# PARAM VISIONS

All about civil construction knowledge- PARAM VISIONS

### How to calculate the length & volume of the segmental arch?

Let us now calculate the length & volume of the segmental arch as shown below.

Given data:

The span of the segmental arch = 3.5m.

Height of arch = h = 1m.

Width of the arch = 300mm.= 0.3m.

Thickness of the arch = 230mm = 0.23m.

First, we will calculate the length of the arch

The arch length is calculated by the formula

=[ ∅ × (2πr ÷ 360°)]

Here,

∅ = angle formed by the arch as shown below.

The given value of ∅ 120°  for the segmental arch.

r = Radius of the arch.

The formula for calculating the radius of the arch

= [ a2+ h2 ÷ 2h]

Here,

a = half of the arch span

= [3.5m. ÷ 2 ]

= 1.75m.

Putting the values of a & h in the above formula,

r = [ (1.75 2+ 12)÷ 2 × 1 ]

=[ (3.0625 + 1) ÷ 2]

=[ 4.0625 ÷ 2]

= 2.031m.

1.   The arch length

=[ ∅ × {(2πr) ÷ 360°}]

=[120° × {(2 × 3.142 × 2.031)÷ 360°}]

=[120° × {12.764 ÷ 360°}]

(By cancelling 120° & 360° with each other)

= [ 12.764 ÷ 3 ]

= 4.255m.

Now,

2. The volume of the segmental arch

= [length × breadth × thickness]

= [4.255m. × 0.3m. × 0.23m.]

=0.294 CUM.