ERT252: GEOMATIC ENGINEERING
TUTORIAL 1
1. A tape of 30 m length suspended in catenary measured the length of a base line. After
applying all corrections the deduced length of the base line was 1462.36 m. Later on it
was found that the actual pull applied was 155 N and not the 165 N as recorded in the
field book. Correct the deduced length for the incorrect pull.
The tape was standardized on the flat under a pull of 85 N having a mass of 0.024 kg/m
and cross-sectional area of 4.12 mm2. The Young’s modulus of the tape material is
152000 MN/m2 and the acceleration due to gravity is 9.806 m/s2.
2. The depth of a mine shaft was measured as 834.66 m using a 1000 m steel tape having a
cross-section of 10 mm2 and a mass of 0.08 kg/m. Calculate the correct depth of the mine
shaft if the tape was standardized at a tension of 182 N. The Young’s modulus of
elasticity of the tape material is 21 × 104 N/mm2 and g = 9.806 m/s2.
3. A steel tape of nominal length 30 m was used to check the distance between two offset
pegs A1 and A2. The following results were obtained.
Length recorded Height
Temperature
Tension applied
on tape
A1
A2
23.512 m
21.50 m 23.50 m
28oC
100 N
Compared to 25.000 m baseline, the tape read 24.994 m with 50 N tensions applied to at
15oC. The cross sectional area of the tape is 2.0 mm2 and it wigh 4.5 N.
Calculate the horizontal length A1 to A2.
4. A line was measured with a steel tape 30 m long, standardized at 15°C with a pull of
100 N. If the temperature at the time of measurement was 20°C and the pull exerted was
160 N, calculate the correction per tape length
Weight of 1 cm3 steel = 0.0786 N
Weight of tape = 8 N
Modulus of elasticity = 2.10 × 105 N/mm2
Coefficient of expansion of tape/°C = 7.1 x 107
TUTORIAL 2
1.
Given the profile data shown below, you are required to calculate the elevation and
check your level calculation.
2.
Compute the interior angles for the trapezoidal layout. Show your calculation steps.
3.
A six-sided traverse has the following coordinates: A (559.319 N, 207.453 E),
B (738.562 N, 666.737 E), C (541.742 N, 688.350 E), D (379.861 N, 839.008 E),
E (296.099 N, 604.048 E), F (218.330 N, 323.936 E).
i) Determine the distance and bearing of each side.
ii) Calculate the area (in hectares) enclosed by the traverse.
4.
Select a suitable levelling method and reduce the levels given in Table Q5a.
Table Q5a
BS
1.729
IS
FS
0.832
0.971
1.002
1.459
1.031
1.600
1.621
2.138
2.076
1.730
5.
REMARKS
TBM 71.025
200 m
210 m
220 m
230 m
240 m
250 m
260 m
270 m
280 m
TBM 71.025
The horizontal circle readings shown in Table Q5b were taken using 5” reading
theodolite that has correctly set up and levelled at point T. Arrange the readings in a
suitable format and calculate values for the horizontal angles.
Table Q5b
POINT
FACE LEFT
FACE RIGHT
A
B
C
D
00o 17’ 35”
38 o 22’ 20”
69 o 30’ 10”
137 o 09’ 55”
180o
218 o
249 o
317 o
A
B
C
D
45 o 39’ 10”
83 o 43’ 20”
114 o 52’ 00”
182 o 31’ 30”
225 o 38’ 55”
263 o 43’ 00”
294 o 51’ 50”
02 o 31’ 10”
17’
22’
29’
09’
15”
00”
40”
40”
TUTORIAL 3
1. A line XY is measured at both ends as follows:
Instrument at X, slope distance = 879.209 m; vertical angle = +1o26’50”
Instrument at Y, slope distance = 879.230 m; vertical angle = -1o26’38”
The height of instrument, reflector and target are equal for each observation.
i) Compute the horizontal distance XY
ii) If the elevation at A is 163.772m, calculate the elevation at position Y.
2. From point D three points A, B and C have been observed as Table 6 follows:
Table Q6
Staff Point
Bearing
Vertical Angles
Stadia Readings
A
B
C
85o30’
125o10’
104o30’
5o12’
0
9o30’
)1.10,1.65,2.20
)2.30,2.95,3.60
)1.45,2.15,2.85
If the reduced level of D is 150.10 m, HI = 1.40 m and the tacheometeric constant = 100:
i) Calculate the horizontal distance to the staff points and their reduced levels
ii) Calculate the distance AB , BC and CA
3. A tacheometric observation was carried out at an intermediate station C of the line AB
and the following readings were obtained:
Staff Station Vertical Angle
[Stesen Staf] [Sudut Pugak]
θ
A
B
- 06o25’40”
+ 04o 36’ 10”
Staff Reading
[Bacaan Staf]
Lower
[Bawah]
0.445
0.950
Middle
[Tengah]
1.675
1.880
Upper
[Atas]
2.905
2.810
The instrument was fitted with an anallactic lens and the constant was 100. Find the
gradient of the line joining stations A and B.
4. To determine the distance between two points A and B, a tacheometer was setup at P and
the following observations were recorded as in Table Q5.
Table Q5
Staff reading
Vertical Angle
Horizontal Angle
Elevation
Staf at A
2.225, 2.605, 2.985
+ 7°54′
+ 68°32′30″
315.600 m
Staff at B
1.640, 1.920, 2.200
– 1°46′
i) Illustrate by diagrams to show how the horizontal distance AB, vertical distance and
the reduced level of point B are deduced.
ii) Calculate the distance AB and the elevation of B.
5. A road is to run on an embankment between chainages 230m and 307m. The crosssectional area every 10m of chainage is shown in Table Q1 below. Determine the volume
of fill required, by both the trapezoidal and prismoidal method.
Table Q1
Chainage (m)
230
240
250
260
270
280
290
300
307
(m2)
0.0
20.5
45.7
96.6
127.3
125.9
88.9
45.2
0.0
Area