In buckling of flat, thin compression elements in beams and columns, the flat-width ratio w/ t is an important factor. It is the ratio of width w of a single flat element, exclusive of any edge fillets, to the thickness t of the element (Fig. 8.4). Local buckling of elements with large w/ t may be resisted with stiffeners or bracing.
Flat compression elements of coldformed structural members are accordingly classified as stiffened or unstiffened.
Stiffened compression elements have both edges of the element parallel to the direction of stress stiffened by a web, flange, or stiffening lip. If the sections in Fig. 8.1a to n are used as compression members, the webs are considered as stiffened compression elements.
The wide, lipless flange elements and the lips that stiffen the outer edges, however, are unstiffened elements. Any section can be broken down into a combination of stiffened and unstiffened elements.
Only part of an element may be considered effective under compression in computation
of net section properties. The portion that may be treated as effective depends on w/ t for the element.
The cold-formed structural cross sections shown in Fig. 8.5 indicate that the effective portions b of the width of a stiffened compression element are considered to be divided into two parts, located next to the two edge stiffeners of that element.
(A stiffener may be a web, another stiffened element, or a lip in beams. Lips in these examples are presumed to be fully effective.) In computation of net section properties, only the effective portions of stiffened compression elements are used and the ineffective portions are disregarded. For beams, because flange elements subjected to uniform compression may not be fully effective, reduced section properties, such as moments of inertia and section moduli, must be used. For computation of the effective widths of webs, see Art. 8.7. Effective areas of column cross sections are based on full cross-sectional areas less all ineffective portions for use in the formula for axially loaded columns, Eq. (8.22), in Art. 8.13.
The critical load, Pcr , kips, for elastic flexural buckling of a bar of uniform cross section, concentrically end loaded as a column, is given by the Euler formula: