C-F2F2 Doubly symmetric compact I-shaped members and channels bent about their major axis

Section F2 applies to members with compact I-shaped or channel cross sections subjected to bending about their major axis; hence, the only limit state to consider is lateral-torsional buckling. Almost all rolled wide-flange shapes listed in the AISC Steel Construction Manual (AISC, 2017) are eligible to be designed by the provisions of this section, as indicated in the User Note in this section.

The flexural strength equations in Section F2 are nearly identical to the corresponding equations in Section F1 of the 1999 LRFD Specification (AISC, 2000b), and are the same as those that have been in the Specification since 2005 (AISC, 2005b). Table C-F2.1 gives the list of equivalent equations.

The only difference between the 1999 LRFD Specification and this Specification is that the stress at the interface between inelastic and elastic buckling has been changed from $F_{y}-F_{r}$ in the 1999 edition to $0.7 F_{y}$. In the Specifications prior to the 2005 AISC Specification, the residual stress, $F_{r}$, for rolled and welded shapes was different, namely 10 ksi (69 MPa) and 16.5 ksi (110 MPa), respectively, while since the 2005 AISC Specification the residual stress has been taken as $0.3 F_{y}$ so that the value of $F_{y}-F_{r}=0.7 F_{y}$ is adopted. This change was made in the interest of simplicity; in addition, this modification provides a slightly improved correlation with experimental data (White, 2008).

The elastic lateral-torsional buckling stress, $F_{c r}$, of Equation F2-4,

(C-F2-1)

is identical to Equation F1-13 in the 1999 LRFD Specification:

(C-F2-2)

This equation may be rearranged to the form,

(C-F2-3)

By using the definitions,

$r_{t s}^{2}=\frac{\sqrt{I_{y} C_{w}}}{S_{x}}, C_{w}=\frac{I_{y} h_{o}^{2}}{4}$, and $c=1$

for doubly symmetric I-shaped members, Equation C-F2-1 is obtained after some algebraic rearrangement. Section F2 provides an alternative definition for $c$, based on the expression for $C_{w}$ of channels, which allows the use of Equation C-F2-1 for channel shapes.

TABLE C-F2.1 Comparison of Equations for Nominal Flexural Strength

Equation F2-5 is the same as F1-4 in the 1999 LRFD Specification and Equation F2-6 corresponds to F1-6. It is obtained by setting Fcr = 0.7Fy in Equation F2-4 and solving for Lb. The format of Equation F2-6 was changed for the 2010 AISC Specification (AISC 2010) so that it is not undefined at the limit when J = 0; other- wise, it gives identical results. The term rts can be approximated accurately as the radius of gyration of the compression flange plus one-sixth of the web.

These provisions are much simpler than the previous ASD provisions and are based on a more informed understanding of beam limit states behavior (White and Chang, 2007). The maximum allowable stress obtained in these provisions may be slightly higher than the previous limit of 0.66Fy, because the true plastic strength of the member is reflected by use of the plastic section modulus in Equation F2-1. The Section F2 provisions for unbraced length are satisfied through the use of two equations: one for inelastic lateral-torsional buckling (Equation F2-2), and one for elastic lateral-torsional buckling (Equation F2-3). Previous ASD provisions placed an arbitrary stress limit of 0.6Fy when a beam was not fully braced and required that three equations be checked with the selection of the largest stress to determine the strength of a laterally unbraced beam. With the current provisions, once the unbraced length is determined, the member strength can be obtained directly from these equations.