Technological University of the Philippines

Ayala Boulevard, Ermita Manila

College of Engineering

Civil Engineering Department

CE 25-2C

Elementary and Higher Surveying I, Lec.

Assignment No. 3

Measurement of Horizontal Distances

Ardiente, Margie Lou V.

13-205-017

Date of Submission: February 10, 2015

Engr. Jesus Ray M. Mansayon

Instructor

Pages 525-528

1. PACING. In walking along a 75-m course, the pacer of a field party counted 43.50, 44.00, 43.50, 43.75, 44.50, and 43.25 strides. Then 105.50, 106.00, 105.75, and 106.25 strides were counted in walking from one marker to another established along a straight and level course. Determine the distance between the two markers.

One stride= 2 paces

X X

2. PACING. A student paces a 50-m length five times the following results: 57.00 56.75, 56.50, 58.00 and 56.25 paces. Determine how many paces must he step off in order to establish a distance of 450 meters on level ground.

X X

3. PACING. Determine the length of a line negotiated in 208 paces by a person whose pace is 0.76 meters long.

4. DISTANCE BY SUBTENSE BARS With the use of a 1-sec theodolite positioned at the center of a six-sided lot the following readings were taken on a 2-m subtense bar set up at each corner: . Determine the distance of each corner from the instrument position.

5. DISTANCE BY SUBTENSE BARS. A 2-m long subtense bar was first set up at A and subsequently at B, and the subtended angles to the bar, as read from a theodolite positioned somewhere along the middle of line AB, were recorded as , respectively. Determine the length of AB.

A B

6. SLOPE MEASUREMENT. A traverse line was measured in three sections: 295.85 m at slope , 149.58 m at slope , and 373.48 m at slope . Determine the horizontal

length of the line.

Horizontal length

7. SLOPE MEASUREMENT. A slope measurement of 545.38 m is made between points A and B. The elevation of A is 424.25 m and that of B is 459.06 m. Determine the horizontal distance between the two points.

H

A B

8. MEASUREMENTS WITH TAPE. The sides of a rectangular parcel of property were measured and recorded as 249.50 m and 496.85 m. It was determined, however, that the 30-m tape used in measuring was actually 30.05 m long. Determine the correct area of the rectangle in hectares.

496.85 m

249.50 m

9. MEASUREMENTS WITH TAPE. A 30-m steel tape when compared with a standard is actually 29.95 m long. Determine the correct length of a line measured with this tape and found to be 466.55 m.

NL CL=?X X

ML

10. LAYING OUT DISTANCES. A track and field coach wishes to lay out for his a 200-m straightaway course. If he uses 50-m tape known to be 50.20 m long, determine the measurements to be made so that the course will have the correct length.

NL CL=?

X X

ML

11. LAYING OUT DISTANCES. It is required to lay out a building 80 m by 100 m with a 30-m long metallic tape which was found to be 0.15 m too short. Determine the correct dimensions to be used in order that the building shall have the desired measurements.

12. LAYING OUT DISTANCES. A steel tape whose nominal length is supposed to be 30 m long was found to be 30.02 m long when compared with an invar tape during standardization. If the tape is to be used in laying out a 520 m by 850 m rectangular parking lot, determine the actual dimensions to be laid out.

13. CORRECTION DUE TO TEMPERATURE. A 30-m steel tape is of standard length at 20 C. If the coefficient of thermal expansion of steel is 0.0000116/1 C, determine the distance to be laid out using this tape to establish two points exactly 1235.65 m apart when the temperature is 33 C.

ML

14. CORRECTION DUE TO TEMPERATURE. A steel tape having a correct length at 22 C was used to measure a base line and the recorded readings gave the total of 856.815 m. If the average temperature during the measurement was 18 C, determine the correct length of the line.

ML @

15.CORRECTION DUE TO TENSION. A heavy 30-m tape having a cross-sectional area of has been standardized at a tension of 5 kg. If E= , calculate the

elongation of the tape for an increase in tension from 5.5 kg to 20 kg.

NL=30

16. CORRECTION DUE TO TENSION. A steel tape is 30.0-m long under a pull of 6.0 kg when supported throughout. It has a cross-sectional area of 0.035 and is applied fully supported

with a 12-kg pull to measure a line whose recorded length is 308.32 m. Determine the correct length of the line if E= .

