rights Reserved. Design by Strategico.