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

Definition: This calculator determines the angle of rotation caused by shear forces acting on an arch dam, considering material properties and geometry.

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

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( \Phi \) — Angle of rotation (radians)
• \( F_s \) — Shear force (N)
• \( K5 \) — Constant depending on b/a ratio and Poisson ratio
• \( E \) — Elastic modulus of rock (Pa)
• \( t \) — Horizontal thickness of arch (m)

Explanation: The rotation angle is directly proportional to the shear force and constant K5, and inversely proportional to the rock's stiffness and arch thickness.

3. Importance of Rotation Calculation

Details: Accurate rotation estimation ensures structural integrity, predicts stress distribution, and helps in dam design optimization.

4. Using the Calculator

Tips: Enter shear force in Newtons, constant K5, elastic modulus in Pascals, arch thickness in meters, and optional tolerance percentage (default ±5%).

5. Frequently Asked Questions (FAQ)

Q1: What is constant K5?
A: K5 is a dimensionless constant that depends on the arch geometry (b/a ratio) and the Poisson's ratio of the material.

Q2: How is the tolerance applied?
A: The tolerance creates a range around the calculated value (±5% by default) to account for material variations and uncertainties.

Q3: What are typical values for elastic modulus of rock?
A: Common values range from 10 GPa (soft rock) to 100 GPa (hard rock), depending on rock type.

Q4: Why measure rotation in radians?
A: Radians are the natural unit for angular measurement in engineering calculations involving trigonometric functions.

Q5: How does arch thickness affect rotation?
A: Thicker arches resist rotation better, resulting in smaller angular displacements under the same shear force.

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