1. What is Radius of Gyration?

The radius of gyration is a geometric property of a cross-section that measures the distribution of the cross-sectional area in relation to an axis. It is defined as the root mean square distance of the object's parts from either its center of gravity or a given axis.

2. How Does the Calculator Work?

The calculator uses the radius of gyration formula:

Where:

• \( k \) — Radius of gyration (m)
• \( I \) — Moment of inertia (m⁴)
• \( A \) — Cross-sectional area (m²)

Explanation: The formula calculates how far the area would be concentrated from the axis if the entire area were located at a single point.

3. Importance of Radius of Gyration

Details: Radius of gyration is crucial in structural engineering for analyzing column buckling, determining the slenderness ratio, and evaluating the stability of structural members under compression.

4. Using the Calculator

Tips: Enter the moment of inertia in m⁴ and cross-sectional area in m². Both values must be positive numbers greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between radius of gyration and moment of inertia?
A: Moment of inertia measures resistance to bending, while radius of gyration describes how the area is distributed relative to an axis.

Q2: How does radius of gyration affect buckling?
A: Larger radius of gyration means better resistance to buckling as the area is distributed farther from the axis.

Q3: Can radius of gyration be calculated for different shapes?
A: Yes, but the formula differs based on shape. This calculator is specifically for rectangular sections.

Q4: What are typical values for radius of gyration?
A: Values vary significantly based on cross-sectional dimensions. For a rectangle, k = h/√12 about its centroidal axis, where h is the height.

Q5: How is radius of gyration used in real-world applications?
A: It's essential in designing columns, struts, and other compression members to ensure they don't buckle under load.