Let us calculate the volume of concrete in a pipe culvert cradle as shown below.
Given data:
OD of RCC pipe = 1640mm.
ID of RCC pipe = 1400mm.
RCC cradle width = 2240mm.= 2.24m.
RCC cradle length = 12m.= 12000mm.
Cradle depth = 720mm.=0.72m.
Calculation:
Let us divide the cradle into two parts having rectangular sections AEFD & EBCF as shown in the below drawing.
The volume of concrete in the cradle
= [cradle length × { area of section EBCF + area of section AEFD}]
Now, the area of section EBCF
= [cradle width × section depth]
= [2.24m. × 0.32m]
= 0.7168 sqm.
The area of the section AEFD
= [(cradle width × section depth) - (an area of pipe embedded in cradle)]
We have to deduct the (red-colored) area of the embedded pipe as shown below.
To calculate the area of the embedded pipe in the culvert, let us follow the following steps.
Length of GI = radius of pipe(r)
= [outer diameter of pipe ÷ 2]
= [1640mm. ÷ 2]
= 820mm.
Length of side GL = side GI = side HG = 820mm., as all are outer radius ( r ) of the pipe.
Side GK = [length of GL - embedded depth of pipe ]
= [ 820mm. - 400mm.]
= 420mm.
By Pythagoras theorem,
GI2= (GK )2 +( KI )2
(820)2= (420)2 +( KI )2
KI = √(820)2 - (420)2
KI = √ 4,96,000
KI = 704.27mm.
Length of side HI = [2 × side KI]
= [2 × 704.27mm.]
= 1408.54mm.
Area of triangle GHI
= [1/2 × base × height]
= [1/2 × side HI × side GK]
= [1/2 × 1408.54mm. × 420mm.]
= 295,793.4 sq mm.
= 0.295 sq m.
sinθ1 = [opposite side ÷ hypotenuse]
= [side KI ÷ side GI]
= [ 704.27mm. ÷ 820mm.]
= 0.8588
θ1 = 59.18°
Area of a sector of a circle GHLI
= [ (θ ÷ 360°) × π r2]
Where θ is the sector angle as shown in the drawing.
Here, θ = 2 × θ1
= 2 × 59.18°
= 118.36°
Area of a sector of a circle GHLI
= [ (118.36° ÷ 360°) × 3.142 × 8202 ]
=[ 0.2877 × 2,112,680]
= 607,818.27sq mm.
= 0.6078 sq m.
Now, the embedded area of pipe in the cradle
= [area of sector GHLI - the area of triangle GHI]
= [ 0.6078 sq m. - 0.295 sq m.]
= 0.3128 sq m.
The area of the section AEFD
= [(cradle width × section depth) - (an area of pipe embedded in cradle)]
= [(2.240m. × 0.4m.) - (0.3128)]
= [0.896 sq m. - 0.3128 sqm.]
= 0.5832 sq m.
The volume of concrete in the cradle
= [cradle length × { area of section EBFC + area of section AEFD}]
= [12m. × { 0.7168 + 0.5832}]
= [12m. × 1.3 sq m.]
= 15.60 cum.
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Thank you for going through these calculation steps❤. Have a good day 😄.
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