Bearing Capacity Factor Dependent on Unit Weight for Rectangular Footing Calculator

Formula:

\[ N_γ = \frac{q_{fc} - \left( (C \times N_c) \times (1 + 0.3 \times \frac{B}{L}) + (σ_s \times N_q) \right)}{0.4 \times B \times γ} \]

Ultimate Bearing Capacity (q_fc):

kPa

Cohesion (C):

kPa

Bearing Capacity Factor (N_c):

Width of Footing (B):

Length of Footing (L):

Effective Surcharge (σ_s):

kPa

Bearing Capacity Factor (N_q):

Unit Weight of Soil (γ):

kN/m³

Bearing Capacity Factor (N_γ):

1. What is Bearing Capacity Factor Dependent on Unit Weight?

Definition: This factor (N_γ) is a dimensionless parameter used in geotechnical engineering to calculate the ultimate bearing capacity of rectangular footings considering the unit weight of soil.

Purpose: It helps engineers determine the safe load-bearing capacity of soil for foundation design.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ N_γ = \frac{q_{fc} - \left( (C \times N_c) \times (1 + 0.3 \times \frac{B}{L}) + (σ_s \times N_q) \right)}{0.4 \times B \times γ} \]

Where:

\( N_γ \) — Bearing capacity factor dependent on unit weight
\( q_{fc} \) — Ultimate bearing capacity in soil (kPa)
\( C \) — Cohesion in soil (kPa)
\( N_c \) — Bearing capacity factor dependent on cohesion (±5%)
\( B \) — Width of footing (m)
\( L \) — Length of footing (m)
\( σ_s \) — Effective surcharge (kPa)
\( N_q \) — Bearing capacity factor dependent on surcharge (±5%)
\( γ \) — Unit weight of soil (kN/m³)

3. Importance of Bearing Capacity Factor

Details: Accurate calculation of N_γ is crucial for designing safe and economical foundations that won't fail under load.

4. Using the Calculator

Tips: Enter all required parameters. The bearing capacity factors (N_c and N_q) typically have ±5% uncertainty. All values must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: Why is the ±5% included for N_c and N_q?
A: These factors are empirically derived and typically have about 5% uncertainty in their values.

Q2: What's a typical range for N_γ?
A: Values typically range from 0 to 50 depending on soil type and conditions.

Q3: How does footing shape affect the calculation?
A: The B/L ratio accounts for rectangular footing effects (1+0.3×(B/L) term.

Q4: What units should be used?
A: Consistent SI units are required (kPa for stresses, m for dimensions, kN/m³ for unit weight).

Q5: How accurate is this calculation?
A: It provides a theoretical estimate; actual field conditions may require adjustments.