Length of Column given Euler Load Calculator

Column Length Formula:

\[ l = \sqrt{\frac{\pi^2 \times E \times I}{P_E}} \]

Modulus of Elasticity (E):

Moment of Inertia (I):

kg·m²

Euler Load (P_E):

Safety Factor (±%):

Column Length (m):

With Safety Factor (m):

Definition: This calculator determines the maximum unsupported length a column can have before buckling under a given Euler load.

Purpose: It helps structural engineers design columns that can support loads without buckling failure.

The calculator uses Euler's buckling formula:

\[ l = \sqrt{\frac{\pi^2 \times E \times I}{P_E}} \]

Where:

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

Details: Proper column length estimation prevents structural failure due to buckling and ensures safe load-bearing capacity.

Tips: Enter the modulus of elasticity, moment of inertia, Euler load, and safety factor (default ±5%). All values must be > 0.

Q1: What is Euler buckling load?
A: The maximum axial load a column can bear before buckling occurs.

Q2: Why include a safety factor?
A: To account for material imperfections, unexpected loads, and other real-world variables.

Q3: What's a typical safety factor for columns?
A: Typically 5-10%, but depends on building codes and specific application.

Q4: How do I find the moment of inertia?
A: It depends on the column's cross-section shape. Use standard formulas for rectangles, circles, etc.

Q5: Does this work for all materials?
A: Yes, as long as you use the correct modulus of elasticity for your material.