How to work out the materials quantities in a segmental arch
In this civil engineering article, you will learn the calculation process for determining the quantity of materials in a segmental arch.
There are normally two types of arches like segmental arch and semi-circular arch.
The calculation is made based on the following values for segmental arch and cross sectional area :-
Breadth of the arch is given as 1 feet
Thickness of the arch is given as 1 feet
Central Angle of the arch is given as 105 degree
The height of the arch is given as 3 feet
Spacing of the arch is given as 8 feet
Now, it is required to determine the volume of arch with the following formula :-
Cross-section of arch x Length of arch
Here, the value of breadth and thickness is given but the value of length is unknown.
Cross section area = Thickness of arch (T) x Breadth of arch (B)
The following formula is used to calculate the length of the arch :-
Length of arch = θπr / 180
The value of r can be calculated as follow :-
R = (a2 + b2) / 2h (the value of a = half of the span i.e. 8/2 = 4)
After putting the value of A, we get the following result :-
R = (42 + 32) / 2 x 3 = 25/6 = 4.16 ft.
Now, put the value of R in the above formula :-
Length of arch = (105 x 3.142 x 4.16) / 180 = 7.6368 [θ = 1050; π = 3.142]
As we know, quantity of materials in arch = L x B x T
So, after putting all the values, we get = 7.6368 x 1 x 1= 7.6368 cft