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 = ?pr / 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 [? = 1050; p = 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