Civil Engineering November 2020
Surveying has to do with the determination of the
relative spatial location of the points on or near the
surface of the earth. It is the art of measuring
horizontal and vertical distances between objects,
of measuring angles between lines, of determining
the direction of lines, and of establishing points by
predetermined angular and linear measurement.
Geodetic Surveying - the type of surveying
which takes into account the true shape of the
earth. Surveys employing the principles of
geodesy are of high precision and generally
extended over large areas.
Plane Surveying - the type of surveying in
which the mean surface of the earth is
considered as a plane, or in which its spheroidal
shape is neglected.
Units of Measurement
•Sexagecimal units of angular measurement are
the degree, minute, and second. A plane angle
extending completely around a point equals 360
degrees; 1 degree = 60 minutes, 1 minute = 60
seconds.
•Centesimal units, the grad, or grade, is the angular
unit. 400 grads = 360 degrees. 1 grad = 100
centesimal minutes; 1 centesimal minute = 100
centesimal seconds.
METHODS OF SURVEYING:
•Control Survey - Made to establish the horizontal
and vertical positions of arbitrary points.
•Boundary Survey - Made to determine the length
and direction of land lines and to establish the
position of these lines on the ground.
•Topographic Survey - Made to gather data to
produce a topographic map showing the
configuration of the terrain and the location of
natural and man-made objects.
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•Hydrographic Survey - The survey of bodies of
water made for the purpose of navigation, water
supply, or sub-aqueous construction.
•Mining Survey - Made to control, locate and map
underground and surface works related to mining
operations.
•Construction Survey - Made to lay out, locate and
monitor public and private engineering works.
•Route Survey - Refers to those control,
topographic, and construction surveys necessary
for the location and construction of highways,
railroads, canals, transmission lines, and pipelines.
•Photogrammetric Survey - Made to utilize the
principles of aerial photogrammetry, in which
measurements made on photographs are used to
determine the positions of photographed objects.
•Astronomical survey - generally involve imaging
or "mapping" of regions of the sky using telescopes.
Problem 1:
Line AB 100 m long was paced by a surveyor four
times with the following data: 144, 145, 143, and
146. Another line CD was paced for four times
again with the following results: 893, 892, 894, and
895.
a. Find the pace factor of the surveyor.
b. Determine the actual length of line CD.
c. If line CD was at elevation of 478 m above the
sea level and the radius of the earth is 6400 km,
determine the reduced distance of line CD along
the sea level.
Problem 2:
A rectangular lot having a dimension of 217.3 m by
148.5 m was measured by a 30 m tape which is
0.04m too long.
a. What is the correct width of the lot?
b. Find the error in the area.
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Surveying 1
c. If the same tape is used to set a baseline with
length of 837.5m, determine the actual distance
to be laid out.
Problem 3:
A 100 m steel tape is used to measure the distance
of the line and found to be 1539.28 m long. During
measurement, the tape is supported at the ends
under a pull of 10 kg and the observed mean
temperature is 31ᵒC. The tape is of standard length
at 20ᵒC and a tension of 12 kg. The cross-sectional
area of the tape is 0.035 cm2. The coefficient of linear
expansion is 0.0000116/ᵒC. and the modulus of
elasticity of steel is 2.0x106 kg/cm2. The tape weighs
1.5 kg.
a. Determine the total correction for
temperature.
b. Find the total correction due to pull/tension.
c. Determine the total correction due to sag.
d. What is the correct length of the line?
𝐏𝐚𝐜𝐞 𝐅𝐚𝐜𝐭𝐨𝐫 =
Length(or Distance)
Average No. of Paces
Error in Tape:
Measure
Layout
Too Long
Add
Subtract
Lcorrect = Linitial ± e(
Too Short
Subtract
Add
Linitial
Ltape
)
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Civil Engineering November 2020
Tape Correction
1. Correction due to Temperature
C T = L (T − To )
α – coefficient of linear (or thermal) expansion
– use 11.6 x 10-6/°C if not given
L – measured length/length of tape
T – temperature during measurement
To – standard temperature
2. Correction due to Pull
CP =
(P − Po )L
aE
P – applied pull/tension
Po – standard pull/tension
L – measured length/length of tape
a – cross-sectional area of tape
E – elastic modulus of steel
3. Correction due to Sag
CS =
w 2L3
24P 2
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Problems for Practice:
1. The taped distance of a line was 99.812 m using a
100m steel tape weighing 2 kg at a pull of 10 kg and
temp of 320C. The difference in elevation between
the end points is 45cm. The tape is exactly 100m at
a temp of 280C and standard pull of 10 kg. If the
coefficient of expansion of the tape is 0.0000118/0C
and the tape was supported at the ends and at 25m
interval during measurement find the correct
horizontal distance of the line.
Answer: 99.805m
Surveying 1
4. A 50 m steel tape was standardized and
supported throughout its whole length and found
to be 0.00205 m longer at an observed temperature
of 31.80C and a pull of 10 kg. This tape was used to
measure a line which was found to be 662.702 m at
an average temperature of 24.60C using the same
pull. Use coefficient of expansion of 11.6 x 10 -6/0C.
a. Compute the standard temperature.
b. Compute the total temperature correction.
c. Compute the correct length of the line.
Answers: a) 28.270C; b) -0.028 m; c) 662.67 m
2. A 100 m tape is suspended at the ends under a
pull of 15 kg. It has also supports at 30 m and 75 m
marks. What is the total correction due to sag if the
tape weighs 2.4 kg?
Answer: 0.014 m
3. In five trials of walking along a 90 m course on
fairly level ground, a pacer for a survey party
counted 51, 52.5, 51.5, 52.5 and 51.5 strides
respectively. He then started walking an unknown
distance XY in four trials which were recorded as
follows: 88.5, 89, 88 and 87 strides. Determine the
following:
a. Pace factor of the pacer.
b. Length of line XY.
c. Percentage of error in the measurement if the
taped length of XY is 150.5 meters.
Answers: a) 0.869 m/pace; b) 153.16 m; c) 1.77%
w – linear weight of tape
L – distance between supports
P – applied pull/tension
Manila FB: @ReviewInnovationsOfficial
 (02) 8735-9161
0919-227-9194
Cebu FB: Excel-RI CE Review Specialist Inc.
 (032) 268-5989 0919-822 -5048
Davao FB: Review Innovations Davao Branch
 (082) 221-1121 0930-256-0998