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OFFSHORE  LOCATION  BY TRIANGULATION
LAND SURVEYING - 14070_228

Engineering Aid 1 - Advanced Structural engineering guide book
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in each bent are 10 feet apart; bents are identified by letters;  and  piles,  by  numbers.  The  distance  between adjacent transit setups in the base line is 10/sin 84°, or 10.05 feet. Bents  are  located  20  feet  apart.  The  distance from  the  center-line  base  line  transit  setup  at  station 7 + 41.05 to pile No. 3 is 70 feet. The distance from station 7 + 51.10 to pile No. 2 is 70 + 10 tan 6°, or 70  +  1.05,  or  71.05  feet.  The  distance  from  station 7 + 61.15 to pile No. 1 is 71.05 + 1.05, or 72.10 feet. The distance from station 7 + 31.00 to pile No. 4 is 70 - 1.05, or 68.95 feet; and from station 7 + 20.95 to pile No. 5 is 68.95 – 1.05, or 67.90 feet. You can determine the angle you turn, at a control station,  from  the  base  line  to  any  pile  location  by triangle solution. Consider pile No. 61, for example. This pile is located 240 + 72.10, or 312.10 feet, from station 7 + 61.15 on the base line. Station 7 + 61.15 is located 1,038.83 – 761.15, or 277.68 feet, from control station 10 + 38.83. The angle between the line from station 7 + 61.15 through pile No. 61 and the base line measures 180°- 84°, or 96°. Therefore, you are dealing with the triangle  ABC shown in figure 10-31. You want to know the size of angle A. First solve for b by the law of cosines, in which  b2  = a2 + c2- 2ac cos B, as  follows: b2 =  312.102  +  277.682-  2(312.10)(277.68)  cos  96° b = 438.89 feet Knowing the length of b, you can now determine the size of angle  A by the law of sines. Sin  A = 312.10 sin 96°/438.89, or 0.70722. This means that angle  A measures, to the nearest minutes, 45°00´. Figure 10-31.—Trigonometric solution for pile No. 61. Figure 10-32.—Trigonometric solution for pile No. 65. To  determine  the  direction  of  this  pile  from control station 4 + 43.27, you would solve the triangle DBC shown in figure 10-31. You do this in the same manner as described above. First solve for  b using the law of cosines and then solve for angle  D using  the law of sines. After doing this, you find that angle  D equals  47°26´. It would probably be necessary to locate in this fashion only the two outside piles in each bent; the piles between these two could be located by measuring off  the  prescribed  spacing  on  a  tape  stretched  be- tween the two. For the direction from control station 10 + 38.83 to pile No. 65 (the other outside pile in bent M), you would solve the triangle shown in figure 10-32. Again, you solve for  b using  the  law  of  cosines and then use the law of sines to solve for angle  A. For each control station, a  pile location sheet like the one shown in figure 10-33 would be made up. If desired, the direction angles for the piles between No. 61 and No. 65 could be computed and inserted in the intervening  spaces. Figure 10-33.—File location sheet. 10-29







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