Elastic Modulus of Rock given Deflection due to Moments on Arch Dam Calculator

Elastic Modulus Formula:

\[ E = \frac{M_t \times K5}{\delta \times T} \]

Moment acting on Arch Dam:

Joule

Constant K5:

Deflection due to Moments:

Thickness of Circular Arch:

Elastic Modulus of Rock (Pascal):

1. What is Elastic Modulus of Rock?

Definition: Elastic Modulus of Rock is defined as the linear elastic deformation response of rock under deformation.

Purpose: It helps engineers understand how much a rock will deform under stress in arch dam construction.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ E = \frac{M_t \times K5}{\delta \times T} \]

Where:

\( E \) — Elastic Modulus of Rock (Pascal)
\( M_t \) — Moment acting on Arch Dam (Joule)
\( K5 \) — Constant depending on b/a ratio and Poisson ratio (±5%)
\( \delta \) — Deflection due to Moments on Arch Dam (m)
\( T \) — Thickness of Circular Arch (m ±5%)

Explanation: The moment multiplied by constant K5 is divided by the product of deflection and thickness to determine the rock's elastic modulus.

3. Importance of Elastic Modulus Calculation

Details: Proper calculation ensures structural stability of arch dams by understanding how the foundation rock will respond to stresses.

4. Using the Calculator

Tips: Enter the moment, constant K5 (±5%), deflection, and thickness (±5%). All values must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: What is the typical range for K5 constant?
A: K5 typically ranges between 0.5 to 10 depending on the arch dam geometry and Poisson ratio.

Q2: Why is there a ±5% variation for some inputs?
A: The ±5% accounts for measurement uncertainties and natural variations in material properties.

Q3: How do I determine the moment acting on an arch dam?
A: The moment can be calculated from water pressure distribution and dam geometry using structural analysis methods.

Q4: What units should be used for input values?
A: Use consistent SI units: Joules for moment, meters for deflection and thickness.

Q5: How accurate is this calculation?
A: The calculation provides an estimate with ±5% accuracy if input values are precise.