1. What is Elastic Modulus of Rock given Deflection due to Shear?

Definition: This calculator determines the elastic modulus of rock based on the deflection caused by shear forces on an arch dam.

Purpose: It helps civil engineers and geotechnical professionals assess the rock's stiffness supporting an arch dam.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( E \) — Elastic modulus of rock (Pascal)
• \( F_s \) — Shear force (Newtons)
• \( K_3 \) — Constant depending on b/a ratio and Poisson ratio
• \( \delta \) — Deflection due to moments (meters)

Explanation: The elastic modulus is calculated by multiplying the shear force with constant K3, then dividing by the measured deflection.

3. Importance of Elastic Modulus Calculation

Details: The elastic modulus indicates how much the rock will deform under stress, which is crucial for dam stability and safety assessments.

4. Using the Calculator

Tips: Enter the shear force in Newtons, constant K3, and deflection in meters. All values must be > 0. Results have ±5% tolerance.

5. Frequently Asked Questions (FAQ)

Q1: What is typical elastic modulus for dam foundation rock?
A: It varies widely but generally ranges from 10-70 GPa for competent rock suitable for dam foundations.

Q2: How is constant K3 determined?
A: K3 depends on the arch dam's geometry (b/a ratio) and the rock's Poisson ratio, typically obtained from engineering tables.

Q3: Why is there a ±5% tolerance?
A: This accounts for measurement uncertainties in field conditions and material variability.

Q4: How does deflection affect the calculation?
A: Greater deflection with the same force indicates lower elastic modulus (softer rock).

Q5: What units are used in this calculator?
A: SI units are used throughout - Newtons for force, meters for deflection, and Pascals for elastic modulus.

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