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El t Element ary Surveying Tape corrections

El tElementary SuSu ey grveying - mindthreshold · 04-07-2011  · More problems • A rectangular building 250.00m by 130.00m is to be laid out with a 30‐m long steel tape. If

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Page 1: El tElementary SuSu ey grveying - mindthreshold · 04-07-2011  · More problems • A rectangular building 250.00m by 130.00m is to be laid out with a 30‐m long steel tape. If

El tElementary SurveyingSu ey g

Tape corrections

Page 2: El tElementary SuSu ey grveying - mindthreshold · 04-07-2011  · More problems • A rectangular building 250.00m by 130.00m is to be laid out with a 30‐m long steel tape. If

Prepared by: Andre‐Paul C. Ampong 3

Page 3: El tElementary SuSu ey grveying - mindthreshold · 04-07-2011  · More problems • A rectangular building 250.00m by 130.00m is to be laid out with a 30‐m long steel tape. If

Correction due to incorrect tape lengthCorrection due to incorrect tape length

• When measuring the distance between twoWhen measuring the distance between two points:– With a tape too long add the correction– With a tape too long, add the correction– With a tape too short, subtract the correction 

Wh l i t li f d i d l th• When laying out a line of desired length:– With a tape too long, subtract the correction– With a tape too short, add the correction

Prepared by: Andre‐Paul C. Ampong 4

Page 4: El tElementary SuSu ey grveying - mindthreshold · 04-07-2011  · More problems • A rectangular building 250.00m by 130.00m is to be laid out with a 30‐m long steel tape. If

Correction due to incorrect tape lengthCorrection due to incorrect tape length

Prepared by: Andre‐Paul C. Ampong 5

Page 5: El tElementary SuSu ey grveying - mindthreshold · 04-07-2011  · More problems • A rectangular building 250.00m by 130.00m is to be laid out with a 30‐m long steel tape. If

Correction due to incorrect tape lengthCorrection due to incorrect tape length

Prepared by: Andre‐Paul C. Ampong 6

Page 6: El tElementary SuSu ey grveying - mindthreshold · 04-07-2011  · More problems • A rectangular building 250.00m by 130.00m is to be laid out with a 30‐m long steel tape. If

Correction due to incorrect tape lengthCorrection due to incorrect tape length

Prepared by: Andre‐Paul C. Ampong 7

Page 7: El tElementary SuSu ey grveying - mindthreshold · 04-07-2011  · More problems • A rectangular building 250.00m by 130.00m is to be laid out with a 30‐m long steel tape. If

Correction due to incorrect tape lengthCorrection due to incorrect tape length

NLTL −=Corr

IMLC ⎟

⎞⎜⎛= CorrI

CMLCLNL

C

±

⎟⎠

⎜⎝

Corr

ICMLCL ±=

Prepared by: Andre‐Paul C. Ampong 8

Page 8: El tElementary SuSu ey grveying - mindthreshold · 04-07-2011  · More problems • A rectangular building 250.00m by 130.00m is to be laid out with a 30‐m long steel tape. If

Correction due to incorrect tape lengthCorrection due to incorrect tape length

• A rectangular lot was measured using a 50‐mA rectangular lot was measured using a 50 m steel tape which was found out to be 0.025 m too short If the recorded length and width oftoo short. If the recorded length and width of the lot are 180.455 m and 127.062 m, respectively determine the following:respectively, determine the following:– Actual dimensions of the lotError in area introduced due to the erroneous– Error in area introduced due to the erroneous length of tape

Prepared by: Andre‐Paul C. Ampong 9

Page 9: El tElementary SuSu ey grveying - mindthreshold · 04-07-2011  · More problems • A rectangular building 250.00m by 130.00m is to be laid out with a 30‐m long steel tape. If

Correction due to incorrect tape lengthCorrection due to incorrect tape length

• A building 38 m x 45 m is to be laid out with aA building 38 m x 45 m is to be laid out with a 50‐m long metallic tape. If during standardization the tape is found to be onlystandardization the tape is found to be only 49.950 m, determine the following:– Dimensions to be laid out using the tape in order– Dimensions to be laid out, using the tape, in order that the building have the desired dimensions

– Using the same tape what should the diagonalsUsing the same tape what should the diagonals read?

