Thrust at Crown of Arch Dam Calculator

Thrust Formula:

\[ F = (p \times r) \times \left(1 - \frac{2 \times \theta \times \sin\left(\theta \times \frac{(T_b/r)^2}{12}\right)}{D}\right) \]

Normal Radial Pressure (p):

N/m²

Radius to Center Line (r):

Angle (θ):

rad

Base Thickness (T_b):

Diameter (D):

Tolerance:

Thrust of Abutments (F): N

1. What is Thrust at Crown of Arch Dam?

Definition: The horizontal force exerted by an arch dam against its supporting abutments at the crown (top) of the dam.

Purpose: This calculation helps engineers ensure the dam structure can withstand the forces acting upon it and design appropriate abutments.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ F = (p \times r) \times \left(1 - \frac{2 \times \theta \times \sin\left(\theta \times \frac{(T_b/r)^2}{12}\right)}{D}\right) \]

Where:

\( F \) — Thrust of Abutments (N)
\( p \) — Normal Radial Pressure (N/m²)
\( r \) — Radius to Center Line of Arch (m)
\( \theta \) — Angle (radians)
\( T_b \) — Base Thickness (m)
\( D \) — Diameter (m)

3. Importance of Thrust Calculation

Details: Proper thrust calculation ensures structural stability of the dam and prevents failure of the abutments.

4. Using the Calculator

Tips: Enter all required parameters. The tolerance field (default ±5%) allows you to specify an acceptable range for the result.

5. Frequently Asked Questions (FAQ)

Q1: What is normal radial pressure?
A: It's the pressure acting perpendicular to the dam surface at the center line, typically calculated from water pressure and other loads.

Q2: How do I determine the radius to center line?
A: This is the radius of the circular arc that forms the center line of the arch dam's cross-section.

Q3: What angle should I use for θ?
A: This is the central angle subtended by the arch, typically between 90° to 130° (1.57 to 2.27 radians) for most arch dams.

Q4: Why include a tolerance?
A: Engineering calculations often include safety factors and tolerances to account for material variations and construction tolerances.

Q5: How does base thickness affect thrust?
A: Thicker bases generally distribute thrust over a larger area but may increase total thrust due to greater mass.