Least Radius of Gyration given Crippling Load and Rankine's Constant Calculator

Least Radius of Gyration Formula:

\[ r_{least} = \sqrt{\frac{\alpha \times L_{eff}^2}{\frac{\sigma_c \times A}{P} - 1}} \]

Rankine's Constant:

Effective Column Length:

Column Crushing Stress:

Column Cross Sectional Area:

m²

Crippling Load:

Least Radius of Gyration (m):

Definition: The least radius of gyration is the smallest value of the radius of gyration used for structural calculations of columns.

Purpose: It helps determine the column's resistance to buckling under compressive loads.

The calculator uses Rankine's formula:

\[ r_{least} = \sqrt{\frac{\alpha \times L_{eff}^2}{\frac{\sigma_c \times A}{P} - 1}} \]

Where:

Explanation: The formula relates the geometric properties of a column to its buckling behavior under load.

Details: Proper calculation ensures structural stability and prevents column failure due to buckling.

Tips: Enter all required values with appropriate units. The ±5% indicates the typical tolerance range for these calculations.

Q1: What is Rankine's constant?
A: It's an empirical constant that depends on the column material (e.g., 0.00038 for mild steel).

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 if I get "Invalid input"?
A: This occurs when the denominator is ≤0, meaning the inputs don't satisfy Rankine's formula conditions.

Q4: Why is radius of gyration important?
A: It measures the column's resistance to buckling - smaller radius means greater buckling risk.

Q5: How accurate are these calculations?
A: They're theoretical estimates - actual values may vary by ±5% due to material imperfections.