lOMoARcPSD|36000955
Plate No. 2 Errors in Measurement Solutions
BS Civil Engineering (University of the East (Philippines))
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lOMoARcPSD|36000955
Plate No. 2 – Errors in Measurement
1. A 30 m steel tape is of standard length @ 20°C. If the coefficient of thermal
expansion of steel 11.6 x 10-6/°C, what distance should be laid-out using this tape to
establish two point exactly 1234.5 m apart when tape is @ 29°C.
Given:
Solution:
𝒕
𝒕
𝒕
Laying Out
𝟔
𝒐
𝟑
Req’d:
T (laying out)
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lOMoARcPSD|36000955
Plate No. 2 – Errors in Measurement
2. A 30 m steel tape weighing 1.45 kg is of standard length under a pull of 5 kg. supported for
full length. The tape was used in measuring a line 938.55m long on a smooth level ground
under a steady pull of 10 kg. Assuming E = 2.0 x 106 kg/cm2 and the unit weight of steel be
7.9 x 10-3 kg/cm3. Determine,
a. Cross sectional area of the tape
Given:
b. Correction for increase in tension (total)
c. Correct length of the line measured
Req’d:
a. A
b. Cp(total)
c. T
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lOMoARcPSD|36000955
Plate No. 2 – Errors in Measurement
Solution:
Solution:
(
)
.
( . ×
)
𝟐
Solution:
(𝑷 𝑷𝒐 )
𝑨𝑬
𝒑
.
𝒑(𝒕𝒐𝒕𝒂𝒍)
c.
(
)
( . ×
𝒑(𝒕𝒐𝒕𝒂𝒍)
𝒑(𝒕𝒐𝒕𝒂𝒍)
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(per tape meter length)
𝒑
lOMoARcPSD|36000955
Plate No. 2 – Errors in Measurement
3. A 50 m steel tape weighing 0.04 kg/m and is supported at its endpoints and at the 8-m and
25-m marks. If the pull of 6 kg is applied, determine the following:
a. Correction due to sag between the 0-m & 8-m mark, 8-m & 25-m mark and 25-m & 50-m
marks
b.Correction due to sag for one tape length
Given:
c. Correct distance between the ends of the tape
Req’d:
b. Cs(total)
c. T
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lOMoARcPSD|36000955
Plate No. 2 – Errors in Measurement
Solution:
𝐬
𝐬𝟏
Solution:
𝐰 𝟐 𝐋𝟑
𝟐𝟒𝐏 𝟐
𝟒
𝐬𝟐
𝐬𝟑
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𝟑
𝟐
lOMoARcPSD|36000955
Plate No. 2 – Errors in Measurement
Solution:
𝒔(𝒕𝒐𝒕𝒂𝒍)
(
𝒔𝟏
)
𝒔𝟐
𝒑(𝒕𝒐𝒕𝒂𝒍)
Solution:
c.
𝒔𝟑 (per tape meter length)
(
𝟐
)
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lOMoARcPSD|36000955
Plate No. 2 – Errors in Measurement
4. A steel tape weighing 0.85 kg has a cross-sectional area of 0.05cm2. The tape measures
exactly 30 m when supported throughout its length under a standard pull of 5.5 kg. If the
modulus of elasticity is 2.10 x 106 kg/cm2, determine the tension required to make the tape
equal to its nominal length when supported only at the end points.
Given:
Solution:
(by trial and error)
𝑵
Try PN = 16 kg
.
Req’d:
( .
) ( .
𝑵
.
)( .
×
𝒔
)
…so try PN in between 16 and 17 kg
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lOMoARcPSD|36000955
Plate No. 2 – Errors in Measurement
Solution:
by using shift-solve in calculator)
𝑵
Try PN = 16.7512 kg
𝑵
𝒔
𝑵
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lOMoARcPSD|36000955
Plate No. 2 – Errors in Measurement
5. A 50 m tape of standard length has a weight of 0.05 kg/m with a cross sectional area of 0.04
sq. cm. It has a modulus of elasticity of 2.10 x 106 kg/cm2. The tape is of standard length under
a pull of 5.5 kg when supported throughout its length and a temperature of 20°C. This tape
was use to measure a distance of 458.65m long. At the time of measurement the pull applied
was 8 kg with the tape supported only at its end points and the temperature observed was
18°C. Assuming that the Coefficient of thermal expansion of the tape is 11.6 x 10-6/°C.
a. Compute the correction due to applied pull of 8 kg.
b.Compute the correction due to the weight of the tape
c. Compute the true length of the measured distance due to the combined effects of tension, sag
and temperature.
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lOMoARcPSD|36000955
Plate No. 2 – Errors in Measurement
Given:
Req’d:
b. Cs
c. T
Solution:
𝒑
𝒑
(𝑷 𝑷𝒐 )
𝑨𝑬
.
(per tape meter length)
.
( . ×
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)
𝟑
lOMoARcPSD|36000955
Plate No. 2 – Errors in Measurement
Solution:
Solution:
𝐬
𝐬
𝐰 𝟐 𝐋𝟑
𝟐𝟒𝐏 𝟐
𝟔
𝒕
𝟏
(
)
Measuring
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