Question

QUESTION 3 a) With the aid of diagrams, describe four (4) errors in leveling. (C01, PO1) (C3) (8 marks) b) Table Q3(b) shows extracted data of leveling work from Bench Mark (BM) 3/24 to Bench Mark 5/25, located at one construction site. Reduced level of BM 3/24 is 44.244 m, BM 5/25 is 43.446 m above Mean Sea Level, and interval distance between stations is 20 m. (CO2, PO4) (C4) Table Q3(b): Leveling Data IS FS BS 1.756 RL 44.244 2.321 2.782 2.231 2.671 Distance 0 20 40 60 80 100 120 140 160 Station BM 3/24 1 2 3 4 5 6 7 BM 5/25 2.012 -3.045 2.125 1.991 2.321 2.254 43.446 i) Calculate the allowable error. ii) Carry out arithmetical checking for this leveling work. iii) Calculate the Final RL for every station by Rise and Fall method. iv) Find the gradient from station 2 to station 5. (17 marks)

please i need help asap , i need the full answers , i want to study it back soon

Answer 1

A) Source 1. Instrumental error

a) Imperfect adjustment - the essential requirement in leveling work is that the line of collimation must be horizontal when instrument is levelled.

b) Defective level tube- If the bubble is sluggish it may remain in centre even though the bubble axis is not horizontal.

c) Shaky tripod- shaky tripod makes the instrument unstable. So tripod must be examined and loose joints must be tightened.

d) Incorrect graduation of the staff.

Source 2. Error of manipulation

a) Careless levelling of the instrument.

b) The bubble not being central at the time of taking reading.

c) Parallax not removed properly- This error is due to imperfect focussing the eye-piece and of the object glass.

d) The staff not being held vertical.

Source 3. Error due to natural causes.

a) Curvature and Refraction- Curvature of the earth causes the objects sighted lower than they actually.

Refraction makes them appear higher then they actually.

b) Wind

c) Sun

Source 4.Common mistakes in leveling

a) Entry a reading in the wrong column.

b) Reading the wrong numbers.

c) Levelling staff not being fully extended.

B) 1) Allowable error of closure depends on the precision required(first,second,or third) most differential leveling (Plane survey) is third order work.

Allowable error in feet is=0.050√(length of the level in miles)

In this question length is 160 meter.

1km = 0.623miles.

160m or 0.160km=0.0994miles.

Allowable error in feet =0.050√(0.0994)

=0.0157 feet

=0.0048 meter (1m=3.28 feet).

2)Arithmetical check = summation of back sight - summation of fire sight=last station RL - first station RL.

Summation of back sight=1.756+2.231+2.125

=6.112

Summation of fore sight = 2.671+1.991+2.254

=6.916

Last station RL= 43.446

First stationRL= 44.244

Put all values in formula

Check

Summation of back sight - summation of fore sight

=6.112-6.916=-0.804

RL of last station - RL of first station  

=43.446- 44.244=- 0.798.

-0.804 not equal to -0.798 so check is not OK.

B.s IS 1.756 DISTANCE STATION |Bm 3/24 20 2.321 2:782 2 2.231 40 60 3 12-012 FS RISE FALL RL 44.244 0.565 143.679 0.461 43-218 | 2.671 0.11 143.329 0.219 | 43-548 5.057 148.605 1.991 5.036 143.569 0.196 143.373 2.254 0.067 143.44 16.916 15.454 16-258 80 4 1-3-045 joo 2-125 5 6 120 140 2-321 160 Bm 5/25 6-112 summation CHECK Summation of B.S - Summation F:S = Summanin of Rise - Summation of fall R-L of Last Station - RL of first station 56-112 -6-916 = 5.454 – 6-258 = 43-44 – 44-244 = -0.804 OK Scanned with CamScanner CS

ERROR = 43.44-43-446 -0.006 Error is Negative so correction is positive Correction at Station - Error X Distance Correction - Error X Distance between the starting Bm and Intermediate Bm Distance between the starting and closing BM Distance between the starting and closing BM 3 16om 0.006 x 20 correction for station 1 = 160 0.00075 m Final RL: 43.679 + 0.000 75 .. 43.67975 m Correction for station 2 = 0.006X40 760 -0.0015 m Final R2 = 43-218 + 0.0015 . 43.2195 m 0.006 X 60 correction for station 3 = 160 -0.00225 43. 329+ 0.00225 final RL : ; 43-33125 m correction for Station 4 - 0.006X 80 Too = 0.003m Final RL = 43.548 +0.003 CS Scanned with 43-551m CamScanner

correction for stations ; 0.00 6 X 100 160 = 0.00375 m Final RL = 48.605+ 0.00375 = 48.60875 m correction for station 6 0.00 6 X 120 160 = 0.0045m Final RL: 43.569 +0.0045 43-5735m correction for station 7: 0.006x 140 Too 0.00525 m Final RL = 43-373 + 0.00525 = 43.37825 m correction for station 5 = 0.006 x 160 25 160 Co-006 m final RL = 43-44 +0.006 43.446 m OK CS Scanned with CamScanner

Summary B'S 1-56 IS F.S RISE FALL-RL 144.244 - 12.321 2-782 2.231 [2.671 0-11) 143.329 CORRECTION FINAL RL DISTANCE STATION Bm3/24 O 0-565 43.67910.00075 43•67975 20 10.461 43.218 0.0015 143-2195 40 2 0.00225 43.33/25 60 143.5480.003 143.55) 80 4 48-605 0.00375 148-60875 loo 5 5.036 43.5690-0045 143.5735 120 6 0-196 43-373 0.00525 143-37825 140 7 | 43-44-0-006 143-446 160 BM5251 12.012 0.219 1-3.045 5. 057 2.125 1.991 2-321 2-254 0-067 Station 5 Gradient from station 2 to Gradient from Station 2 to Station 5 : RLof station 5 - RL of station 2 Distance between Station 542 Final RL of station 5 = 48-60875 Final RL OF Station 23 Distance between station 542= 48-60875-43-2195 60 = 0.0898 43.2195 [the means Rising] Erising] Ang Gradient from station 2 to station 5= 0.0898 CS Scanned with CamScanner