Engineering Surveying

Civil & Environmental Engineering Department 1

EGCE 214 – Surveying

Homework For due date, please check your syllabus

Homework #1

A steel tape with a cross sectional area of 0.040 cm2 and weight of 1.5 kg has a length of 30.050 m between the zero and the 30m marks, when supported throughout at 200C and subjected to a tension of 5 kg. This tape is used to measure a distance along a slope of 5% gradient and is supported throughout during the measurement. The tension applied is 10 kg. The temperature of the tape is 200C. The measured slope distance is recorded as 400 m. What is the corrected horizontal distance?

Consider E = 2.1 x 106 kg/cm2

K = 6.45 x 10 -6 /0F Homework #2

Shown in figure is a differential leveling sketch to determine the difference in elevations at two sides of a hill. Leveling work was started from BM 1 and was ended to the BM 2.

a. Please complete the level book and calculate elevations of points A and B. Also check the accuracy of your calculation. b. What was the leveling error of the job? . c. A foresight was taken from X to the bottom of the creek and the reading was 13.54 ft. Likewise, a foresight reading was taken from Y to the bottom of the cliff and the reading was 13.77 ft. Please calculate the depth of creek and the height of cliff?

Civil & Environmental Engineering Department 2

Homework #3 A closed traverse surveying was conducted in front of Engineering building of the CSUF and results i.e. internal angles and bearing of one line are presented in the figure below. Please check the closing of internal angles and compute the azimuths and bearings of all traverse lines.

Homework #4

Shown in the following table are the azimuths and lengths of sides of a four sided traverse. Please calculate the north and east coordinates of those traverse stations and check the accuracy of survey and your calculation. North and east coordinates of station C are 800 ft and 1000 ft, respectively.

Station Azimuth Length (ft)

C D 14902’ 583.095 A 4500’ 565.685 B 31500’ 424.264 C 243026’ 447.213

Homework #5

Shown in the figure are the latitudes and departures of a four sided traverse. Please calculate the latitude, departure, and length of line AD.

Station Latitude (ft) Departure (ft)

A B 290.00 -310.00 C -210.00 -390.00 D -480.00 280.00 A

Civil & Environmental Engineering Department 3

Homework #6 Mapping of a ground in front of CSUF Engineering building was done with a four sided closed traverse. Assuming that the angle measurement is accurate, interior angles of only three traverse stations were measured. Northing, Easting, and Elevation of stations C and D were measured with GPS device. Rest of the surveying was done with the total station. The results obtained with field surveying are shown in the following tables. With the provided information, please calculate the Northing, Easting, and Elevation of stations A and B. Please calculate the precision of distance measurement with the total station. Also calculate the error in elevation measurement. Table 1: Northing, Easting, and Elevation obtained from GPS Survey

Traverse Station

Northing (ft)

Easting (ft)

Elevation (ft)

C 5500.000 8300.000 246.885 D 5933.013 8550.000 248.993

Table 2: Data recorded in the field book from the survey with Total Station

Instrument Station

Prism Station

Horizontal Angle

Horizontal Distance

(ft)

Vertical Distance

(ft)

Height of Instrument

(ft)

Height of prism

(ft) B A 0o0′ B C 73o45′ 740.920 +3.7 5.015 7.055

D C 0o0′ D A 140o18′ 280.000 -5.885 5.125 7.553

A D 0o0′ A B 100o22′ 401.850 +5.856 5.222 6.556

Civil & Environmental Engineering Department 4

Homework #7 Make contour lines of 50 ft, 60 ft, 70 ft, and 80 ft. for the spot heights shown in the figure (page 2). Please calculate the width and gradient of the “Tokyo Road” shown in the plan. Is the road constructed in cutting or in filling? Is the road ascending towards north-east?

Civil & Environmental Engineering Department 5

Homework #8 Problem 1

Shown in the following figure is a plot near Box Canyon and is on sale. All dimensions are in ft. Please calculate the area of the plot using the Simpson’s 1/3 Rule method and estimate the cost of the land if the cost of land per square ft. is $100.00.

Problem 2

Cross-sections of a sector of a highway project were calculated at different chainages and presented in the following table. Earthwork quantities for the sector indicate a transition from cut to fill. Please calculate:

a) Volume of fill required for this section of road. b) Volume of cut required for this section. c) Cumulative quantity of earthwork. d) If the total labor and equipment cost of cutting and filling are separately $1000 per cubic yard and $2000 per cubic yard, respectively, please calculate the total cost of cutting and filling.

In the region where there is a transition from fill to cut use pyramid rule.

Station (ft) Cut area (ft2) Fill area (ft2)

20+00 500 0

20+80 300 200

22+50 0 500

24+30 200 0

28+60 0 100

Civil & Environmental Engineering Department 6

Homework #9 Problem 1

Shown in the following figure is a highway alignment. Azimuth of line AB is 80o. The highway alignment deflects from B to C and the azimuth of line BC is 100o. We have to set a circular horizontal curve from A to C. Angle subtended by 100 ft arc of that curve at the center of that circle is 6o . Station of B is 100+00. Please calculate

a. The stations of A and C. b. If a 40 ft x 40 ft size building is observed at 50 ft below the point of intersection (B), please check if the center of the building comes along or above or below the center line of the curve alignment. The drawing is not in scale. c. Direct distance from A to C.

Problem 2

A back tangent of +4% gradient meets with a forward tangent of -3% gradient in a vertical curve. Station and elevation of Point of Vertical Intersection (PVI) are 70+00 and 270 ft, respectively. Horizontal length of the curve is 1000 ft. Calculate the elevation and tangent offset at station 74+00. Also, calculate the station in the curve that has maximum elevation, and corresponding maximum elevation.