In this article, I will discuss how two calculate quantity of materials in arch.
1. Semi Circular Arch:
Given:
Span = 8 ft
Height = 4 ft
Thickness = 1 ft
Breadth = 1ft
To calculate the quantity of materials in semi circular arch we need to calculate the volume of arch.
Volume of arch = Cross-section of arch x Arch length
We know Cross-section area = Thickness of arch x Breadth of arch = T x B
From the above image, you can see the thickness and breadth are 1 ft.
Cross-section of arch = 1 x 1 = 1 ft²
Now Arch length = Circumference of half circle (The arch is semi circular)
We know circumference of circle = 2πR
Circumference of half circle = 2πR/2 = πR
We don’t what is R. So we need to find out the ‘R’.
R = Half span + Thickness/2 = 4 +1/2 = 4.5 ft.
Arch length = πR =3.14 x 4.5 = 14.13 ft.
Quantity of materials in arch = 1 x 14.13 = 14.13 cft.
2. Segmental Arch:
Given:
Span = 8 ft
Height = 2ft
Thickness = 1 ft
Breadth = 1ft
Central angle = 105°
Solution:
Volume arch = Cross-section of arch x Arch length
We know Cross-section area = Thickness of arch x Breadth of arch = T x B
Arch length = θπR/180
Now R = (a² + h²)/2h [a =half span = 8/2 =4]
=(4² + 3²)/2 x 3 = 25/6 =4.16 ft.
Arch length = (105 x 3.14 x 4.16)/180 = 7.61
Quantity of materials in arch = 1 x 7.61 = 7.61 cft.
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