It is necessary to apply the following corrections to the measured length of a line in order to obtain its true length: 1. Correction for Absolute Length 2. Correction for Temperature 3. Correction for Pull 4. Correction for Sag 5. Correction for Slope.
1. Correction for Absolute Length:
The absolute length of a tape is expressed as its standard length plus or minus a correction
The correction for the measured length is given by the formula:
Where Ca= the correction for absolution length.
L= the measured length of a line
I= the standard length of a tape.
C= the correction to a tape length
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This correction may be +ve or -ve depending upon the type of correction needed by the tape.
2. Correction for Temperature (+ve or – ve):
It is necessary to apply this correction since the measurements are not made at a temperature at which the tape is standardised. The length of a tape increases or decreases with the increase or decrease in temperature than the standardising temperature.
If Ct= the correction for temperatures in m
α = the co-efficient of thermal expansion
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Tm = the mean temperature during measurement
Ts = the temperature at which the tape is standardized
L= the measured length in m.
The sign for correcting is plus or minus according as Tm is greater or less than Ts. The average values of coefficients of expansion for steel and invar are 12 x 10-6 and 0.9 x 10-6 per degree centigrade respectively.
3. Correction for Pull (+ve or – ve):
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The correction is necessary when the pull applied during measurement is different from that at which the tape is standardised.
If Cp= the correction for pull in m
Pa= the pull applied during measurement in kg
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Ps= the pull at which the tape is standardized in kg
L= the measured length in m
A= the cross sectional area of the tape in sq.cm
E= the modulus of Elasticity of the tape material.
The correction may be +ve or -ve according as Pa is greater or less than Ps. The general values of E for steel and invar are 2.1 x 106 kg/sq. cm and 1.54 x 106 kg/sq. cm respectively.
4. Correction for Sag (-ve) (Fig. 2.24):
When a tape is stretched between two supports, it takes the form of a catenary which is assumed to be a parabolic curve. The correction for sag is the difference in length between the are and the subtending chord. It is required only when the tape during measurement is kept suspended. Since the effect of sag is to make the measured length too great, this correction is always —ve.
If Csg= the correction for sag in m
I1= the distance between supports in m
w= the weight of the tape in kg per m
Pa= the pull applied in kg.
Normal Tension:
The tension at which effect of pull and sag are neutralised is called the normal tension. It may be obtained by equating the corrections for pull and sag.
5. Correction for Slope (-ve) (Fig. 2.25):
The correction-is required when the points of supports are not at the same level.
If Csi=the correction for slop in m
I= the length measured along slope in m
h= the vertical distance supports in m
θ= the angle of slope
Examples on Tape Corrections:
Example 1:
A steel tape was standardised as 30 m at 18°C. A line was measured as 460.4 m with temperature during measurement as 30°C. Calculate the true distance of the line.
Co-efficient of expansion for steel = 0.000012 per degree rise of temperature.
Solution:
Example 2:
A line was measured with a steel tape which was exactly 30 m at a pull of 5 kg and the measured length was 229.621 m. The pull applied during measurement was 10 kg and the tape was uniformly supported. Find the true length of the line if the cross- sectional area of tape was 0.02 cm2 and the modulus of Elasticity = 2.1 x 106 kg per cm2.
Solution:
Example 3:
A 50 m tape is suspended between the ends under a pull of 15 kg. The weight of the tape is 1.5 kg. Find the corrected length of the tape between its ends.
Solution:
Example 4:
A steel tape was exactly 30 m long at 18°C when supported throughout its length under a pull of 8 kg. A line was measured with a tape under a pull of 12 kg and found to be 1602 m. The mean temperature during the measurement was 26°C.
Assuming the tape to supported at every 30 m, Calculate the true length of the line, given that cross-sectional area of the tape = 0.04 cm2, the weight of 1 cu. cm is 0.0077 kg, the co-efficient of expansion = 0.000012 per 1°C and the modulus of elasticity = 2.1 x 106 kg/cm2.
Solution:
