Quick Notes And Exercises

THEODOLITE TRAVERSE/DCC20063

10. Calculate the final bearing of theodolite traverse data in Behrang land lot table below by
second class traverse.

Line Bearing Distance(M)

2-1 Datum from Prismatic Compass, PC 243 30 00

2-3 077° 30’ 00” 257° 30’ 20”

3-4 173° 44’ 00” 353° 43’ 20”

4-5 231° 55’ 20” 051° 54’ 40”

5-1 322° 20’ 40” 142° 21’ 00”

1-2 063° 31’ 00” 243° 30’ 00”

Stn Bearing Min From Stn Final Bearing To Stn

Face Left Face Right Bearing

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THEODOLITE TRAVERSE/DCC20063

11. A 2nd class traverse survey fieldwork has been formatted at FIVE (5) station. The observation
data from the theodolite are recorded in table below. Calculate the bearing adjustment and
determine the final bearing for each line of the traverse.

Stn Bearing Min From Stn Final Bearing To Stn
Bearing 2 1200 30’ 00’’ 1
1 Face Left Face Right 2 3
2 3 4
Datum from pc 1200 30’ 00’’ 4 5
3 5 1
2 1200 30’ 00’’ 3000 30’ 00’’ 1 2
3
4 3230 52’ 27’’ 1430 53’ 08’’
3
4 360 44’ 58’’ 2160 44’ 56’’
5
4 1320 03’ 49’’ 3120 05’ 22’’
5
1 2250 21’ 21’’ 450 20’ 00’’
5
1 3000 30’ 40’’ 1200 30’ 60’’
2

12. Calculate the missing bearing and complete the booking form of the traverse.

Bearing/Angle Line
Face Right Final Bearing
Station Face Left Min Bearing To Vertical
From Angle

Datum from PA 1234 2250 30’ 00” 2 2250 30’ 00” 1
BKL BKL

1 2250 30’ 00” a) 980 47’ 00”
k)
2 BKL 2780 47’ 00” 2 p) 3
3 b) 2100 25’ 30” 3 q) 4
l) 4 r) 5
2 c) 980 47’ 00” 5 s) 1
2490 15’ 40” 1 450 30’ 00” 2
3 m)

4 2100 25’ 40” d) 2800 09’ 20”
n)
3 300 25’ 30” e)
450 31’ 10”
4 o)

5 f) 690 15’ 40”

4 690 15’ 40” g)

5

1 h) 1000 09’ 30”

5 i) 2800 09’ 20”

1

2 450 31’ 10” j)

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THEODOLITE TRAVERSE/DCC20063

LATITUDE & DEPARTURE, BOWDITCH’S METHOD

13. Table below shows data for theodolite booking at site. Based on this information, solve:
i. Latitude and departure for each line
ii. Calculate the Arithmetical sum of departure and latitude
iii. Calculate the closing error

Line Bearing Length(M)
AB 343° 54’ 00’’ 235.00
BC 87° 52’ 00’’ 317.50
CD 172° 42’ 00’’ 215.00
DE 265° 14’ 00’’ 281.50

14. a) List five(5) steps in theodolite traverse field works

b) Table below shows the bearings and distances for a close traverse, calculate the latitude

and departure of each line.

Table

LINE BEARING DISTANCE(M)

AB 63° 30’ 00’’ 63.264

BC 77° 25’ 00’’ 75.119

CD 173° 43’ 30’’ 82.147

DE 231° 55’ 00’’ 87.273

EA 322° 19’ 00’’ 114.829

15. Table below shows the bearing and distance for closed traverse. Calculate latitude and
departure for this traverse. Based on the data, calculate the corrected latitude and departure by
using Bowditch method.

