Civil Engineering November 2020 Surveying has to do with the determination of the relative spatial location of the points on or near the surface of the earth. It is the art of measuring horizontal and vertical distances between objects, of measuring angles between lines, of determining the direction of lines, and of establishing points by predetermined angular and linear measurement. Geodetic Surveying - the type of surveying which takes into account the true shape of the earth. Surveys employing the principles of geodesy are of high precision and generally extended over large areas. Plane Surveying - the type of surveying in which the mean surface of the earth is considered as a plane, or in which its spheroidal shape is neglected. Units of Measurement •Sexagecimal units of angular measurement are the degree, minute, and second. A plane angle extending completely around a point equals 360 degrees; 1 degree = 60 minutes, 1 minute = 60 seconds. •Centesimal units, the grad, or grade, is the angular unit. 400 grads = 360 degrees. 1 grad = 100 centesimal minutes; 1 centesimal minute = 100 centesimal seconds. METHODS OF SURVEYING: •Control Survey - Made to establish the horizontal and vertical positions of arbitrary points. •Boundary Survey - Made to determine the length and direction of land lines and to establish the position of these lines on the ground. •Topographic Survey - Made to gather data to produce a topographic map showing the configuration of the terrain and the location of natural and man-made objects. Manila FB: @ReviewInnovationsOfficial (02) 8735-9161 0919-227-9194 Review Innovations •Hydrographic Survey - The survey of bodies of water made for the purpose of navigation, water supply, or sub-aqueous construction. •Mining Survey - Made to control, locate and map underground and surface works related to mining operations. •Construction Survey - Made to lay out, locate and monitor public and private engineering works. •Route Survey - Refers to those control, topographic, and construction surveys necessary for the location and construction of highways, railroads, canals, transmission lines, and pipelines. •Photogrammetric Survey - Made to utilize the principles of aerial photogrammetry, in which measurements made on photographs are used to determine the positions of photographed objects. •Astronomical survey - generally involve imaging or "mapping" of regions of the sky using telescopes. Problem 1: Line AB 100 m long was paced by a surveyor four times with the following data: 144, 145, 143, and 146. Another line CD was paced for four times again with the following results: 893, 892, 894, and 895. a. Find the pace factor of the surveyor. b. Determine the actual length of line CD. c. If line CD was at elevation of 478 m above the sea level and the radius of the earth is 6400 km, determine the reduced distance of line CD along the sea level. Problem 2: A rectangular lot having a dimension of 217.3 m by 148.5 m was measured by a 30 m tape which is 0.04m too long. a. What is the correct width of the lot? b. Find the error in the area. Cebu FB: Excel-RI CE Review Specialist Inc. (032) 268-5989 0919-822 -5048 Surveying 1 c. If the same tape is used to set a baseline with length of 837.5m, determine the actual distance to be laid out. Problem 3: A 100 m steel tape is used to measure the distance of the line and found to be 1539.28 m long. During measurement, the tape is supported at the ends under a pull of 10 kg and the observed mean temperature is 31ᵒC. The tape is of standard length at 20ᵒC and a tension of 12 kg. The cross-sectional area of the tape is 0.035 cm2. The coefficient of linear expansion is 0.0000116/ᵒC. and the modulus of elasticity of steel is 2.0x106 kg/cm2. The tape weighs 1.5 kg. a. Determine the total correction for temperature. b. Find the total correction due to pull/tension. c. Determine the total correction due to sag. d. What is the correct length of the line? 𝐏𝐚𝐜𝐞 𝐅𝐚𝐜𝐭𝐨𝐫 = Length(or Distance) Average No. of Paces Error in Tape: Measure Layout Too Long Add Subtract Lcorrect = Linitial ± e( Too Short Subtract Add Linitial Ltape ) Davao FB: Review Innovations Davao Branch (082) 221-1121 0930-256-0998 Civil Engineering November 2020 Tape Correction 1. Correction due to Temperature C T = L (T − To ) α – coefficient of linear (or thermal) expansion – use 11.6 x 10-6/°C if not given L – measured length/length of tape T – temperature during measurement To – standard temperature 2. Correction due to Pull CP = (P − Po )L aE P – applied pull/tension Po – standard pull/tension L – measured length/length of tape a – cross-sectional area of tape E – elastic modulus of steel 3. Correction due to Sag CS = w 2L3 24P 2 Review Innovations Problems for Practice: 1. The taped distance of a line was 99.812 m using a 100m steel tape weighing 2 kg at a pull of 10 kg and temp of 320C. The difference in elevation between the end points is 45cm. The tape is exactly 100m at a temp of 280C and standard pull of 10 kg. If the coefficient of expansion of the tape is 0.0000118/0C and the tape was supported at the ends and at 25m interval during measurement find the correct horizontal distance of the line. Answer: 99.805m Surveying 1 4. A 50 m steel tape was standardized and supported throughout its whole length and found to be 0.00205 m longer at an observed temperature of 31.80C and a pull of 10 kg. This tape was used to measure a line which was found to be 662.702 m at an average temperature of 24.60C using the same pull. Use coefficient of expansion of 11.6 x 10 -6/0C. a. Compute the standard temperature. b. Compute the total temperature correction. c. Compute the correct length of the line. Answers: a) 28.270C; b) -0.028 m; c) 662.67 m 2. A 100 m tape is suspended at the ends under a pull of 15 kg. It has also supports at 30 m and 75 m marks. What is the total correction due to sag if the tape weighs 2.4 kg? Answer: 0.014 m 3. In five trials of walking along a 90 m course on fairly level ground, a pacer for a survey party counted 51, 52.5, 51.5, 52.5 and 51.5 strides respectively. He then started walking an unknown distance XY in four trials which were recorded as follows: 88.5, 89, 88 and 87 strides. Determine the following: a. Pace factor of the pacer. b. Length of line XY. c. Percentage of error in the measurement if the taped length of XY is 150.5 meters. Answers: a) 0.869 m/pace; b) 153.16 m; c) 1.77% w – linear weight of tape L – distance between supports P – applied pull/tension Manila FB: @ReviewInnovationsOfficial (02) 8735-9161 0919-227-9194 Cebu FB: Excel-RI CE Review Specialist Inc. (032) 268-5989 0919-822 -5048 Davao FB: Review Innovations Davao Branch (082) 221-1121 0930-256-0998