1. What is Slenderness Ratio?

The slenderness ratio (λ) is a measure of the propensity of a column to buckle. It's defined as the ratio of the effective length of the column (L_e) to its radius of gyration (r). Higher slenderness ratios indicate a greater tendency to buckle under compressive loads.

2. How Does the Calculator Work?

The calculator uses the slenderness ratio formula:

Where:

• \( \lambda \) — Slenderness ratio (dimensionless)
• \( L_e \) — Effective length of the column (m)
• \( r \) — Radius of gyration (m)

Explanation: The effective length accounts for end conditions, while the radius of gyration represents the distribution of the cross-sectional area.

3. Importance of Slenderness Ratio

Details: Slenderness ratio is crucial in structural engineering for:

• Determining column buckling strength
• Classifying columns as short, intermediate, or long
• Designing safe and efficient structural elements
• Complying with building codes and standards

4. Using the Calculator

Tips:

• Enter effective length in meters (consider end conditions)
• Enter radius of gyration in meters (calculated from cross-section properties)
• Both values must be positive numbers

5. Frequently Asked Questions (FAQ)

Q1: What is effective length (L_e)?
A: The effective length is the length between inflection points (points of zero moment) in the buckled shape, depending on end conditions.

Q2: How do I find radius of gyration (r)?
A: \( r = \sqrt{I/A} \), where I is the moment of inertia and A is the cross-sectional area.

Q3: What are typical slenderness ratio values?
A: Values vary by material and application, but generally:

• λ < 50: Short columns (fail by crushing)
• 50 < λ < 200: Intermediate columns
• λ > 200: Long columns (fail by buckling)

Q4: How do end conditions affect L_e?
A: Common effective length factors (K):

• Pinned-pinned: K = 1.0
• Fixed-fixed: K = 0.5
• Fixed-pinned: K = 0.7
• Fixed-free: K = 2.0

Q5: What's the difference between λ and KL/r?
A: KL/r is the modified slenderness ratio where K is the effective length factor accounting for end conditions.