Buckling of parallel purlins in standing seam or screw-fastened roofs

Purlins are usually connected to roof sheeting by sliding-clips, while wall sheeting is often screw-fastened to girts. This paper investigates the buckling of such two types of parallel purlin/girt systems inter-connected by multiple lines of sag rods. One single purlin braced by one sag rod at any place along the span is first analyzed, and its buckling deformation at any cross-section is seen as a flexibility coefficient which is then used to study the buckling of the purlin braced by multiple sag rods along span. A flexibility matrix is constructed, whose eigenvalues are the base of critical equations. In the case where the sag rods are placed with equal spaces along span, the eigenvalues are expressed in explicit forms, of which each represents one buckling mode. Threshold stiffness of the sag rods are presented for multiple sag rod bracings for these two types of sheet-to-purlin connection. Based on the findings of this paper, the differences of buckling behaviors between these two types of purlin systems have been revealed. The effect of local deformation of the web at the sag rod connecting points on the sag rod stiffness is also included. Parallel purlin systems are then investigated in a compact matrix form. After carrying out matrix operations and slight approximations, a key parameter is found to be used to reflect the effect of the number of purlins and zig-zag layout of sag rods in adjacent bays on the effective sag rod stiffness.