Deflection due to Shear on Arch Dam Calculator

Deflection Formula:

\[ \delta = \frac{F_s \times K_3}{E} \]

Deflection (δ): m

1. What is Deflection due to Shear on Arch Dam?

Definition: This calculator estimates the deflection caused by shear forces on an arch dam structure.

Purpose: It helps civil engineers and structural designers evaluate the deformation characteristics of arch dams under shear loading.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \delta = \frac{F_s \times K_3}{E} \]

Where:

\( \delta \) — Deflection due to shear (meters)
\( F_s \) — Shear force (Newtons)
\( K_3 \) — Constant depending on b/a ratio and Poisson ratio (±5%)
\( E \) — Elastic modulus of rock (Pascals)

Explanation: The shear force multiplied by the arch dam constant K3, divided by the elastic modulus of the rock gives the deflection.

3. Importance of Deflection Calculation

Details: Accurate deflection calculation is crucial for ensuring structural integrity, safety, and proper functioning of arch dams under load.

4. Using the Calculator

Tips: Enter the shear force in Newtons, constant K3 (with ±5% accuracy), and elastic modulus in Pascals. All values must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: What is constant K3?
A: K3 is a dimensionless constant that depends on the arch dam's geometry (b/a ratio) and the Poisson ratio of the material.

Q2: Why is there a ±5% on K3?
A: The ±5% accounts for typical variations in material properties and geometric approximations in real-world applications.

Q3: How do I determine the elastic modulus of rock?
A: The elastic modulus is typically determined through laboratory testing of rock core samples from the dam site.

Q4: What's a typical range for deflection in arch dams?
A: Deflection varies greatly but is typically in millimeters to centimeters range for large dams.

Q5: Does this include all deflection components?
A: No, this calculates only the shear component. Total deflection would include bending and other effects.