Width of Footing given Shape Factor Calculator by Tons of Concrete

Width of Footing given Shape Factor Calculator

Width of Footing Formula:

\[ B = \frac{q_f - (s_c \times C \times N_c + \sigma' \times N_q)}{0.5 \times N_\gamma \times \gamma \times s_\gamma} \]

Ultimate Bearing Capacity:

Shape Factor (Cohesion):

Cohesion:

Bearing Capacity Factor (Cohesion):

Effective Surcharge:

Bearing Capacity Factor (Surcharge):

Bearing Capacity Factor (Unit Weight):

Unit Weight of Soil:

N/m³

Shape Factor (Unit Weight):

Width of Footing (m):

1. What is Width of Footing given Shape Factor?

Definition: This calculator determines the required width of a footing based on soil bearing capacity factors and shape factors.

Purpose: It helps civil engineers and construction professionals design proper foundation dimensions for structural stability.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ B = \frac{q_f - (s_c \times C \times N_c + \sigma' \times N_q)}{0.5 \times N_\gamma \times \gamma \times s_\gamma} \]

Where:

\( B \) — Width of Footing (m)
\( q_f \) — Ultimate Bearing Capacity (Pa)
\( s_c \) — Shape Factor dependent on Cohesion (±5%)
\( C \) — Cohesion (Pa)
\( N_c \) — Bearing Capacity Factor dependent on Cohesion (±5%)
\( \sigma' \) — Effective Surcharge (Pa)
\( N_q \) — Bearing Capacity Factor dependent on Surcharge (±5%)
\( N_\gamma \) — Bearing Capacity Factor dependent on Unit Weight (±5%)
\( \gamma \) — Unit Weight of Soil (N/m³)
\( s_\gamma \) — Shape Factor dependent on Unit Weight (±5%)

3. Importance of Footing Width Calculation

Details: Proper footing width ensures structural stability, prevents settlement, and distributes loads appropriately to the underlying soil.

4. Using the Calculator

Tips: Enter all required parameters. Default values are provided for typical conditions. All values must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: What are typical values for shape factors?
A: Shape factors typically range from 1.0 to 1.3 for rectangular footings and 1.3 to 1.7 for square footings.

Q2: How do I determine soil cohesion?
A: Cohesion is determined through geotechnical testing (e.g., triaxial or unconfined compression tests).

Q3: What affects the bearing capacity factors?
A: Bearing capacity factors depend on soil friction angle and are typically obtained from geotechnical tables.

Q4: Why is there a ±5% variation on some factors?
A: These factors have inherent variability due to soil heterogeneity and testing methods.

Q5: How does footing shape affect the calculation?
A: Different shapes (strip, rectangular, square, circular) require different shape factors in the calculation.