Crippling Load given Moment of Section if One End of Column is Fixed and Other is Free Calculator

Crippling Load Formula:

\[ P = \frac{M_t}{a - \delta} \]

Column Crippling Load:

1. What is Crippling Load?

Definition: Column Crippling Load is the load over which a column prefers to deform laterally rather than compressing itself.

Purpose: This calculation helps structural engineers determine the maximum load a column can bear before buckling occurs.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ P = \frac{M_t}{a - \delta} \]

Where:

\( P \) — Column Crippling Load (Newtons)
\( M_t \) — Moment of Section (Newton Meter)
\( a \) — Deflection of Free End (Meters)
\( \delta \) — Deflection at Section (Meters ±5%)

Explanation: The moment is divided by the difference in deflection between the free end and the section to determine the crippling load.

3. Importance of Crippling Load Calculation

Details: Proper calculation ensures structural stability and prevents column failure due to buckling under load.

4. Using the Calculator

Tips: Enter the moment of section, deflection at free end, and deflection at section (with ±5% tolerance). All values must be > 0 and free end deflection must be greater than section deflection.

5. Frequently Asked Questions (FAQ)

Q1: What is the significance of ±5% for deflection at section?
A: This accounts for measurement uncertainties and material variations in real-world applications.

Q2: When does this formula apply?
A: Specifically when one end of the column is fixed and the other end is free.

Q3: What units should I use?
A: Use consistent SI units - Newtons for force, Meters for length, and Newton Meters for moment.

Q4: What if my deflection difference is very small?
A: A small denominator leads to large crippling loads, which may indicate an unstable condition approaching buckling.

Q5: How does this differ from other end conditions?
A: Different end conditions (both fixed, pinned, etc.) require different formulas for accurate calculation.