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Length of Column given Initial Deflection at Distance X from end A Calculator

Length of Column Formula:

\[ l = \frac{\pi \cdot x}{\sin^{-1}\left(\frac{y'}{C}\right)} \]

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1. What is Length of Column given Initial Deflection?

Definition: This calculator determines the length of a column based on its deflection characteristics at a specific point.

Purpose: It helps structural engineers analyze column behavior under load and design appropriate supports.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ l = \frac{\pi \cdot x}{\sin^{-1}\left(\frac{y'}{C}\right)} \]

Where:

  • \( l \) — Length of column (meters)
  • \( x \) — Distance of deflection from end A (meters)
  • \( y' \) — Initial Deflection at distance x (meters)
  • \( C \) — Maximum initial deflection (meters)

Explanation: The formula calculates column length using trigonometric relationships between deflection points.

3. Importance of Column Length Calculation

Details: Accurate column length determination is crucial for structural stability, load-bearing capacity, and preventing buckling.

4. Using the Calculator

Tips: Enter the distance from end A, initial deflection, maximum deflection (all in meters), and optional tolerance percentage (±5%).

5. Frequently Asked Questions (FAQ)

Q1: What is the tolerance field for?
A: The tolerance allows for a ±5% adjustment to account for material variations or safety factors.

Q2: What units should I use?
A: All length measurements should be in consistent units (typically meters).

Q3: What if I get an error?
A: Ensure y'/C ratio is between -1 and 1, as arcsin is undefined outside this range.

Q4: How accurate is this calculation?
A: It provides theoretical values; actual measurements may vary based on material properties.

Q5: Can I use this for any column material?
A: Yes, but material properties affect actual deflection behavior.

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