How To Calculate The length And volume Of Semi Circular Arch
Let us now calculate the length & volume of the semicircular arch as shown below.
Given data:
The span of the semicircular arch = 2m.
Height of arch = 1m.
Width of the arch = 300mm.= 0.3m.
Thickness of the arch = 230mm = 0.23m.
First, we will calculate the length of the arch
The arch length is calculated by the formula
=[ ∅ × (2πr ÷ 360°)]
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Here
∅ = angle formed by the arch as shown below.
For a semicircular arch, the value of ∅ = 180°
r = Radius of the arch.
Calculate the volume of the arch, let us calculate the radius of the center line as shown below.
Radius
= [{arch span + (half of the arch width on both sides.)}÷ 2 ]
= [{2m. + ( 2nos.×0.5 × 0.3m.)} ÷ 2]
= [{2m. + ( 0.3m.)} ÷ 2]
= [2.3m ÷ 2]
r = 1.15m.
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1. The arch length
=[ ∅ × {(2πr) ÷ 360°}]
=[180° × {(2 × 3.142 × 1.15)÷ 360°}]
=[180° × {7.227÷ 360°}]
(By cancelling 180° & 360° with each other)
= [ 7.227 ÷ 2 ]
= 3.613m.
Now,
2. The volume of the semicircular arch
= [length × breadth × thickness]
= [3.613m. × 0.3m. × 0.23m.]
=0.249 CUM.
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