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Length of Column given Crippling Load if Both Ends of Column are Fixed Calculator

Column Length Formula:

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

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m⁴
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1. What is Column Length given Crippling Load Calculator?

Definition: This calculator determines the maximum length a column can have before it buckles under a given load, when both ends are fixed.

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

2. How Does the Calculator Work?

The calculator uses Euler's buckling formula for fixed-fixed columns:

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

Where:

  • \( l \) — Effective length of column (meters)
  • \( E \) — Modulus of elasticity (Pascals)
  • \( I \) — Moment of inertia (m⁴)
  • \( P \) — Crippling load (Newtons)

Explanation: The formula calculates the maximum length where the column remains stable under the given load.

3. Importance of Column Length Calculation

Details: Proper column length calculation prevents structural failure due to buckling and ensures safety in building designs.

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.

5. Frequently Asked Questions (FAQ)

Q1: What is crippling load?
A: The maximum load a column can bear before it starts to buckle or deform laterally.

Q2: Why is modulus of elasticity important?
A: It measures the column material's stiffness and resistance to deformation under load.

Q3: What does moment of inertia represent?
A: It measures the column's resistance to bending and depends on its cross-sectional shape.

Q4: Why include a tolerance percentage?
A: It provides a safety margin accounting for material imperfections and real-world conditions.

Q5: What if my column has different end conditions?
A: Different end conditions (pinned, free, etc.) require modified versions of Euler's formula.

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