The following corrections are to be applied to the linear measurements with a chain or a tape where such accuracy is required.
1) Correction for Standard Length of Tape
Before using a tape, its actual length is ascertained by comparing it with a standard tape of known length. The designated nominal length of a tape is its designated length e.g. 30m or 100m. The absolute length of a tape is its actual length under specified conditions. Incorrect length of a tape can be one of the most important errors. It is systematic. An error due to incorrect length of a tape occurs each time the tape is used. If the true length, known by standardization, is not exactly equal to its nominal value of 100.00 m recorded for every full length, the correction can be determined and applied from the formula given below.
Where,
l - Actual tape length at the field
l’ - Nominal tape length
L - Measured length of the line
Sometimes, the changes in length are quite small and of little importance in many types of surveys. The actual length of a working tape must be compared with a standard tape periodically. When its actual length is known, the tape is said to be standardized. A correction must be added or subtracted to a measured distance whenever its standardized length differs from its nominal or graduated length. In measuring unknown distances with a tape that is too long, a correction must be added. Conversely, if the tape is too short, the correction will be minus, resulting in decrease.
2) Correction for Temperature
This correction is necessary because the length of the tape or chain may be increased or decreased due to rise or fall of temperature during measurement. Steel tapes are standardized for 680F or 200C. A temperature higher than or lower than this value causes a change in length that must be considered. The coefficient of thermal expansion and contraction of steel used in ordinary tapes is approximately 1.16 x 10-5 per length per 0C. For any tapes the correction for temperature can be computed and applied using the formula.
Ct = πΌ (Tm – T0) L
Corrected Length = L + Ct
Where,
Ct - Correction in length of a line due to nonstandard temperature
πΌ− Coefficient of thermal expansion and correction of the tape
Tm - Tape temperature at the time of measurement
To - Tape temperature when it has standard length
L - Measured length of the line
3) Correction for Pull / Tension
During measurement the applied pull may be either more or less than the pull at which the chain or tape was standardized. Due to the elastic property of materials the strain will vary according to the variation of applied pull and hence necessary correction should be applied. When a steel tape is pulled with a tension greater than its standard, the tape will stretch and be no longer than its standard length. Conversely, if less than standard pull is used, the tape will be shorter than its standard length. The modulus of elasticity of the tape regulates the amount that it stretches. Correction pull can be computed and applied using the following formula.
Corrected Length = L + Cp
Where,
Cp - Total elongation in tape length due to the pull, in meter.
P1- Pull applied to the tape, in Kg.
P - Standard pull for the tape, in Kg.
A - Cross sectional area of the tape.
E - Modulus of elasticity of the steel.
L - Measured length of the line in meter.
4) Correction for Sag
In case of suspended measurement across a span L the chain or tape sag to take the form of curve known as catenary. Sag shortens the horizontal distance between end graduations, because the tape length remains the same. Sag can be diminished but not eliminated unless the tape is supported throughout. The following formulas are used to compute the sag correction.
Where,
Cs - Correction for sag in meter.
Ls - Unsupported length of the tape in meter.
w - Weight of the tape per meter of length.
W - Total weight of the tape between the supports in Kg.
P1 - Pull on the tape in Kg.
In measuring lines of unknown length, the sag correction is always negative. After a line has been measured in several segments and a sag correction has been calculated for each segment, the corrected length is given by
Corrected Length = L + Ξ£Cs
Where,
L - Recorded length of the line
Ξ£Cs - Sum of individual sag corrections.
5) Normal Tension
By equating equations Cs = Cp,
i.e. the elongation due to increase in tension is made equal to the shortening due to sag; thus, the effect of the sag can be eliminated. The pull that will produce this condition, called Normal Tension Pn is given by the formula.
Where,
Pn - Normal tension
P - Standard pull for the tape, Kg
W - Total weight of the tape between the support, Kg
A - Cross sectional area of tape
E - Modulus of elasticity of steel
6) Correction for Alignment
Generally, a survey line is set out in a continuous straight line. Sometimes, it becomes necessary due to obstruction to follow a bent line which may be composed of two or more straight portions subtending an angle other than 180ΒΊ as shown in Fig. 1.
Let AC = L1, CB= L2
< BAC = π1, BAC = π2
Length AB = L1 cos π1 + L2 cos π2
The required correction = (L1+ L2) - (L1 cos π1 + L2 cos π2)
7) Correction for Slope
The distance measured along the slope between two stations is always greater than the horizontal distance between them. The difference in slope distance and horizontal distance is known as slope correction which is always subtractive.
Let,
L - Slope distance AB
D - Horizontal distance AC
H - Difference in reduced levels of A and B
Question 1
The length of a survey line measured with a 30m chain was found to be 631.5m. When the chain was compared with a standard chain, it was found to be 0.1m too long. Find the true length of the survey line.
Solution
L’ = 30.1m. L = 30m
Measured length of the survey line = 631.5m
Thus, true length of the survey line = 30.130 x 631.5
= 633.603 m.
Question 2
A 20m chain was found to be 4 cm too long after chaining 1400m. It was 8 cm too long at the end of day’s work after chaining a total distance of 2420m. If the chain was correct before commencement of the work, find the true distance.
Solution
The correct length of the chain at commencement = 20m
The length of the chain after chaining 1400m = 20.04 m
The mean length of the chain while measuring = (20+20.04)/2
= 20.02m
The true distance for the wrong chainage of 1400m = (20.02/20)x1400
= 1401.4 m
The remaining distance = 2420-1400
= 1020m
The mean length of chain while measuring the remaining distance = (20.08+20.04)/2
= 20.06m
The true length of remaining 1020m = (20.06/20) x 1020
=1023.06m
Hence, the total true distance = 1401.4 + 1023. 06
= 2424.46 m
Question 3
A line was measured with a steel tape which was exactly 30 meters at 20℃ at a pull of 100N, the measured length being 1650.00 meters. The temperature during measurement was 30°C and the pull applied was 150N. Find the length of the line, if the cross-sectional area of the tape was 0.025 sq.cm. The co-efficient of expansion of the material of the tape per 1 ΒΊC = 3.5x10-6 and the modulus of elasticity of the material of the tape = 2.1x105 N/mm2.
Solution
i) Correction of temperature per tape length
Ct = πΌ (Tm – T0) L
= 0.0000035 (30 – 20) x 30
= 0.00105m (+ve)
ii) Correction for pull per tape length
CP = ((P-P0) x L)/(A E)
= ((150-100) x 30)/(2.5x2.1x105)
= 0.00286m (+ve)
Combined correction = 0.00105+0.00286
= 0.00391m
True length of the tape = 30+0.0039
=30.0039m
True length of the line = (30.0039x1650.00)/30
=1650.21m
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