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Thrust at Crown of Arch Dam given Moment at Abutments Calculator

Thrust of Abutments Formula:

\[ F = \frac{M_t}{r \times \left(\frac{\sin(\theta)}{\theta - \cos(\theta)}\right)} + p \times r \]

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1. What is Thrust at Crown of Arch Dam?

Definition: The thrust at the crown of an arch dam is the horizontal force exerted by the arch structure against its supporting abutments, calculated considering the moment at abutments and normal radial pressure.

Purpose: This calculation is crucial for designing arch dams to ensure structural stability and proper load distribution.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ F = \frac{M_t}{r \times \left(\frac{\sin(\theta)}{\theta - \cos(\theta)}\right)} + p \times r \]

Where:

  • \( F \) — Thrust of Abutments (N)
  • \( M_t \) — Moment acting on Arch Dam (J)
  • \( r \) — Radius to Center Line of Arch (m)
  • \( \theta \) — Theta angle (radians)
  • \( p \) — Normal Radial Pressure (N/m²)

3. Importance of Thrust Calculation

Details: Proper thrust estimation ensures the dam's structural integrity, prevents abutment failure, and helps in designing appropriate reinforcement.

4. Using the Calculator

Tips: Enter the moment, radius, theta angle (in radians), normal radial pressure, and optional tolerance percentage (default ±5%).

5. Frequently Asked Questions (FAQ)

Q1: What is the typical tolerance percentage?
A: Engineering calculations often use ±5% tolerance, but this can vary based on project requirements.

Q2: How do I convert degrees to radians?
A: Multiply degrees by π/180 (approximately 0.0174533) to get radians.

Q3: What affects normal radial pressure?
A: Water depth, dam curvature, and material properties all influence normal radial pressure.

Q4: Why is theta angle important?
A: Theta represents the angular span of the arch and significantly affects the thrust distribution.

Q5: How does radius impact thrust calculations?
A: Larger radii generally result in lower thrust values for the same moment and pressure.

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