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The section's radius of gyration about its minor (weak) axis, from the shape tables.
Read it from the shape table; it is not worth deriving. It is the property lateral-torsional buckling turns on, and a deep girder's weak-axis radius is small — often a twentieth of its depth — which is exactly why an unbraced long span buckles sideways long before it fails in bending. If you find yourself wanting a larger number here, the answer is bracing rather than a different table.
The girder steel's specified minimum yield strength.
The SPECIFIED MINIMUM for the grade, not a mill certificate's actual value — design works from the specified minimum and using a tested figure produces a capacity nobody can rely on for the next piece. Grade 350 and Grade 250 are not interchangeable in a buckling check: the limiting unbraced length falls as the yield rises, so stronger steel buckles sooner.
The steel's modulus of elasticity — 200,000 MPa (29,000,000 psi) is standard for structural steel.
Effectively a constant for structural steel and the same for every grade — strength varies between grades, stiffness does not. That is worth knowing here because it means a higher-grade steel does not buckle later or deflect less; it is the same stiffness with a higher yield, which is why buckling and deflection checks so often govern a design that passes on strength.
Limiting unbraced length (Lp)
5.3 ft
This checks only whether your unbraced length is within Lp (full plastic capacity retained). It is NOT a full moment capacity calculator — once the unbraced length exceeds Lp, the actual reduced capacity requires Lr, Cb, Fcr, and Sx per AISC 360 Eqs. F2-2 through F2-6, which a structural engineer should evaluate.
They open the calculator with your figures already in it
Steel Girder Lateral-Torsional Buckling Limit (Lp) Calculator: 5.3 ft — shown in imperial, US market. The link sets both, so the result they see is the one on your screen.
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How this was calculated
Formula source(s)
- AISC 360 Chapter F, Eq. F2-5: Lp = 1.76×ry×√(E/Fy), the limiting laterally unbraced length below which lateral-torsional buckling does not reduce a doubly-symmetric compact I-shaped member's nominal moment capacity below Mp
Inputs used
- Minor-Axis Radius of Gyration ry
- 1.5 in
- Steel Yield Strength Fy
- 50038.02 psi
- Modulus of Elasticity E
- 29007547.55 psi
Confidence note: This checks only whether your unbraced length is within Lp (full plastic capacity retained). It is NOT a full moment capacity calculator — once the unbraced length exceeds Lp, the actual reduced capacity requires Lr, Cb, Fcr, and Sx per AISC 360 Eqs. F2-2 through F2-6, which a structural engineer should evaluate.
What this calculation does not cover
- Lp is a property of the section and the grade — the only inputs are ry and Fy — so it is a yardstick, not a verdict. What it is compared against is Lb, the distance between points that hold the COMPRESSION flange against lateral movement and against twist, and AISC Appendix 6 puts strength and stiffness requirements on those braces. A joist merely bearing on the top flange, or a tie that sways with it, is not a brace point; assume one that does not qualify and the real Lb is double the length checked here.
- Over a support in a continuous beam, and along a cantilever, the moment reverses and the compression flange is the BOTTOM one — which the slab or deck above does not brace at all. The unbraced length that governs there runs between bottom-flange restraints or torsional restraints at the support, and it routinely decides a beam that looks fully braced along its span.
- Lp moves in direct proportion to ry but only with the square root of E/Fy, so the grade barely lengthens it and readily shortens it: substituting Grade 50 steel for Grade 36 cuts Lp by about 15 per cent. Upgrading the steel to gain moment capacity therefore tightens the bracing that capacity depends on, and a bracing layout drawn for the original grade can be too loose for the stronger one.
Computed in your browser — nothing you enter is uploaded. Presented in US customary units and US trade terminology. Where a formula follows a published standard, that standard and its edition are cited beside it on this page; where none governs, the page says so. Local amendments override model codes — verify against the code in force where you build.
Sources checked 2026-09-06 · in the site-wide review of 2026-09-06 · v1.0.1
Regulatory standards & verification citations1
- AISC 360 Chapter F, Eq. F2-5: Lp = 1.76×ry×√(E/Fy), the limiting laterally unbraced length below which lateral-torsional buckling does not reduce a doubly-symmetric compact I-shaped member's nominal moment capacity below Mp
Which documents these citations point at
Standards referenced: AISC 360 (American Institute of Steel Construction, United States).
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