Surveying civil engineering, engineering homework help

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rffn901

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Hello, please i need help with this lab. you need to fill out the last table and find out the angels, also you need to follow the assignments steps well.

I provided all materials needed

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10/31/2016 Traverse Surveying (CE 302) Instructor: Dr. Yonas Demissie Semester: Fall, 2016 Washington State University – Tri-cities Objectives • Misclosure errors (angle and distance errors) in Traverse surveying • Traverse Computation (misclosure adjustment) • Angle adjustment using balanced distribution method. • Length (distance) adjustment using compass rule. • Reading: Chapter 9 and 10 1 10/31/2016 Recall • Traverse surveying needs measuring distance and angle • As in the case of all our measurements, the angle and distance measurements have errors (also called Misclosure). • Angle misclosure • For Interior angle: 𝑆𝑢𝑚 𝑜𝑓 𝑖𝑛𝑡𝑒𝑟𝑖𝑜𝑟 𝑎𝑛𝑔𝑙𝑒 = 𝑛 − 2 180𝑜 • For exterior angle: 𝑆𝑢𝑚 𝑜𝑓 𝑒𝑥𝑡𝑒𝑟𝑖𝑜𝑟 𝑎𝑛𝑔𝑙𝑒 = 𝑛 + 2 180𝑜 • For deflection angle: 𝑆𝑢𝑚 𝑜𝑓 𝑑𝑒𝑓𝑙𝑒𝑐𝑡𝑖𝑜𝑛 𝑎𝑛𝑔𝑙𝑒 = 360𝑜 Permissible Angle Misclosure 𝐹𝑒𝑑𝑒𝑟𝑎𝑙 𝐺𝑒𝑜𝑑𝑒𝑡𝑖𝑐 𝐶𝑜𝑛𝑡𝑟𝑜𝑙 𝑆𝑢𝑏𝑐𝑜𝑚𝑚𝑖𝑡𝑡𝑒𝑒 (𝐹𝐺𝐶𝑆) 𝑟𝑒𝑐𝑜𝑚𝑚𝑒𝑛𝑑𝑠: ‒ 𝐾 = 1.7” 𝑓𝑜𝑟 𝑓𝑖𝑟𝑠𝑡 − 𝑜𝑟𝑑𝑒𝑟 𝑠𝑢𝑟𝑣𝑒𝑦 𝑐=𝐾 𝑛 ‒ 𝐾 = 3” 𝑓𝑜𝑟 𝑠𝑒𝑐𝑜𝑛𝑑 − 𝑜𝑟𝑑𝑒𝑟 𝑐𝑙𝑎𝑠𝑠 𝐼 𝑠𝑢𝑟𝑣𝑒𝑦 ‒ 𝐾 = 4.5” 𝑓𝑜𝑟 𝑠𝑒𝑐𝑜𝑛𝑑 − 𝑜𝑟𝑑𝑒𝑟 𝑐𝑙𝑎𝑠𝑠 𝐼𝐼 𝑠𝑢𝑟𝑣𝑒𝑦 ‒ 𝐾 = 10” 𝑓𝑜𝑟 𝑡ℎ𝑖𝑟𝑑 − 𝑜𝑟𝑑𝑒𝑟 𝑐𝑙𝑎𝑠𝑠 𝐼 𝑠𝑢𝑟𝑣𝑒𝑦 ‒ 𝐾 = 12” 𝑓𝑜𝑟 𝑡ℎ𝑖𝑟𝑑 − 𝑜𝑟𝑑𝑒𝑟 𝑐𝑙𝑎𝑠𝑠 𝐼𝐼 𝑠𝑢𝑟𝑣𝑒𝑦 𝑤ℎ𝑒𝑟𝑒: 𝑛 𝑖𝑠 𝑡ℎ𝑒 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑠𝑖𝑑𝑒𝑠 or angles of the ploygon Horizontal Control Accuracy Standards for Traverse (By FGCS) Order 1st 2nd Class ′′ Angular Closure 𝟏. 𝟕 𝐧 Linear Closure (after angle adj.) 1:100,000 𝟑. 𝟎 3rd I II ′′ ′′ 𝐧 1:50,000 𝟒. 𝟓 I 𝐧 1:20,000 II 𝐧 𝟏𝟐. 𝟎′′ 𝐧 1:10,000 1:5,000 𝟏𝟎. 𝟎 ′′ 2 10/31/2016 Misclosure Errors • Linear Misclosure 1) On a closed loop traverse, the sum of the Latitudes should equal zero as should the sum of the Departures. − Latitude is the north-south component of a line (North latitudes are positive, South are negative); − departure the east-west (East departures are positive, West are negative). The latitude of line AB is North (+), its departure is East (+). The latitude of line CD is South (-), its departure is West (-). Misclosure Errors • Linear Misclosure 1) On a closed loop traverse, the sum of the Latitudes should equal zero as should the sum of the Departures. There is no Misclosure Error There is Misclosure Error 3 10/31/2016 Misclosure for Closed Link Traverse • The algebraic sum of departures should be equal to the departure between the starting and ending control points. • The same conditions applies to latitudes as well. dep(AB) B lat(AB) D(BM) dep(BC) lat(CD) lat(BC) lat(BC) C A(BM) dep(CD) dep(AB) dep(AB) = dep(AB) + dep(BC) + dep(CD) lat(AB) = lat(AB) + lat(BC) + lat(CD) Traverse Computations (Adjustment of Misclosure) • Checking and adjusting geometric closure of angles and lengths are important part of traverse surveying. 