Calculating the concrete quantity for an octagon footing is crucial in construction projects to ensure the correct volume of materials is used, preventing shortages or excess costs. This article provides a comprehensive, step-by-step guide to accurately compute the required concrete for an octagonal footing based on given dimensions.
An octagonal footing is a widely used structural element in buildings and bridges, offering greater load distribution than square or rectangular footings. The octagonal shape provides improved stability and strength, making it a preferred choice for foundations in various soil conditions.
Given Data
- All sides are equal
- Length of each side (a) = 2 m
- Height (h) = 0.6 m
Step 1: Calculate the Area of the Octagon
The formula for the area (A) of a regular octagon is:
A = 2(1 + 1.414) x 4 = 19.312 m²
Thus, the area of the octagonal base is 19.312 m².
Step 2: Calculate the Volume of the Octagonal Footing
The volume (V) of the footing is calculated using the formula:
V = A x h
Substituting the values:
V = 19.312 x 0.6
V = 11.5872 m³
So, the total concrete volume required is 11.5872 cubic meters.
Step 3: Convert Volume into Bags of Cement, Sand, and Aggregate
For M20 grade concrete mix (1:1.5:3), the materials required per 1 cubic meter are:
Before determining the material requirements, we must calculate the total volume of ingredients used in 1 cubic meter (1m³) of concrete.
Total parts of mix = 1 + 1.5 + 3 = 5.5
However, when concrete is mixed with water, it shrinks due to compaction and setting. Civil engineers apply a shrinkage factor of 1.54 to 1.57 to compensate for this.
Dry Volume of Concrete Calculation:
- Given 1 m³ of wet concrete,
- Dry volume = 1 x 1.54 = 1.54 m³
- Cement = 1/5.5 × 1.54 x 1 m³ = 0.28 m³
- Sand = 1.5/5.5 x 1.54 × 1 m³ = 0.42 m³
- Aggregate = 3/5.5 x 1.54 × 1 m³ = 0.84 m³
Now, multiplying by the total volume (11.5872 m³):
- Cement = 0.28 × 11.5872 = 3.24 m³
- Sand = 0.42 × 11.5872 = 4.86 m³
- Aggregate = 0.84 × 11.5872 = 9.73 m³
Convert Cement Volume into Bags
One bag of cement (50 kg) = 0.0347 m³.
Number of cement bags required:
Step 4: Water Requirement
The water-cement ratio for M20 concrete is 0.5.
Total cement = 93 bags × 50 kg = 4650 kg.
Water required:
4650 × 0.5 = 2325 liters
Additional Considerations
1. Wastage Factor
Always account for 5-10% extra concrete due to spillage, formwork absorption, and compaction losses. Therefore, the total concrete required:
11.5872 + (11.5872 + 0.05) = 12.16m³
2. Formwork and Shuttering
Using plywood or steel shuttering ensures accurate shape retention and minimal leakage during pouring.
3. Concrete Curing
Curing for 7 to 14 days is essential to achieve the desired compressive strength and durability.
