Thrust given Extrados Stresses on Arch Dam Calculator

Thrust of Abutments Formula:

\[ F = S \times T_b + \frac{6 \times M_t}{(T_b^2)} \]

Intrados Stresses (S):

kN/m²

Base Thickness (T_b):

Moment (M_t):

Tolerance:

Thrust of Abutments (F):

1. What is Thrust of Abutments?

Definition: Thrust of Abutments refers to the horizontal force exerted by an arch, vault, or similar structure against its supporting abutments.

Purpose: It helps engineers design proper support structures for arch dams to ensure stability and safety.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ F = S \times T_b + \frac{6 \times M_t}{(T_b^2)} \]

Where:

\( F \) — Thrust of Abutments (N)
\( S \) — Intrados Stresses (kN/m²)
\( T_b \) — Base Thickness (m)
\( M_t \) — Moment acting on Arch Dam (J)

Explanation: The formula combines the direct stress component and the bending moment component to calculate the total thrust.

3. Importance of Thrust Calculation

Details: Proper thrust estimation ensures dam stability, prevents structural failure, and helps design adequate abutments.

4. Using the Calculator

Tips: Enter the intrados stresses, base thickness, moment, and tolerance percentage (default ±5%). Base thickness must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: What are typical values for intrados stresses?
A: Values vary but typically range from 0.1 to 1.0 kN/m² depending on dam design and water pressure.

Q2: How does base thickness affect thrust?
A: Thicker bases generally reduce thrust by distributing the load over a larger area.

Q3: Why include a tolerance percentage?
A: Engineering calculations often include safety margins to account for material variations and unexpected loads.

Q4: How is moment on an arch dam determined?
A: Moment is calculated from water pressure, dam weight, and other forces acting on the structure.

Q5: What units should I use?
A: Use consistent units: kN/m² for stress, meters for thickness, and joules for moment.