Vertical Normal Stress at Upstream Face Calculator

Vertical Stress Formula:

\[ \sigma_z = \frac{F_v}{144 \times T} \times \left(1 - \frac{6 \times e_u}{T}\right) \]

Vertical Component of Force:

Thickness of Dam:

Eccentricity at Upstream:

Tolerance:

Vertical Stress at Point (Pa):

Acceptable Range (±5%):

1. What is Vertical Normal Stress at Upstream Face?

Definition: This calculator determines the vertical normal stress at the upstream face of a dam based on force components and geometric properties.

Purpose: It helps civil engineers assess stress distribution in dam structures for stability analysis.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \sigma_z = \frac{F_v}{144 \times T} \times \left(1 - \frac{6 \times e_u}{T}\right) \]

Where:

\( \sigma_z \) — Vertical stress at point (Pa)
\( F_v \) — Vertical component of force (N)
\( T \) — Thickness of dam (m)
\( e_u \) — Eccentricity at upstream (m)

Explanation: The formula accounts for both the vertical force component and the eccentricity effect on stress distribution.

3. Importance of Vertical Stress Calculation

Details: Proper stress analysis ensures dam structural integrity, prevents failure, and helps in design optimization.

4. Using the Calculator

Tips: Enter the vertical force component, dam thickness, eccentricity, and tolerance percentage (default ±5%). Thickness must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: What is eccentricity in this context?
A: Eccentricity is the distance from the point of force application to the center of the dam base.

Q2: Why is the 144 factor included?
A: The 144 factor is a conversion constant when working with mixed units (imperial and metric).

Q3: What does negative eccentricity mean?
A: Negative eccentricity indicates the force is applied towards the upstream face.

Q4: How is the tolerance percentage used?
A: The tolerance shows the acceptable range of stress values (±% of calculated value).

Q5: What are typical values for dam thickness?
A: Dam thickness varies widely but is typically several meters for small to medium dams.