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.

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