What is the significance of slenderness ratio?

Slenderness ratio KL/r determines whether column fails by yielding (short, KL/r 120). AISC limit: KL/r ≤ 200 for compression members to prevent excessive lateral deflection.

What effective length factor K should I use?

Theoretical K: pinned-pinned = 1.0, fixed-free (flagpole) = 2.0, fixed-pinned = 0.7, fixed-fixed = 0.5. AISC recommends conservative K: pinned = 1.0, fixed ends = 0.65-0.80 for real imperfect fixity.

Which axis governs column buckling?

Column buckles about the weaker axis (smaller r). For W-sections: r_x >> r_y. Column may be braced in y-direction reducing KL_y; compare KL_x/r_x vs KL_y/r_y and use the larger ratio for design.

Column Slenderness Ratio Calculator

Calculate column slenderness ratio λ = KL/r. Effective length factors K: pinned-pinned K=1.0, fixed-free K=2.0, fixed-pinned K=0.7, fixed-fixed K=0.5. Maximum λ for steel: 200 (compression members), 300 (tension).

2D stress state at a point. All stresses in MPa.

σx — Normal Stress X (MPa)

σy — Normal Stress Y (MPa)

τxy — Shear Stress (MPa)

⚙ Mechanical Note: Results are based on standard textbook formulas and ISO/AASHTO references. Always verify critical designs with applicable codes (ISO 898, AASHTO 1993, AISC, Eurocode 3) and a qualified engineer.

How to Use

Enter the values for the patient or scenario you are assessing. Calculate column slenderness ratio λ = KL/r. Effective length factors K: pinned-pinned K=1.0, fixed-free K=2.0, fixed-pinned K=0.7, fixed-fixed K=0.5. Maximum λ for steel: 200 (compression members), 300 (tension). Use the slenderness ratio result to inform your clinical assessment.

Related Calculators

Euler Buckling

Engineering

Moment of Inertia

Engineering

Section Modulus

Engineering

Column Slenderness Ratio Calculator

How to Use

Related Calculators

Frequently Asked Questions

What is the significance of slenderness ratio?

What effective length factor K should I use?

Which axis governs column buckling?