Total Vertical Force for Vertical Normal Stress at Upstream Face Calculator

Vertical Force Formula:

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

Vertical Component of Force: N

1. What is Total Vertical Force for Vertical Normal Stress?

Definition: This calculator determines the vertical component of force acting on a dam based on vertical stress, dam thickness, and upstream eccentricity.

Purpose: It helps civil engineers analyze the force distribution in dam structures for stability assessment.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

\( F_v \) — Vertical component of force (N)
\( \sigma_z \) — Vertical stress at a point (Pa)
\( T \) — Thickness of dam (m)
\( e_u \) — Eccentricity at upstream (±5%)

Explanation: The formula accounts for the stress distribution and eccentric loading conditions at the upstream face of the dam.

3. Importance of Vertical Force Calculation

Details: Accurate force calculation is crucial for dam stability analysis, preventing overturning, and ensuring structural integrity.

4. Using the Calculator

Tips: Enter the vertical stress in Pascals, dam thickness in meters, and eccentricity (with ±5% tolerance). Thickness cannot be zero.

5. Frequently Asked Questions (FAQ)

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

Q2: Why is the ±5% important for eccentricity?
A: It accounts for uncertainties in load distribution and construction tolerances.

Q3: What units should I use for input?
A: Use Pascals for stress, meters for thickness, and the same units for eccentricity.

Q4: How does dam thickness affect the result?
A: Thicker dams generally distribute forces more evenly, reducing stress concentrations.

Q5: What if I get a negative result?
A: Negative values indicate upward (tensile) forces, which may require design adjustments.