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Figure  14-13.-Differersthd  leveling.
Reciprocal  Leveling

Engineering Aid 3 - Beginning Structural engineering guide book
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TBM  16.  The  BS  reading  of  +6.659  is  added  to the  elevation  of  BM  35  and  gives  the  resulting  HI (139.822). The rod is moved to Peg 16 (which later becomes  TBM  16).  The  FS  reading  of  –4.971  is subtracted from the HI to get the elevation of Peg 16. Note that the distance (220 ft each way) is also recorded  for  balancing.  The  process  continues until BM 19 is reached. LEVEL  COMPUTATIONS.—  ln making level computations, you should be sure to check on the notes  for  a  level  run  by  verifying  the  beginning BM;  that  is,  by  determining  that  you  used  the correct BM and recorded its correct elevation, as required. Then,  you  should  check  on  the  arithmetical accuracy with which you added BSs and subtracted FSs. The difference between the sum of the BSs taken  on  BMs  or  TPs  and  the  sum  of  the  FSs taken on BMs or TPs should equal the difference in  elevation  between  the  initial  BM  or  TP  and  the final  BM  or  TP. Balanced BS and FS distances are shown in figure   14-14.   The   distance   used   for   the   first instrument  setup  was  220  ft.  The  first  BS  (rod reading on  El 35) was 6,659 ft. The first FS (rod reading on 0 16) was 4.971. Notice that the plus sign (+) appears at the top of the BS column and that the minus sign (–) appears at the top of the FS column in the field notebook. This helps you to  remember  that  BSs  are  added  and  FSs  are subtracted  as  you  compute  the  new  elevations. The BS taken on a point added to the elevation of  the  point  gives  the  HI.  This  establishes  the elevation  of  the  line  of  sight  so  that  an  FS  can then  be  taken  on  any  point  (BM,  TBM,  or  TP). The level line is extended as far as desired with as many instrument setups as may be necessary by  a  repetition  of  the  process  used  in  the  first setup. The elevation of  El 35 is 133.163 ft. The first HI is 133.163  +  6,659  =  139.822  ft. The  FS  subtracted  from  the  HI, 139.822  –  4.971  =  134.851  ft, gives the elevation of 0, the first established. Following  through  with  a  similar  computation  for each setup, notice that the elevation of El 19 was found  to  be  136.457  ft. Look  now  at  the  notes  in  figure  14-14.  The sum  of  all  the  BSs  is  24.620  ft.  The  sum  of  all the FSs is 21.326 ft. The difference between the sum  of  the  BSs  and  the  sum  of  the  FSs  is 24.620  –  21.326  =  3.294  ft. This difference should agree with the difference between  the  actual  elevation  of  BM  35  and  the elevation  already  found  for  BM  19;  that  is, 136.457  –  133.163  =  3.294  ft. This  provides  a  check  on  the  step-by-step computation   of   elevations. ADJUSTMENT OF INTERMEDIATE BENCH MARK ELEVATIONS.—  Level lines that begin and  end  on  points  that  have  fixed  elevations,  such as  BMs,  are  often  called  level  circuits.  When leveling is accomplished between two previously established BMs or over a loop that closes back on  the  starting  point,  the  elevation  determined  for the final BM will seldom be equal to its previously established   elevation.   The   difference   between these two elevations for the same BM is known as  the  ERROR  OF  CLOSURE.  The  Remarks column of figure 14-14 indicates that the actual elevation of BM 19 is known to be 136.442 ft. The elevation found through differential leveling was 136.457   ft.   The   error   of   closure   of   the   level circuit is 136.457  –  136.442  =  0.015  ft. It  is  assumed  that  errors  have  occurred progressively along the line over which the leveling was done so that adjustments for these errors are distributed  proportionally  along  the  line  as  shown by  the  following  example:  Referring  to  figure 14-14,  you  will  notice  that  the  total  distance between BM 35 and BM 19, over which the line of levels was run, was 2,140 ft. The elevation on the closing BM 19 was found to be 0.015 ft greater than  its  known  elevation.  You  must  therefore adjust the elevations found for the intermediate TBMs  16,  17,  and  18. The  amount  of  correction  is  calculated  as follows: TBM 16 is 440 ft from the starting BM. The total length distance between the starting and closing BMs is 2,140 ft. The error of closure is 0.015 ft. 14-14







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