Elastic Stability Of Cold-formed C And Z Purlins Under Wind Suction

An unfavorable state of purlins appears in the situation under wind suction. The common used cold formed channel and z purlins are non-biaxial symmetrical sections and in most cases being thin-walled and open sections, and are extremely flexible and weak in resistance to torsion, so that they are often liable to suffer torsional-flexural buckling. The current achievements of purlins are mainly obtained by numerical means or experiments so that cannot grasp key points of torsional-flexural buckling. This paper analyzed the instability of cold-formed C-and Z-purlins under wind suction and established a theoretical model of purlins whose lateral displacement of top flange is prohibited, with ignoring the rotation restraint supplied by the sheeting. Based on the buckling theory of thin-walled members, this paper derived the total potentials of cold-formed purlins by considering nonlinear strains. Applying the Galerkin’s technique, the buckling moments of the purlins without bracing and purlins with an anti-sag bar at mid-span section were obtained. The results were compared with numerical results using shell elements of ANSYS. Through multiplying the linear horizontal reaction factors with a correction coefficient, the obtained formulae were found to be in excellent agreement with ANSYS. As to purlins with an anti-sag bar at mid-span section, the method of judging critical moments of different buckling mode was got also. The effects of anti-sag bars were analyzed by contrasting the critical moments of purlins without bracing and purlins with an anti-sag bar at mid-span section. The variation laws of critical moments with the anti-sag bar on different locations of the web was obtained too.