Eccentricity given Vertical Normal Stress at Upstream Face Calculator

Eccentricity Formula:

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

Vertical Stress at a Point:

psi

Vertical Component of Force:

lb/ft

Thickness of Dam:

Tolerance:

Eccentricity at Upstream (ft):

1. What is Eccentricity at Upstream Face?

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

Purpose: It helps determine the distribution of vertical normal stress on the upstream face of a dam.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

\( e_u \) — Eccentricity at upstream face (ft)
\( \sigma_z \) — Vertical stress at a point (psi)
\( F_v \) — Vertical component of force (lb/ft)
\( T \) — Thickness of dam (ft)

Explanation: The formula calculates how far the resultant force is offset from the center of the dam base based on stress distribution.

3. Importance of Eccentricity Calculation

Details: Proper eccentricity calculation ensures structural stability of the dam and helps predict stress distribution patterns.

4. Using the Calculator

Tips: Enter the vertical stress (psi), vertical force component (lb/ft), dam thickness (ft), and tolerance percentage (default ±5%). All values must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: What does negative eccentricity indicate?
A: Negative eccentricity means the resultant force is located upstream from the center of the base.

Q2: Why include a tolerance percentage?
A: The tolerance accounts for measurement uncertainties and material variations in real-world applications.

Q3: What's a typical acceptable eccentricity range?
A: Most designs aim to keep eccentricity within ±T/6 of the base center (middle third rule).

Q4: How does eccentricity affect dam stability?
A: Excessive eccentricity can cause uneven stress distribution leading to potential cracking or overturning.

Q5: What units should be used for inputs?
A: Use consistent units: psi for stress, lb/ft for force, and feet for thickness.