1 Surveyed closed travers data (angles and lengths) 6 Correct the linear misclosure using Compass Rule 7 Determine the rectangular coordinates for all the stations 2 Adjust angles for geometric conditions 5 Determine the linear misclosure and relative precision 8 Determine length and directions for all the traverse lines using departures and latitudes, or coordinates 3 Determine preliminary azimuths /bearings for the traverse lines 4 Determine departures and latitudes for the traverse lines 9 Final adjustment of the angles 4 10/31/2016 Example: Loop Traverse From field surveying: 151°52‘24" 234°17'18" 2) Balancing Angles • The first step is to balance (adjust) the angels to the proper geometric total. • Angels of a closed traverse can be adjusted to the correct geometric total by applying one the following methods. • Method 1: Applying an average correction to each angle where observing conditions were approximately the same at all stations. • Method 2: Making larger corrections to angles where poor observing conditions were present. • Of these two methods, the first method is most common. 5 10/31/2016 Check for Angle Misclosure and Correct 𝐴𝑛𝑔𝑙𝑒 𝑀𝑖𝑠𝑐𝑙𝑜𝑠𝑢𝑟𝑒 = sum(interior angles) – (5-2)*180 = 540𝑜 00′ 11" – 540 = 11" 𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝐶𝑜𝑟𝑟𝑒𝑐𝑡𝑖𝑜𝑛 = 𝐴𝑛𝑔𝑙𝑒 𝑀𝑖𝑠𝑐𝑙𝑜𝑠𝑢𝑟𝑒 11" = = −2.2" 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑎𝑛𝑔𝑙𝑒𝑠 5 ** Noted that the algebraic signs of the corrections are opposite to the misclosures 3) Determine Preliminary Azimuths or Bearings • After balancing the angles, the next step in traverse computation is calculation of either preliminary azimuths or preliminary bearings. • This requires the direction of at least one course within the traverse to be either known or assumed. 6 10/31/2016 4) Determine Departures and Latitudes • After balancing the angels and calculating preliminary azimuth (or bearings), traverse linear closure is checked by computing the departure and latitude of each line (course). • Departures are sometimes called eastings (+ve) or westings (-ve). • Latitude is also called northing (+ve) or southing (-ve). 𝐷𝑒𝑝𝑎𝑟𝑡𝑢𝑟𝑒 = 𝐿 sin 𝛼 𝐿𝑎𝑡𝑖𝑡𝑢𝑑𝑒 = 𝐿 cos 𝛼 • It is more convenient to use azimuths than bearings for traverse computations. 4) Determine Departures and Latitudes 7 10/31/2016 5) Traverse Linear Misclosure and Relative Precision 𝑙𝑖𝑛𝑒𝑎𝑟 𝑚𝑖𝑠𝑐𝑙𝑜𝑠𝑢𝑟𝑒 = 𝑑𝑒𝑝𝑎𝑟𝑡𝑢𝑟𝑒 𝑚𝑖𝑠𝑐𝑙𝑜𝑠𝑢𝑟𝑒 𝑙𝑖𝑛𝑒𝑎𝑟 𝑚𝑖𝑠𝑐𝑙𝑜𝑠𝑢𝑟𝑒 = 𝑟𝑒𝑙𝑎𝑡𝑖𝑣𝑒 𝑝𝑟𝑒𝑐𝑖𝑠𝑖𝑜𝑛 = 0.026 2 + 0.077 2 + 𝑙𝑎𝑡𝑖𝑡𝑢𝑑𝑒 𝑚𝑖𝑠𝑐𝑙𝑜𝑠𝑢𝑟𝑒 2 2 = 0.081 𝑓𝑡 𝑙𝑖𝑛𝑒𝑎𝑟 𝑚𝑖𝑠𝑐𝑙𝑜𝑠𝑢𝑟𝑒 𝑡𝑟𝑎𝑣𝑒𝑟𝑠𝑒 𝑙𝑒𝑛𝑔𝑡ℎ 1 0.081 0.081 1 1 0.081 𝑟𝑒𝑙𝑎𝑡𝑖𝑣𝑒 𝑝𝑟𝑒𝑐𝑖𝑠𝑖𝑜𝑛 = = = = 1 2466.00 2466.00 30444 30,000 0.081 6) Traverse Adjustment • For any closed traverse the linear misclosure must be adjusted (or distributed) through out the traverse to close or balance the figure. • The Compass rule (Bowditch method) is the most commonly used method. • Compass (Bowditch) Rule: ‒ This method adjusts the departures and latitudes of traverse courses in proportions of their lengths. 