prismoidal formula
Formula untuk volume prismoid. A rumus khas, digunakan untuk menghitung volume dipotong
atau mengisi yang berbentuk seperti prismoid, adalah V = L (A + 4B + C) / 6, di mana V adalah
volume, A dan C adalah area cross sectional ujung, B adalah luas penampang silang di tengah
dipotong atau mengisi, dan L adalah panjang sebagian seragam meruncing dipotong atau
mengisi. Formula yang digunakan, misalnya, dalam penilaian jalur rel kereta api atau jalan Raya.
EQUATIONS - EARTHWORK FORMULAS
Area
Area by Coordinates
Area = [XA(YB - YN) + XB(YC - YA) + XC(YD - YB) + ...+ XN(YA - YN-
1)]/2
Trapezoidal Rule
Area = w[(h1 + hn)/2 + h2 + h3 + h4 + .... + hn-1]
w = common interval length
Simpson's 1/3 Rule
w = common interval length
n must be odd number of measurements
Volume
Average End Area
Formula
V = L(A1 + A2)/2
A = section area
L = length between areas 1 and 2
V = volume
Prismoidal Formula
V = L(A1 + 4Am + A2)/6
Am = area at mid section
see Prismoid in Measuration Equations
Pyramid or Cone
V = h(area of base)/3
h = cone height
Volume Calculation for Areas Found Using Section Method
Volume Calculation for Areas found using Section Method
Once the section wise area calculation is done using section method, any of the 3 Volume calculation
methods can be used for Volume Calculation
1. Average End Area Method
2. Prismoidal Rule
3. Simpsons 1/3rd Rule
Average End Area Volume Calculation (Trapezoidal Method)
The formula for calculation of volume by average end area:
Volume = L x 1/2 (A1 + A2) cubic meter
L Distance in meters A1 and A2 area in Square meters
The average end area calculation is used to calculate volume between two cross sections i.e., Two cross
sectional areas are averaged and multiplied by the length (distance) between two cross sections to get
the volume.
If there are a series of areas A1, A2, A3,.An at regular interval L, V=L/2[(A1+An)+2A2+A3+..+An-1)]
Prismoidal Formula
Prismoidal formula is accurate in finding the volume of prisms, pyramids, wedges, and prismoids having
irregular end sections. The estimation of earthwork gives nearly an accurate volume.
The formula given is V=d/3[Sum of areas of end two sections+ 4(sum of the even sections) +2(sum of the
remaining sections)]
Example 7:
In this example, we have found out the area of cutting and filling for all the 6 Sections using Trapezoidal
Method at formation level 20.
The area calculation details are as below:
Sl. Section Cutting Filling
No. No. Area Area
1 729 1.85 2.45
2 732 17.10
3 735 78.90
4 738 20.85
5 741 72.00
6 744 14.70
Total 1.85 206.00
Volumes
Volume calculations for rectangular prism and pyramid are shown below:
A truncated pyramid is a pyramid
which top has been cut off.
If the A1+A2 is almost equal in size
then the following formula can be used
instead:
V = h (A1 + A2) / 2
A prismoid is as a solid whose end
faces lie in parallel planes and consist
of any two polygons, not necessarily
of the same number of sides as shown
opposite, the longitudinal faces may
take the form of triangles,
parallelograms, or trapeziums.
Areas
Area calculations refer usually to rectangular and triangular shapes. If you need the trigonometric
function for calculations click here.
There are different ways to calculate the area of
the opposite figure. Try to minimise the amount
of calculation. The figure could be divided in
three distinct areas
a=10.31x5.63+
b=6.25x5.76+
c=10.39x4.79
or the whole rectangle minus the hole (d)
A =16.67x10.31-6.25x4.55.
As you can see the 2nd method is easier. Look
at the shape and try to shorten the calculations.
If you know only the sides of a triangle then use the formula given in the figure below.
An area can usually be divided it in
triangles (rectangles, parallelograms,
trapeziums etc).
Parallelograms has opposite sides
parallel and equal. Diagonals bisect
the figure and opposite angles are
equal..
The trapezium has one pair of
opposite sides parallel.
(A regular trapezium is symmetrical about
the perpendicular bisector of the parallel
sides.)
An arc is a part of the circumference of a circle; a part proportional to the central angle.
If 360 corresponds to the full circumference. i.e. 2 r then for a central angle of (see opposite
figure) the corresponding arc length will be b = /180 x r .
