Radial Thickness of Element given Rotation due to Shear on Arch Dam Calculator

Radial Thickness Formula:

\[ t = \frac{F_s \times K_5}{E \times \Phi} \]

Shear Force (F_s):

Constant K₅:

Elastic Modulus (E):

Angle of Rotation (Φ):

rad

Radial Thickness (t):

1. What is Radial Thickness of Element given Rotation due to Shear on Arch Dam?

Definition: This calculator determines the radial thickness of an arch dam element based on the rotation caused by shear forces.

Purpose: It helps civil engineers design arch dams by calculating the required thickness to withstand shear-induced rotations.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ t = \frac{F_s \times K_5}{E \times \Phi} \]

Where:

\( t \) — Radial thickness (meters)
\( F_s \) — Shear force (Newtons)
\( K_5 \) — Constant depending on b/a ratio and Poisson ratio (±5%)
\( E \) — Elastic modulus of rock (Pascals)
\( \Phi \) — Angle of rotation (radians)

Explanation: The formula relates the thickness to the shear forces, material properties, and resulting rotation.

3. Importance of Radial Thickness Calculation

Details: Proper thickness calculation ensures structural integrity of the arch dam against shear forces and rotations.

4. Using the Calculator

Tips: Enter the shear force, constant K5 (with ±5% tolerance), elastic modulus, and rotation angle. All values must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: What is constant K5?
A: K5 is a dimensionless constant that depends on the arch geometry (b/a ratio) and the Poisson ratio of the material.

Q2: Why is there a ±5% tolerance on K5?
A: The ±5% accounts for variations in material properties and geometric approximations in real-world applications.

Q3: How do I determine the angle of rotation?
A: The angle of rotation is typically determined through structural analysis or field measurements of the dam's deformation.

Q4: What units should I use?
A: Use consistent SI units: Newtons for force, Pascals for elastic modulus, and radians for angles.

Q5: Does this calculation account for safety factors?
A: No, engineers should apply appropriate safety factors to the calculated thickness based on design standards.