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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.

Structural Analysis
Structural Analysis
6th Edition
ISBN:9781337630931
Author:KASSIMALI, Aslam.
Publisher:KASSIMALI, Aslam.
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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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.
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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