Eccentricity for Vertical Normal Stress at Downstream Face Calculator

Eccentricity Formula:

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

Eccentricity at Downstream:

1. What is Eccentricity at Downstream Face?

Definition: Eccentricity at downstream face is the distance from the point of application of the resultant force to the center of the dam base.

Purpose: It helps determine the distribution of vertical normal stress in dams and other hydraulic structures.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

\( e_d \) — Eccentricity at downstream face
\( \sigma_z \) — Vertical stress at a point (±5%)
\( F_v \) — Vertical component of force (±5%)
\( T \) — Thickness of dam (±5%)

Explanation: The formula calculates the eccentricity based on the relationship between vertical stress, vertical force, and dam thickness.

3. Importance of Eccentricity Calculation

Details: Proper eccentricity calculation ensures structural stability and helps prevent excessive stress concentrations in dams.

4. Using the Calculator

Tips: Enter the vertical stress, vertical force, and dam thickness. All values must be > 0. Results are accurate within ±5%.

5. Frequently Asked Questions (FAQ)

Q1: What does eccentricity indicate in dam design?
A: Eccentricity shows how far the resultant force is offset from the center, affecting stress distribution.

Q2: Why is the ±5% tolerance important?
A: It accounts for variations in material properties and measurement uncertainties.

Q3: What units should I use for inputs?
A: Use consistent units (typically psi for stress, kips for force, and feet for thickness).

Q4: How does eccentricity affect dam stability?
A: Higher eccentricity can lead to uneven stress distribution and potential stability issues.

Q5: When would this calculation be needed?
A: During dam design, safety assessments, and structural evaluations.