1. What is the Radius of Wheel Given Shear Stress Formula?

The formula calculates the radius of a fully worn-out wheel based on contact shear stress and static load. It is particularly useful in railway engineering for determining wheel dimensions under specific stress conditions.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( R_w \) — Radius of Wheel (mm)
• \( F_s \) — Contact Shear Stress (kgf/mm²)
• \( F_a \) — Static Load (tf)

Explanation: The formula establishes the relationship between wheel radius, contact shear stress, and the static load applied to the wheel.

3. Importance of Radius Calculation

Details: Accurate wheel radius calculation is crucial for railway maintenance, ensuring proper wheel-rail contact, and preventing excessive wear and stress concentrations.

4. Using the Calculator

Tips: Enter contact shear stress in kgf/mm² and static load in tf. Both values must be positive numbers greater than zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is contact shear stress?
A: Contact shear stress is the shear stress at the contact point between wheel and rail, typically measured in kgf/mm².

Q2: How is static load defined in this context?
A: Static load refers to the stationary load applied to the wheel, used for stress and moment calculations, measured in metric ton-force (tf).

Q3: Why is this formula specific to fully worn-out wheels?
A: The formula is designed to calculate the radius under worst-case scenario conditions when the wheel is fully worn, ensuring safety margins in design calculations.

Q4: What are typical values for contact shear stress?
A: Contact shear stress values vary depending on materials and conditions, but typically range from 5-15 kgf/mm² for railway applications.

Q5: Can this formula be used for other types of wheels?
A: While primarily designed for railway wheels, the formula may be adapted for other wheel types with appropriate modifications and validation.