INTRODUCTION Cold-formed steel lipped channel (C-) and Z-purlins are used widely in the roofs of metal buildings. They are easy and economical to fabricate and erect. However these sections are weak in the lateral direction and in torsion. In order to use their full bending capacity in the strong direction, they must be braced in the lateral direction and against twisting. Roof panels which are connected to the purlins do provide to some extent such bracing effect by virtue of their shear rigidity and resistance to local bending at the connections. Wind uplift is an important design condition for roof purlins. The objective of the research reported herein was to develop simple design equations for C- and Z-purlins subjected to uplift. The previous work reported in Refs. 2 through 4 based on the classical theory of torsional-flexure resulted in computer programs for the analysis of the problem. The classical theory of torsional-flexure due to its complexity was not suitable for treating the effects of local buckling and post-buckling behavior on the overall behavior. Furthermore, this approach was not extended to include the effects of initial sweep and twist of purlins. The importance of these parameters was observed in several large scale tests. The theory was shown to be satisfactory for predicting deflections but not the ultimate loads. The discrepancies were larger for thinner sections indicating the importance of local behavior of the component plate elements of the sections. In the first phase of the present research reported in Ref. 1, work was initiated to include the above parameters in a design formulation. The basic approach used in Ref. 1 was that given in Section 3 of Part III of Ref. 5. This approach also has several deficiencies. First, a sudden bifurcation type is the basic behavior mode assumed in that approach. Namely, it is assumed that the compression flange of a purlin does not deflect laterally until failure. The actual behavior is clearly not so. The compression flange deflects laterally from the start of loading. Second, the effect of initial sweep and twist is not accounted for. These and several other additional deficiencies of that approach have been eliminated by the new approach derived in the present research. This new approach will be discussed in detail in Chapter 2. Failure criteria will also be discussed in this chapter. Simplications to the general solutions obtained in Chapter 2 will be presented in Chapter 3. Large scale and component tests by the authors and by a steel manufacturer will be described in Chapter 4. The experimental and analytical results will be compared in Chapter 5. Finally, a summary of the work and the conclusions will be presented in Chapter 6.


Civil, Architectural and Environmental Engineering

Research Center/Laboratory(s)

Wei-Wen Yu Center for Cold-Formed Steel Structures


American Iron and Steel Institute
Metal Building Manufacturers Association



Publication Date


Document Version

Final Version

Document Type

Report - Technical

File Type




Technical Report Number

Report No. 81-2