Chapter 8 - Bending Members
© 2006, 2007, 2008, 2011 T. Bartlett Quimby
Compression Flange Local Buckling Limit State
Last Revised: 07/30/2011
Local buckling of the compression flange (FLB) occurs when the width/thickness ratio of the plate elements is high. The general concept was discussed in some detail in the notes on plate buckling. The specific application to flexural members is found in SCM Chapter F. Using SCM Table User Note F1.1 as a reference, one or the other of FLB appears in SCM F3, F4, F5, F6, F7, and F9.
Note that there are a limited number of rolled sections which have problems with FLB and WLB. The SCM user notes in F2, F3, and F6 point out the sections that are likely to have problems with WLB and FLB for a given range of Fy. As Fy increases, more sections become non-compact and slender, thus invoking WLB and FLB limits on strength.
The Limit State
The basic limit state follows the standard form. The statement of the limit states and the associated reduction factor and factor of safety are given here:
The values of Mu and Ma are the LRFD and ASD factored loads, respectively, applied to the flexural member.
In this case Mn is the nominal FLB limited flexural strength of the member. Since this is a buckling phenomenon, limits need to be found for the three strength regions: plastic, inelastic buckling, and elastic buckling as shown in Figure 220.127.116.11.
The General Form
The general form of the FLB limit state follows the typical buckling curve. The slenderness parameter used is width/thickness ratio (b/t) as specified in SCM B4.
The limits of the buckling regions are specified by the terms lp (the limit of the plastic region) and lr (the limit of the inelastic buckling region). Hence:
Figure 18.104.22.168 illustrates the concept.
Both lp and lr are computed using the appropriate cases and equations from SCM Table B4.1.
The moment at the interface of the elastic and inelastic ranges, Mr, is found embedded in the linear interpolation function found in several of the specification sections used to compute the strength in the inelastic buckling range.
As noted above, when l < lp FLB does not happen. Consequently in the plastic range, Mn equals Mp.
In-elastic Buckling Range
Mn = min [(Mp - (Mp - Mr)*(l - lp)/(lr - lp)), Mp]
Mn = FcrRpgSxc = min [(Fy - 0.3Fy (l - lp)/(lr - lp)), Fy] RpgSxc
Mn = min [(Mp - (Mp - Mr)*(l - lp)/(lr - lp)), 1.6My]
Elastic Buckling Range
The nominal moment capacity, Mn, in the elastic range is found by computing the elastic moment that creates the critical buckling stress, Fcr, in the compression flange.
Mn = min[FcrSxc, Mp]
A modified Euler type function is used to the compute the critical buckling stress, Fcr.
Mn = FySe
The following spreadsheet example computes the major axis flexural capacity, Mnx, including FLB effects, for a typical W section. The input values are in the grey shaded cells and the result in the yellow highlighted cell.