Prepared by: Andre‐Paul C. Ampong 10

Page 10: El tElementary SuSu ey grveying - mindthreshold · 04-07-2011  · More problems • A rectangular building 250.00m by 130.00m is to be laid out with a 30‐m long steel tape. If

Correction due to slopeCorrection due to slope

Prepared by: Andre‐Paul C. Ampong 11

Page 11: El tElementary SuSu ey grveying - mindthreshold · 04-07-2011  · More problems • A rectangular building 250.00m by 130.00m is to be laid out with a 30‐m long steel tape. If

Correction due to slopeCorrection due to slope

• For gentle slopes (less than 20%)For gentle slopes (less than 20%)hCh 2

2

=

• For steep slopes (between 20% and 30%sh 2

3

42

82 sh

shCh +=

• For very steep slopes (greater than 30%)82 ss

Prepared by: Andre‐Paul C. Ampong 12

( )θcos1−= sCh

Page 12: El tElementary SuSu ey grveying - mindthreshold · 04-07-2011  · More problems • A rectangular building 250.00m by 130.00m is to be laid out with a 30‐m long steel tape. If

Correction due to alignmentCorrection due to alignment

• Considered of less importance compared toConsidered of less importance compared to the other errors

• Can be calculated using slope correction• Can be calculated using slope correction formulas

Prepared by: Andre‐Paul C. Ampong 13

Page 13: El tElementary SuSu ey grveying - mindthreshold · 04-07-2011  · More problems • A rectangular building 250.00m by 130.00m is to be laid out with a 30‐m long steel tape. If

Correction due to temperatureCorrection due to temperature

( )TTLC −=α ( )st TTLC =α

Prepared by: Andre‐Paul C. Ampong 14

Page 14: El tElementary SuSu ey grveying - mindthreshold · 04-07-2011  · More problems • A rectangular building 250.00m by 130.00m is to be laid out with a 30‐m long steel tape. If

ProblemProblem

• A steel tape known to be of standard length atA steel tape known to be of standard length at 20oC, is used in laying out a runway 2,500.00 m long If its coefficient of linear expansion ism long.  If its coefficient of linear expansion is 0.0000116/oC, determine the temperature correction and the correct length to be laidcorrection and the correct length to be laid out when the temperature is 42oC.

Prepared by: Andre‐Paul C. Ampong 15

Page 15: El tElementary SuSu ey grveying - mindthreshold · 04-07-2011  · More problems • A rectangular building 250.00m by 130.00m is to be laid out with a 30‐m long steel tape. If

Correction due to tensionCorrection due to tension

( )LPPC sm −=AE

Cp =

Prepared by: Andre‐Paul C. Ampong 16

Page 16: El tElementary SuSu ey grveying - mindthreshold · 04-07-2011  · More problems • A rectangular building 250.00m by 130.00m is to be laid out with a 30‐m long steel tape. If

ProblemProblem

• A heavy 50‐m tape having a cross‐sectionalA heavy 50 m tape having a cross sectional area of 0.05 cm2 has been standardized at a tension of 5 5 kg If E = 2 10 x 106 kg/cm2tension of 5.5 kg.  If E = 2.10 x 10 kg/cm , determine the elongation of the tape if a pull of 12 kg is appliedof 12 kg is applied.

Prepared by: Andre‐Paul C. Ampong 17

Page 17: El tElementary SuSu ey grveying - mindthreshold · 04-07-2011  · More problems • A rectangular building 250.00m by 130.00m is to be laid out with a 30‐m long steel tape. If

Correction due to sagCorrection due to sag

32LC ω= 224P

Cs =

Prepared by: Andre‐Paul C. Ampong 18

Page 18: El tElementary SuSu ey grveying - mindthreshold · 04-07-2011  · More problems • A rectangular building 250.00m by 130.00m is to be laid out with a 30‐m long steel tape. If

ProblemProblem

• A 30‐m tape is supported only at the ends andA 30 m tape is supported only at the ends and under a steady pull of 8 kg.  If the tape weighs 0 91 kg determine the sag correction and the0.91 kg, determine the sag correction and the correct distance between the ends of the tapetape.

