Radius of Gyration given Effective Length and Crippling Load Calculator

Radius of Gyration Formula:

\[ r_{least} = \sqrt{\frac{P \times L_{eff}^2}{\pi^2 \times \varepsilon_c \times A_{sectional}}} \]

Column Crippling Load:

Effective Column Length:

Modulus of Elasticity:

Cross Sectional Area:

m²

Tolerance:

Least Radius of Gyration:

1. What is Radius of Gyration?

Definition: The radius of gyration is the distance from the axis of rotation to a point where the total mass of the body is assumed to be concentrated.

Purpose: It helps in structural engineering to determine the buckling resistance of columns and other compression members.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ r_{least} = \sqrt{\frac{P \times L_{eff}^2}{\pi^2 \times \varepsilon_c \times A_{sectional}}} \]

Where:

\( r_{least} \) — Least radius of gyration (meters)
\( P \) — Column crippling load (Newtons)
\( L_{eff} \) — Effective column length (meters)
\( \varepsilon_c \) — Modulus of elasticity (Pascals)
\( A_{sectional} \) — Cross sectional area (square meters)

Explanation: The formula calculates the minimum radius of gyration required to prevent buckling under the given load and conditions.

3. Importance of Radius of Gyration Calculation

Details: Proper calculation ensures structural stability, prevents buckling failures, and helps in designing efficient structural members.

4. Using the Calculator

Tips: Enter the column crippling load, effective length, modulus of elasticity, cross-sectional area, and tolerance percentage (default ±5%). All values must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: What is the significance of the least radius of gyration?
A: It determines the column's resistance to buckling - a smaller radius means greater susceptibility to buckling.

Q2: How does effective length affect the radius of gyration?
A: Longer effective lengths require larger radii of gyration to prevent buckling under the same load.

Q3: What's a typical modulus of elasticity for steel columns?
A: For structural steel, it's typically around 200 GPa (200 × 10⁹ Pa).

Q4: Why include a tolerance percentage?
A: The tolerance accounts for material imperfections, construction tolerances, and safety factors.

Q5: How do I determine the crippling load for my column?
A: The crippling load can be calculated using Euler's formula or determined through structural analysis based on expected loads.