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Normal Radial Pressure at Centerline given Moment at Crown of Arch Dam Calculator

Radial Pressure Formula:

\[ P_v = \frac{F_C \times r \times \left(1 - \frac{\sin(\theta)}{\theta}\right) - M_t}{r^2 \times \left(1 - \frac{\sin(\theta)}{\theta}\right)} \]

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1. What is Normal Radial Pressure at Centerline?

Definition: This calculator determines the normal radial pressure at the centerline of an arch dam based on thrust, radius, angle, and moment at the crown.

Purpose: It helps engineers assess the pressure distribution in arch dams, which is crucial for structural integrity analysis.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ P_v = \frac{F_C \times r \times \left(1 - \frac{\sin(\theta)}{\theta}\right) - M_t}{r^2 \times \left(1 - \frac{\sin(\theta)}{\theta}\right)} \]

Where:

  • \( P_v \) — Radial pressure (Pa/m²)
  • \( F_C \) — Thrust at crown (N)
  • \( r \) — Radius to center line (m)
  • \( \theta \) — Angle (radians)
  • \( M_t \) — Moment at crown (J)

3. Importance of Radial Pressure Calculation

Details: Proper pressure estimation ensures dam stability, prevents structural failure, and helps in optimizing design parameters.

4. Using the Calculator

Tips: Enter all required parameters including the tolerance percentage (default ±5%). The calculator provides both the exact value and acceptable range.

5. Frequently Asked Questions (FAQ)

Q1: What is typical thrust at crown for arch dams?
A: Thrust values vary significantly based on dam size and water pressure, typically ranging from thousands to millions of newtons.

Q2: How to determine the angle θ?
A: θ is the central angle subtended by the arch, calculated from the dam geometry and centerline radius.

Q3: Why include tolerance?
A: Tolerance accounts for material variations, construction tolerances, and safety factors in engineering design.

Q4: What if denominator becomes zero?
A: The formula is undefined when θ = 0 or when the term (1 - sinθ/θ) = 0. These are edge cases that shouldn't occur in practical dam designs.

Q5: How does moment affect the pressure?
A: Higher moments at the crown reduce the radial pressure, as seen in the numerator of the formula.

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