Vertical Stress on Surface of Prism given Normal Stress Component Calculator

Vertical Stress Formula:

\[ \sigma_{z(kp)} = \frac{\sigma_n}{\cos\left(\frac{i \times \pi}{180}\right)} \]

Vertical Stress (σ_z(kp)):

1. What is Vertical Stress on Surface of Prism?

Definition: This calculator determines the vertical stress acting on the surface of a prism based on the normal stress component and the angle of inclination.

Purpose: It helps geotechnical engineers and construction professionals analyze stress distribution in soil structures.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \sigma_{z(kp)} = \frac{\sigma_n}{\cos\left(\frac{i \times \pi}{180}\right)} \]

Where:

\( \sigma_{z(kp)} \) — Vertical stress at a point (kPa)
\( \sigma_n \) — Normal stress component (kPa)
\( i \) — Angle of inclination to horizontal (degrees)

Explanation: The normal stress is divided by the cosine of the inclination angle (converted to radians) to obtain the vertical stress component.

3. Importance of Vertical Stress Calculation

Details: Accurate vertical stress calculation is crucial for stability analysis of slopes, retaining walls, and other geotechnical structures.

4. Using the Calculator

Tips: Enter the normal stress in kPa, angle of inclination in degrees (0-90), and tolerance percentage (default ±5%). All values must be valid.

5. Frequently Asked Questions (FAQ)

Q1: What is the physical meaning of vertical stress?
A: Vertical stress represents the force per unit area acting perpendicular to the horizontal plane in a soil mass.

Q2: Why do we need to consider angle of inclination?
A: The angle affects how much of the normal stress translates into vertical stress due to the orientation of the surface.

Q3: What does the tolerance percentage represent?
A: It shows the acceptable range (±%) around the calculated value to account for measurement or calculation uncertainties.

Q4: What happens at 0° inclination?
A: At 0°, the vertical stress equals the normal stress since cos(0°) = 1.

Q5: What's the maximum valid angle?
A: The calculator accepts angles up to 90°, but values approaching 90° result in extremely high vertical stresses.