𝐶𝑜𝑟𝑟𝑒𝑐𝑡𝑖𝑜𝑛 𝑖𝑛 𝑑𝑒𝑝𝑎𝑟𝑡𝑢𝑟𝑒 𝑓𝑜𝑟 𝐴𝐵 = − 𝐶𝑜𝑟𝑟𝑒𝑐𝑡𝑖𝑜𝑛 𝑖𝑛 𝑙𝑎𝑡𝑖𝑡𝑢𝑑𝑒 𝑓𝑜𝑟 𝐴𝐵 = − 𝑡𝑜𝑡𝑎𝑙 𝑑𝑒𝑝𝑎𝑟𝑡𝑢𝑟𝑒 𝑚𝑖𝑠𝑐𝑙𝑜𝑠𝑢𝑟𝑒 𝑙𝑒𝑛𝑔𝑡ℎ 𝑜𝑓 𝐴𝐵 𝑡𝑟𝑎𝑣𝑒𝑟𝑠𝑒 𝑝𝑒𝑟𝑖𝑚𝑒𝑡𝑒𝑟 𝑡𝑜𝑡𝑎𝑙 𝑙𝑎𝑡𝑖𝑡𝑢𝑑𝑒 𝑚𝑖𝑠𝑐𝑙𝑜𝑠𝑢𝑟𝑒 𝑙𝑒𝑛𝑔𝑡ℎ 𝑜𝑓 𝐴𝐵 𝑡𝑟𝑎𝑣𝑒𝑟𝑠𝑒 𝑝𝑒𝑟𝑖𝑚𝑒𝑡𝑒𝑟 ** Noted that the algebraic signs of the corrections are opposite to the misclosures 8 10/31/2016 6) Traverse Adjustment • Example – Apply Compass (Bowditch) Rule to correct the departure and latitude for AB: 𝐶𝑜𝑟𝑟𝑒𝑐𝑡𝑖𝑜𝑛 𝑖𝑛 𝑑𝑒𝑝𝑎𝑟𝑡𝑢𝑟𝑒 𝑓𝑜𝑟 𝐴𝐵 = − 𝐶𝑜𝑟𝑟𝑒𝑐𝑡𝑖𝑜𝑛 𝑖𝑛 𝑙𝑎𝑡𝑖𝑡𝑢𝑑𝑒 𝑓𝑜𝑟 𝐴𝐵 = − 0.026 647.25 = −0.007 𝑓𝑡 2466 0.077 647.25 = −0.020 𝑓𝑡 2466 6) Traverse Adjustment 9 10/31/2016 7) Compute Rectangular Coordinates • Used to determine relative positions of points. • State plane coordinate systems are mostly used as the basis for rectangular coordinates in plane surveys. • Given the X and Y coordinates or any starting points A 𝑋𝐵 = 𝑋𝐴 + 𝑎𝑑𝑗𝑢𝑠𝑡𝑒𝑑 𝑑𝑒𝑝𝑎𝑟𝑡𝑢𝑟𝑒 𝐴𝐵 𝑌𝐵 = 𝑌𝐴 + 𝑎𝑑𝑗𝑢𝑠𝑡𝑒𝑑 𝑙𝑎𝑡𝑖𝑡𝑢𝑑𝑒 𝐴𝐵 7) Compute Rectangular Coordinates 10 10/31/2016 8) Lengths and Directions of Lines from Departures and Latitudes, or Coordinates • If the departure and latitude of a line AB are known tan(𝑎𝑧𝑖𝑚𝑢𝑡ℎ 𝑜𝑟 𝑏𝑒𝑎𝑟𝑖𝑛𝑔 𝑜𝑓 𝐴𝐵) = 𝑑𝑒𝑝𝑎𝑟𝑡𝑢𝑟𝑒 𝐴𝐵 𝑙𝑎𝑡𝑖𝑡𝑢𝑑𝑒 𝐴𝐵 length of AB = 𝑑𝑒𝑝𝑎𝑟𝑡𝑢𝑟𝑒 𝐴𝐵 sin(𝑎𝑧𝑖𝑚𝑢𝑡ℎ 𝑜𝑟 𝑏𝑒𝑎𝑟𝑖𝑛𝑔 𝑜𝑓 𝐴𝐵) = 𝑙𝑎𝑡𝑖𝑡𝑢𝑑𝑒 𝐴𝐵 cos(𝑎𝑧𝑖𝑚𝑢𝑡ℎ 𝑜𝑟 𝑏𝑒𝑎𝑟𝑖𝑛𝑔 𝑜𝑓 𝐴𝐵) = 𝑑𝑒𝑝𝑎𝑟𝑡𝑢𝑟𝑒 𝐴𝐵 2 + 𝑙𝑎𝑡𝑖𝑡𝑢𝑑𝑒 𝐴𝐵 2 9) Computing Final Adjusted Traverse Lengths and Directions • Example 11 10/31/2016 9) Computing Final Adjusted Angles • Because the final adjusted azimuths are different from their preliminary values, the preliminary adjusted angles need to be adjusted. 12 Lab 08 – Traverse Data Collection and Adjustment Lab Work: The lab will be performed as a group in the field. The Traverse adjustment will be done individually Submission: The lab report will be turned individually at the beginning of the next lab. Objectives and Outcomes The purpose of this lab is to perform a closed traverse using a total station in the field and adjust the closed traverse for possible angle and linear misclosure errors. After completing this lab, students will be able to survey traverse for defining property boundary and perform all necessary error and correction calculations to ensure its accuracy. Concepts A traverse survey includes taking distance and angular measurement to establish traverse stations and courses. It has very wide applications, including for route, boundary, and topographic surveys. When using a total station it matters where you set up the instrument because horizontal position is being measured. While traversing, you always set up the instrument on the point you just shot, and measure each angle twice using direct and reverse reading to ensure accuracy. In this lab, we will perform a closed traverse, which begins and ends at the same benchmark (SC). When a traverse is measured there