• Home
  • Download PDF
  • Order CD-ROM
  • Order in Print
Computations - 14070_368
ADJUSTING A CHAIN OF QUADRILATERALS - CONTINUED

Engineering Aid 1 - Advanced Structural engineering guide book
Page Navigation
  342    343    344    345    346  347  348    349    350    351    352  
Table  15-7.—Figure  Adjustment  for  Chain  of  Triangles,  Figure  15-27 measured angles around each station, determine the extent to which it differs from 360°, and distribute this difference over the angles around the station according to the number of angles. Figure 15-27 shows a chain of triangles. Station adjustment for this chain of triangles is given in table 15-6. At station A, as you can see, the sum of the observed interior angles 3, 5, and 8 plus the observed exterior closing  angle  12  comes  to  360°00´25´´.  This  differs from  360°  by  25  seconds.  The  number  of  angles around the station is four; therefore, the correction for each angle is one fourth of 25, or 6 seconds, with 1 second left over. The sum of the observed angles is in excess  of  360°;  therefore,  6  seconds  was  subtracted from the observed value of each interior angle and 7 seconds from the observed value of the exterior angle. The angles around the other stations were similarly adjusted,  as  shown. The next step is the figure adjustment for each of the triangles in the chain. For a triangle, the sum of the interior angles is 180°. The figure adjustment for each of the three triangles illustrated in figure 15-27 is shown in  table  15-7. As  you  can  see,  the  sum  of  the  three  adjusted observed  interior  angles  in  triangle  ABC (angles 1, 2, and 3) comes to 179°59´40´´.  This is 20 seconds less than 180°,  or  20/3,  or  6  seconds  for  each  angle,  with 2 seconds left over. Therefore, 6 seconds was added to the station adjusted value of angle 1, and 7 seconds each was added to the measured values of angles 2 and  3.  The  angles  in  the  other  two  triangles  were similarly  adjusted. ADJUSTING   A   CHAIN   OF   QUADRI- LATERALS.—  The station adjustment for a chain of quadrilaterals is the same as that for a chain of triangles. The next step is a figure adjustment like that for a chain of triangles, except that the sum of the interior angles of a quadrilateral is (4 - 2) 180°, or 360°. Next,  for  a  quadrilateral,  comes  another  figure adjustment, based on the four overlapping triangles within the quadrilateral. To understand this figure adjustment, study the quadrilateral shown in figure 15-28. The diagonals in this quadrilateral intersect to Figure 15-28.—Quadrilateral. 15-35







Western Governors University

Privacy Statement
Press Release
Contact

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