Post on 20-May-2022
SURVEYING & LEVELLING
Lecture # 2 Civil Engineering Dept.
CHAINING ON LEVEL GROUND
To chain the line, the leader moves forward by dragging
the chain and by taking with him a ranging rod and arrows.
The follower stands at the starting station by holding the
other end of the chain
When the chain is fully extended, Leader holds the
ranging rod and the ranging process is done with the help
of directions given by the follower
Then the follower holds the zero end of the chain by
touching the station point
The leader stretches the chain and finally place it on the
line. Once done he inserts an arrow in the ground at the
end of the chain
Now the leader moves forward by dragging the chain with
arrows and the ranging rod and the whole process is
repeated again but this time there should be a surveyor on
the starting station to conduct the ranging operation
Chaining (contd.) On Sloping Ground
There are two methods. Direct and Indirect Method
Direct Method
The distance is measured in small horizontal stretches. Say a1, a2
…an. with suitable length of chain or tape. This method is direct one.
Finally the total horizontal distances are added to get the required
distances.
w
x
y
z
c
b
a
Chaining (contd.)
Chaining (contd.)
Indirect Method:
Horizontal distance of the segment is calculated by knowing sloping
length of the segment and angle of inclination of that with horizontal.
If the elevation difference between 2 terminals points and the sloping
distance between 2 terminal points is known the horizontal distance D
can be calculated as
D = (l²-h²)
Chaining (contd.) Indirect method (Vertical angle measured) Clinometer to measure vertical angle
D1 = s1×cosΦ1
The e ui ed ho izontal distance D =∑s cosΦ
D2
Φ1
Φ2
s1
s2
C
B
A
D1 Indirect method (difference in height)
D = √( s 2 - h 2 ) D
h
s A
B C
Indirect method (Hypotensual allowance)
B
A’
C
A
θ
1 chain
BA / = BC = 1 CHAIN
BA = 1 CHAIN × sec θ
AA / = BA - BA / = 1 CHAIN ( sec θ – 1)
TAPE CORRECTIONS
1. TEMPERATURE CORRECTION
This correction is necessary because the length of the
tape or chain may be increased or decrease due to rise
or fall of temperature, respectively, during
measurement
The sign of correction may be positive or negative
Coefficient of thermal expansion for the steel tape can
be assumed to be 11 x 10-6 per degree centigrade, if
not known
Where,
Ct Correction for temperature (m)
Tm Temperature during measurement (oC)
To Temperature at which tape was standardized (oC)
L Length of the tape (m)
Coefficient of thermal expansion (oC-1)
𝐶 = 𝛼 𝑇 − 𝑇 𝐿
2. PULL CORRECTION
Due to the elastic properties of the tape material,
when pull is applied, the strain will vary according to
the variation of applied pull, and hence necessary
correction should be applied
The sign of correction may be positive or negative
Modulus of elasticity of the tape may be assumed to be
2.1 x 106 kg/cm2, if not known
Where,
Cp Pull Correction (m)
Pm Pull applied during measurement (kg)
Po Pull at which tape was standardized (kg)
L Length of the tape (m)
E Modulus of elasticity (kg/cm2)
A Cross-sectional area of tape (cm2)
𝐶 = 𝑃 − 𝑃 𝐿𝐴 𝐸
3. SLOPE CORRECTION 𝐶ℎ = 𝐿 − 𝐿 cos 𝜃
Where,
Ch Slope correction (m)
h Vertical distance between
two points (m)
𝐶ℎ = 𝐿 − 𝐿 − ℎ 𝐶ℎ = ℎ2𝐿
h L
Ch (always negative)
A
B
C
(APPROXIMATE)
(EXACT)
(EXACT)
4. SAG CORRECTION
This correction is necessary when the measurement is
taken with tape in suspension (always negative)
𝐶 = 𝐿 𝐿24 𝑛 𝑃 = 𝐿𝑊24 𝑛 𝑃
Where,
Cs Correction for sag (m)
Pm Pull applied during measurement (kg)
n number of spans
w weight of tape per unit length (Kg/m)
W Total weight of the tape (kg)
5. NORMAL TENSION
The tensions at which the effect of pull is neutralized
by the effect of sag is known as normal tension
At this the elongation due to pull is balanced by the
shortening due to sag. Mathematically, 𝐶 = 𝐶 𝐿𝑊24 𝑛 𝑃 = 𝑃 − 𝑃 𝐿𝐴 𝐸
𝑊24 𝑃 = 𝑃 − 𝑃𝐴 𝐸
Let, Pn be the Normal tension or pull, then
(Considering n = 1)
𝑊 𝐴 𝐸24 = 𝑃 𝑃 − 𝑃
By substituting the values of Po, W, A and E, we get the
final equation of the following form, 𝑃 ± 𝑃 ± 𝐶 = 0
Pn is determined by trial and error method
CHAIN CORRECTIONS
1. CORRECTION FOR INCORRECT LENGTH 𝐿 = 𝐿′𝐿 𝐿
Where,
L Standard/ true length of chain (m)
Lm Measured length of the line (m)
Lt True length of the line (m)
L’ True length error (m)
(Positive when chain is too long and negative when chain is too short)
2. CORRECTION FOR INCORRECT AREA
𝐴 = 𝐿′𝐿 𝐴
Where,
L Standard/ true length of chain (m)
L’ True length error (m)
Am Measured length of the line (m2)
At True area (m2)
Numerical 1
A 20 m chain was used to measure the distance between two
stations, which was found to be 2500 m. Then same distance
when measured with a 30 m chain was found to be 2495 m. If
the 20 m chain was 0.07 m too long, what was the error in the
30 m chain?
𝐻𝑖𝑛𝑡: 𝐿 = 𝐿′𝐿 𝐿
(Ans. 0.17 m)
Numerical 2
A line was measured by a 20 m chain which was accurate
before starting the day’s work. After chaining 900 m, the
chain was found to be 6 cm too long. After chaining a total
distance of 1, 575 m, the chain was found to be 14 cm too long.
Find the true distance of the line.
𝐻𝑖𝑛𝑡: 𝐿 = 𝐿′𝐿 𝐿
(Ans. 1,579.72 m)
Numerical 3
An old map was plotted to a scale of 40 m to 1 cm. Over the
years, this map has been shrinking, and a line originally 20 cm
long is only 19.5 cm long at present. Again the 20 m chain was 5
cm too long. If the present area of the map measured by
planimeter is 125.50 cm2, find true area of the land surveyed.
𝐻𝑖𝑛𝑡: 𝐴 = 𝐿′𝐿 𝐴
(Ans. 21.23 hectares)
CONCLUDED