Stn Bearing Distance, m

1 13.358
2 540 13’ 30’’ 16.510
3 1170 01’ 10’’ 17.989
4 1960 53’ 50’’ 24.380
5 2710 04’ 00’’ 16.941
1 130 52’ 50’’

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THEODOLITE TRAVERSE/DCC20063

16. Calculate the latitude and departure based on the data and correction by Bowditch method.

Line Bearing Distance, m
1-2 850 23’ 53”
2-3 1680 45’ 22” 32.124
3-4 2550 13’ 56” 51.445
4-1 48.587
40 40’ 20” 60.451

17. A close traverse theodolite in the table below has the following distance and bearings. Calculate
:
i. Latitude and departure of the lines.
ii. Adjustment for latitudes and departure by using Bowditch rule.
iii. Linear misclosure

Line Bearing Distance, m
2-3 1140 53’ 30” 203.117
3-4 1140 57’ 10” 43.853
4-5 2390 05’ 20” 211.971
5-1 3120 49’ 50” 175.630
1-2 420 50’ 00” 127.456

18. Refer to the table above, calculate the adjustment for the latit and depart by using transit
method.

Station Latitude Departure
NS EW
1
2 236.045 88.896
3 62.386 277.278
4
64.696 363.121 127.1
1 239.06

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THEODOLITE TRAVERSE/DCC20063

TRAVERSE FORM

Bearing/Angle Line
Face Right Final Bearing
Station Face Left Min Bearing To Vertical
From Angle

TRAVERSE FORM

Bearing/Angle Line
Face Right Final Bearing
Station Face Left Min Bearing To Vertical
From Angle

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THEODOLITE TR

Stn Bearing Distance Latitude LATIT &
(Azimuth) (Meters) NS
Depart
E

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RAVERSE/DCC20063

& DEPART

tures Final Latitude Final Departures Coordinate
W
N/S E/W

THEODOLITE TR

Stn Bearing Distance Latitude LATIT &
(Azimuth) (Meters) NS
Depart
E

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RAVERSE/DCC20063

& DEPART

tures Final Latitude Final Departures Coordinate
W
N/S E/W

THEODOLITE TR

Stn Bearing Distance Latitude LATIT &
(Azimuth) (Meters) NS
Depart
E

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RAVERSE/DCC20063

& DEPART

tures Final Latitude Final Departures Coordinate
W
N/S E/W

SETTING OUT/DCC20063

SETTING OUT

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SETTING OUT/DCC20063

Building Plan

Setting Out Building

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SETTING OUT/DCC20063

1. Explain FIVE (5) responsibilities of a setting out engineer.

2. Traveler and sight rail are an instrument that are used to fill and cut for construction of
earthwork. Explain how both instruments are used with the aid of a diagram.

3. Explain with sketch FOUR (4) equipment of setting out.
4. Explain four (4) general procedures of setting out.
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SETTING OUT/DCC20063

5. Refer table below, show the leveling booking for culvert setting out project. The culvert distance
from A to E is 100.00 meter. Gradient 1 in 100.

FS IS BS H.O.C R.L CHAINAGE REMARKS
0.520
1.12 2.010 100 BM1 (RL=100)
2.810 2.835 1.32
1.215 0A
1.685
1.835 INVERT LEVEL A
1.905
25 B

50 C

75 D

100 E

CP

BM2 (RL=100)

i. Complete the table
ii. If traveler level = 3.00m, calculate the height of rail above ground level at point A, B, C, D &

E.

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SETTING OUT/DCC20063
6. Figure below shows an underground drainage stop at point J and will be joined to point K

with the gradient of 1:100 downward. Point J and K were marked with a wood picket on the
ground. If the traveler height is 3.1 m and invert level at K is 95.458 m, calculate.
i. Reduce level of ground at J and K
ii. Reduce level of rail at J and K
iii. Depth of excavation at J and K

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SETTING OUT/DCC20063

7. An existing sewer at P is to be continued to Q and R on a falling gradient of 1 in 150 for plan
distances of 27.12m and 54.11 m consecutively where there positions of P, Q and R are defined
by wooded uprights.

Given the following level observations, calculate the difference in level between the top of each

upright and the position at which the top edge sight rail must be set at P, Q and R a 2.5m

traveler is to be used.

Level reading to staff on TBM on wall (RL 89.52 m) 0.39m

Level reading to staff on top of upright at P 0.16m

Level reading to staff on top of upright at Q 0.35m

Level reading to staff on top of upright at R 1.17m

Level reading to staff on invert of existing sewer at P 2.84m

All reading were taken from the same instrument position.

