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.

The thickness of the arch = 230mm = 0.23m.

Calculation:

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 canceling 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.

To go through the articles on Estimation & calculation in civil engineering, click here.

Thank you for going through these calculation steps❤. Have a good day 😄.

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