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Area Measurement

Area Measurement. Mohammed Ali Ihsan Saber PhD. In Structural Engineering. Objectives. In this lecture we will learn about: The formulae used to calculate the area of regularly shapes. The formulae used to calculate the area of irregularly shapes by: Simpson’s rule. Trapezoidal rule.

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Area Measurement

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  1. Area Measurement Mohammed Ali Ihsan Saber PhD. In Structural Engineering

  2. Objectives • In this lecture we will learn about: • The formulae used to calculate the area of regularly shapes. • The formulae used to calculate the area of irregularly shapes by: • Simpson’s rule. • Trapezoidal rule. • Methods of calculating area from survey field notes and from coordinates.

  3. Area Measurement • Even on the smallest site, calculations have to be made of a wide variety of area. • Site area itself. • Design of any construction. • Estimation of costs. • Calculation of volumes, earthworks, capacity…..

  4. Regular areas • Measuring area directly by using mathematical formula, Ex. Square, triangle,…. • Split it in to figures in order to calculate its area.

  5. Regular areas

  6. Irregular areas • The trapezoidal rule,(General, low accuracy). • The trapezoidal rule is usually expressed thus: • Area = strip width x (average of first and last offsets + sum of others) • Note. (a) The offsets must be at regular intervals.

  7. Irregular areas • Simpson's rule,(only odd off set, more accurate). • The area can be found slightly more accurately by Simpson's rule. • Area = ⅓ strip width (first + last offsets + twice sum of odd offsets + four times sum of even offsets). • Note. (a) The offsets must be at regular intervals. • (b) There must be an odd number of offsets.

  8. Trapezoidal VS Simpson

  9. Area from field notes • Linear surveys: In linear survey the area is divided into triangles, and the length of the three sides of each triangle are measured. The area contained any one triangle ABC is found from the formula: Where s is the semi-perimerter

  10. Total coordinate products • Method of total coordinate products The following is the sequence of operations in the calculation of the area of any polygon: • Write the array of easting and northing as shown above. Note that E₁ and N₁ are repeated at the bottom of the columns. • Multiply the departure of each station by the latitude of the preceding station and find the sum. • Multiply the departure of each station by the latitude of the following station and find the sum. • Find the algebraic difference between operations 2 and 3 above. • Halve this figure to give the area of the polygon.

  11. Total coordinate products

  12. Summery • The formulae used to calculate the area of regularly shapes. • The formulae used to calculate the area of irregularly shapes by: • Trapezoidal rule.(General, low accuracy) • Simpson’s rule.(only odd off set, more accurate) • Methods of calculating area from survey field notes and from coordinates

  13. References: • Willima Irvine and finlaymaclennan "surveying for construction" fifth edition. • W.Schofield and M.Breach "engineering surveying" sixth edition. • Moffitt Bouchard "surveying" eighth edition

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