Normal Radial Pressure at Centerline Calculator

Normal Radial Pressure at centerline given Thrust at Abutments of Arch Dam Calculator

Radial Pressure Formula:

\[ P_v = \frac{P + F \cdot \cos(\theta)}{r - (r \cdot \cos(\theta))} \]

Thrust from Water (P):

N/m

Thrust of Abutments (F):

Angle (θ):

rad

Radius to Center Line (r):

Tolerance:

Radial Pressure (Pv): Pa/m²

Tolerance Range (±5%): Pa/m²

1. What is Normal Radial Pressure at Centerline?

Definition: This calculator computes the normal radial pressure at the centerline of an arch dam based on water thrust, abutment thrust, angle, and radius.

Purpose: It helps civil engineers determine the pressure distribution in arch dams for structural analysis and design.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ P_v = \frac{P + F \cdot \cos(\theta)}{r - (r \cdot \cos(\theta))} \]

Where:

\( P_v \) — Radial pressure (Pa/m²)
\( P \) — Thrust from water (N/m)
\( F \) — Thrust of abutments (N)
\( \theta \) — Angle (radians)
\( r \) — Radius to center line (m)

3. Importance of Radial Pressure Calculation

Details: Accurate pressure calculation ensures dam stability, proper load distribution, and structural integrity under hydrostatic forces.

4. Using the Calculator

Tips: Enter all required values with proper units. The tolerance field (default ±5%) allows for acceptable pressure range calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is typical abutment thrust for arch dams?
A: Abutment thrust varies widely but typically ranges from 10,000 to 100,000 N depending on dam size and water pressure.

Q2: How do I convert degrees to radians?
A: Multiply degrees by π/180 (approximately 0.0174533). Many calculators have a degree-to-radian conversion function.

Q3: Why include a tolerance percentage?
A: Engineering designs often account for material variations and safety factors, making tolerance ranges important.

Q4: What's a typical radius for arch dams?
A: Radius depends on canyon geometry but often ranges from 50m to 300m for large dams.

Q5: How does water thrust vary with depth?
A: Water thrust increases linearly with depth, calculated as P = ½·ρ·g·h² where ρ is water density, g is gravity, and h is depth.