FORMULA FOR CLCULATION OF VOLUME

 

FORMULA FOR CLCULATION OF VOLUME

 

D = Common distance between sections.

 Trapezoidal rule or average end area rule.

 

Volume (Cutting or Filling),

 

                           V = D/2[A₁ + An + 2(A₂ + A₃ + A₄ + … +An-₁)]

 

i.e.   Volume = Common distance {Area of 1^st section + Area of last section

                                  2              

                                                + 2(Sum of area of other sections)}

 

Prismoidal rule.

 

Volume (Cutting or Filling),

 

          V = D/3[(A₁+An) + 4(A₂+A₄+...+ An-₂) + 2(A₃+A₅+... + An-₁)]

 i.e.   Volume = Common distance {Area of 1^st section + Area of last section

                                  3              

                                                 + 4(Sum of area of even sections)

                                                 + 2(Sum of area of odd sections)}

 

This formula is applicable when there are an odd number of sections.

 

PRISMOIDAL CORRECTION FOR TRAPEZOIDAL OR AVERAGE END AREA RULE

 

i.             Prismoidal correction for level section:

 

            Cp = D x s (h – h)²    (Considering, transverse slope= 1 in n side slope= S : 1)

                        6       

 

 

 

 

ii.            Prismoidal correction for two level section:

 

            Cp = D x s    n²      x (h₁ – h₂)²

                        6    n² - s     

 

iii.          Prismoidal correction for three level section:

 

            Cp = D  (h₁ – h₂)    (Whole width of 1^st section – Whole width of 2^nd section)

                           12

 

iv.          Prismoidal correction for Side-hill two level or Part cut-part fill:

 

(a)        Cp (for cutting) =      D       x n²(h₁ – h₂)²    (side slope= s₁ : 1)

                                              12(n – s₁)

 

(b)        Cp (for filling) =      D       x n²(h₁ – h₂)²    (side slope= s₂ : 1)

                                           12(n – s₂)

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