Radial Thickness of Element given Deflection due to Moments on Arch Dam Calculator

Radial Thickness Formula:

\[ t = \frac{M_t \times K_5}{E \times \delta} \]

Moment acting on Arch Dam:

Constant K5:

Elastic Modulus of Rock:

Deflection due to Moments:

Radial Thickness (m):

1. What is Radial Thickness of Element given Deflection?

Definition: This calculator determines the radial thickness of an arch dam element based on moment, material properties, and deflection.

Purpose: It helps civil engineers design arch dams by calculating the required thickness to withstand moments and deflections.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ t = \frac{M_t \times K_5}{E \times \delta} \]

Where:

\( t \) — Radial thickness (meters)
\( M_t \) — Moment acting on Arch Dam (Joules)
\( K_5 \) — Constant depending on b/a ratio and Poisson ratio
\( E \) — Elastic Modulus of Rock (Pascals)
\( \delta \) — Deflection due to Moments (meters)

Explanation: The formula calculates the required thickness to resist bending moments while accounting for material properties and allowable deflection.

3. Importance of Radial Thickness Calculation

Details: Proper thickness calculation ensures structural integrity, prevents excessive deflection, and maintains dam stability under load.

4. Using the Calculator

Tips: Enter the moment, constant K5, elastic modulus, and deflection. All values must be > 0. The ±5% indicates typical tolerance ranges.

5. Frequently Asked Questions (FAQ)

Q1: What is constant K5?
A: K5 is a dimensionless constant that depends on the arch geometry and material's Poisson ratio.

Q2: How is deflection measured?
A: Deflection is typically measured at the crown of the arch dam under maximum load conditions.

Q3: Why is elastic modulus important?
A: It quantifies the rock's stiffness and its resistance to elastic deformation under stress.

Q4: What affects the moment on an arch dam?
A: Water pressure, temperature changes, and seismic activity all contribute to moments.

Q5: How accurate are these calculations?
A: Results are theoretical; actual construction should include safety factors and field verification.