is inherent error in each measurement (both angle and distance). For a closed traverse it is possible to check and reduce these errors. The traverse computation method discussed in the class will allow you to check and correct for the misclosure errors of angle and distance. Procedure for surveying the traverse The following procedure will explain the traverse going counter clockwise. The same idea is applied for the clockwise traverse, except that instead of taking interior angle measurement, we will be taking exterior angle measurement when we do clockwise traverse. Note that the phrase “a shot is taken of point A” means that the horizontal distance and angle to point A are measured and recorded. All measurements must be recorded in your notes. 1) Identify the reference line with known direction (or azimuth, Hz) that you are going to use as a reference direction for the rest of the traverse lines. In our case, we will use the SC-SH line as reference. Since we knew the geographical coordinates for SC and SH points from our previous lab, one can easily determine the direction or horizontal angle of the line connecting the two points. Set up the TS over SC control point using "orientation by coordinate” method 1| Page and the coordinates of SC and SH given in Table 1 below. Take measurement and record the azimuth angle. 2) Make a reading to a next point (e.g. A) and record the azimuth and the horizontal distance. 3) Mark the SC point on the ground, and move the TS to A and set up the instrument using "orientation by angle” and aim to SC and make Hz = 0 along this line of sight 4) Aim at the next point (station) on your traverse line take both direct and reverse azimuth and distance readings and record your reading in your notes. 5) Repeat 3 and 4 (mark the station before moving to the next station so that the prism can be hold to set up Hz=0 line, and make direct and reverse reading to the next station) till you finish the loop. 6) As a final step, you will need to make angle measurement at SC It help to reduce error in the misclosure error when you make direct and reverse angle measurements as shown in figure below. If there is no error in the angle measurements, the direct angle should be equal to reverse angle minus 180 (direct angle = reverse angle - 180). The average angle is: Average Angle direct angle + (reverse angle – 180) 2 = Step 1: Reverse Reading Direct Reading Step 2: Direct angle measurement Reverse angle measurement involves first rotating the lens vertically by 180 degrees and then rotating the TS head horizontally by 180 degrees. These will make the reading panel to be opposite to the reader. Now you can make reading by pressing F4 and record the value. 2 Page Procedures for Traverse Adjustment Follow the following procedures and provide the required tables for each step in your report. Use the table format used for the class discussion. 