1. What is Slenderness Ratio?

The slenderness ratio (sr) is a measure of the propensity of a column to buckle. It's defined as the ratio of the length of the column to the radius of gyration of its cross section.

2. How Does the Calculator Work?

The calculator uses the slenderness ratio formula:

Where:

• \( l \) — Length of the column (m)
• \( r \) — Radius of gyration (m)
• \( sr \) — Slenderness ratio (dimensionless)

Explanation: The ratio compares the column's length to its cross-sectional stiffness, indicating how susceptible it is to buckling under compressive loads.

3. Importance of Slenderness Ratio

Details: Slenderness ratio is crucial in structural engineering for designing columns. Higher ratios indicate greater tendency to buckle, requiring different design approaches than short, stocky columns.

4. Using the Calculator

Tips: Enter the column length and radius of gyration in meters. Both values must be positive numbers. The calculator will compute the dimensionless slenderness ratio.

5. Frequently Asked Questions (FAQ)

Q1: What is considered a high slenderness ratio?
A: Generally, ratios above 200 are considered high, but critical values depend on material and end conditions.

Q2: How does radius of gyration relate to cross-section?
A: Radius of gyration is calculated as \( r = \sqrt{I/A} \), where I is moment of inertia and A is cross-sectional area.

Q3: Why is slenderness ratio important in construction?
A: It helps determine whether a column will fail by crushing (low ratio) or buckling (high ratio), guiding material selection and design.

Q4: Does slenderness ratio apply to all materials?
A: Yes, but different materials have different critical slenderness ratios where behavior changes from crushing to buckling.

Q5: How do end conditions affect slenderness ratio?
A: Effective length (used in ratio) depends on end fixity - pinned, fixed, or free ends modify the effective length.