Slenderness Ratio Calculator

What Is Slenderness Ratio?

Slenderness ratio λ compares a column's unsupported length to its radius of gyration. It is a key indicator of whether a structural member will fail by buckling rather than by material crushing or yielding.

Slenderness Ratio Formula

$$\lambda = \frac{L}{k}, \quad k = \sqrt{\frac{I}{A}}$$

$L$ is the effective column length, $k$ is the radius of gyration, $I$ is the second moment of area, and $A$ is the cross-sectional area. A higher λ means the column is more slender and more susceptible to buckling.

Buckling Classification

Short columns ($\lambda < 50$) tend to fail by crushing or yielding. Intermediate columns (50 to 200) require code-based reduction factors. Long columns ($\lambda > 200$) follow elastic Euler buckling behavior.

Related tools: Buckling Calculator and Moment of Inertia Calculator.

Frequently Asked Questions

What is the radius of gyration?

It is the distance from the centroid at which the entire area could be concentrated while keeping the same moment of inertia. It measures how spread out the cross-section is.

How do I find k from section properties?

Compute k = √(I/A) using the moment of inertia and cross-sectional area of the member.

Does effective length differ from actual length?

Yes. End fixity changes the effective length. This calculator uses the length you enter as the effective buckling length.

Are the classification thresholds universal?

The ranges shown are typical guides for steel. Always verify against your design code and material properties.

Why is slenderness ratio dimensionless?

Both L and k have units of length, so their ratio has no units. It is a pure geometric measure of slenderness.

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Slenderness Ratio Calculator

What Is Slenderness Ratio?

Slenderness Ratio Formula

Buckling Classification

Frequently Asked Questions

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