How To Calculate The length And volume Of Semi Circular Arch
Let us now calculate theĀ length & volumeĀ 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
=[Ā ā Ā Ć (2ĻrĀ Ć· 360Ā°)]
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Here
ā = angle formed by the arch as shown below.
For a semicircular arch, the value ofĀ ā Ā =Ā 180Ā°
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.)}Ć· 2 ]
= [{2m. + ( 2nos.Ć0.5 Ć 0.3m.)} Ć· 2]
= [{2m. + ( 0.3m.)} Ć· 2]
= [2.3m Ć· 2]
rĀ =Ā 1.15m.
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1.Ā Ā The arch length
=[Ā ā Ā Ć {(2Ļr) Ć· 360Ā°}]
=[180Ā° Ć {(2 Ć 3.142 Ć 1.15)Ć· 360Ā°}]
=[180Ā° Ć {7.227Ć· 360Ā°}]
(By cancelling 180Ā° & 360Ā° with each other)
= [ 7.227 Ć· 2 ]
=Ā 3.613m.
Now,
2.Ā The volume of the semicircular arch
= [length Ć breadth Ć thickness]
= [3.613m. Ć 0.3m. Ć 0.23m.]
=0.249 CUM.
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