How to work out the volume of a segmental arch

In this useful construction video tutorial, you will learn how to measure the quantity of materials in a segmental arch.

There are two types of arches i.e. segmental arch and semi circular arch.

The calculation is done on the basis of the following dimensions:-

Span of the arch is given as = 8 feet
Height of the arch is given as = 3 feet
Density of the arch is given as = 1 feet
Breadth of the arch is given as = 1 feet
Central Angle of arch is given as = 105 degree

The volume of arch can be measured with the following formula :-

Cross-section of arch x length of arch
Here, the values for breadth and thickness are provided, hence it is required to determine the length.
It is known cross-section area = thickness of arch x breadth of arch
= T x B

The following formula should be used to determine the length of the arch :-

Length = ØπR/180
So, you have to find out the value of R.
R = (a² + h²)/2h [a = half span = 8/2 = 4]

After putting all the values, we get the following :-

(4² + 3²) /2 x 3 = 25/6 = 4.16 feet
So, length of arch = (105 x 3.142 x 4.16)/180 = 7.6368 [Ø = central angle of arch & π = 3.142]

Now, the quantities of materials in arch will be determined with the following formula :-

Length x Breadth x Thickness = 7.6368 x 1 x 1 = 7.6368 cft

It will be the volume of the segmental arch.

Video Source: Civil Study