Width of Footing given Factor of Safety and Safe Bearing Capacity Calculator

Footing Width Formula:

\[ B = \frac{(q_{sa} \times FS) - (FS \times (\gamma \times D)) - (C_s \times N_c + (\gamma \times D) \times (N_q - 1))}{0.5 \times \gamma \times N_\gamma} \]

Safe Bearing Capacity (q_sa):

Factor of Safety (FS):

Unit Weight of Soil (γ):

N/m³

Depth of Footing (D):

Cohesion of Soil (C_s):

Bearing Capacity Factor (N_c):

Bearing Capacity Factor (N_q):

Bearing Capacity Factor (N_γ):

Width of Footing (B): m

1. What is Footing Width Calculation?

Definition: This calculator determines the required width of a footing based on safe bearing capacity, soil properties, and safety factors.

Purpose: It helps civil engineers design stable foundations that can safely support structural loads without soil failure.

2. How Does the Calculator Work?

The calculator uses the bearing capacity formula:

\[ B = \frac{(q_{sa} \times FS) - (FS \times (\gamma \times D)) - (C_s \times N_c + (\gamma \times D) \times (N_q - 1))}{0.5 \times \gamma \times N_\gamma} \]

Where:

\( B \) — Width of footing (meters)
\( q_{sa} \) — Safe bearing capacity (Pascals)
\( FS \) — Factor of safety
\( \gamma \) — Unit weight of soil (N/m³)
\( D \) — Depth of footing (meters)
\( C_s \) — Cohesion of soil (Pascals)
\( N_c, N_q, N_\gamma \) — Bearing capacity factors

Explanation: The formula accounts for soil properties, surcharge effects, and safety margins to determine minimum footing width.

3. Importance of Footing Width Calculation

Details: Proper footing design prevents excessive settlement, bearing capacity failure, and ensures structural stability.

4. Using the Calculator

Tips: Enter all required parameters. Default values are provided for typical conditions. Factors marked with ±5% indicate typical variability.

5. Frequently Asked Questions (FAQ)

Q1: What's a typical factor of safety for footings?
A: Usually 2.5-3.0 for permanent structures, but may vary based on soil conditions and importance of structure.

Q2: How do I determine bearing capacity factors?
A: They depend on soil friction angle - use standard geotechnical tables or laboratory testing.

Q3: What if my soil has no cohesion?
A: Set cohesion (C_s) to zero and use appropriate bearing capacity factors for granular soils.

Q4: How does footing depth affect the calculation?
A: Deeper footings benefit from greater surcharge and may require less width, but consider excavation costs.

Q5: Should I round up the calculated width?
A: Yes, always round up to nearest standard construction dimension (e.g., 0.1m increments).