Visayas State UniversityCollege of Engineering

DEPARTMENT OF CIVIL ENGINEERINGBaybay, Leyte

GEng 112General Surveying II

Name: Joycelyn H. Uy Date Performed: December 6, 2012Course and Year: BSCE-3 Date Submitted: January 3, 2013

TRIANGULATION FOR A BRIDGE SITELaboratory Exercise No. 5

I. Introduction:The method of surveying called triangulation is based on the trigonometric

proposition that if one side and two angles of a triangle are known, the remaining sides can be computed. Furthermore, if the direction of one side is known, the directions of the remaining sides can be determined. A triangulation system consists of a series of joined or overlapping triangles in which an occasional side is measured and remaining sides are calculated from angles measured at the vertices of the triangles. The vertices of the triangles are known as triangulation stations. The side of the triangle whose length is predetermined, is called the base line. The lines of triangulation system form a network that ties together all the triangulation stations.

II. Objective(s):1. To establish the control points for a low order triangulation system

(consisting of a single quadrilateral) needed to stake out a site for a short-span bridge.

2. To learn how to apply the approximate method of adjusting a quadrilateral and how to determine length of the bridge and the lengths of other unknown sides of the quadrilateral.

III. Instruments and Accessories:Engineer’s Transit, Stadia rod, Chaining pins, and Hubs or Pegs

IV. Procedure:1. The two end points defining the length of a proposed (or imaginary) bridge was established and two other points within the vicinity of the bridge site in order to form a triangulation figure in the shape of a quadrilateral. These points were called A, B, C, and D with line AB defining the length and centerline of the proposed bridge. Pegs or hubs were used to mark these points.

2. Lines AD and BC were designated as the base line and check base, respectively. Their respective lengths were measured accurately twice and the mean measurements were recorded as the actual length of each line.

3. The instrument was set up and leveled at A and each horizontal angle about the station was measured in two repetitions. The observed values were recorded accordingly.

4. In a similar process, the horizontal angles at stations D, B, and C were also measured.

5. The observed and calculated values were then tabulated accordingly.

V. Results and Discussion: Table 1. Data for Station Adjustment

STATION ANGLE MEASURED VALUE CORRECTION ADJUSTED VALUE

A

123

SUM

284°35’20”60°30’20”14°54’20”

360°00’00”

0

284°35’20”60°30’20”14°54’20”

360°00’00”

B

456

SUM

259°45’00”15°37’20”84°48’20”

360°10’40”

- 3’ 33.33”

259°41’26.67”15°33’46.67”84°44’46.66”360°00’00”

C

789

SUM

263°55’20”77°14’00”18°56’20”

360°05’40”

- 1’ 53.33”

263°53’26.67”77°12’6.67”

18°54’26.66”360°00’00”

D

101112

SUM

272°04’00”19°40’00”68°14’00”

359°58’00”

40”

272°04’40”19°40’40”68°14’40”

360°00’00”

SAMPLE CALCULATIONS:In Station A:

Sum = 284o35’20” + 60o30’20” + 14o54’20” = 360o

Discrepancy = 360 - 360o = 0Correction = 0

Table 2. Data for Figure Adjustment

QUADRILATERAL ANGLEADJUSTED ANGLE FROM STATION

ADJ.CORRECTION

ADJUSTED VALUE

ABCD

2 60o30’20”

1’51.67”

60o32’11.67”3 14o54’20” 14o56’11.67”5 15o33’46.67” 15o35’38.34”6 84o44’46.67” 84o46’38.3”8 77o12’6.67” 77o13’58.34”9 18o54’26.67” 18o56’18.34”

11 19o40’40” 19o42’31.67”12 68o14’40” 68o16’31.67”

SUM 359o45’6.68” 14’53” 360

SAMPLE COMPUTATIONS:

Sum = 60o30’20” + 14o54’20” + 15o33’46.67” + 84o44’46.67” + 77o12’6.67”+ 18o54’26.67”+ 19o40’40” + 68o14’40” = 359o45’6.68”

Discrepancy = 360 - 359o45’6.68” = 14’53”Error = 14’53” / 8 = 1’51.67”

