Lateral-torsional buckling modification factor Cb to AISC 360-16 Section F1, Eq. F1-1, from quarter-point moments. Open the free template and run it.
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About this Lateral-Torsional Buckling Modification Factor Calculator
This calculator gives the lateral-torsional buckling modification factor C_b for a nonuniform moment diagram between braced points, to AISC 360-16 Section F1, Eq. F1-1. C_b raises the lateral-torsional buckling strength of a segment whose moment varies along its length: a uniform moment gives the base value, and a steeper moment gradient gives more. Enter the absolute values of the maximum moment and the moments at the quarter, centre and three-quarter points of the unbraced segment.
- Steel beam designer gets C_b for each unbraced segment before checking flexural strength under Sections F2 to F5.
- Connection and bracing engineer sees how adding or moving a brace point changes the moment shape and the benefit C_b gives.
- Plan checker confirms the C_b used in a submission from the four moments, with the moment ordinates drawn to scale.
A diagram shows the moments at the quarter points against the maximum moment for the segment. It is an engineering-grade calculation you can duplicate and adapt in a CalcTree workspace.
More info on the Lateral-Torsional Buckling Modification Factor
Inputs
The inputs are the absolute values of four moments in the unbraced segment: the maximum moment M_max, and M_A, M_B and M_C at the quarter point, centreline and three-quarter point. The segment is taken between braced points, with both ends braced.
Equation F1-1
C_b is 12.5 M_max divided by the sum of 2.5 M_max, 3 M_A, 4 M_B and 3 M_C. The factor weights the maximum moment against the moments at the quarter points, and the centreline moment carries the most weight.
Using C_b in Chapter F
C_b multiplies the lateral-torsional buckling strength of Sections F2 to F5. The resulting strength remains capped at the plastic moment, so C_b cannot raise the nominal flexural strength beyond it. C_b may conservatively be taken as 1.0 in all cases.
Common Calculation Errors to Avoid
- Using signed moments Eq. F1-1 takes absolute values of all four moments. Entering a negative moment for a reversing diagram gives a wrong, sometimes very large, factor.
- Taking moments over the whole span instead of the segment M_A, M_B and M_C are at the quarter points of the unbraced segment between braces, not of the beam span.
- Letting C_b push strength past the plastic moment The amplified lateral-torsional buckling strength is capped at the plastic moment.
- Applying Eq. F1-1 to a cantilever with a free unbraced end For a cantilever or overhang whose free end is unbraced, take C_b as 1.0.
Engineering templates
Common calculators
Design guides
FAQs
What does C_b represent?
It accounts for the benefit of a nonuniform moment diagram on lateral-torsional buckling. A segment under uniform moment is the worst case, and a segment whose moment varies along its length buckles at a higher moment, which C_b reflects.
Can I just use 1.0?
Yes. AISC 360-16 Section F1 allows C_b to be taken conservatively as 1.0 in all cases. Calculating it is worth it when the moment varies along the segment and lateral-torsional buckling governs.
Why are the moments absolute values?
Eq. F1-1 is written for absolute values of M_max, M_A, M_B and M_C. This keeps the factor meaningful for diagrams that change sign within the segment.
Where are the quarter points measured?
Along the unbraced segment between braced points, not along the full beam span. If you add a brace, the segment and its quarter points change.
What about cantilevers?
For a cantilever or overhang whose free end is unbraced, take C_b as 1.0.
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