Sum of Tangential Component given Factor of Safety Calculator

Sum of Tangential Component Formula:

\[ F_t = \frac{(c_u \times L) + (\Sigma N \times \tan(\phi))}{FOS} \]

Unit Cohesion (c_u):

Length of Slip Arc (L):

Sum of Normal Components (ΣN):

Angle of Internal Friction (φ):

Factor of Safety (FOS):

Sum of Tangential Component (F_t):

1. What is Sum of Tangential Component in Soil Mechanics?

Definition: The sum of all tangential components represents the total shear force acting along a potential slip surface in soil mechanics analysis.

Purpose: It's crucial for slope stability analysis and determining the factor of safety against sliding.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ F_t = \frac{(c_u \times L) + (\Sigma N \times \tan(\phi))}{FOS} \]

Where:

\( F_t \) — Sum of tangential components
\( c_u \) — Unit cohesion of soil
\( L \) — Length of slip arc
\( \Sigma N \) — Sum of all normal components
\( \phi \) — Angle of internal friction
\( FOS \) — Factor of safety

Explanation: The formula combines cohesive and frictional components of shear strength, divided by the factor of safety.

3. Importance of Tangential Component Calculation

Details: Accurate calculation helps engineers assess slope stability and design appropriate retaining structures.

4. Using the Calculator

Tips: Enter all required parameters with appropriate units. The ±5% indicates typical measurement tolerances.

5. Frequently Asked Questions (FAQ)

Q1: What is unit cohesion?
A: Unit cohesion is the shear strength of soil due to cohesive forces between particles, independent of normal stress.

Q2: How is slip arc length determined?
A: It's the length of the critical slip surface identified through stability analysis.

Q3: What's a typical factor of safety?
A: For slopes, FOS typically ranges from 1.3 to 1.5 depending on project requirements.

Q4: Why include angle of internal friction?
A: It represents the frictional component of soil shear strength.

Q5: How accurate are these calculations?
A: Results are estimates; field verification is recommended for critical applications.