1. Preliminary adjustment of the traverse angles assuming observation conditions were the same for all stations. Prepare and show your calculations using a similar table used for the example problem in the textbook and class. Check the angle sum for proper geometric total. 2. Compute preliminary azimuths. Show your calculations and the sketches you used at each stations. 3. Compute departures and latitudes for all the traverse lines. Prepare and show your calculations using a similar table used for the example problem in the textbook and class. 4. Determine the linear misclosure and relative precision (use the correct ratio representation for the relative precision) 5. Adjust the departures and latitudes using the Compass rule (Bowditch method). Prepare and show your calculations using a similar table used for the example problem in the textbook and class. Check the departures and latitudes for balance. 6. Determine the rectangular coordinates for each traverse stations. Given the rectangular coordinate for SC control point is (365270.76 ft, 1953250.64 ft). Use the SC as reference or starting station to compute the rectangular coordinates for your traverse stations. Prepare and show your calculations using a similar table used for the example problem in the textbook and class. Check for closure. 7. Compute lengths and directions of traverse lines from departures and latitudes, or coordinates. Prepare and show the final adjusted traverse lengths and directions using a similar table used for the example problem in the textbook and class. 8. Computing and show the final adjusted angles using a similar table used for the example problem in the textbook and class. Check the angle sum for proper geometric total. 9. Provide two clear sketches for your traverse, one figure shows the unadjusted lengths and angles, while the other shows the final adjusted lengths and angles. Assignment: The field measurements will be done in group, while the traverse adjustment will be done individually. While performing the traverse you will keep neat field notes, and measure each horizontal angle twice. 1) Check whether, your angle and linear misclosure errors are within the allowable range for Order III Surveying. 2) Submit the tables and calculations used for correcting the misclosure errors. Use the table formats I have used in the lecture or text book. 3) If you have to redo the survey, what two things you will do differently to reduce the misclosure errors. 3 Page RiverfrontiTrail Washington State University INN TE 19 1 SH CONTATT SC Figure 2. Surveying area, showing closed traverse and reference line with known direction. Table 1. Control points to setup the instrument Control Points Latitude (ft) Longitude (ft) Elevation (ft) Sprout + Col (SC) 365270.76 373.82 1953250.64 Sprout +Harries (SH) 365584.10 1952946.76 381.40 4 | Page
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Explanation & Answer

