Shear Stress Component given Submerged Unit Weight Calculator

Shear Stress Formula:

\[ \tau = \gamma' \times z \times \cos(i) \times \sin(i) \]

Submerged Unit Weight (γ'):

kN/m³

Depth of Prism (z):

Angle of Inclination (i):

Safety Factor:

Shear Stress (τ): kN/m²

Shear Stress with Safety Factor (±5%): kN/m²

1. What is Shear Stress Component given Submerged Unit Weight?

Definition: This calculator determines the shear stress component acting on submerged slopes based on submerged unit weight, depth, and inclination angle.

Purpose: It helps geotechnical engineers analyze slope stability under submerged conditions.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \tau = \gamma' \times z \times \cos(i) \times \sin(i) \]

Where:

\( \tau \) — Shear stress component (kN/m²)
\( \gamma' \) — Submerged unit weight (kN/m³)
\( z \) — Depth of prism (m)
\( i \) — Angle of inclination to horizontal (degrees)

Explanation: The formula calculates the shear stress component parallel to the slope in submerged conditions.

3. Importance of Shear Stress Calculation

Details: Proper shear stress estimation is crucial for analyzing slope stability, designing retaining structures, and preventing landslides in submerged conditions.

4. Using the Calculator

Tips: Enter submerged unit weight, depth, inclination angle (0-90°), and safety factor (default 5%). All values must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: What is submerged unit weight?
A: It's the effective unit weight of soil when submerged in water, accounting for buoyancy.

Q2: Why include a safety factor?
A: The safety factor accounts for uncertainties in material properties and loading conditions.

Q3: What's a typical submerged unit weight?
A: For common soils, it ranges from 8-11 kN/m³, but varies with soil type and saturation.

Q4: How does angle affect shear stress?
A: Shear stress peaks at 45° and decreases to zero at 0° and 90°.

Q5: When would I adjust the safety factor?
A: Increase for critical structures or uncertain conditions; decrease for well-characterized materials.