Engineering Surveying

Homework #7 ONLY

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
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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

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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

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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
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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.