8.2approximate inelastic moment redistribution

The required flexural strength of indeterminate beams composed of compact sections, as defined in Section B4.1, carrying gravity loads only, and satisfying the unbraced length requirements provided in this section, is permitted to be taken as nine-tenths of the negative moments at the points of support, produced by the gravity loading and determined by an elastic analysis satisfying the requirements of Chapter C, provided that the maximum positive moment is increased by one-tenth of the average negative moment determined by an elastic analysis. This moment redistribution is not permitted for moments in members with $F_{y}$ exceeding 65 ksi (450 MPa), for moments produced by loading on cantilevers, for design using partially restrained (PR) moment connections, or for design by inelastic analysis using the provisions of Appendix 1.3. This moment redistribution is permitted for design according to Section B3.1 (LRFD) and for design according to Section B3.2 (ASD). The required axial strength shall not exceed $0.15 \phi_{c} F_{y} A_{g}$ for LRFD or $0.15 F_{y} A_{g} / \Omega_{c}$ for ASD, where $\phi_{c}$ and $\Omega_{c}$ are determined from Section E1, $A_{g}=$ gross area of member, in. ${ }^{2}$ $\left(\mathrm{mm}^{2}\right)$, and $F_{y}=$ specified minimum yield stress, ksi (MPa).

The laterally unbraced length, $L_{b}$, of the compression flange adjacent to the redistributed end moment locations shall not exceed $L_{m}$ determined as follows.

• (a) For doubly symmetric and singly symmetric I-shaped beams with $I_{y c}$ of the compression flange equal to or larger than $I_{y t}$ of the tension flange loaded in the plane of the web

(A-8-9)

• (b) For solid rectangular bars and for rectangular HSS and symmetric box beams bent about their major axis

(A-8-10)

where

$F_{y}=$ specified minimum yield stress of the compression flange, ksi (MPa)

$M_{1}=$ smaller moment at end of unbraced length, kip-in. (N-mm)

$M_{2}=$ larger moment at end of unbraced length, kip-in. (N-mm)

(

$\begin{aligned} r_{y} & =\text { radius of gyration about } y \text {-axis, in. (mm) } \\ \left(M_{1} / M_{2}\right) & \text { is positive when moments cause re }\end{aligned}$

$\left(M_{1} / M_{2}\right)$ is positive when moments cause reverse curvature and negative for single curvature

There is no limit on $L_{b}$ for members with round or square cross sections or for any beam bent about its minor axis.

COMMENTARY on the Specification for Structural Steel Buildings

August 1, 2022

(The Commentary is not a part of ANSI/AISC 360-22, Specification for Structural Steel Buildings, but is included for informational purposes only.)

INTRODUCTION

The Specification is intended to be complete for normal design usage.

The Commentary furnishes background information and references for the benefit of the design professional seeking further understanding of the basis, derivations, and limits of the Specification.

The Specification and Commentary are intended for use by design professionals with demonstrated engineering competence.

COMMENTARY SYMBOLS

The Commentary uses the following symbols in addition to the symbols defined in the Specification. The section number in the right-hand column refers to the Commentary sec- tion where the symbol is first used.

COMMENTARY GLOSSARY

The Commentary uses the following terms in addition to the terms defined in the Glossary of the Specification.

• Alignment chart. Nomograph for determining the effective length factor, K, for some types of columns.

Biaxial bending. Simultaneous bending of a member about two perpendicular axes.

Brittle fracture. Abrupt cleavage with little or no prior ductile deformation.

• Column curve. Curve expressing the relationship between axial column strength and slenderness ratio.

• Critical load. Load at which a perfectly straight member under compression may either assume a deflected position or may remain undeflected, or a beam under flexure may either deflect and twist out-of-plane or remain in its in-plane deflected position, as determined by a theoretical stability analysis.

• Drift damage index. Parameter used to measure the potential damage caused by interstory drift.

• Effective moment of inertia. Moment of inertia of the cross section of a member that remains elastic when partial plastification of the cross section takes place, usually under the combination of residual stress and applied stress; also, the moment of inertia based on effective widths of elements that buckle locally; also, the moment of inertia used in the design of partially composite members.

• Effective stiffness. Stiffness of a member computed using the effective moment of inertia of its cross section.

• Fatigue threshold. Stress range at which fatigue cracking will not initiate regardless of the number of cycles of loading.

• First-order plastic analysis. Structural analysis based on the assumption of rigid-plastic behavior—in other words, that equilibrium is satisfied throughout the structure and the stress is at or below the yield stress—and in which equilibrium conditions are formulated on the undeformed structure.

• Flexible connection. Connection permitting a portion, but not all, of the simple beam rotation of a member end.

• Inelastic action. Material deformation that does not disappear on removal of the force that produced it.

• Interstory drift. Lateral deflection of a floor relative to the lateral deflection of the floor immediately below, divided by the distance between floors, $\left(\delta_{n}-\delta_{n-1}\right) / h$.

• Permanent load. Load in which variations over time are rare or of small magnitude. All other loads are variable loads.

• Plastic plateau. Portion of the stress-strain curve for uniaxial tension or compression in which the stress remains essentially constant during a period of substantially increased strain.

• Primary member. For ponding analysis, beam or girder that supports the concentrated reactions from the secondary members framing into it.

• Residual stress. Stress that remains in an unloaded member after it has been formed into a finished product. (Examples of such stresses include, but are not limited to, those induced by cold bending, cooling after rolling, or welding.)

• Rigid frame. Structure in which connections maintain the angular relationship between beam and column members under load.

• Secondary member. For ponding analysis, beam or joist that directly supports the distributed ponding loads on the roof of the structure.

• Sidesway. Lateral movement of a structure under the action of lateral loads, unsymmetrical vertical loads, or unsymmetrical properties of the structure.

• Sidesway buckling. Buckling mode of a multistory frame precipitated by the relative lateral displacements of joints leading to failure by sidesway of the frame.

• Shape factor. Ratio of the plastic moment to the yield moment, $M_{p} / M_{y}$, also given by $Z / S$.

• St. Venant torsion. Portion of the torsion in a member that induces only shear stresses in the member.

• Strain hardening. Phenomenon wherein ductile steel, after undergoing considerable deformation at or just above yield point, exhibits the capacity to resist substantially higher loading than that which caused initial yielding.

• Stub-column. A short compression test specimen utilizing the complete cross section, suf- ficiently long to provide a valid measure of the stress-strain relationship as averaged over the cross section, but short enough so that it will not buckle as a column in the elastic or plastic range.

• Total building drift. Lateral frame deflection at the top of the most occupied floor divided by the height of the building to that level, $\Delta / H$.

• Undercut. Notch resulting from the melting and removal of base metal at the edge of a weld. Variable load. Load with substantial variation over time.

• Warping torsion. Portion of the total resistance to torsion that is provided by resistance to warping of the cross section.