308.32 m

17. CORRECTION DUE TO TENSION. A 30-m steel tape weighing 1.75 kg is of standard length under a pull of 4.55 kg, supported for full length. This tape was used in measuring a line (found to be 1371.50 m) on smooth level ground under a steady pull of 8 kg. Assuming E=

and that the unit weight of steel is , determine the following: cross-

sectional area of the tape, correction for increase in tension for the whole length measured, and the correct length of the measured line.

1371.50 m

18. CORRECTION DUE TO SAG. A 30-m steel tape weighs 1.5 kg and is supported at its end points and at the 5 and 15-m marks. If a pull of 8 kg is applied, determine the correction due to sag between supports and for one tape length.

L1=5m L2=10m L3=15m

0-m 5-m 10-m 15-m

;

19. CORRECTION DUE TO SAG. A 30-m steel tape weighing 0.04 kg/m is constantly supported at its end points, and used to measure a line with a steady pull of 8.5 kg. If the measured length of the line is 2465.18 m, determine the correct length of the line.

…

L1=30m L1=30m L1=30mL2 = ?

L =30m1

20. NORMAL TENSION. Determine the normal tension required to make a tape exactly 30.0 m between its ends when used in an unsupported mode, if the tape has a cross-sectional area of 0.045 and weighs 0.90 kg. Assume that the tape is exactly 30.0 m when supported throughout its length under a standard pull of 6.0 kg, and its modulus of elasticity is

.

30 m

21. NORMAL TENSION. A 30-m steel tape supported at its ends weighs 0.03 kg/m and is of standard length under a pull of 6.5 kg. If the elastic modulus of steel is and its weight density is , determine the tension at which the effect of sag will be eliminated by the elongation of the tape due to increased tension.

30m

22. COMBINED CORRECTIONS. A 30-m tape weighs 12.5 g/m and has a cross section of

. It measures correctly when supported throughout under a tension of 8.0 kg and at a temperature of . When usedd in the field, the tape is only supported at its ends, under a pull of .0 kg, and at an average temperature of . Determine the distance between the zero and 30-m marks.

23.COMBINED CORRECTIONS. A line was found to be 2865.35 m long when measured with a 30-m tape under a steady pull of 6.5 kg at a mean temperature of . Determine the correct length of the line if the tape used is of standard length at under a pull of 5.5 kg. Assume the cross-sectional area of the tape to be , elastic modulus as

, and coefficient of thermal expansion to be

24.MEASURING ANGLES WITH TAPE. The sides of a triangle measure 1063.55, 1840.33, and 1325.05 m. Determine the three angles in the triangle.

25. OBSTRUCTED DISTANCES. In the accompanying sketch it is required to determine the distance between points A and B which spans a wide and deep river. Lines BD and CE, which measure 385.75 m and 52.05 m, respectively, are established perpendicular to line ABC. If the points D and E are lined up with A and the length of BC=210.38 m, determine the required distance.

Page 579-582

1. A pace is defined as the length of a step in walking. It may be measured from a) Heel to toe b) Toe to heel c) Heel to heel d) Mid-heel to mid-toe e) Tip of toe to tip of heel.

Answer: c) Heel to heel

2. The method of measuring or laying out horizontal distances by stretching a calibrated tape between two points and reading the distance indicated on the tape is referred to as

a) Taping b) Pacing c) Tacheometry d) Stadia measurement e) Range finding

Answer: a) Taping

3. The subtense bar is a convenient and practical device used for quick and accurate measurement of horizontal distances. It consists of a rounded steel tube through which runs a thin invar rod and at each end of the frame the target marks are house exactly.

a) 1.00 m apart b) 1.50 m apart c) 3.00 m apart d) 2.00 m apart e) 4.00 m apart

Answer: d) 2.00 m apart

4. The first electronic distance measuring instrument was the geodetic distance meter (geodimeter) which was developed in 1948 by a Swedish physicist named

a) Dr. T.L. Wadley b) Erik Bergstrand c) Sir Edmund Gunter d) Pierre Vernier e) Hipparchus

Answer: b) Erik Bergstrand

5. A special tape made of an alloy of nickel (35%) and steel (65%) with a very low coefficient of thermal expansion, and used only for precise measurements in geodetic work as well as for checking the lengths of other kinds of tape is

a) Engineer’s tape b) Fiberglass tape c) Invar tape d) Nylon-coated tape

e) Builder’s tape

Answer: c) Invar tape

6. The standard practice of measuring short distances on uneven and sloping ground to accumulate a full tape length wherein the tape is held horizontally above ground and plumbed at one or both ends is referred to as

a) Slope taping b) Horizontal taping c) Incremental taping d) Breaking taping e) Partial taping

