### Calculating the volume of concrete in a triangular pile cap having 3-piles.

Let us calculate the volume of concrete in a triangular pile foundation having 3 nos. of the pile, as shown below.

Given data:

Pile diameter = 0.6m.( d )

No. of piles = 3 nos.

Length of pile = 16m. (h )

Depth of the pile cap = 0.9m. (D )

Calculation:

The volume of concrete in the piles

= [3nos.× πr2 h]

Here,

r = radius of the pile.

= [d ÷ 2]

= [0.6m ÷ 2]

r = 0.3m.

h = length of the pile.

The volume of concrete in piles

= [3nos. × 3.142 × (0.3m)2 × 16m.]

13.57 cum.

The volume of concrete in the pile cap :

The volume of  pile cap concrete

=  [Surface area (A ) × depth ( D )]

First, let us calculate the sectional area (A1) of rectangle ABCD, as shown in the below drawing.

Area of rectangle ABCD (A1)

= [L × B]

= [2.2m × 2.0m]

= 4.4 sqm.

To get the surface area ( A) of the pile cap, we have to deduct the area of triangles AEF & GDH from the rectangle area.

Here,

Triangle AEF = triangle GDH

Area of triangle AEF

= [0.5 × base × height.]

= [0.5 × side AE × side AF]

Side AE

= [ ( 1/2 ×side BC ) - (1/2 × side EG )]

=  [ ( 1/2 ×2m. ) - (1/2 × 0.6m. )]

= [ 1m - 0.3 m ]

= 0.7m.

Side AF

= [side AB - side FB]

= [2.2m - 0.7m]

= 1.5m.

I have redrawn the triangle, with the calculated length of the sides AF & AE as shown below.

Area of triangle AEF

= [0.5 × side AE × side AF]

= [0.5 × 0.7m × 1.5m.]

= 0.525 sqm.

The surface area of the pile cap (A )

= [area of rectangle ABCD - (2nos. × area of a triangle AEF )]

= [4.4 sqm. - (2nos. × 0.525sqm.)]

= [4.4 sqm. - 1.05 sqm.]

= 3.35 sqm.

Now,

the concrete vol. of pile cap

= [surface area (A ) × depth (D )]

= [3.35 sqm. × 0.9m.]

= 3.015 cum.

The total concrete volume of the 3-pile foundation

= [The vol. of concrete in pile cap + total vol. of concrete in piles.]

= [3.015 cum + 13.57 cum.]

16.585 cum.

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