PROBLEMS ON BEARINGS

PROBLEMS ON BEARINGS, Basic Civil Engineering

1. PROBLEMS ON BEARING Page 1

QUESTION BANK
PROBLEMS ON BEARINGS

PROBLEMS ON BEARINGS
Types of problems:
Type A) The summation of entire included angle is equal to (2n-4) x 90
0
.
Type B) When the summation of entire included angle is not equal to (2n-4) x 90
0
.

1. Following readings were taken in a closed traverse. Draw a rough traverse showing the included
angles. Calculate the corrected bearings and indicate the stations free from local attraction. Show
specimen calculations. (10 MKS)
Station P Q R S
Line PQ QR RS SP
F.B. 50
0
30’ 140
0
30’ 219
0
00’ 328
0
00’
B.B. 230
0
30’ 319
0
00’ 38
0
00’ 150
0
30’
Sol
n
:
To solve such problem you must know following relations:
 F.B. = Fore Bearing, B.B. = Back Bearing
 F.B. ± B.B. = ± 180
0

Step I:
Take the difference of F.B. and B.B. of respective line and check whether the difference is nearly
equal to a180
0
or not. (Forget about the Sign).
Eg. 50
0
30’ - 230
0
30’ = 180
0
140
0
30’ - 319
0
00’ = 178
0
30
’

219
0
00’ - 38
0
00’ = 181
0

328
0
00’ - 150
0
30’ = 177
0
30’

2. PROBLEMS ON BEARING Page 2


Observed
St
n
Line F.B. B.B. Difference
P PQ 50
0
30’ 230
0
30’ 180
0

Q QR 140
0
30’ 319
0
00’ 178
0
30
’

R RS 219
0
00’ 38
0
00’ 181
0

S SP 328
0
00’ 150
0
30’ 177
0
30’
Step II:
Now with the help of F.B. of Every line draw the rough traverse. From the traverse find out I.A.
(included angle) and take the summation of I.A. This summation will match with (2n - 4) x 90
0
.
Observed
St
n
Line F.B. B.B. Difference I.A.
P PQ 50
0
30’ 230
0
30’ 180
0
100
0

Q QR 140
0
30’ 319
0
00’ 178
0
30
’
90
0

R RS 219
0
00’ 38
0
00’ 181
0
100
0

S SP 328
0
00’ 150
0
30’ 177
0
30’ 70
0

Total 360
0

Step III:
Now select such a line whose difference between the F.B. and B.B. is exactly 180
0
.
For this problem such difference is for the line PQ. That means the difference between 50
0
30’
and 230
0
30’ is 180
0
. Therefore write down both reading as it is in the corrected F.B. and B.B.
column.
Now 50
0
30’ is F.B. at st
n
P, which is correct F.B. reading. That means the B.B. is also correct at
the same station i.e. 150
0
30’. Therefore write down both reading as it is in the corrected F.B. and
B.B. column.
Now 230
0
30’ is B.B. at st
n
Q, which is correct B.B. reading. That means the F.B. is also correct
at the same station i.e. 140
0
30’. Therefore write down both reading as it is in the corrected F.B.
and B.B. column.
See the following table which shows the corrected F.B. and B.B. reading.
Observed Corrected
St
n
Line F.B. B.B. Difference I.A. F.B. B.B.
P PQ 50
0
30’ 230
0
30’ 180
0
100
0
50
0
30’ 230
0
30’
Q QR 140
0
30’ 319
0
00’ 178
0
30
’
90
0
140
0
30’
R RS 219
0
00’ 38
0
00’ 181
0
100
0

S SP 328
0
00’ 150
0
30’ 177
0
30’ 70
0
150
0
30’
Total 360
0

3. PROBLEMS ON BEARING Page 3

Step IV:
Now consider the corrected F.B. at st
n
Q.
Observed Corrected
St
n
Line F.B. B.B. Difference I.A. F.B. B.B. Error
P PQ 50
0
30’ 230
0
30’ 180
0
100
0
50
0
30’ 230
0
30’ Zero at P
Q QR 140
0
30’ 319
0
00’ 178
0
30
’
90
0
140
0
30’ 320
0
0’ Zero at Q
R RS 219
0
00’ 38
0
00’ 181
0
100
0
220
0
30’ 40
0
30’
S SP 328
0
00’ 150
0
30’ 177
0
30’ 70
0
330
0
30’ 150
0
30’

2. Below are the bearings observed in a traverse conducted with a prismatic compass at a place
where local attraction was suspected?
Line FB BB
PQ 191
0
45
’
13
0
0
’

QR 39
0
30
’
222
0
30
’

RS 22
0
15
’
200
0
30’
ST 242
0
45
’
62
0
45’
TP 330
0
15’ 147
0
45’

At what stations do you suspect local attraction? Find the corrected bearings of the lines and also
calculate the included angles. (11)
Solution:
St
n
Line observed Difference IA Corrected
IA
Corrected Remark
FB BB FB BB
P
PQ

