M5-2 MEASUREMENTS WITH TAPE. A rectangular lot was measured using a 50-m steel tape which was found to be 0.025 m too short. If the recorded length and width of the lot are 180.455 m and 127.062 m, respectively, determine the following: a) Actual dimensions of the lot. b) Error in area introduced due to the erroneous length of tape.
M5-2 MEASUREMENTS WITH TAPE. A rectangular lot was measured using a 50-m steel tape which was found to be 0.025 m too short. If the recorded length and width of the lot are 180.455 m and 127.062 m, respectively, determine the following: a) Actual dimensions of the lot. b) Error in area introduced due to the erroneous length of tape.
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:M5-2 MEASUREMENTS WITH TAPE. A rectangular lot was measured using a 50-m
steel tape which was found to be 0.025 m too short. If the recorded length
and width of the lot are 180.455 m and 127.062 m, respectively, determine
the following:
a) Actual dimensions of the lot.
b) Error in area introduced due to the erroneous length of tape.
M5-3 CORRECTION DUE TO SLOPE. A line AB cannot be measured directly
because of an obstruction on line. Accordingly, the two lines AC and CB
were measured as 2,400.850 m and 1,320.420 m, respectively. Point C was
set at a perpendicular distance of 155 m from point D on line AB. Using the
approximate slope correction formula for steep slopes, determine the
length of AB.
M5-4 CORRECTION DUE TO TEMPERATURE. A steel tape, known to be of standard
length at 20°C, is used in laying out a runway 2,500.00 m long. If its
coefficient of linear expansion is 0.0000116/1°C, determine the temperature
correction and the correct length to be laid out when the temperature is
42°C.
M5-5 CORRECTION DUE TO TENSION. 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 938.55 m long on smooth level ground under a
steady pull of 10 kg. Assuming E = 2.0x106 kg/cm2 and the unit weight of
steel to be 7.9x10-3 kg/cm³, determine the following:
a) cross-sectional area of the tape.
b) correction for increase in tension.
c) correct length of the line measured.
M5-6 CORRECTION DUE TO SAG. A 50-m steel tape weighs 0.04 kg/m and is
supported at its end points and at the 8-m and 25-m marks. If a pull of 6 kg
is applied, determine the following:
a) Correction due to sag between the 0-m and 8-m marks, 8-m and 25-m
marks, and the 25-m and 50-m marks.
b) Correction due to sag for one tape length.
c) Correct distance between the ends of the tape.
|
Steel Tape
50m --> P
Om
8m
25m
Support
at end
Intermediate
support
Support at
mid- point
Support
at end
-2
M5-7 NORMAL TENSION. A steel tape having a cross-sectional area of 0.06 cm²
and a modulus of elasticity of 2.0x106 kg/cm², weighs 0.03 kg/m. Its length
is 30.00 m when standardized at a pull of 5 kg and supported throughout its
length. Determine the tension at which the effect of sag will be eliminated
by the elongation of the tape due to increased tension.
Fia. 10-6. Determining normal tension.
-0-m
mark
Steel Tape(Held
above ground)
-30-m
mark
-P= ?
W = wL
2nd Support
Ist Subport
30.00 m
Steel Tope (Supported
throughout on ground surface)
-30-m
mark
mark
--->P = 5 kg
P: 5 kg w
M5-8 COMBINED CORRECTIONS. A 50-m steel tape is of standard length under a
pull of 5.5 kg when supported throughout its entire length. The tape weighs
0.05 kg/m has a cross-sectional area of 0.04 sq.cm, and being made of
steel, its modulus of elasticity is 2.10x106 kg/cm². This tape was used in the
field to measure a distance that was determined to be 458.650 m. At the
time the measurement was made, the constant pull applied was 8 kg with
the tape supported only at its end points. Determine the correct length of
the line.
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