LTB Moment-Gradient Factor Cb (AISC 360 Eq. F1-1)
The moment-gradient factor Cb for a lateral-torsional buckling check, instead of the conservative default of 1.0.
Example
You enter
- Max moment in the unbraced segment Mmax (kip-ft) 100
- Moment at the quarter point MA (kip-ft) 75
- Moment at midspan MB (kip-ft) 100
- Moment at the three-quarter point MC (kip-ft) 75
You get
- Moment-gradient factor Cb 1.136
Details, formula, and sources
AISC 360 Eq. F1-1: Cb = 12.5 Mmax / (2.5 Mmax + 3 MA + 4 MB + 3 MC), the absolute moments at the max and the quarter/mid/three-quarter points of the unbraced segment (Rm = 1, doubly symmetric). It rewards a non-uniform moment: uniform moment gives 1.0, a simple-span uniformly loaded beam braced only at its ends gives 1.14, and a midspan-peaked diagram goes higher -- each a direct multiplier on the LTB nominal moment. Because Mmax is the largest moment in the segment, Cb is at least 1.0. Feed it into the lateral-torsional buckling check; recompute per unbraced segment. A design aid, not the engineer of record's stamped design.
Cb = 12.5 Mmax / (2.5 Mmax + 3 MA + 4 MB + 3 MC), absolute moments at the max and the quarter (MA), mid (MB), and three-quarter (MC) points of the unbraced segment; Rm = 1 (doubly symmetric).
The AISC 360-22 Eq. F1-1 lateral-torsional-buckling moment-gradient factor Cb, by name.
AISC 360 is free to read at aisc.org (Specification for Structural Steel Buildings); Eq. F1-1 is in Chapter F. The four segment moments are the user's own analysis results.
Estimate. AHJ and licensed professional govern.
Field names used by the API: mmax, ma, mb, mc, cb
- Moment-gradient factor Cb = 12.5 Mmax / (2.5 Mmax + 3 MA + 4 MB + 3 MC)AISC 360-22 Eq. F1-1
- Absolute moments MA, MB, MC at the 1/4, 1/2, 3/4 points of the unbraced segment; Rm = 1 for a doubly symmetric shapeAISC 360-22 F1
- Bounds uniform moment -> 1.0; Cb >= 1.0 since Mmax is the segment maximum; feeds steel-beam-ltbAISC 360-22 F1 / scope of this tile