Elastic Modulus of Rock given Rotation due to Twist on Arch Dam Calculator

Elastic Modulus Formula:

\[ E = \frac{M \times K4}{\Phi \times T^2} \]

Cantilever Twisting Moment (M):

N·m

Constant K4:

Angle of Rotation (Φ):

rad

Thickness of Circular Arch (T):

Elastic Modulus of Rock (E):

1. What is Elastic Modulus of Rock given Rotation due to Twist?

Definition: This calculator determines the elastic modulus of rock based on the rotation caused by twisting moments on an arch dam.

Purpose: It helps engineers assess the rock foundation's stiffness when designing arch dams.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ E = \frac{M \times K4}{\Phi \times T^2} \]

Where:

\( E \) — Elastic modulus of rock (Pa)
\( M \) — Cantilever twisting moment (N·m)
\( K4 \) — Constant depending on b/a ratio and Poisson ratio (±5%)
\( \Phi \) — Angle of rotation (radians)
\( T \) — Thickness of circular arch (meters)

Explanation: The twisting moment and constant are multiplied, then divided by the product of rotation angle and squared thickness.

3. Importance of Elastic Modulus Calculation

Details: Accurate elastic modulus determination ensures proper dam design, accounting for rock foundation deformation under twisting forces.

4. Using the Calculator

Tips: Enter the twisting moment, K4 constant (default 10.02 ±5%), rotation angle, and arch thickness. All values must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: What affects the K4 constant value?
A: K4 depends on the arch dam's b/a ratio (width/height) and the Poisson ratio of the rock.

Q2: Why is there a ±5% margin on K4?
A: The constant varies slightly based on specific geometric conditions and material properties.

Q3: How is the angle of rotation measured?
A: Typically measured in radians using precise surveying instruments on the dam structure.

Q4: What's a typical elastic modulus for dam foundations?
A: Values typically range from 10-70 GPa, depending on rock type (granite, sandstone, etc.).

Q5: How does thickness affect the calculation?
A: Thicker arches result in lower calculated elastic modulus as the effect is squared in the formula.