Understanding the method to calculate the length and volume of a semi-circular arch is crucial in construction and architecture. Let’s dive straight into it.

Given Data for the Semi-Circular Arch

• Span of the Arch: 2 meters

• Height of the Arch: 1 meter

• Width of the Arch: 300 mm = 0.3 meters

• Thickness of the Arch: 230 mm = 0.23 meters

Having these values handy, we can now move on to the calculations.

Step 1: Calculating the Radius of the Arch

The first essential step is finding the centerline radius.

Formula to Calculate Radius:

Radius (r) = (Span + Half of the Arch Width on Both Sides) ÷ 2

Now substituting the given values:

r = [2m + (2no. × 0.5 × 0.3m)] ÷ 2

r = [2m + 0.3m] ÷ 2
r = 2.3m ÷ 2
r = 1.15 meters

Thus, the radius of the arch is 1.15 meters.

Step 2: Calculating the Length of the Arch

For a semi-circular arch, the central angle (∅) is 180°.

Formula to Calculate Arch Length:

Length = ∅ × (2πr ÷ 360)

Substituting the values:

Length = 180 × (2 × 3.142 × 1.15 ÷ 360)

Length = 180 × (7.227 ÷ 360)
Length = 7.227 ÷ 2
Length = 3.613 meters

Therefore, the total length of the semi-circular arch is 3.613 meters.

Step 3: Calculating the Volume of the Semi-Circular Arch

Now, with the length determined, we proceed to find the volume.

Formula for Volume:

Volume = Length × Breadth × Thickness

Substituting the calculated and given values:

Volume = 3.613m × 0.3m × 0.23m

Volume = 0.249 cubic meters (CUM)

Hence, the volume of the semi-circular arch comes out to be 0.249 cubic meters.

Quick Summary

• Radius of Arch: 1.15 meters

• Length of Arch: 3.613 meters

• Volume of Arch: 0.249 cubic meters

Key Points to Remember

• Always double-check the conversion of units before beginning the calculation.

• Keep the use of π (Pi) accurate up to three decimal places for better precision.

• Maintain clarity in applying formulas to avoid confusion later.

Click Here To See Accurate Concrete Volume Calculation For Staircase Construction by Imperial System