Lateral bracing has a significant effect on increasing the buckling load of compression members. In the case of wall stud construction, such bracing is provided by wallboards directly attached to the stud along its length and results in increasing the load carrying capacity significantly. The objective of this investigation is to study the behavior of singly symmetric sections braced by shear diaphragms and to apply the theoretical findings verified by experimental results to the design of wall studs. In the present investigation the shear rigidity as well as the rotational restraint of the diaphragm are considered. Using an energy approach, general solutions are obtained for the cases of bracing on one or both sides. Solutions for channel, Z and I-sections are derived as special cases from the general solution. Depending on the relative magnitudes of the diaphragm and column characteristics, higher buckling modes, associated with buckling in more than one half-sine wave, may govern the behavior of the stud. Results of numerical investigations indicate that in some cases of sections braced on one side only, higher buckling modes are as low as 50% of the critical buckling load computed by considering one half-sine wave only. On the other hand, higher buckling modes do not govern the behavior of sections braced on both sides with diaphragms whose characteristics are within the range of wall stud applications. The shear rigidity as well as the rotational restraint of the diaphragm required for prediction of the failure load of the braced stud are determined experimentally using a variety of wallboard materials and fastener spacings. The proposed design procedure is based on the ultimate load capacity of the column, utilizing a conservative estimate of the shear rigidity and rotational restraint of the wallboards acting as bracing diaphragms. The design procedure is applicable to buckling in the elastic and the inelastic domain. Beyond the elastic limit load, the influence of diaphragm bracing is less pronounced and high values of shear rigidity and rotational restraint would be needed to maintain the stability of the stud. Based on the suggested design procedure, four computer programs are prepared for design of wall studs. Design aids in the form of charts and approximate formulas are provided to facilitate the use of the governing equations in predicting the critical buckling load. Tests conducted on a total of 11 double-column assemblies of cold-formed steel sections with diaphragms on one or both sides have shown satisfactory agreement with the theoretical results. This indicates that the proposed design approach appears to be reliable.


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. 353