worked examples

example the positions of the pegs which need to be set out for the construction of a sloping concrete slab are shown in the diagram . Because of site obstructions the tiling level which is used to set the pegs at their correct levels can only be set up at station X which is 100 m from the TBM .

the reduced level of peg A is to be 100 m the slab to have uniform diagonal from A towards j of 1 in 20 downwards .

To ensure accuracy in setting out the levels it was decided to adjust the instrument before using it , but it was found that the correct adjusting tools were missing from the instrument case . A test was therefore carried out to determine the magnitude of any collimation error that may have been present in the level and this error was found  to be 0.04 m per 100 m downwards .

Assuming that the backsight reading from station X to a staff held on TBM was 1,46 m , determine to the nearest 0,01 m the staff reading  which should be obtained on the pegs at A,Fand H , in order that they may be set to correct levels .

Describe fully the procedure that should be adopted in the detemination of the collimation error of the tilting level . (ICE)

The simplest approach to this question is to work out the true readings at A,F and Hand then adjust them for collimation error . Allowing for collimation error the true reading on TBM = 1.46 + 0,04 = 1,50 m 

HPC = 103,48 + 1,50 = 104,98 m 

Example The following reading were observed with a level : 1,143 (BM 112,28 ) 1,765,2,566,3,820 

CP : 1,390 , 2 , 262, 0 ,664 , 0 , 0,433 CP : 3,722 , 2 , 886 , 1,618 ,0,616 TBM

(1) Reduce the levels by the R-and F method .

(2) Calculate the level of the TBM in the line of collimation was tilted upwards at an angle of 6 َ and each BS length was 100 m and FS length 30 m .

(3) Calculate the level of the TBM if in all cases the staff was held not upright but leaning backwards at 5ُ to the vertical .

(1) The answer here relies on knowing once again levelling always commences on a BS and ends on a FS . and that CPs are always FS/BS (see table below )

(2) due to collimation error

Note that the intermediate sights are unnecessary in calculating the value of the TBM : prove it for yourself by simply covering up the IS column and calculating the value of TBM using BS and FS only .

There are three instrument set-ups , and therefore the total net error on BS = 3 × 70 tan 6 َ = 0,366 m

(too great)

level of TBM = 113.666 - 0.366 = 113.300 m

(3)  from the diagram it is seen that the true reading AB = actual reading CB × cos 5 ُ Thus each BS and FS needs to be corrected by multiplying it by cos 5∘ and as one subtracts BS from to get the difference , then

                                                                                 ∘

True difference in level = actual difference × cos  5

                                                              ∘

                                       =  1.386 cos 5           =   1.381 m

           level of TBM      =   112.28  +  1,381  =    113,661 m

One carriageway of motorway running due N is 8 m wide between kerbs and the following surface levels were taken along a section of it . the chainage increasing from S to N A concrete bridge 12 m in width  and having a horizontal soffit ,

carries a minor road actross the motorway from Sw to NE the Centre-line of the minor road passing over that of the motorway carriageway at chainage of 1550 m Taking crown (i.e . centre-line ) level of the motorway carriageway at 1550 m chainage to be 224.000 m :

(a) Reduce the above set of levels and apply the usual arithmetical checks .

(b) Assuming surface and the bridge soffit .

The HPC method of booking is used because of the numerous intermediate sights .

intermediate sight check

2245.723  =  { (224.981 × 7 )   +  ( 226.393 × 3 ) - (5.504 + 2.819 ) }

                 = 1574.867  +  679.179 - 8.323  =  2245.723