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

Radial Pressure Formula:

\[ P_v = \frac{F_C}{r \times \left(1 - \frac{2 \theta \sin\left(\theta \times \frac{(t/r)^2}{12}\right)}{D}\right)} \]

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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 at the crown and other geometric parameters.

Purpose: It helps civil engineers analyze stress distribution in arch dams to ensure structural integrity.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ P_v = \frac{F_C}{r \times \left(1 - \frac{2 \theta \sin\left(\theta \times \frac{(t/r)^2}{12}\right)}{D}\right)} \]

Where:

  • \( P_v \) — Radial pressure (Pa/m²)
  • \( F_C \) — Thrust at crown (N)
  • \( r \) — Radius to center line (m)
  • \( \theta \) — Angle (radians)
  • \( t \) — Horizontal thickness (m)
  • \( D \) — Diameter (m)

3. Importance of Radial Pressure Calculation

Details: Proper calculation ensures the dam can withstand water pressure and other forces without excessive deformation or failure.

4. Using the Calculator

Tips: Enter all required parameters. The tolerance field (default ±5%) helps determine acceptable pressure ranges for safety factors.

5. Frequently Asked Questions (FAQ)

Q1: What is typical thrust at crown for arch dams?
A: Thrust varies greatly by design but typically ranges from 10,000 to 500,000 N depending on dam size.

Q2: How is the angle θ determined?
A: θ is the central angle of the arch segment, calculated from the dam's geometry and design specifications.

Q3: Why include a tolerance percentage?
A: Engineering designs often allow for small variations; the tolerance helps identify acceptable operational ranges.

Q4: What if my result is negative?
A: Negative values may indicate calculation errors or physically impossible input combinations.

Q5: How accurate is this calculation?
A: This provides a theoretical value; actual field measurements may vary due to material properties and environmental factors.

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