Shear Force given Deflection due to Shear on Arch Dam Calculator

Shear Force Formula:

\[ Fs = \frac{\delta \times E}{K3} \]

Shear Force (N):

1. What is Shear Force given Deflection Calculator?

Definition: This calculator determines the shear force acting on an arch dam based on the deflection due to moments, elastic modulus of rock, and a constant factor.

Purpose: It helps civil engineers analyze the structural behavior of arch dams under loading conditions.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ Fs = \frac{\delta \times E}{K3} \]

Where:

\( Fs \) — Shear Force (Newtons)
\( \delta \) — Deflection due to Moments (meters)
\( E \) — Elastic Modulus of Rock (Pascals)
\( K3 \) — Constant depending on b/a ratio and Poisson ratio (±5%)

Explanation: The deflection multiplied by elastic modulus gives the resisting force, which is then divided by the structural constant to determine shear force.

3. Importance of Shear Force Calculation

Details: Accurate shear force determination is critical for dam safety, preventing structural failure, and ensuring proper design specifications.

4. Using the Calculator

Tips: Enter the deflection in meters, elastic modulus in Pascals, and constant K3 (with ±5% tolerance). All values must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: What is typical elastic modulus for dam rock?
A: It varies widely (10-80 GPa) depending on rock type. Granite averages about 50 GPa.

Q2: How is constant K3 determined?
A: K3 depends on the dam's geometry (b/a ratio) and material properties (Poisson's ratio), typically from engineering tables.

Q3: Why is there a ±5% tolerance on K3?
A: This accounts for variations in material properties and measurement uncertainties.

Q4: What causes deflection in arch dams?
A: Water pressure, thermal changes, and seismic activity primarily cause deflections.

Q5: How does shear force affect dam safety?
A: Excessive shear can cause cracking or sliding along construction joints or weak planes in the foundation.