Crippling Load given Effective Length and Radius of Gyration Calculator

Crippling Load Formula:

\[ P = \frac{\pi^2 \times E \times A \times r^2}{L_{eff}^2} \]

Modulus of Elasticity:

Cross Sectional Area:

Least Radius of Gyration:

Effective Column Length:

Column Crippling Load (N):

1. What is a Crippling Load Calculator?

Definition: This calculator determines the crippling load of a column based on the modulus of elasticity, cross-sectional area, radius of gyration, and effective length.

Purpose: It helps structural engineers determine the maximum load a column can bear before buckling occurs.

2. How Does the Calculator Work?

The calculator uses Euler's formula for buckling:

\[ P = \frac{\pi^2 \times E \times A \times r^2}{L_{eff}^2} \]

Where:

\( P \) — Crippling load (N)
\( E \) — Modulus of elasticity (Pa)
\( A \) — Cross-sectional area (m²)
\( r \) — Least radius of gyration (m)
\( L_{eff} \) — Effective column length (m)

Explanation: The formula calculates the critical load at which a slender column will buckle.

3. Importance of Crippling Load Calculation

Details: Proper calculation ensures structural stability and prevents catastrophic failures in columns under compressive loads.

4. Using the Calculator

Tips: Enter all required values with their ±5% tolerance. All values must be > 0 for calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is radius of gyration?
A: It's a measure of a column's resistance to buckling, calculated as the square root of (moment of inertia/area).

Q2: How is effective length determined?
A: It depends on end conditions - pinned-pinned (1.0L), fixed-fixed (0.5L), fixed-pinned (0.7L), etc.

Q3: What materials is this valid for?
A: Primarily for elastic materials that follow Hooke's law up to the buckling point.

Q4: Does this account for imperfections?
A: No, real-world calculations should include safety factors for imperfections.

Q5: What's the ±5% tolerance for?
A: It accounts for material property variations and measurement uncertainties.