Prepared by: Andre‐Paul C. Ampong 19

Page 19: El tElementary SuSu ey grveying - mindthreshold · 04-07-2011  · More problems • A rectangular building 250.00m by 130.00m is to be laid out with a 30‐m long steel tape. If

Correction due to windCorrection due to wind

• Error due to wind is similar in effect to errorError due to wind is similar in effect to error due to sag

• May be avoided by not conducting survey on a• May be avoided by not conducting survey on a windy day

Prepared by: Andre‐Paul C. Ampong 20

Page 20: El tElementary SuSu ey grveying - mindthreshold · 04-07-2011  · More problems • A rectangular building 250.00m by 130.00m is to be laid out with a 30‐m long steel tape. If

Combined corrections (problem)Combined corrections (problem)

• A line was measured to be 2582.35 m using a 30‐m gsteel tape supported throughout its length under a pull of 4 kg.  The mean temperature during the measurement is 35oC The tape used has a crossmeasurement is 35 C.  The tape used has a cross‐sectional area of 0.03 square centimeters and has a standard length at 20oC under a pull of 5 kg.  The 

d l f l f h 6 k / 2 dmodulus of elasticity of the tape is 2 x 106 kg/cm2 and the coefficient of thermal expansion is 0.0000116/oC.– Determine the error due to temperature changeDetermine the error due to temperature change– Determine the error due to tension– Determine the corrected length of the line

Prepared by: Andre‐Paul C. Ampong 21

Page 21: El tElementary SuSu ey grveying - mindthreshold · 04-07-2011  · More problems • A rectangular building 250.00m by 130.00m is to be laid out with a 30‐m long steel tape. If

More problemsMore problems 

• A slope distance of 465 82m is measuredA slope distance of 465.82m is measured between two points with a slope angle of 12o35’ What is the corresponding horizontal35 . What is the corresponding horizontal distance between the points?

• A line measured with a 30 m steel tape was• A line measured with a 30‐m steel tape was recorded as 325.70m. If the tape is found 30 05m long during standardization what is30.05m long, during standardization, what is the correct length of the line?

Prepared by: Andre‐Paul C. Ampong 22

Page 22: El tElementary SuSu ey grveying - mindthreshold · 04-07-2011  · More problems • A rectangular building 250.00m by 130.00m is to be laid out with a 30‐m long steel tape. If

More problemsMore problems 

• A rectangular building 250.00m by 130.00m is to be g g ylaid out with a 30‐m long steel tape. If during standardization the tape is found to be 30.03m, what should be the correct length and width to be laid out?should be the correct length and width to be laid out?

• A line measured with a 50‐m long steel tape was determined to be 645.22m when the average gtemperature during taping was 15.75oC. If the tape is of standard length at 20oC and the coefficient of thermal expansion of steel is 0 0000116/1oC what isthermal expansion of steel is 0.0000116/1 C, what is the correct length of the measured line?

Prepared by: Andre‐Paul C. Ampong 23

Page 23: El tElementary SuSu ey grveying - mindthreshold · 04-07-2011  · More problems • A rectangular building 250.00m by 130.00m is to be laid out with a 30‐m long steel tape. If

More problemsMore problems 

• A steel tape with a cross‐sectional area of 0.03cm2 is p30.00m long under a pull of 5kg when supported throughout. It is used in measuring a line 875.63m long under a steady pull of 10kg Assuming E = 2 0 x 106under a steady pull of 10kg. Assuming E = 2.0 x 10kg/cm2, what is the elongation of the tape due to increase in tension? What is the correct length of the 

d lmeasured line?• A 30‐m steel tape weighs 1.05kg and is supported at its end points and at the 10‐m and 25‐mmarks If a pull ofend points and at the 10‐m and 25‐m marks. If a pull of 6.0kg is applied to the ends of the tape, what is the correction due to sag for a full tape length?

Prepared by: Andre‐Paul C. Ampong 24

Page 24: El tElementary SuSu ey grveying - mindthreshold · 04-07-2011  · More problems • A rectangular building 250.00m by 130.00m is to be laid out with a 30‐m long steel tape. If

HomeworkHomework

• Using a 25‐m tape a square lot was measuredUsing a 25 m tape, a square lot was measured and found to have an area of 1 hectare.  If the total error in area is 4 004 square meter shorttotal error in area is 4.004 square meter short, what is the error in each tape length?

Prepared by: Andre‐Paul C. Ampong 25

Page 25: El tElementary SuSu ey grveying - mindthreshold · 04-07-2011  · More problems • A rectangular building 250.00m by 130.00m is to be laid out with a 30‐m long steel tape. If

HomeworkHomework

• A rectangular lot has a correct area of twoA rectangular lot has a correct area of two hectares.  Its length is twice its width.  It the lengths of the sides were measured with a 50‐lengths of the sides were measured with a 50m tape that is 0.02 m too long, compute the error in the area of the lot in square metererror in the area of the lot in square meter.

Prepared by: Andre‐Paul C. Ampong 26