Angle between Crown and Abutments given Thrust at Abutments of Arch Dam Calculator

Angle Calculation Formula:

\[ \theta = \cos^{-1}\left(\frac{P - P_v \times r}{-P_v \times r + F}\right) \]

Thrust from Water:

N/m

Radial Pressure:

Pa/m²

Radius to Center Line:

Thrust of Abutments:

Angle (radians):

Angle (degrees):

1. What is Angle between Crown and Abutments Calculator?

Definition: This calculator determines the angle between the crown and abutments of an arch dam based on thrust forces and radial pressure.

Purpose: It helps civil engineers design arch dams by calculating the critical angle that affects structural stability.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \theta = \cos^{-1}\left(\frac{P - P_v \times r}{-P_v \times r + F}\right) \]

Where:

\( \theta \) — Angle between crown and abutments (radians or degrees)
\( P \) — Thrust from water retained behind the wall (N/m)
\( P_v \) — Radial pressure (Pa/m²)
\( r \) — Radius to center line of arch (m)
\( F \) — Thrust of abutments (N)

Explanation: The formula calculates the angle using inverse cosine of the ratio between the net thrust and the resisting forces.

3. Importance of Angle Calculation

Details: Proper angle calculation ensures structural integrity of arch dams, optimal force distribution, and safety against water pressure.

4. Using the Calculator

Tips: Enter all required values with appropriate units. The calculator provides results in both radians and degrees. All values must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: Why is this angle important in arch dam design?
A: This angle determines how forces are transferred to the abutments and affects the dam's structural stability.

Q2: What's a typical range for this angle?
A: Most arch dams have angles between 90-130 degrees, but this varies based on design requirements.

Q3: How does water thrust affect the angle?
A: Greater water thrust typically requires a wider angle to properly distribute forces to the abutments.

Q4: What units should I use for inputs?
A: Use consistent SI units: N/m for thrust, Pa/m² for pressure, meters for radius, and N for abutment thrust.

Q5: Why are results shown in both radians and degrees?
A: Radians are mathematically precise, while degrees are more intuitive for visualization and design.