Deflection due to Moments on Arch Dam Calculator

Deflection Formula:

\[ \delta = \frac{M_t \times K5}{E \times t} \]

Moment acting on Arch Dam:

Constant K5:

Elastic Modulus of Rock:

Horizontal Thickness of an Arch:

Deflection due to Moments on Arch Dam (m):

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

Definition: The deflection due to moments on an arch dam is the degree to which the dam structure is displaced under the moment load.

Purpose: This calculation helps engineers assess the structural behavior and safety of arch dams under various loading conditions.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \delta = \frac{M_t \times K5}{E \times t} \]

Where:

\( \delta \) — Deflection due to Moments (meters)
\( M_t \) — Moment acting on Arch Dam (Joules)
\( K5 \) — Constant depending on b/a ratio and Poisson ratio
\( E \) — Elastic Modulus of Rock (Pascals)
\( t \) — Horizontal Thickness of an Arch (meters)

Explanation: The moment is multiplied by the constant K5 and then divided by the product of the elastic modulus and thickness.

3. Importance of Deflection Calculation

Details: Proper deflection estimation ensures structural integrity, safety, and long-term performance of arch dams.

4. Using the Calculator

Tips: Enter the moment, constant K5, elastic modulus, and thickness. All values must be > 0. Note that all inputs have a ±5% tolerance.

5. Frequently Asked Questions (FAQ)

Q1: What is the typical range for constant K5?
A: K5 typically ranges between 0.01 to 10 depending on the arch dam geometry and material properties.

Q2: Why is there a ±5% tolerance on inputs?
A: The tolerance accounts for measurement uncertainties and material property variations.

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

Q4: What affects the horizontal thickness of an arch?
A: The thickness depends on the dam design, water pressure, and geological conditions.

Q5: Is this deflection calculation applicable to all dam types?
A: No, this formula is specific to arch dams due to their unique curvature and load distribution.