Attached.

1

Traverse Surveying and Adjustments
Transverse Surveying and Computation

Transverse surveying is the procedure of measuring angles and measurements from a chosen
control point and the end of the survey ends at the starting point. Due to errors in measurement of
angles and distances from one transverse station to another there will be an error in that the last
transverse station will not coincide with first starting control station. This is known as the
misclosure. The angular and linear misclosure are eliminated by adjusting the angles and distances
of the transverse.
Objectives.
In a transverse survey the objectives are as follows;
a. Take angular measurements using a total station and linear measurements using a tape
measure from one transverse station to the other.
b. Establish the angular and linear misclosures of the transverse survey.
c. Perform computations in order to adjust the misclosure errors. Angular misclosures are
adjusted by balanced distribution of the error to each angle while linear misclosures are
adjusted using the compass(Bowditch) rule.
Data Collected.
Naming the transverse stations as A, B, C, D, E, F assuming the plane takes a seven sided polygon.
For the purpose of reducing angular misclosure we measure the direct and reverse angle. When
there is no angular error, the direct angle should be equal to the reverse angle minus 180 0 .With
these two angles we find an average as shown below,
𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝐴𝑛𝑔𝑙𝑒 =

[𝐷𝑖𝑟𝑒𝑐𝑡 𝑎𝑛𝑔𝑙𝑒 + (𝑅𝑒𝑣𝑒𝑟𝑠𝑒 𝑎𝑛𝑔𝑙𝑒 − 180)]
2

An average of the direct and reverse distances is taken to reduce linear misclosures as follows,
𝐴𝑣𝑣𝑒𝑟𝑎𝑔𝑒 𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒 =

Transvers
e
Lines
SC-SH

Direct
Angle(D)

Reverse
Angle(R)

SC-A

3150 50’36

320 40’28”

A-SC

00 00’00”

A-B

1460 32’01


1350 49’30

2120 44’31

1790 59’44

3260 29’03


𝐷𝑖𝑟𝑒𝑐𝑡 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 + 𝑅𝑒𝑣𝑒𝑟𝑠𝑒 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒
2

Average
[𝐷 + (𝑅 − 180)]
2
3150 50’03”

Direct
Horizonta
l Distance
299.038

Reverse
Horizonta
l Distance
298.929

Average
Horizonta
l Distance
298.9835

320 42’30”

612.883

612.606

612.7445

00 00’08”

611.517

611.524

611.5205

1460 30’32”

279.056

273.737

276.3965

2

Traverse Surveying and Adjustments

C-D

3590 59’00

1380 38’34

3590 58’06

860 33’05”

D-C

890 30’05”

D-E

890 30’05”

E-D

900 04’28”

E-F

1310 02’21

00 00’00”

B-A
B-C
C-B

F-E
F-SC
SC-F

1800 01’54

1310 13’33

1800 00’42

2700 38’55

2700 04’28

2700 31’07

1790 58’57

3100 02’21

2720 11’06
�...


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