Arc Angle given Length of Slip Arc Calculator

Arc Angle Formula:

\[ \delta = \frac{360 \times L'}{2 \times \pi \times d_{radial}} \times \frac{\pi}{180} \]

Arc Angle (δ):

1. What is Arc Angle given Length of Slip Arc?

Definition: This calculator determines the angle (in radians) subtended by a slip arc given its length and radial distance.

Purpose: It's used in geotechnical engineering and soil mechanics to analyze slope stability and failure surfaces.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \delta = \frac{360 \times L'}{2 \times \pi \times d_{radial}} \times \frac{\pi}{180} \]

Where:

\( \delta \) — Arc angle (radians)
\( L' \) — Length of slip arc (meters)
\( d_{radial} \) — Radial distance (meters)
\( \pi \) — Pi constant (≈3.14159)

Explanation: The formula converts the arc length to an angle by considering the full circumference of the circle.

3. Importance of Arc Angle Calculation

Details: Accurate arc angle calculation is crucial for determining the critical failure surface in slope stability analysis.

4. Using the Calculator

Tips: Enter the length of slip arc, radial distance, and tolerance percentage. The calculator provides the angle in radians and the tolerance range.

5. Frequently Asked Questions (FAQ)

Q1: What is a slip arc in geotechnical engineering?
A: A slip arc represents the potential failure surface in slope stability analysis, typically circular in shape.

Q2: Why is the result in radians?
A: Radians are the standard angular measurement in mathematical calculations and many engineering applications.

Q3: What is the purpose of the tolerance field?
A: The tolerance (±%) provides a range to account for measurement uncertainties or safety factors.

Q4: Can I use this for non-circular slip surfaces?
A: No, this calculator assumes a circular slip surface. Other methods are needed for non-circular surfaces.

Q5: How precise should my measurements be?
A: For engineering applications, measure to at least 4 significant figures for reliable results.