Table 3. Data for Adjustment of Opposite AnglesADJUSTED ANGLE FROM

FIGURE ADJSUTMENTOPPOSITE ANGLE(computations)

ADJUSTMENT VALUE

Angle 2 = 60o32’11.67” 2 + 6 = 12 + 860o32’11.67” + 84o46’38.3” = 145o18’49.97”

68o16’31.67” + 77o13’58.34” = 145o30’30.01”Error = 11’40.04”, corr = 2’55.01”

2 60o35’6.68”Angle 3 =14o56’11.67” 3 14o54’30”Angle 5 = 15o35’38.34” 5 15o37’20”Angle 6 = 84o46’38.3” 6 84o49’33.31”

Angle 8 = 77o13’58.34” 3 + 11 = 5 + 914o56’11.67” + 19o42’31.67” = 34o38’43.34”15o35’38.34”+ 18o56’18.34” = 34o31’56.68”

Error = 6’46.66”, corr = 1’41.67”

8 77o11’3.33”Angle 9 = 18o56’18.34” 9 18o58’00”

Angle 11 = 19o42’31.67” 11 19o40’50”Angle 12 = 68o16’31.67” 12 68o13’36.66”

Table 4. Trigonometric ConditionANGLE Log Sin Ө + 10 Diff in 1” Correction Adjusted angle

a b2 9.940061474 1.1871 +56.841” 60o36’3.52”3 9.410394792 7.9084 -56.841” 14o53’33.16”5 9.430225651 7.5298 +56.841” 15o38’16.84”6 9.998226764 0.1907 -56.841” 84o48’36.45”8 9.989044012 0.479 +56.841” 77o12’0.17”9 9.511907439 6.1264 -56.841” 18o57’3.16”

11 9.527340789 5.8867 +56.841” 19o41’46.84”12 9.967856625 0.841 -56.841” 68o12’39.82”

SUM 38.88667193 38.88838562 30.1491 360O

SAMPLE COMPUTATIONS:

In Angle 2:

Log Sin<2 + 10Log Sin(60o35’6.68”) + 10 = 9.940061474

diff in 1” = [logsin(<2 + 1”)]-[logsin(<2) + 10] = [logsin(60o35’6.68” + 1”)]-[logsin(60o35’6.68”) + 10]

diff in 1” = 1.1871 x 10-6

For Correction:

Correction =

= =

Correction = 56.841”

DETERMINING THE LENGTH OF THE BRIDGE AND OTHER UNKNOWN SIDE:

Using the two (2) routes:Route 1:

BC =

=

BC = 35.8749 m

Route 3:

BC =

=

BC = 35.8749 m

Therefore, the mean distance of BC is 35.8749 m.

RELATIVE PRESICION:

RP = =

RP = or =

DISCUSSION:

Table 1 and 2 shows the station and figure adjustment, respectively. In the first adjustment, all the observed horizontal angles about a station were just added. The sum was then subtracted from 360o. The difference was then divided by the number of angles about the station. The resulting value is then added algebraically to each angle in order to make the sum of all angles about each station equal to 360o. While in the second adjustment, the sum of the interior angles of the quadrilateral must be equal to (n-2)180o, where ‘n’ represents the number of sides. In the third table, the opposite angles at the intersection of the diagonals should be equal. The values of these angles were previously adjusted in earlier adjustments and were compared and the difference between them was divided by 4. The computed correction was then added to smaller pair of angles and subtracted to the larger pair. In the last table, it shows the trigonometric condition. It was satisfied by the means of computations involving the sines of the angles. The angles were adjusted so that the computed length of an unknown side opposite a known side will be the same regardless of which of the four routes is used. In this manner, route 1 and 3 were computed and its average will then represent as the computed distance of BC or the check base.

VI. Conclusion:Therefore, the control points for a low order triangulation system (consisting of a single

quadrilateral) needed to stake out a site for a short-span bridge was established. The application of the approximate method of adjusting a quadrilateral was also learned, so as to determine the length of the bridge and the lengths of other unknown sides of the quadrilateral.

VII. Sketch:

VIII. Reference(s): http://surveying.wb.psu.edu/sur162/control/control.htm

http://www.icmsurveysystems.com/surveying_techniques.htm

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