'/THE INSTITUTION OF ENGINEERS SRI LANKA

PART 11 EXAMINATIONS -Jut1e2013203- SURVEYING

Instructions:

Answer any five questions Duration: 03 hours

Question 01

Five bays of a line AB were measured under a tension of 53N and the following data in Table -Ql were obtained.

Table -Ql

Bay Measured Ternp.I''C) Level differencelength(m) (m)

1 29.899 22.0 0.0272 29.901 21.5 0.1953 29.882 20.1 0.1254 29.950 22.20 0.0555 29.852 21.0 0.338

The tape has a density of 7700 kg/rrr' and a cross sectional area of 6 mm''. It was standardized onthe flat at 21°C under a pull of 112 N. The coefficient of linear expansion for the material of thetape is o.oooou/c, and Young's modulus is 20.7 x 104 MN/m2. The mean level of the line is54.50 m above the mean sea level. Determine the absolute length of the survey line, reduced tothe sea level.

Tension correction = (P-Ps) L lAESag correction = ~L3 I 24 p2Temperature correction = a L (t-ts)Slope correction = h2/2 LReduction to mean sea level = L H IRRadius of the earth = 6367 km

(20 Marks)Question 02

(a) Derive an expression for the error due to curvature of the earth in terms of thedistance L and radius R.

(3 Marks)(b) Assuming that the error due to refraction is one seventh of that due to curvature( in (a» ,

determine at what approximate distance would the combined correction for curvatureand refraction be 5mm. Assume the radius of earth (R ) as 6367 ·km.

(3 Marks)(c) Describe the two- peg method for testing of a level for collimation error. Also explain

how it is corrected when detected.1

(5 Marks)(d) Reciprocal observations while leveling across a wide river gave the following readings

on to staves held vertical at R and S from instruments stationed at P and Q.

Reading of staff at R from P = l.332 mReading of staff at S from P = l.016 mReading of staff at R from Q = 1.614 mReading of staff at S from Q = 1.278 m

Rand P were close to each other on one bank with S and Q similarly situated on the otherBank. If the reduced level ofS is 50.248 m AOD, what is the level ofR?

(9 Marks)

Question 03

a) A line of levels at 20 m centers, running from a point at the top of a quarry face, aroundthe edge of the excavation, and then across it to a point immediately below the startingpoint, yielded the bookings givens in the table below. Complete the Level Book by theRise and Fall method, and apply the usual checking.

Station BS IS FS RL DistanceA 0.44 0B l.64 20C 2.94 40D 0.17 3.98 60E 2.12 80F 0.32 4.11 100G 0.54 3.88 120H 0.11 4.08 140I 4.00 3.96 149.73 160J 2.44 180K 3.86 0.11 200L 0.59 220

(10 Marks)

b) A level set up at C in a position 30m from a staff held at A and 60 m from a staff held atB, gave readings of l.914 and 2.23 m respectively, the bubble having been brought to thecentre of its run before each reading. The level was then taken to D, 30 m from B and 60111 from A, and staff readings of l.874 m and 2.141 m respectively were obtained fit Aand B . The level stations and staff station lay in a straight line.Determine the collimation error of the level, the corrected difference in level between Aand B, and the staff readings obtained from D when the instrument had been placed inadjustment.

(10 Marks)

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Question 04

a) Explain advantages and disadvantages of Line of Collimation method over Rise and Fallmethod, in Levelling.

(4 Marks)b) Briefly explain the following:

(i). Mean Sea Level(3 Marks)

(ii). Line of Collimation(3 Marks)

(iii). Errors in chain survey(6 Marks)

(iv). Equipment used in tape and offset surveying(4 Marks)

Question 05

(a) The following data in Table-Q5 were obtained for a closed traverse ABCDEFA. Adjustthe traverse using? the Bowditch method and find coordinates of all points in the traverseif coordinates of A are 10000N, 10000E, and find the area enclosed by the polygonABCDEFA.

Table-Q5

Line Length ~E ~NAB 183.89 +183.89 0.000BC 160.02 +98.05 + 128.72CD 226.77 -140.85 + 177.56...--DE 172.52 -153.34 -76.46EF 177.00 0.000 -178.00FA 53.00 +12.08 -51.39

(12Marks)

(b) In a tape and offset survey the following offsets were taken to a fence from a survey line.

Chainage 0 20 40 60 80 100 120 140 160 180(m)

Offset 0 8.32 5.56 5.43 3.45 3.54 7.85 4.52 6.87 8.54(m)

Find the area between the fence and the survey line using Simpson's and Trapezoidal rule.

(8 Marks)

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Question 06

(a) Explain the procedure of reading a horizontal angle using a T-1 theodolite.(6 Marks)

(b) The Table Q-06 indicates the lines, mean included angles and lengths of the legs of aclosed traverse. The whole circle bearing of line AB is 30° 02' 20".

Table Q-06

Line Mean Included Angle Length (m)AB eA 151°53'56" 94.420BC es 102° 36' 01" 67.970CD 8c 108 ° 44' 46" 67.475DE 8D 153° 09' 51" 89.173EF eE 112° 22' 48" 78.125FA eF 91° 12' 25" 82.273

(i). Use the appropriate method of checking and find whether there is any error in angularmeasurements.

(2 Marks)(ii). Compute the closing error in distance measurements.

(4 Marks)(iii).Calculate the final coordinates value of all traverse points. Co-ordinate values of a

point A are 2000.0 Nand 2000.0 E (in meters).(8 Marks)

Question 07

a) Tabulate data needed to set out by theodolite and tape a circular curve of a radius 600 mto connect two straights having a deflection angle of 30° 18', the chainage of theintersection point being 4440.0 m .

(10 Marks)

b) The following readings were taken on a vertically held staff. Calculate the horizontaldistance between the theodolite and the staff, and the elevation at the staff station if theheight of the instrument is 37.36 m above datum.

Vertical angle Staff reading(Middle)

+4u 13' 30" 1.00+5u58' 20" 3.00

(10 Marks)

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Question 08

Table Q8-(a) Indicates three collinear ground control points A, Band C, established by theSurvey Department. A theodolite was set up at station X, eastward of ABC, and three stationmeasurements were taken and recorded (see Table Q8-(b».

Table Q8-(a)

point East(m) North(m)

A 1000.00 1500.00

B 1112.75 1668.91

C 1350.31 2025.47

Table Q8-(b)

Station Staff Station Horizontal Vertical Angle Stadia ReadingsAngle

A OUO'O" +2u 00' 00" 1.2, AI,A2X B 13u40'40" +3u 00' 00" 1.2, BI,B2

C 46u 13' 12" _4u00' 00" 1.2, CI,C2

Estimate the values of AI, A2, BI, B2, CI and C2 obtained on a staff held vertically.Multiplication constant and Additive constant of the tacheometer were 100 and 0.23, respectively.

(20 Marks)

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