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

Column Length Formula:

\[ l = \sqrt{\frac{\pi^2 \times E \times I}{4 \times P}} \]

Modulus of Elasticity (E):

Moment of Inertia (I):

m⁴

Crippling Load (P):

Tolerance:

Column Length (l):

1. What is Column Length given Crippling Load?

Definition: This calculator determines the maximum length a column can have before it buckles under a given load, when one end is fixed and the other is free.

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

2. How Does the Calculator Work?

The calculator uses Euler's formula for buckling:

\[ l = \sqrt{\frac{\pi^2 \times E \times I}{4 \times P}} \]

Where:

\( l \) — Column length (meters)
\( E \) — Modulus of Elasticity (Pascals)
\( I \) — Moment of Inertia (m⁴)
\( P \) — Crippling Load (Newtons)

Explanation: The formula calculates the critical length at which a column will buckle under the given load, considering the material properties and cross-section.

3. Importance of Column Length Calculation

Details: Proper column length calculation prevents structural failure due to buckling, ensures safety, and optimizes material usage.

4. Using the Calculator

Tips: Enter the modulus of elasticity, moment of inertia, crippling load, and tolerance percentage (default ±5%). All values must be > 0 except tolerance which can be 0.

5. Frequently Asked Questions (FAQ)

Q1: What is a crippling load?
A: The crippling load is the maximum load a column can bear before it buckles or fails due to instability.

Q2: Why is one end fixed and the other free?
A: This is one of several end conditions that affect buckling behavior. The fixed-free condition is common in cantilever columns.

Q3: What's a typical modulus of elasticity for steel?
A: For structural steel, E is typically around 200 GPa (200 × 10⁹ Pa).

Q4: How do I determine moment of inertia?
A: Moment of inertia depends on the cross-section shape and can be calculated using standard formulas or found in engineering tables.

Q5: What does the tolerance percentage mean?
A: The tolerance provides a safety range (±%) around the calculated length to account for material variations and safety factors.