0.16 levelTBM 89.52m0.35 1.17
0.39 Wooden stake
R
Staff Invert 2.84 P Q Horizontal
sloping at 27.12m 54.11m
1:150

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SETTING OUT/DCC20063
8. A 110m long drainage water system is to be build with a slope of 1:100 reduced from point A to

B. The reduced level for starting point A is 20.222m and point B is 20.195m. The invert level at the
starting point of excavation (penggalian) of A is 19.123m. The length of the traveler is 3m.
calculate the following:
i- Invert level at the end of point B
ii- Height of sight rail needed to be set up on the ground of both A and B points.
iii- The depth should be dug at points A and B.

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SETTING OUT/DCC20063
9. A straight length of sewer is to be laid between THREE (3) manholes A, B and C as shown in

figure. The following information are shown in table below.

Calculate :
i. The invert level at B and C.
ii. The reduce levels of the sight rails at A, B and C if a 3m traveler is to be used to locate the
sewer invert.
iii. The height of sight rail above ground level at A, B and C.
iv. The depth of excavation at A, B and C.

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SETTING OUT/DCC20063

10. The data for setting out of propose drainage in primary school project are as follow:

Invert level at point A = 28.321 m
Gradient drainage from point A to B = 1 :75 (decreased)
Distance from point A to B = 50 m
TBM = 32.41 m
Back sight (staf on TBM) = 1.122 m
Intermediate sight (staf at point A) = 2.232 m
Fore sight (staf at drain point B) = 3.100 m
Traveler height = 3.0m

Calculate :

i. Height of rail at point A and point B
ii. Depth of excavation at point A and point B

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CURVE/DCC20063

CURVE RANGING

In the geometric design of motorways, railways, pipelines, etc. The design and
setting out of curves is an important aspect of the engineer’s work.

The initial design is usually based on a series of straight sections whose
positions are defined largely by the topography of the area. The intersections
of pairs of straights are then connected by horizontal curves.

In the vertical design, intersecting gradients are connected by curves in
the vertical plane.

Circular curves are used to join intersecting straight lines (or tangents). Circular
curves are assumed to be concave. Horizontal circular curves are used to
transition the change in alignment at angle points in the tangent (straight)
portions of alignments. An angle point is called a point of intersection or PI
station; and the change in alignment is defined by a deflection angle, Δ.

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CURVE/DCC20063

curve horizontal circular curve
curve
transition
vertical curve curve

combined
curve

intersection
of 2 gradient

Vertical Curve Horizontal Curve

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CURVE/DCC20063

1. State the purpose of curve ranging
a.
b.
c.
d.

2. State the formula used for the following terms in circular curve.
i. Tangent length
ii. Chainage of beginning curve

iii. Length of curve

3. Explain by sketching a diagram four (4) elements of a simple circular curve.

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CURVE/DCC20063
4. Identify the suitable term related to the circular curve of geometry as in figure below.

Offsets From Long Chord
5. Calculate the set out the curve based on the data, θ = 590 58’. Radius = 64 m and interval is 7
m.

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CURVE/DCC20063
6. Two road having a deviation angle of 450 at apex point, I are to be joined by a 200 m radius circular

curve. If the chainage of apex point is 1839.2 m, calculate the necessary data to set the curve by
long chord. Using 10 m interval.

7. Two straight line road with deflection angle θ is 300 00’ 00” crossed at the point of crossing. One
circular curve with radius 450 m need to be constructed to join the both road. Using the long
chord offset method and the interval of ranging is 15 m. Calculate the ranging data table.

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CURVE/DCC20063
Offsets From Tangent

8. From the data , radius is 64.7 m, angle of intersections is 450 45’. The peg interval is 5 m. Calculate
the setting out of the curve.

9. Two road having a deviation angle of 450 at apex point I are to be joined by a 200 m radius circular
curve. If the chainage of apex point is 1839.2 m, calculate the necessary data to set the curve by
tangent method and their interval is 30 m.

