Crippling Load by Euler's Formula Calculator

Euler's Buckling Load Formula:

\[ P_E = \frac{\pi^2 \times E \times I}{(L_{eff})^2} \]

Modulus of Elasticity (E):

Moment of Inertia (I):

m⁴

Effective Length (L_eff):

Safety Factor (±%):

Euler's Buckling Load (N):

With Safety Factor (±5%):

1. What is Euler's Buckling Formula?

Definition: Euler's formula calculates the critical axial load at which a slender column will buckle.

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:

\[ P_E = \frac{\pi^2 \times E \times I}{(L_{eff})^2} \]

Where:

\( P_E \) — Euler's buckling load (Newtons)
\( E \) — Modulus of elasticity (Pascals)
\( I \) — Moment of inertia (m⁴)
\( L_{eff} \) — Effective column length (meters)

Explanation: The formula shows that buckling load is directly proportional to stiffness (EI) and inversely proportional to the square of the effective length.

3. Importance of Buckling Calculation

Details: Proper buckling analysis prevents structural failures in columns, especially slender ones under compressive loads.

4. Using the Calculator

Tips: Enter the modulus of elasticity (typically 200 GPa for steel), moment of inertia, effective length, and safety factor (default ±5%). All values must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: What is effective length?
A: It's the length between inflection points of the buckled shape, depending on end conditions (pinned, fixed, etc.).

Q2: Why include a safety factor?
A: Safety factors account for imperfections, eccentric loads, and material variations not considered in the ideal formula.

Q3: What's a typical modulus for steel?
A: Structural steel typically has E ≈ 200 GPa (200×10⁹ Pa).

Q4: When is Euler's formula applicable?
A: For long, slender columns where buckling dominates over material failure (slenderness ratio > critical value).

Q5: How to find moment of inertia?
A: For standard sections, use tables. For custom shapes, calculate using I = ∫y²dA or CAD software.