Radial Distance from Centre of Rotation given Moment of Resistance Calculator

Radial Distance Formula:

\[ d_{radial} = \frac{M_R}{c_u \times L'} \]

Resisting Moment (M_R):

kN·m

Unit Cohesion (c_u):

kPa

Length of Slip Arc (L'):

Tolerance:

Radial Distance (d_radial):

1. What is Radial Distance from Centre of Rotation?

Definition: This calculator determines the radial distance from the center of rotation based on the resisting moment, unit cohesion, and length of the slip arc.

Purpose: It helps geotechnical engineers analyze slope stability and rotational failures in soil mechanics.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ d_{radial} = \frac{M_R}{c_u \times L'} \]

Where:

\( d_{radial} \) — Radial distance from center of rotation (meters)
\( M_R \) — Resisting moment (kN·m)
\( c_u \) — Unit cohesion (kPa)
\( L' \) — Length of slip arc (meters)

Explanation: The resisting moment is divided by the product of unit cohesion and slip arc length to determine the radial distance.

3. Importance of Radial Distance Calculation

Details: Accurate calculation of radial distance is crucial for analyzing rotational slope failures, designing retaining structures, and assessing soil stability.

4. Using the Calculator

Tips: Enter the resisting moment in kN·m, unit cohesion in kPa, length of slip arc in meters, and tolerance percentage. All values must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: What is resisting moment?
A: Resisting moment is the moment that counteracts rotational forces, preventing slope failure.

Q2: How is unit cohesion determined?
A: Unit cohesion is typically measured through laboratory tests like unconfined compression tests or vane shear tests.

Q3: What does the length of slip arc represent?
A: It's the curved length along which potential failure might occur in rotational slope failures.

Q4: Why include a tolerance percentage?
A: The tolerance accounts for measurement uncertainties and material variability in geotechnical calculations.

Q5: Can this be used for non-circular slip surfaces?
A: This formula specifically applies to circular slip surfaces. Other methods are needed for non-circular failures.