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How to Accurately Calculate Trapezoidal Footing Volume: A Detailed Tutorial

How to Calculate the Volume of a Trapezoidal Structure

How to Calculate the Volume of a Trapezoidal Structure

Step 1: Volume of the Rectangular Base

The rectangular base is a prism. Its volume is calculated as:

Vrect = Length × Width × Depth

Input Data:

  • Length (L) = 6 meters
  • Width (b) = 5.6 meters
  • Depth (d) = 0.450 meters

Calculation:

Vrect = 6 × 5.6 × 0.450

Vrect = 15.12 m³

The volume of the rectangular base is 15.12 cubic meters.

Step 2: Volume of the Trapezoidal Frustum

The trapezoidal frustum is a truncated pyramid. Its volume is calculated as:

Vfrustum = (h / 3) × (A1 + A2 + √(A1 × A2))

Step 2.1: Calculate Area of the Bottom Base (A1)

Input Data:

  • Length (L1) = 6 meters
  • Width (b1) = 5.6 meters

Calculation:

A1 = 6 × 5.6 = 33.6 m²

The area of the bottom base is 33.6 square meters.

Step 2.2: Calculate Area of the Top Base (A2)

Input Data:

  • Length (L2) = 1.450 meters
  • Width (b2) = 1.3 meters

Calculation:

A2 = 1.450 × 1.3 = 1.885 m²

The area of the top base is 1.885 square meters.

Step 2.3: Calculate the Geometric Mean (√(A1 × A2))

Calculation:

√(A1 × A2) = √(33.6 × 1.885) = √63.396 ≈ 7.967 m²

The geometric mean is 7.967 square meters.

Step 2.4: Substitute Values into the Formula

Substitute the values:

Vfrustum = (0.500 / 3) × (33.6 + 1.885 + 7.967)

Step 2.5: Simplify the Expression

Calculate the sum of areas:

33.6 + 1.885 + 7.967 = 43.452

Divide the height by 3:

0.500 / 3 = 0.1667

Multiply the results:

Vfrustum = 0.1667 × 43.452 = 7.242 m³

The volume of the trapezoidal frustum is 7.242 cubic meters.

Step 3: Total Volume of the Structure

The total volume is the sum of the rectangular base and trapezoidal frustum volumes:

Vtotal = Vrect + Vfrustum

Substitute the values:

Vtotal = 15.12 + 7.242

Final Calculation:

Vtotal = 22.362 m³

The total volume of the structure is 22.362 cubic meters.

Watch this video for a complete explanation by Er. Afroz on the Afroz Civil YouTube channel.

👉 Click here to watch

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