Actual Length given Slenderness Ratio Calculator

Length of Column Formula:

\[ l = \lambda \times r_L \]

Length of Column:

1. What is Actual Length given Slenderness Ratio?

Definition: This calculator determines the actual length of a column based on its slenderness ratio and least radius of gyration.

Purpose: It helps structural engineers and designers calculate column lengths for stability analysis in construction projects.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ l = \lambda \times r_L \]

Where:

\( l \) — Length of Column (meters)
\( \lambda \) — Slenderness Ratio (dimensionless, ±5%)
\( r_L \) — Least Radius of Gyration (meters)

Explanation: The slenderness ratio multiplied by the least radius of gyration gives the effective length of the column.

3. Importance of Column Length Calculation

Details: Proper column length calculation is crucial for determining buckling strength and overall structural stability.

4. Using the Calculator

Tips: Enter the slenderness ratio (±5%) and least radius of gyration (in meters). Both values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is slenderness ratio?
A: It's the ratio of a column's effective length to its least radius of gyration, indicating its susceptibility to buckling.

Q2: Why is there a ±5% note?
A: The slenderness ratio often has a tolerance of ±5% in practical applications to account for variations.

Q3: How do I find the least radius of gyration?
A: It's calculated as \( r = \sqrt{I/A} \), where I is the smallest moment of inertia and A is cross-sectional area.

Q4: What's a typical slenderness ratio range?
A: For steel columns, it's typically between 20-200, but varies by material and design requirements.

Q5: Does this calculate effective or actual length?
A: This calculates the actual length based on the slenderness ratio and radius of gyration.