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Areas and Volumes Introduction

Faculty of Applied Engineering and Urban Planning. Civil Engineering Department. Surveying. 2 nd Semester 2008/2009. Areas and Volumes Introduction. Areas and Volumes. Planimeters. Digital Planimeter. Optical Polar Planimeter. Planimeters.

vladimir-zimmerman
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Areas and Volumes Introduction

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  1. Faculty of Applied Engineering and Urban Planning Civil Engineering Department Surveying 2nd Semester 2008/2009 Areas and Volumes Introduction

  2. Areas and Volumes

  3. Planimeters Digital Planimeter Optical Polar Planimeter

  4. Planimeters

  5. Note : the accuracy of the results obtained from using planimeter in the measurement of areas depends mainly on the original accuracy drawn map, as well as on the experience of the operator when tracing boundary of the figure.

  6. Questions?!

  7. Areas • Regular Figures • Mathematical Formulae • Method of Coordinates • Irregular Figures • Graphical Method • Trapezoidal Rule • Simpson’s One-Third Rule

  8. Mathematical Formulae

  9. Mathematical Formulae

  10. Mathematical Formulae 20 m 15 m

  11. Questions?!

  12. Areas by Method of Coordinates

  13. Areas by Method of Coordinates

  14. Areas by Method of Coordinates

  15. Areas by Method of Coordinates

  16. Areas by Method of Coordinates Area = 0.5(| 136840.01 – (-84890.94) |) = 110865.48 ft2

  17. Questions?!

  18. Content • Areas of Irregular Figures • Graphical Method • Trapezoidal Rule • Simspon’s One-Third Rule

  19. Graphical Method

  20. Trapezoidal Rule

  21. Trapezoidal Rule

  22. Trapezoidal Rule

  23. Example

  24. Simspon’s One-Third Rule Offset Intercept ONLY used with Odd number of offsets (i.e. Even number of Intercepts)

  25. Simspon’s One-Third Rule

  26. Example

  27. Trapezoidal Rule Area Calculation Simspon’s One-Third Rule

  28. Content • Volumes by: • Average-End-Area Method • Prismoidal Method • Contour Maps • Volume from Spot Levels

  29. Cut and Fill

  30. Average-End-Area Method

  31. Average-End-Area Method

  32. Prismoidal Method

  33. Calculating Volumes from Contour Map

  34. Calculating Volumes from Contour Map

  35. Calculating Volumes from Contour Map

  36. Questions?!

  37. Volume from Spot Levels

  38. Volume from Spot Levels

  39. Volume from Spot Levels

  40. Mass Haul Diagram A mass haul diagram is of great value both in planning and construction. The diagram is plotted after the earthwork quantities have been computed, the ordinates showing aggregate volumes in cubic metres while the horizontal base line, plotted to the same scale as the profile, gives the points at which these volumes obtain.

  41. Mass Haul Diagram Most materials are found to increase in volume after excavation ('bulking'), but after being re-compacted by roller or other means, soils in particular might be found to occupy less volume than originally, i.e. a 'shrinkage' has taken place when compacted in the in situ volume.

  42. Mass Haul Diagram

  43. Mass Haul Diagram

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