Width of Footing for Local Shear Failure given Bearing Capacity Factor Calculator

Footing Width Formula:

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

Ultimate Bearing Capacity (q_fc):

kPa

Cohesion (C):

kPa

Bearing Capacity Factor (N_c):

Unit Weight of Soil (γ):

kN/m³

Depth of Footing (D_footing):

Bearing Capacity Factor (N_q):

Bearing Capacity Factor (N_γ):

Footing Width (B): m

1. What is Footing Width Calculation for Local Shear Failure?

Definition: This calculator determines the required width of a footing to prevent local shear failure in soil, based on bearing capacity factors and soil properties.

Purpose: It helps geotechnical engineers and construction professionals design stable foundations that won't experience local shear failure.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

\( B \) — Width of footing (meters)
\( q_{fc} \) — Ultimate bearing capacity in soil (kPa)
\( C \) — Cohesion in soil (kPa)
\( N_c, N_q, N_\gamma \) — Bearing capacity factors
\( \gamma \) — Unit weight of soil (kN/m³)
\( D_{footing} \) — Depth of footing (meters)

Explanation: The formula accounts for soil cohesion, surcharge from soil above footing depth, and soil unit weight to determine the minimum footing width needed.

3. Importance of Footing Width Calculation

Details: Proper footing width calculation prevents local shear failure, ensures structural stability, and optimizes material usage in foundation construction.

4. Using the Calculator

Tips: Enter all required parameters. Note that ±5% tolerance is assumed for most parameters. All values must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: What is local shear failure?
A: Local shear failure occurs when only the soil immediately beneath the footing fails, while soil beyond this zone remains intact.

Q2: How do I determine bearing capacity factors?
A: These depend on soil friction angle. Use standard geotechnical tables or our Bearing Capacity Factor Calculator.

Q3: Why is there a 2/3 factor on cohesion?
A: This accounts for the reduced mobilization of shear strength in local shear failure compared to general shear failure.

Q4: What's a typical range for cohesion values?
A: Clay soils: 10-200 kPa, silt soils: 5-50 kPa, sandy soils: 0-10 kPa (with ±5% variation).

Q5: How does footing depth affect the calculation?
A: Deeper footings benefit from more surcharge (N_q term) but may require wider bases to distribute loads.