# How to measure the volume or quantity of material in a segmental arch

Parag Pal, the eminent civil engineer, comes up with another useful video tutorial for civil engineering students. In this video, he teaches how to work out the materials quantities of a segmental arch.

Here, the segmental area of the arch is given.

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

The span of the arch is taken as 8 feet

The height of the arch is taken as 3 feet

The thickness of the arch is taken as 1 feet

The breadth of arch is taken as 1 feet

The central angle of the arch is taken as 105 degree

The volume is determined with the following formula :-

Cross section of arch x the length of the arch

Initially, it is required to determine the cross sectional area of arch with the following formula :-

Thickness of arch x breadth of arch = T x B

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

ØπR/180 (here, the value of R is unknown)

So, R = (a2 + h2)/2h (here, a denotes half span i.e. 8/2 = 4 feet)

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

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

Now, the length of the arch will be as follow :-

ØπR/180 = 105 x 3.142 x 4.16 (as central angle = 105 degree; standard value of π = 3.142) = 7.63 feet

The volume or quantity of material of segmental arch will be determined as follow :-

Length x breadth x thickness = L x B x T

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

7.63 x 1 x 1 = 7.63 cubic feet

For online demonstration, go through the following youtube video.

Video Source: Parag Pal