When properly attached, shear-rigid light-gage metal diaphragms, such as roof decking or wall sheathing, can be very effective as lateral bracing for slender columns and beams. At present, limited design use is made of this fact, because of inadequate information on the effectiveness and reliability of such bracing. In this thesis, previous theory on the stability of Isection beams and columns braced with shear-rigid diaphragms has been extended. Two energy methods are used, one employing the Euler-Lagrange conditions from the calculus of variations, and the other the Rayleigh-Ritz method. The problem initially considered is that of an I-section beam-column eccentrically loaded in the plane of the web. This problem is later reduced to two extreme conditions, a column centrally loaded, and a beam sUbjected to uniform bending moment, for which explicit solutions are obtained. A method for handling the beam-column problem is indicated. For a centrally loaded elastic column with continuous shear-rigid bracing symmetrically disposed with respect to the column centroid, previous investigators have determined the augmented weak-axis buckling load as p = pyy + Q where Pyy is the weak-axis buckling load of the unbraced column, and Q is the effective shear rigidity of the bracing. In this investigation, a theoretical solution is obtained for centrally loaded columns with a single diaphragm at any location, considering possible twist of the column. A solution for the torsional-flexural buckling load for centrally loaded columns symmetrically braced by diaphragms is presented also. In addition, previous results for diaphragm-braced columns buckling into multiple half sine waves are modified, and a solution is obtained for buckling of diaphragm-braced columns with an enforced axis of rotation. For diaphragm-braced beams subjected to uniform bending moment, theoretical results are presented for both simply supported end conditions (ends fixed against rotation about the longitudinal axis only), and for ends fixed also against lateral displacement. Inelastic behavior of diaphragm-braced beams and columns is considered. Theoretical results are compared with 16 tests of concentrically loaded double-column assemblies, and 5 tests of diaphragm-braced dOUble-beam assemblies subjected to uniform bending moment. For columns in the elastic range, test results are consistently about 10 percent below predicted values, while the magnitude of the increase over the unbraced strength is several-fold. It is shown that diaphragm bracing can reliably increase the carrying capacity of slender columns up to the elastic limit load. Above the elastic limit load, the influence of diaphragm bracing is much less pronounced, and somewhat less predictable. For beams in the elastic range, test results exceed predicted values obtained neglecting the cross-bending rigidity of the diaphragms, again with a several-fold increase in carrying capacity. The yield moment of beams appears to be readily attainable using shear-rigid diaphragm bracing.


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. 321