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

Definition: This calculator computes the angle of rotation caused by twisting moments on an arch dam, considering material properties and geometry.

Purpose: It helps civil engineers assess the deformation behavior of arch dams under torsional loads.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( \Phi \) — Angle of rotation (radians)
• \( M \) — Cantilever twisting moment (N·m)
• \( K4 \) — Constant depending on b/a ratio and Poisson ratio (±5%)
• \( E \) — Elastic modulus of rock (GPa)
• \( t \) — Horizontal thickness of the arch (m)

Explanation: The twisting moment is multiplied by the geometry constant K4, then divided by the product of elastic modulus and squared thickness.

3. Importance of Rotation Calculation

Details: Accurate rotation estimation ensures structural integrity assessment, helps predict stress distribution, and verifies design safety margins.

4. Using the Calculator

Tips: Enter the twisting moment, K4 constant (default 10.02 ±5%), elastic modulus (default 10.2 GPa), and thickness (default 1.2 m). All values must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: What is the typical range for K4 constant?
A: K4 typically ranges between 9-12 for most arch dams, with ±5% variation depending on specific geometry.

Q2: How does rock elasticity affect rotation?
A: Higher elastic modulus (stiffer rock) results in smaller rotation angles for the same twisting moment.

Q3: Why is thickness squared in the formula?
A: The squared relationship accounts for both the cross-sectional area and moment of inertia effects.

Q4: How to measure twisting moment on a dam?
A: Twisting moments are typically calculated from water pressure distribution and dam geometry using structural analysis.

Q5: What's an acceptable rotation angle?
A: Acceptable values depend on design standards, but typically less than 0.01 radians for safety.

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