Rotation due to Moment on Arch Dam Calculator

Angle of Rotation Formula:

\[ \Phi = \frac{M_t \times K_1}{E \times t \times t} \]

Moment acting on Arch Dam:

Constant K1:

Elastic Modulus of Rock:

Horizontal Thickness:

Angle of Rotation (rad):

1. What is Rotation due to Moment on Arch Dam?

Definition: This calculator determines the angle of rotation at the base of an arch dam caused by applied moments.

Purpose: It helps civil engineers assess the deformation behavior of arch dams under loading conditions.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \Phi = \frac{M_t \times K_1}{E \times t \times t} \]

Where:

\( \Phi \) — Angle of rotation (radians)
\( M_t \) — Moment acting on arch dam (J)
\( K_1 \) — Constant depending on b/a ratio and Poisson ratio
\( E \) — Elastic modulus of rock (Pa)
\( t \) — Horizontal thickness of arch (m)

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

3. Importance of Rotation Calculation

Details: Accurate rotation calculation ensures structural integrity assessment and helps prevent excessive deformation that could compromise dam safety.

4. Using the Calculator

Tips: Enter the moment value, constant K1 (with ±5% uncertainty), elastic modulus, and horizontal thickness (with ±5% uncertainty). All values must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: Why is there a ±5% uncertainty on some values?
A: Material properties and measurements often have inherent variability that should be accounted for in calculations.

Q2: How is constant K1 determined?
A: K1 depends on the arch geometry (b/a ratio) and the Poisson ratio of the material, typically obtained from engineering tables.

Q3: What's a typical elastic modulus for dam rock?
A: It varies widely (10-80 GPa) depending on rock type, with granite typically around 50 GPa.

Q4: How does thickness affect rotation?
A: Rotation decreases with the square of thickness - doubling thickness reduces rotation by a factor of four.

Q5: What's an acceptable rotation angle?
A: This depends on design standards, but typically very small (fractions of a degree) to maintain structural integrity.