Crippling Load by Euler's Formula given Crippling Load by Rankine's Formula Calculator

Euler's Buckling Load Formula:

\[ P_E = \frac{P_c \times P_r}{P_c - P_r} \]

Euler's Buckling Load (P_E):

1. What is Euler's Buckling Load?

Definition: Euler's Buckling Load is the axial load at which a perfectly straight column or structural member starts to bend.

Purpose: This calculator determines Euler's Buckling Load when you know both the crushing load and Rankine's critical load.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ P_E = \frac{P_c \times P_r}{P_c - P_r} \]

Where:

\( P_E \) — Euler's Buckling Load (N)
\( P_c \) — Crushing Load (N)
\( P_r \) — Rankine's Critical Load (N)

Explanation: The formula combines both crushing and Rankine's loads to determine the critical buckling load according to Euler's theory.

3. Importance of Buckling Load Calculation

Details: Accurate buckling load calculation is crucial for structural stability, preventing column failure, and ensuring safety in construction projects.

4. Using the Calculator

Tips: Enter the crushing load and Rankine's critical load in Newtons. The tolerance field (default ±5%) lets you specify an acceptable range around the calculated value.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between crushing load and buckling load?
A: Crushing load is when material fails by compression, while buckling load is when the structure fails by bending under axial load.

Q2: Why include a tolerance percentage?
A: Tolerance accounts for material variations, imperfections, and safety factors in real-world applications.

Q3: What units should I use?
A: All loads should be in Newtons (N) for consistent results.

Q4: Can I use this for any column material?
A: Yes, as long as you have accurate crushing and Rankine's load values for that material.

Q5: What if P_c equals P_r?
A: The formula becomes undefined (division by zero), indicating the column would fail immediately under any load.