Answer: d) Breaking tape 7. Normal tension is defined as the applied pull which will lengthen the tape to equal the

a) Decrease in standard pull b) Shortening due to temperature c) Increase in length due to the absence of intermediate supports d) Shortening caused by sag e) Increase in gravitational forces

Answer: d) Shortening caused by sag

8. A surveyor counted 50, 52, 53, 51, 53, and 51 paces in walking along a 45-m course laid out on a concrete pavement. He then took 768, 771, 772, 770, 769 and 770 paces in walking an unknown distance XY. His pace factor should be equal to

a) 1.148 m/pace b) 0.001 m/pace c) 14.904 m/pace d) 0.067 m/pace e) 0.871 m/pace

X X

Answer: e) 0.871 m/pace9. In question 8, the length of XY based on the pace factor of the surveyor is equal to

a) 670.67 m b) 883.6 m c) 11476.08 m d) 51.59 m e) 715.67 m

10. Two points, A and B, are established along the same direction from a theodolite station. If the subtended angle read on a subtense bar held at A and B are , respectively, the horizontal distance between the two point is

a) 82.73 m b) 165.45 m c) 206.98 m d) 289.70 m e) 124.25 m

A B

Answer: b) 165.45 m

11. A slope distance of 465.82 m is measured between two points with a slope angle of . The corresponding horizontal distance between the points is

a) 101.48 m b) 454.63 m c) 103.98 m d) 358.70 m e) 207.14 m

slope angle of .

465.82 m

slope

H

Answer: b) 454.63 m

12. A line measured with a 30-m steel tape was recorded as 325.70 m. If the tape is found to be 30.5 m long during standardization, the correct length of the line is

a) 325.16 m b) 325.70 m c) 327.45 m d) 325.44 m e) 326.24 m

325.7 m

Answer: e) 326.24 m

13. A rectangular building 250.00 m by 130.00 m is to laid out with a 30-m long steel tape. If during the standardization the tape is found to be 30.03 m, the correct length and width to be laid out should be

a) 249.75 m by 129.87 m b) 250.25 m by 130.13 m c) 249.87 m by 129.75 m d) 250.00 m by 130.00 m e) 249.97 m by 129.97 m

L

W

Answer: a) 249.75m by 129.87m

14. A line measured with a 50-m long steel tape was determined to be 645.22 m when the average temperature during taping was . If the tape is of standard length at and the coefficient of thermal expansion of steel is , the correct length of the measured line is

a) 645.23 m b) 645.22 m c) 645.24 m d) 645.19 m e) 645.21 m

ML

Answer: D. 645.19 m

15. A steel with a cross-sectional area of is 30.00 m long under a pull of 5 kg when supported throughout. It is used in measuring a line 874.63 m long under a steady pull of 10 kg.

Assuming E= , the elongation of the tape due to increase in tension isa) 0.0730 m b) 0.730 m c) 0.50 m d) 0.043 m e) 0.0025 m

Answer: e) 0.0025 m

16. In question 15, the correct length of the measured line is a) 875.56 m b) 875.63 m c) 875.68 m d) 875.60 m e) 875.70 m

Answer: b) 875.63 m

17. A 30-m steel tape weighs 1.05 kg and is supported at its end points and at the 10-m and 25-m marks. If a pull of 6.0 kg is applied at the ends of the tape, the correction due to sag for a full tape length is

a) 0.038 m b) 0.006 m

c) 0.050 m d) 0.45 m e) 0.06 m

Answer: e) 0.06m

18. In a triangular-shaped lot ABC, the two sides and the included angle are: CA= 90.95 m, BC=73.80 m, and angle C= . The length of the remaining side AB is

a) 62.77 m b) 117.13 m c) 153.28 m d) 82.38 m e) 81.93 m

A

?

C B

Answer: a) 62.77 m

19. In question 18, the relationship between angle C and the two remaining angles, A and B, of the triangle could expressed correctly as

a) A < C > B b) A > C > B c) C = A – B d) C = A + B e) A > C < B

20. In the accompanying sketch it is desired to determine the length of AB across a wide and deep river.

C

D A B

Line AC which measures 471.48 m, is established perpendicular to AB; CD is similarly established perpendicular to BC with point D on the prolongation of line AB. If the length of AD is 322.35 m, the length of AB is equal to

a) 689.60 m b) 220.39 m c) 389.85 m d) 453.40 m e) 517,23 m

Answer: a) 689.60 m