Analysis and Design Assumptions for Continuous Cold-Formed Purlins

In the design of continuous roof purlins or wind girts made of cold-formed steel members, several assumptions in analysis and design are commonly made. Typically, these continuous members are Z- or C­ shaped. Continuous through fastening between cold-formed decks or panels and one of the flanges of the purlin or girt has been the usual method of providing lateral bracing. With the increasing popularity of standing-seam roofs, discrete point bracing of the underlying roof purlins is becoming fairly common. In either case, because the bending moment changes sign in these continuous elements, there are regions where the compression flange is not continuously braced. The lateral-torsional buckling mode of failure frequently governs design strength. This paper addresses the assumptions made in the analysis and design of these continuous elements, shows the effects and questions the appropriateness of many of the assumptions, and presents safety concerns. The examples presented are for continuous Z-purlins subjected to gravity loading. The conclusions reached, however, are entirely applicable to other shapes, other loading, and other applications, such as continuous girts. Typical cold-formed steel construction of roofing or siding is accomplished with continuous roof purlins or wind girts supporting the outer skin of the structure. Cold-formed C- and Z-sections are well suited to this application because they are easily nested. Therefore, continuity over a support can easily be accomplished by overlapping the sections and field bolting them together. The Z-section has the additional advantage of being able to have large quantities nested for ease of trans­ porting to the site. Furthermore, both flanges of the Z are eas­ ily accessible for attachment to the skin as well as the sup­ porting structure. Z-sections will be used for the examples in this paper, but all the methods used and conclusions reached are applicable to other shapes. Consider a continuous beam having Z-shaped cross sections such as the one shown in Fig. 1. Most suppliers of these Z­ sections will have an array of shapes with the same overall dimensions (D, B, d, and 8), but of varying thickness (gauge), t. This enables an ease of lapping such purlins, as shown by the dashed lines in this figure. Fig. 2 shows a typical span of a continuous row of purl ins. Most programs used in the design of the purlins permit each individual span to have its own purlin size as well as individual left and right lap lengths. This paper uses continuous purlins as illustrations, but it should be noted that continuous girts subjected to wind pressure loading present exactly the same problems addressed in this paper. The American Iron and Steel Institute (AISI) presents spec­ ifications for designing these bending elements. The 1986 edi­ tion of the AISI "Specification for the Design of Cold-Formed Steel Structural Members" (AISI 1986), published in 1986 (with an addendum in 1989), was the governing specification until very recently. In 1993, AISI published a guide for pre­ liminary design of cold-formed steel C- and Z-members (AISI 1993). The current edition of the specification is dated 1996 (AISI 1996), but had a first printing in June 1997. AISI pre-