Shear Force given Rotation due to Shear on Arch Dam Calculator

Shear Force Formula:

\[ F_s = \frac{\Phi \times E \times t}{K5} \]

Angle of Rotation (Φ):

rad

Elastic Modulus of Rock (E):

Horizontal Thickness (t):

Constant K5:

Shear Force (Fs): N

1. What is Shear Force given Rotation due to Shear on Arch Dam?

Definition: This calculator determines the shear force acting on an arch dam based on the rotation angle caused by shear, material properties, and geometric factors.

Purpose: It helps civil engineers analyze the structural behavior of arch dams under shear forces.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ F_s = \frac{\Phi \times E \times t}{K5} \]

Where:

\( F_s \) — Shear Force (N)
\( \Phi \) — Angle of Rotation (rad)
\( E \) — Elastic Modulus of Rock (Pa)
\( t \) — Horizontal Thickness of an Arch (m)
\( K5 \) — Constant depending on b/a ratio and Poisson ratio

Explanation: The formula relates the rotational deformation to the shear force through material stiffness and geometric properties.

3. Importance of Shear Force Calculation

Details: Accurate shear force calculation is crucial for dam safety, preventing structural failure, and ensuring proper design of arch dams.

4. Using the Calculator

Tips: Enter the angle of rotation in radians, elastic modulus in Pascals, horizontal thickness in meters, and constant K5 (±5%). All values must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: What is the typical range for constant K5?
A: K5 typically ranges between 5-15 depending on the arch geometry and material properties.

Q2: How is angle of rotation measured?
A: The angle is measured in radians from the original position to the deformed position due to shear.

Q3: Why is elastic modulus important?
A: It represents the rock's stiffness and determines how much it resists deformation under load.

Q4: What affects horizontal thickness?
A: It depends on the dam's design, water pressure, and geological conditions at the site.

Q5: How accurate is this calculation?
A: The calculation provides an estimate with ±5% accuracy depending on K5 value precision.