Moments given Rotation due to Twist on Arch Dam Calculator

Cantilever Twisting Moment Formula:

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

Elastic Modulus of Rock:

Horizontal Thickness of an Arch:

Angle of Rotation:

rad

Constant K4:

Cantilever Twisting Moment (N·m):

1. What is Cantilever Twisting Moment?

Definition: The twisting moment that occurs in an arch dam due to rotational deformation caused by water pressure or other forces.

Purpose: This calculation helps structural engineers assess the rotational stresses in arch dams to ensure structural integrity.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

\( M \) — Cantilever Twisting Moment (N·m)
\( E \) — Elastic Modulus of Rock (Pa)
\( t \) — Horizontal Thickness of an Arch (m)
\( \Phi \) — Angle of Rotation (radians)
\( K4 \) — Constant depending on b/a ratio and Poisson ratio

Explanation: The formula calculates the twisting moment based on material properties, arch geometry, and rotational deformation.

3. Importance of Twisting Moment Calculation

Details: Accurate calculation helps prevent structural failure in arch dams by ensuring the design can withstand rotational forces.

4. Using the Calculator

Tips: Enter the elastic modulus, arch thickness, rotation angle, and constant K4 (default 10.02). Note that angle and K4 have ±5% uncertainty.

5. Frequently Asked Questions (FAQ)

Q1: What is typical value for elastic modulus of rock?
A: It varies widely (5-100 GPa) depending on rock type. Granite is typically 50-70 GPa.

Q2: How is angle of rotation measured?
A: It's typically determined through structural analysis or field measurements with ±5% accuracy.

Q3: Where does constant K4 come from?
A: K4 is derived from arch dam geometry (b/a ratio) and material properties (Poisson ratio).

Q4: Why is thickness squared in the formula?
A: The squared relationship accounts for how both width and depth contribute to resistance against twisting.

Q5: How critical is the ±5% uncertainty?
A: For safety-critical structures like dams, engineers typically apply safety factors to account for these uncertainties.