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CURVE/DCC20063
10. Calculate the horizontal curve ranging data by using the tangent line offset method if the radius,

R is 500 m, the deflection angle θ is 200 30’ 00” and the intervals for ranging is 15 m each.

11. The two straight lines intersects at an angle of 320 30’ 00” are connected by a circular curve with
500 m radius. Given chainage of intersection point is 1900 m, calculate tangent length, chainage
of beginning curve, length of curve and chainage of end of curve. Prepare the suitable table setting
out using the offset from tangent where the sub chord is 20 m interval. Draw a suitable sketch for
this method.

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CURVE/DCC20063
Offset From a Deflection Angle By Using One Theodolite (Circular Curve)

12. Two straight tangent lines is extended to meet at point of intersection, I. The obtained
intersection angle is 180 24’ 00”. If tangent line is corrected to a circular curve with a radius of
640 m, interval is 20 m and intersection chainage is 3025.62 m by using the deflection angle
method, calculate the deflection angle.
i. Tangent length, T and curve length, Lc
ii. Chainage of T1 and chainage of T2
iii. Calculate the data for setting out circular curve

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CURVE/DCC20063
13. Two straight lines A1 and B1 meet at chainage of 4350m. a simple circular curve of 200m radius

joins them and the deflection angle between the two straight lines OS 500. If the chord interval
is 35m, calculate the data needed to design the curve using deflection angle method.

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CURVE/DCC20063
14. Two straight lines that intersect at a deflection angle 500 00’ 00” are connected by a circular curve

with radius 400 m. Chainage at the intersection point is 1692.020 m. Calculate the setting out at
25 m interval. Given bearing at T1I is 600 00’ 00”. Prepare the suitable table. Find :

i. Tangent length and length of circular curve.
ii. Chainage and deflection angle with one theodolite.

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CURVE/DCC20063
15. A circular curve of 500 m radius is connected between two straight roads, which intersect with

an angle of 14° 00' 20". During the design of the curve, the chainage of intersection point is 3500.00
m.

i. Draw THREE (3) types of circular curve.
ii. With the aid of diagram, explain FIVE (5) terminologies used to describe a

circular curve.
iii. Calculate the data for setting out circular curve at 22 m interval.

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CURVE/DCC20063
Offset From Deflection Angle By Using Two Theodolite (Circular Curve)
16. A horizontal circular curve of radius 150 m and the chord of bearing is 350 00’ 00”. Derive

and tabulate the data for deflection angles required to set out a curve from tangent TI, of
chainage 2068.321, from small chord each is 20 m. Obtain :
i. The tangent length
ii. The curve length
Calculate the cumulative deflection angles and total curve length for checking, by using two
theodolite.

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CURVE/DCC20063
17. Tabulate the necessary data to set out the right handed simple circular curve of 250 m radius

connecting two straights having a point of intersection at a chainage 3450 m by two theodolite
method. The deflection angle between the two straights is 500. Take peg interval is 20 m.

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Norayahati Ngagiman. The writer is a lecturer in the
Department of Civil Engineering, Sultan Azlan Shah Polytechnic,
Behrang Station, Tanjung Malim, Perak Darul Ridzuan since
2004, with 15 years of teaching experience in Civil Engineering
Department, she specializes in Engineering Survey Course.

Nafisah Harun. The writer is a lecturer in the Department of
Civil Engineering, Sultan Azlan Shah Polytechnic, Behrang
Station, Tanjung Malim, Perak Darul Ridzuan since 2006 and
Tuanku Sultanah Bahiyah Polytechnic for two years (2004-
2005, with 15 years of teaching experience in Civil Engineering
Department, she specializes in Engineering Survey Course.

Hasliza Yusof. The writer is a lecturer in the Department of
Civil Engineering, Sultan Azlan Shah Polytechnic Behrang
Station, Tanjung Malim, Perak Darul Ridzuan since 2008.
Merlimau Polytechnic for two years (2004-2005) and Sultan
Haji Ahmad Shah Polytehnic for two years (2006-2007), with 12
years of teaching experience in Civil Engineering Department.