Q
QR

R
RS

S
ST

T
TP

4. PROBLEMS ON BEARING Page 4

3. The following bearings were taken in running a closed compass traverse: (10)

Station A B C D E
Line AB BC CD DE EA
F.B. 80
0
10' 120
0
20' 170
0
50' 230
0
10' 310
0
20'
B.B. 259
0
0' 301
0
50' 350
0
50' 49° 30' 130
0
15'
Compute the interior angles and correct them for observational errors. Assuming the bearing of
line CD is correct. Adjust the bearing of the remaining sides.
St
n
Line observed Difference IA Corrected
IA
Corrected Remark
FB BB FB BB
A
B
C
D
E

4. The observed whole circle bearings in a closed traverse ABCD are given below:
Line AB BC CD DA
FB 46
0
10’ 119
0
20’ 169
0
30’ 280
0
20’
BB 226
0
10’ 298
0
40’ 351
0
10’ 99
0
20’

Calculate the included angle and apply correction for local attraction and find corrected F.B. and
B.B. Draw a sketch of the traverse. Specimen calculations must be given. (10)
Stn Line observed Difference IA Corrected
IA
Corrected Remark
FB BB FB BB
A
B
C
D
E

5. PROBLEMS ON BEARING Page 5

5. The following bearings were taken in running a closed compass traverse:
Line AB BC CD DA EA
FB 80
0
10’ 120
0
20’ 170
0
50’ 230
0
10’ 310
0
20’
BB 259
0
0’ 301
0
50’ 350
0
50’ 49
0
30’ 130
0
15’

Compute the Included angle and correct them for observational errors. Assuming bearing of the
line CD is correct. Adjust the bearing of the remaining sides.
St
n
Line observed Difference IA Corrected
IA
Corrected Remark
FB BB FB BB
A
B
C
D
E

6. Following bearings were taken with a prismatic compass for a closed traverse. Compute the
interior angles and correct them (8)
Line AB BC CD DE EA
F.B. 120°30' 30° 330°30' 260°30' 210°
B.B. 300° 209° 150°30' 80° 31
0


St
n
Line observed Difference IA Corrected
IA
Corrected Remark
FB BB FB BB
A
B
C
D
E

6. PROBLEMS ON BEARING Page 6

7. Following readings are taken in a closed compass traverse. Draw the original traverse. Calculate
the included angles. Check for angular error. Calculate the corrected bearings. Tabulate the
results in tabular form. State the corrections to local attraction of each station. (6)

Station A B C D

F.B. N 10°30’ E N 80° W S 40° W S 80° E
B.B N 81° W S 11° W S 80° E N40
0
30’E
8. Following bearings were observed while running a closed transverse in the
clockwise direction:






Draw a rough traverse. Calculate included angles and check for angular error. Calculate corrected
bearings. Indicate stations free from local attraction and corrections at other stations. (9)

9. Following readings are taken in a closed compass traverse. Draw a rough traverse. Calculate the
induced angles and check for angular error. Calculate the induced angles and check for angular
error. Calculate the corrected bearings. Also indicate the stations free from local attraction

Station A B C D

F.B. N 10°30’ E N 80° W S 40° W S 80° E
B.B N 81° W S 11° W S 80° E N40
0
30’E

10. Following table shows bearings observed for a closed traverse. (9)

Line AB BC CD DA
F.B. 75°30' 19
o
45' 289°30' 359°00'
B.B. 260°00' 10°15' 109°30' 176°
Calculate:
i) Included angles of the traverse.
ii) Corrected bearings of each line.
iii) Tabulate the results and draw a neat sketch of the traverse.

Line AB BC CD DA
F.B. N 74° 30' W N 32° E S 31° E S 18°30' W
B.B. S 74° 30' E S 30
0
W N 28°30' W N 18° E

7. PROBLEMS ON BEARING Page 7

11. Below are the bearings observed in a traverse survey conducted with a prismatic compass at a
place where local attraction was suspected?
Line FB BB
PQ 124
0
30’ 304
0
30,
QR 68
0
15’ 246
0
0’
RS 310
0
30’ 135
0
15’
SP 200
0
15’ 17
0
45’
At what station do you suspect local attraction? Find the corrected bearings of the lines and also
calculate the IA.
12. The following readings were taken in a closed traverse. Draw a rough traverse. Calculate the
included angle and check for angular error. Calculate the corrected I.A. Also indicate the stations
free from local attraction.
Line AB BC CD DA
FB N66
0
15’E S50
0
15’E S38
0
30’W N53
0
15’W
BB S 64
0
W N 47
0
W N 37
0
30’E S 53
0
15’E

13. Below are the bearings observed in a traverse conducted with a prismatic compass at a place where
local attraction was suspected? At what stations do you suspect local attraction? Find the corrected
bearings of the lines and also calculate the included angles. (10)
Line F.B. B.B.
PQ

191
0
45’ 13
0
00’
QR

39
0
30’ 222
0
30’
RS

22
0
15’ 200
0
30’
ST

242
0
45’ 62
0
45’
TP 330
0
15’ 147
0
45’

8. PROBLEMS ON BEARING Page 8

14. The following bearings are the observed bearings of the lines of a traverse ABCDEA with a
compass in a place where local attraction was suspected. Find the included angles and correct
bearings of the lines. (10)
Line F.B B.B
AB 140⁰45' 318⁰15'
BC 216⁰30' 38⁰00'
CD 209⁰15' 30⁰15'
DE 319⁰45' 139⁰45'
EA 60⁰15' 240⁰15'