ADJUSTING A CHAIN OF QUADRILATERALS

ADJUSTING A CHAIN OF QUADRILATERALS - CONTINUED

Engineering Aid 1 - Advanced Structural engineering guide book
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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

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