For a member subjected to flexure, the bending strength depends on the shape of the member, width/ thickness or depth/ thickness ratios of its elements, location and direction of loading, and the support given to the compression flange.

Higher strengths are assigned to symmetrical and compact shapes. Flexural strength may be reduced, however, based on the spacing of lateral supports that prevent displacement of the compression flange and twist of the cross section.

## Compact Shapes

The AISC LRFD and ASD specifications define compact sections similarly: Compact sections are sections capable of developing a fully plastic stress distribution and possess a rotation capacity of about 3 before the onset of local buckling. Rotational capacity is the incremental angular rotation that a section can accept before local failure occurs, defined as R = ( @u / @p) - 1, where @u is the overall rotation attained at the factored-load state and @p is the idealized rotation corresponding to elastic-theory deformations for the case where the moment equals Mp , the plastic bending moment (Sec. 6.17.2).

A section is considered compact if its flanges are continuously connected to its web or webs and the width/ thickness or depth/ thickness ratios of its compression elements do not exceed the following: for the flanges of beams, rolled or welded, and channels, 65/F , y and for the flanges of box and hollow structural sections of uniform thickness, 190/F , y where Fy is the minimum specified yield stress of the flange steel. The limiting depth/ thickness ratio of webs is 640/F . (See also Art. 6.23 and Table 6.28.) y For flanges of I-shaped members and tees, the width is half the full nominal width for rolled shapes and the distance from the free edge to the first line of fasteners or welds for built-up sections. For webs, the depth is defined in LRFD as the clear distance between flanges less the fillet or corner radius for rolled shapes; and for built-up sections, the distance between adjacent lines of fasteners or the clear distance between flanges when welds are used. In ASD, the depth is defined as the full nominal depth.

## LRFD Bending Strength

According to the AISC LRFD specification, the flexural design strength for a compact shape is determined by the limit state of lateral-torsional buckling with an upper limit of yielding of the cross section.

For singly symmetrical I-shaped members with the compression flange larger than the tension flange, use Sxc (section modulus referred to compression flange) instead of Sx in Eqs. (6.53) and (6.54).

For noncompact shapes, consideration should be given to the reduction in flexural strength because of local buckling of either the compression flange or the compression portion of the web. Appendix F and Appendix G of the AISC LRFD specification provide design guidance for evaluating the strength of such members.

Because of the enhanced lateral stability of circular or square shapes and shapes bending about their minor axis, the nominal moment capacity is defined by Mn Mp , where Mp is evaluated for the minor axis and @ = 0.90. Also, Mp is limited to 1.5Fy .

## ASD Bending Stresses

The ASD requirements for bending strength follow, in concept, the LRFD provisions in that allowable stresses are defined based on the member cross section, the width/ thickness and depth/ thickness ratios of its elements, the direction of loading, and the extent of lateral support provided to the compression flange.

The allowable bending stress for a compact shape depends on the laterally unsupported length L of the compression flange. The allowable stress also depends on the stiffness of the compression part of the cross section as measured by L/ rT , where rT is the radius of gyration of a section comprising the compression flange and one-third of the web area in compression,

taken about an axis in the plane of the web.

The largest bending stress permitted for a compact section symmetrical about and loaded in the plane of its minor axis is

The AISC specifications for structural steel buildings do not require lateral bracing for members having equal strength about both major and minor axes, nor for bending about the weak axis when loads pass through the shear center.

For I- and H-shape members symmetrical about both axes, with compact flanges continuously connected to the web and solid rectangular sections subjected to bending about the minor axis, the allowable bending stress is

Fb = 0.75Fy

This stress is also permitted for solid round and square bars.

For shapes not covered in the preceding, refer to the AISC specifications for structural steel buildings.