Euler Load Calculator

Euler Load Formula:

\[ PE = \frac{\pi^2 \times \epsilon_{column} \times I}{l^2} \]

Modulus of Elasticity:

Moment of Inertia:

kg·m²

Column Length:

Safety Factor (±5%):

Euler Load (N):

With Safety Factor (N):

1. What is Euler Load?

Definition: Euler load is the compressive load at which a slender column will suddenly bend or buckle.

Purpose: It helps engineers determine the critical buckling load for columns in structural design.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ PE = \frac{\pi^2 \times \epsilon_{column} \times I}{l^2} \]

Where:

\( PE \) — Euler load (Newtons)
\( \epsilon_{column} \) — Modulus of elasticity (Pascals)
\( I \) — Moment of inertia (kg·m²)
\( l \) — Column length (meters)

Explanation: The formula calculates the critical buckling load based on material stiffness, cross-section properties, and column length.

3. Importance of Euler Load Calculation

Details: Proper calculation ensures structural stability and prevents catastrophic buckling failures in columns.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: What is the safety factor for?
A: The safety factor accounts for material imperfections and uncertainties in loading conditions.

Q2: What's a typical modulus of elasticity for steel?
A: For structural steel, it's typically around 200 GPa (200 × 10⁹ Pa).

Q3: How does column length affect Euler load?
A: Euler load decreases with the square of the column length - longer columns are much more prone to buckling.

Q4: What end conditions does this assume?
A: This formula assumes pinned-pinned end conditions. Other end conditions require modification factors.

Q5: When is Euler's formula applicable?
A: For long, slender columns where buckling occurs before material yielding (slenderness ratio > critical value).