The behavior of thin-walled cold formed channel and Z-sections, braced on their upper flange by light-gage steel diaphragms under static loading is studied. The objective of the study is to obtain mathematical solutions, to verify these solutions by tests, and to derive design formulations for the bending behavior of channel and Z-section beams with various boundary conditions. This type of structural element is encountered as purlins and girts to support the roof cover and siding of metal buildings. The roof cover is connected to the upper flange of the purlins and gives rise to the case of braced compression flange when the system is under gravity loading. Similarly, for the uplift caused by wind forces, the beam is braced on its tension flange. The bracing capability of the diaphragms is due to their shear rigidity and/or due to the rotational restraints at the beam diaphragm connection. The effect of the shear rigidity as well as of the rotational restraint on the load carrying capacity of the beams have been investigated. Since in some applications, the lower flange of the beam which is not connected to the diaphragm is braced by X-bracings or sag rods, the additional effect of this discrete bracing is also included in this study. The differential equation of the diaphragm braced channel and Z-section beams have been derived and a series solution has been obtained by the Galerkin Method. Based on these studies, a computer program is written for the determination of the yield load of the beam. The program is capable of considering any desired number of terms in the series solution and in many cases, it is sufficient to use but a few terms of the series. The computer program is sufficiently general to include the effect of all geometric parameters. Using a single term solution of the differential equation, design formulas for the yield moment are derived for the beams considered. The designer is thus given the choice of using these simple formulas or the computer program if he desires more accurate analysis. Based on theoretical and experimental results, pertinent conclusions are obtained and recommendations for further studies are included.


Civil, Architectural and Environmental Engineering

Research Center/Laboratory(s)

Wei-Wen Yu Center for Cold-Formed Steel Structures



Publication Date


Document Version

Final Version

Document Type

Report - Technical

File Type