PREFACE The present Report No. 356 deals with the inelastic reserve strength of cold-formed beams with stiffened compression flanges. The usual elastic design criterion regards the initiation of yielding in the outer fibers as defining failure. This criterion is used in Part I of the A.I.S.C. Specification and in the A.I.S.I. Specification for the design of steel structures. On the other hand, for so-called compact sections, as defined in the A.I.S.C. Specification, it is known that the actual maximum moment of a cross-section exceeds the initial yield moment and is reached only when yielding spreads over the entire section (complete plastification). It is also known that the carrying capacity of continuous compact beams and frames exceeds that calculated from the initial yield criterion, because of (a) the higher carrying capacity of the cross-section and (b) plastic moment redistribution subsequent to plastic hinge formation. Cold-formed sections generally do not fall into the category of compact sections, which should make their inelastic reserve strength smaller than that of hot-rolled shapes. At the same time their neutral axis is frequently not located at mid-depth, which produces initial yielding in one flange only; also, because of constant thickness their web area is frequently relatively larger than in hot-rolled sections. Both these factors tend to increase the inelastic reserve strength as compared to that of doubly symmetrical hot-rolled shapes. It is this situation which necessitates developing an approach very different from that of conventional plastic design. To enable the economical utilization of this reserve strength in design, such an approach is developed and supported by tests in this report. The report covers all phases of this investigation, regardless of whether one or the other particular phase is, at this time, ready for direct application to practical design problems. To enable a design-oriented reader to digest those parts which have the most direct practical implications, this preface attempts to guide such a reader to the relevant portions only. For this purpose, at the end of this preface, those groups of pages are listed which contain the essential portions of the work, omitting subsidiary topics and necessary but complicating refinements of theory. Most stiffened compression flanges with w/t significantly exceeding (w/t)lim as defined in the A.I.S.I. Specifications, do in fact fail when yielding initiates. These flanges, and therefore beams with such compression flanges, have no inelastic reserve capacity if yielding begins in the compression rather than the tension flange. However, flanges with w/t of the order of, or significantly smaller than (w/t)lim continue to carry their compression load after initial yielding is reached and when further yielding occurs. In this case yielding will spread into the web, causing significant inelastic reserve strength. Hence, Chapter II is devoted to the important determination of the amount of additional strain beyond initial yielding which can be sustained before failure by stiffened flanges of moderate or small w/t-ratios. The most important information is contained in Fig. 2-9 and in Eqs. 2.6 and 2.7 on p. 60. As was mentioned before, the inelastic reserve strength of such sections depends not only on this inelastic strain capacity (denoted as critical strain) of the compression flange but also on the location of the neutral axis, i.e., whether yielding will occur first in tension or compression, and also on the relative magnitude of the web area as compared to the flange areas. Chapter III, therefore, determines the ultimate moment of cross-sections, depending on these three enumerated factors. For cross-sections of the general shape of Fig. 3.1 the most important information is contained in Figs. 3.2 through 3.6 which show that inelastic reserve strength, in terms of ultimate moments, of up to 30% and more are entirely realistic. The developed methodology is easily applied to other cross-sectional shapes. These experimentally confirmed reserve strengths can be applied directly to statically determinate beams, i.e., simple, single-span beams or cantilevers. On this basis it would be possible in the Specification to permit conservative increases in allowable bending stresses for beams with stiffened compression flanges of low and moderate w/t-ratios. This may not be desirable at this time until similar information has been obtained for unstiffened compression flanges, which is being developed in a research project now under way at Cornell University. For continuous beams, additional reserve strength can be developed through partial moment redistribution, somewhat similarly as in conventional plastic design of compact, hot-rolled continuous beams. However, the full development of plastic hinges, on which such plastic design is based, is generally not attainable in cold-formed sections with their thinner flanges. Therefore, the amount of moment redistribution that can be attained depends on the amount of rotation or curvature which such sections can develop, beyond initial yielding but prior to compression flange failure. This is the subject of Chapter IV. Chapter V then develops a fairly involved analytical method for calculating the strength of continuous beams based on these plastic rotation capacities. The methodology is general and the most specific information is contained in Fig. 5.5a. It is seen that, for the investigated system, the preponderant portion of the inelastic load factors comes from the inelastic reserve strength of the cross-section (Ch. III), and only a small additional gain is obtained through inelastic moment redistribution. However, this purely analytical information is obtained for beams on idealized knife-edge supports, and it is shown that for realistic beams of finite width of support, significantly larger gains can be achieved (pp. 149-151). Methodology for this is given, but without graphical or otherwise directly usable information. Also, the entire treatment of continuous beams is purely analytical, without experimental confirmation. Therefore, at this time, it is not ready for practical use. It is hoped that time and funds in the previously mentioned research project at Cornell University will permit further work on this sub-topic. With this exposition as a general guide, it is suggested that those readers who want to familiarize themselves only with the essential generalities and details of this report, while omitting information which is secondary either in general or at this time, concentrate on the following portions: Introduction pp. 1-3. Summary pp. 160-165. Ch. I: pp. 4 - 11, 16 - 19, 26 - 28. Ch. II : pp. 29 - 36, 39, 43 - 47, 51 - 66. Ch. III : pp. 67 - 70, 73 - 77, 80 - 86. Ch. IV: pp. 87 - 88, 94 bottom, 96 - 99, 101 - 103. Ch. V: pp. 104 - 109, 129 - 132, 149 - 151. Ch. VI: pp. 162 - 169. This report was originally a thesis presented to the Faculty of the Graduate School of Cornell University for the degree of Doctor of Philosophy, for conferment in June 1974. The research project covered by this report was sponsored by the American Iron and Steel Institute. The valuable cooperation of the Sheet Committees of the American Iron and Steel Institute is gratefully acknowledged.


Civil, Architectural and Environmental Engineering

Research Center/Laboratory(s)

Wei-Wen Yu Center for Cold-Formed Steel Structures


American Iron and Steel Institute



Publication Date


Document Version

Final Version

Document Type

Report - Technical

File Type




Technical Report Number

Report No. 356