Assessment of purlins with paired torsion bracing in sloped roof systems: Direct strength method approach

Abstract

A Direct Strength Method based methodology has been developed by the authors for the prediction of local buckling and distortional buckling strength of purlins with paired torsion bracing. In a previous study, the methodology was presented and discussed for zero slope roof systems in by the authors. In this paper, the authors reformulated the developed methodology to include the effect of slope in the structural behavior of the roof systems. Equations have been developed for the strength prediction of sloped roof systems for simple span and multi-span interior conditions (fixed support conditions at both ends). As downslope forces are introduced to the sloped roof systems, the lateral displacement of the diaphragm is affected, and the stress distributions are impacted along the purlin cross sections. Typically, with the increase in the roof slope, the lateral diaphragm deflection decreases during which the stress distributions approach the constrained bending distribution increasing the strength. When the roof slope is increased further and the lateral deflection of the purlins moves downslope, there is a considerable decrease in the predicted strength. Therefore, for steep roof slopes, a considerable inelastic reserve capacity is observed which when accounted for will improve the predicted strength. The component stiffness method is utilized in the process, considering displacement compatibility for the calculation of the anchorage forces within the purlin system. Partial restraint of the diaphragm that is provided by the sheathing is considered in the procedure. The developed methodology herein this paper incorporates the effects of first-order and approximate second-order torsion for the prediction of the actual stress distributions along purlin cross sections. This stress distribution may significantly differ from the conventionally assumed constrained bending distributions which may result in substantial differences in the predicted local buckling and distortional buckling strengths for purlin systems.