In this exclusive civil engineering article, you will learn how to measure the quantity of materials in a segmental arch.

Normally, there are two types of arches like semi-circular arch and segmental arch.

A segmental arch stands for a type of arch that contains a circular arc of below 180 degrees. It is sometimes known as a scheme arch. The segmental arch is treated as one of the harder arches due to its ability to withstand thrust.

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

The breadth of the arch is taken as 1 feet.

The thickness of the arch is taken as 1 feet.

The height of the arch is given as 3 feet.

The span is given as 8 feet.

The central angle is taken as 105 degree.

Now, the volume of arch will be determined with the following formula:-

Cross-section of arch x Arch length

It is known that cross-section of arch = Thickness of arch x breadth of arch = T x B

But, the length of arch is unknown.

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

Arch length = θπR/180

Now, it is required to work out the radius first as follow:-

R = (a² + h²)/2h [here, a = half span = 8/2 = 4]

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

= (4² + 3²) / 2 x 3 = 25/6 = 4.16 feet

Now, θ = 105⁰ and π = 3.142

So, θπR/180 = (105 x 3.142 x 4.16) / 180 = 7.6368

To determine the quantity of materials in arch, the following formula will be applied.

Length x Breadth x Thickness = L x B x T = 7.6368 x 1 x 1

So, the volume of material required in a segmental arch = 7.6368 cft