Ultimate Bearing Capacity for Rectangular Footing given Shape Factor Calculator

Ultimate Bearing Capacity Formula:

\[ q_{fc} = (C \times N_c \times (1 + 0.3 \times \frac{B}{L})) + (\sigma_s \times N_q) + (0.5 \times \gamma \times B \times N_\gamma \times (1 - 0.2 \times \frac{B}{L})) \]

Cohesion in Soil (C):

kPa

Bearing Capacity Factor (Nc):

Width of Footing (B):

Length of Footing (L):

Effective Surcharge (σs):

kPa

Bearing Capacity Factor (Nq):

Unit Weight of Soil (γ):

N/m³

Bearing Capacity Factor (Nγ):

Ultimate Bearing Capacity (q_fc): kPa

1. What is Ultimate Bearing Capacity for Rectangular Footing?

Definition: The ultimate bearing capacity is the maximum pressure that a soil can withstand before shear failure occurs under a rectangular footing.

Purpose: This calculation is essential for foundation design to ensure structural stability and prevent soil failure.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ q_{fc} = (C \times N_c \times (1 + 0.3 \times \frac{B}{L})) + (\sigma_s \times N_q) + (0.5 \times \gamma \times B \times N_\gamma \times (1 - 0.2 \times \frac{B}{L})) \]

Where:

\( q_{fc} \) — Ultimate bearing capacity (kPa)
\( C \) — Cohesion in soil (kPa)
\( N_c \) — Bearing capacity factor for cohesion (dimensionless)
\( B \) — Width of footing (m)
\( L \) — Length of footing (m)
\( \sigma_s \) — Effective surcharge (kPa)
\( N_q \) — Bearing capacity factor for surcharge (dimensionless)
\( \gamma \) — Unit weight of soil (N/m³)
\( N_\gamma \) — Bearing capacity factor for unit weight (dimensionless)

Explanation: The formula accounts for three components of bearing capacity: cohesion term, surcharge term, and soil weight term, with shape factors for rectangular footings.

3. Importance of Bearing Capacity Calculation

Details: Proper bearing capacity calculation ensures safe foundation design, prevents excessive settlement, and maintains structural integrity.

4. Using the Calculator

Tips: Enter all required parameters. The bearing capacity factors (Nc, Nq, Nγ) include ±5% uncertainty. All values must be ≥ 0 with denominators > 0.

5. Frequently Asked Questions (FAQ)

Q1: Why are there shape factors in the formula?
A: Shape factors account for the rectangular footing's geometry, as bearing capacity differs from strip footings.

Q2: What are typical values for Nc, Nq, Nγ?
A: Common defaults are Nc=9, Nq=2.01, Nγ=1.6, but these vary with soil friction angle.

Q3: How does footing shape affect bearing capacity?
A: Rectangular footings generally have higher capacity than strip footings due to 3D confinement effects.

Q4: What is effective surcharge?
A: It's the vertical stress from soil or other loads above the footing base level.

Q5: How accurate is this calculation?
A: The calculation provides theoretical capacity; actual values may vary ±5% due to soil variability.