Width of Footing given Bearing Capacity for Local Shear Failure Calculator

Width of Footing Formula:

\[ B = \frac{q_{fc} - \left(\left(\frac{2}{3} \times C \times N_c\right) + \left(\sigma_s \times N_q\right)\right)}{0.5 \times N_\gamma \times \gamma} \]

Ultimate Bearing Capacity (q_fc):

kPa

Cohesion (C):

kPa

Bearing Capacity Factor (N_c):

Effective Surcharge (σ_s):

kPa

Bearing Capacity Factor (N_q):

Bearing Capacity Factor (N_γ):

Unit Weight of Soil (γ):

kN/m³

Width of Footing (B): m

1. What is Width of Footing given Bearing Capacity for Local Shear Failure?

Definition: This calculator determines the required width of a footing based on soil bearing capacity parameters for local shear failure conditions.

Purpose: It helps geotechnical engineers and foundation designers ensure footings are properly sized to prevent local shear failure in soil.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ B = \frac{q_{fc} - \left(\left(\frac{2}{3} \times C \times N_c\right) + \left(\sigma_s \times N_q\right)\right)}{0.5 \times N_\gamma \times \gamma} \]

Where:

\( B \) — Width of footing (meters)
\( q_{fc} \) — Ultimate bearing capacity in soil (kPa)
\( C \) — Cohesion in soil (kPa)
\( N_c \) — Bearing capacity factor dependent on cohesion (±5%)
\( \sigma_s \) — Effective surcharge (kPa)
\( N_q \) — Bearing capacity factor dependent on surcharge (±5%)
\( N_\gamma \) — Bearing capacity factor dependent on unit weight (±5%)
\( \gamma \) — Unit weight of soil (kN/m³)

Explanation: The formula accounts for soil cohesion, surcharge, and unit weight to determine the minimum footing width needed to prevent local shear failure.

3. Importance of Footing Width Calculation

Details: Proper footing width ensures structural stability, prevents excessive settlement, and avoids shear failure in the supporting soil.

4. Using the Calculator

Tips: Enter all required parameters. Default values are provided for bearing capacity factors (with ±5% accuracy). All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is local shear failure?
A: Local shear failure occurs when only a portion of the soil beneath the footing reaches failure, causing excessive settlement.

Q2: How do I determine the ultimate bearing capacity (q_fc)?
A: q_fc is typically determined through soil testing or empirical correlations based on soil properties.

Q3: Why are bearing capacity factors given with ±5%?
A: These factors are empirically derived and can vary slightly depending on soil conditions and analysis methods.

Q4: What if my soil has no cohesion (C=0)?
A: For cohesionless soils, simply enter 0 for cohesion. The calculation will still work.

Q5: How does surcharge affect footing width?
A: Higher surcharge (σ_s) reduces the required footing width as it contributes to bearing capacity.