What is a Sloped Footing?
A sloped or stepped footing is designed to save concrete material by reducing the thickness towards the edges, where the bending moment and shear stresses are lowest. This tool helps engineers calculate the exact volume of the truncated pyramid and the required reinforcement.
Truncated Pyramid Volume Formula
The total volume is the sum of the rectangular base (V1) and the sloped truncated pyramid (V2). V2 is calculated using the areas of the base (A1) and the top (A2).
Practical Example
For a footing with Base 2x2m, Top 0.5x0.5m, Base thickness 0.2m, and Sloped thickness 0.3m: Base Vol = 2×2×0.2 = 0.8m³. Top Area = 0.25m². Sloped Vol = 0.3/3 × (4 + 0.25 + √(4×0.25)) = 0.1 × (4.25 + 1) = 0.525m³. Total Volume = 1.325m³.
Frequently Asked Questions
Why use a sloped footing instead of a flat isolated pad?
Sloped footings require significantly less concrete while providing the same structural safety, making them highly economical for large scale projects.