F1General provisions

The design flexural strength, fbMn, and the allowable flexural strength, Mn Ω, shall b be determined as follows:

(a) For all provisions in this chapter

φb = 0.90 (LRFD) Ωb = 1.67 (ASD)

and the nominal flexural strength, $M_{n}$, shall be determined according to Sections F2 through F13.

• (b) The provisions in this chapter are based on the assumption that points of support for beams and girders are restrained against rotation about their longitudinal axis.
• (c) For singly symmetric members in single curvature and all doubly symmetric members

The lateral-torsional buckling modification factor, $C_{b}$, for nonuniform moment diagrams when both ends of the segment are braced is determined as follows:

(F1-1)

where

• $\begin{aligned} M_{\max } & =\text { absolute value of maximum moment in the unbraced segment, kip-in. } \\ & \text { (N-mm) }\end{aligned}$
• $\begin{aligned} M_{A} & =\text { absolute value of moment at quarter point of the unbraced segment, } \\ & \text { kip-in. (N-mm) }\end{aligned}$
• $\begin{aligned} M_{B} & =\text { absolute value of moment at centerline of the unbraced segment, kip- } \\ & \text { in. (N-mm) }\end{aligned}$
• $\begin{aligned} M_{C} & =\text { absolute value of moment at three-quarter point of the unbraced segment, kip-in. (N-mm) }\end{aligned}$

User Note: For doubly symmetric members with no transverse loading between brace points, Equation F1-1 reduces to 1.0 for the case of equal end moments of opposite sign (uniform moment), 2.27 for the case of equal end moments of the same sign (reverse curvature bending), and to 1.67 when one end moment equals zero. For singly symmetric members, a more detailed analysis for $C_{b}$ is presented in the Commentary. The Commentary provides additional equations for $C_{b}$ that provide improved characterization of the effects of a variety of member boundary conditions.

For cantilevers where warping is prevented at the support and where the free end is unbraced, $C_{b}=1.0$.

• (d) In singly symmetric members subjected to reverse curvature bending, the lateral-torsional buckling strength shall be checked for both flanges. The available flexural strength shall be greater than or equal to the maximum required moment causing compression within the flange under consideration.