Steel Beam Lateral-Torsional Buckling (AISC 360 F2)
The moment the actual bracing allows - the check steel-beam-flexure defers: an unbraced compression flange buckles sideways below the plastic moment. AISC F2 grades the unbraced length against Lp = 1.76 ry sqrt(E/Fy) and the F2-6 Lr; between them Mn falls linearly, beyond Lr the elastic Fcr governs. A W18x50 braced every 10 ft drops from 421 to 360 kip-ft, and at 20 ft to 200 - less than half the braced number, the cliff that forces a brace or a heavier shape. Doubly-symmetric compact I-shapes, entered Cb. A design aid, not the engineer of record's stamped design.
Formula and source
Mp = Fy Zx; Lp = 1.76 ry sqrt(E/Fy); Lr per AISC Eq. F2-6 (c = 1); Lb <= Lp: Mn = Mp; Lp < Lb <= Lr: Mn = Cb[Mp - (Mp - 0.7 Fy Sx)(Lb - Lp)/(Lr - Lp)] <= Mp; Lb > Lr: Fcr = Cb pi^2 E/(Lb/rts)^2 sqrt(1 + 0.078 Jc/(Sx ho)(Lb/rts)^2), Mn = Fcr Sx <= Mp. ASD = Mn/1.67; LRFD = 0.90 Mn. (E = 29,000 ksi)
The AISC 360-22 Section F2 lateral-torsional buckling provisions for a doubly-symmetric compact I-shape bending about its strong axis (Lp, the Eq. F2-6 Lr, the linear inelastic branch, and the Eq. F2-4 elastic critical stress with c = 1), by name; E = 29,000 ksi and the Omega_b = 1.67 / phi_b = 0.90 factors are named constants.
Audience
This tile is built for trades and the adjacent professions in the Carpentry and Construction group. The interactive calculator runs entirely in your browser. No account, no fee, no advertising, no tracking.
Related tools
Posture
Rough Logic answers the math question the working professional asks on the job. The site is a calm, fast, ad-free, account-free, ever-free reference. It does not interpret code. It does not replace the licensed professional. It does not store your inputs. The Authority Having Jurisdiction governs all installations and inspections.