Effective Length of Column given Crippling Load and Rankine's Constant Calculator

Effective Column Length Formula:

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

Column Crushing Stress (σ_c):

Column Cross Sectional Area (A):

m²

Crippling Load (P):

Least Radius of Gyration (r_least):

Rankine's Constant (α):

Effective Column Length (L_eff): m

1. What is Effective Column Length?

Definition: Effective length of a column is the length of an equivalent pin-ended column having the same load-carrying capacity as the member under consideration.

Purpose: It helps structural engineers determine the buckling capacity of columns under compressive loads.

2. How Does the Calculator Work?

The calculator uses Rankine's formula:

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

Where:

\( L_{eff} \) — Effective column length (meters)
\( \sigma_c \) — Column crushing stress (Pascals)
\( A \) — Cross-sectional area (m²)
\( P \) — Crippling load (Newtons)
\( r_{least} \) — Least radius of gyration (meters)
\( \alpha \) — Rankine's constant (dimensionless)

Explanation: The formula combines Euler's buckling theory with Rankine's empirical approach for short columns.

3. Importance of Effective Length Calculation

Details: Proper calculation ensures structural stability, prevents buckling failures, and helps in economical column design.

4. Using the Calculator

Tips: Enter all required parameters with correct units. Rankine's constant typically ranges from 0.0002 to 0.0005 (default 0.00038 ±5%).

5. Frequently Asked Questions (FAQ)

Q1: What is Rankine's constant?
A: It's an empirical constant that depends on column material and end conditions.

Q2: How to determine least radius of gyration?
A: It's the minimum value of √(I/A), where I is moment of inertia and A is cross-sectional area.

Q3: What's typical Rankine's constant for steel?
A: For mild steel, it's approximately 0.00038 ±5%.

Q4: When does this formula apply?
A: For intermediate columns where both crushing and buckling are significant.

Q5: How does end condition affect effective length?
A: Different end conditions require different effective length factors (not shown in this formula).