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Calculation Of Area & Volume - Coggle Diagram
Calculation Of Area & Volume
Area calculation from plans
Irregular boundaries
Mathematics
Trapezoidal
If there are n offsets
Simpson
For n offsets
Trapezoidal vs Simpson
Simpson approximate boundaries as curve sections
Preference should be given to Simpson. In cases where offsets are even numbers, partly calculate using Simpson (up to odd offsets) and trapezoidal for the remaining offsets
therefore better approximation than trapezoidal
Mechanical
Planimeter : mechanical instrument specifilcally designed to calculate irregular areas from plans and maps.
Graphical
‐Uses grids and counting squares
Combination of regular & irregular
:
Regular boundaries
Area can be calculated using formulas for triangle or coordinates
Area from coordinates
Calculating cross-sectional areas
the reduced levels of these
points are determined determined using any suitable suitable method
reduced levels of points that lie to the left and right of the centre line at right angle are also observed, thus, creating cross‐sections
Setting‐out of roads, highways, railway track, etc., are normally done at regular intervals along the centre line
Volume estimation
Spot heights
Example ‐ cutting and filling of earth for basement (car park), underground water tanks, to obtain required formation levels, etc
A grid is f d orme over the area, and the reduce levels
of the grid points are determined
Used in ‘localised’ construction, such as earthwork for
the construction of buildings.
The difference between the grid heights and the proposed heights are obtained in order to estimate volumes
Contours
Suitable to be used when large volume is involved, such as, volumes of water contained in a dam, soil such as, volumes of water contained in a dam, soil
The area of a contour contour surface surface is determined determined. The contour’s surface can be treated as a cross‐section whose areas can be calculated either graphically or mechanically
Cross‐sections
End‐Areas
Prismoidal
Cross Sections
& Longitudinal Sections
LONGITUDINAL SECTION
Reduced level of the centre‐line observed produced longitudinal sections
Determine the
vertical curve
CROSS SECTION
Observations of reduced levels at point that lie at right angle of the centre‐line produced cross‐sections
Calculated by
Mathematical formula (software)
Grid & Counting Squares (manual)
Planimeter (manual – easy)
