All about civil construction knowledge- PARAM VISIONS

How to calculate the volume of concrete in trapezoidal footing? /Trapezoidal footing volume calculation.

Let us calculate the volume of concrete in a trapezoidal footing as shown below.



The volume of the trapezoidal footing is calculated into 2 parts as it is made of two different shapes.

Part-1 of the footing is known as a truncated pyramid ( as shown below )




and part 2 of the footing is known as cuboid ( as shown below )


The volume of the trapezoidal footing 

   = [ (volume of the truncated pyramid ) + ( volume of the cuboid.) ]

   = [ ( 1/3(a1 +a2 + √ a1 × a2 ) × h )   + ( L × B × H ) ]

Here,

        a1 =  top surface area of truncated pyramid ( part-1 )

             = l × b

      a 2 = base surface area of a truncated pyramid ( part-1 )

            = L × B 


Now, for the calculation purpose, let us redraw the above drawings with mathematical dimensions. 


a. The volume of the cuboid ( part-2 ) :


Cuboid


Given data :

 Length L = 750mm.

Breadth B = 600mm.

Height H = 300 mm.


The volume of the cuboid 

   =  [L × B × H]

   = [750mm × 600mm × 300mm]

   = [0.75 m × 0.6m × 0.3m]

   =0.135 cum.


b. The volume of the truncated pyramid ( part-1 ) :


 Given data :

Base surface length L = 750mm ( same as cuboid )

Base surface breadth B = 600 mm. ( same as cuboid )

Top surface length l = 450 mm

Top surface breadth b = 300mm.

Height h = 200mm.


The volume of the truncated pyramid (part-1 )

  = [1/3(a1 +a2 + √ a1 × a2 ) × h]

Here,

    a1 = l × b

        = 450mm × 300mm

        = 0.45 m × 0.3 m

       = 0.135 sqm.


a2 = L × B

    = 750 mm × 600mm

   = 0.75m × 0.6 m

  = 0.45 sqm.

The volume of the truncated pyramid ( part -1)

  = 1/3 (0.135 sqm + 0.45 sqm + √ 0.135sqm × 0.45sqm ) × 0.2 m

  = 1/3 ( 0.585  +  √ 0.06075 ) × 0.2

  = 1/3 (0.585 + 0.2465 ) × 0.2

 = 1/3 × 0.8315 × 0.2

 = 0.0554 cum.


The volume of concrete in trapezoidal footing 

  = vol. of cuboid ( part-2 ) + vol. of truncated pyramid ( part-1 )

  = 0.135 cum + 0.0554 cum

  = 0.1904 cum.

  =6.725 cu ft.  ( 1 cu ft = 35.315 cum )

 

Thank you for going through these calculation steps. Have a good day 😄.











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