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Moment at Crown of Arch Dam Calculator

Moment Formula:

\[ M_t = -r \times ((p \times r) - F) \times \left(1 - \left(\frac{\sin(A)}{A}\right)\right) \]

m
N/m²
N
°
%

1. What is Moment at Crown of Arch Dam?

Definition: This calculator determines the bending moment at the crown (center) of an arch dam based on structural parameters.

Purpose: It helps civil engineers analyze the structural behavior of arch dams under various loading conditions.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ M_t = -r \times ((p \times r) - F) \times \left(1 - \left(\frac{\sin(A)}{A}\right)\right) \]

Where:

  • \( M_t \) — Moment at crown (Joules)
  • \( r \) — Radius to center line (meters)
  • \( p \) — Normal radial pressure (N/m²)
  • \( F \) — Thrust of abutments (Newtons)
  • \( A \) — Angle between crown and abundant radii (degrees)

Explanation: The formula accounts for the arch geometry, water pressure, and abutment reactions to determine the bending moment.

3. Importance of Moment Calculation

Details: Accurate moment calculation ensures dam stability, proper material selection, and safety against structural failure.

4. Using the Calculator

Tips: Enter all required parameters. The tolerance field (default ±5%) helps account for measurement uncertainties.

5. Frequently Asked Questions (FAQ)

Q1: What is normal radial pressure?
A: It's the water pressure acting perpendicular to the dam surface at the center line.

Q2: How is thrust of abutments determined?
A: It's calculated from the horizontal component of the water pressure and arch geometry.

Q3: Why include a tolerance range?
A: To account for measurement errors, material variations, and construction tolerances.

Q4: What angle should be used?
A: The angle between the crown radius and the radius at the abutment, typically 30-45°.

Q5: What units should be used?
A: Consistent SI units - meters for length, Newtons for force, and degrees for angles.

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