# Damage Analysis and Evaluation of Light Steel Structures Exposed to Wind Hazards
## 3 Purlin-Sheeting System (Roof/Wall Systems)  
Research of girt and purlin design for wind loads has been investigated for over 50 years. For building structural systems, purlin is a type of secondary element acting as an intermediate member to transfer load from the roof sheeting to the primary frame structure. Common types of purlin sections include channel, zed, and sigma shapes. The open and thin-walled cross section may lead to a high susceptibility to various types of buckling failure, such as local, distortion, and lateral torsional buckling. Roof sheeting, which is normally attached to purlins using self-drilling screws, can enhance a purlin's load resistance by supplying it with a certain degree of lateral and rotational restraining effect. [PERSON] and [PERSON] [29; 30] concluded that the restraints of sheeting to the purlins included four different types of restraining actions: minor axis deflection, minor axis rotation, axial rotation, and warping of the member. The lateral buckling of purlins with diaphragm restraints was studied using finite element analysis. The results show that the effectiveness of diaphragm restraints depends not only on their stiffness but also on their height above the shear center axis of the purlin, and the buckling resistance is significantly increased when the loads act below the shear center. [PERSON] and [PERSON] [31; 32] also proposed a non-linear analysis model that could provide nonlinear response data for screw-fastened purlins under wind uplift loading. Moreover, several experimental tests for both bridged and unbridged Z- and C-section purlins under uplift loads were compared with the model. [PERSON] et al. [33; 34] developed both full and simplified models to study the interaction between the sheeting and purlins using finite element methods. It is found that the simplified model can account for the cross-sectional distortion of the purlin, the shear and rotational restraining effects of the sheeting, and failure of the purlin by local buckling or yielding. Research has continued to focus on validation of the rotational stiffness. [PERSON] and [PERSON] [35] proposed a nonlinear finite element model to estimate the rotational restraint provided by sandwich sheeting. Moreover, the model could be used for parametric studies to investigate the influencing factors. Based on the study of the redistribution of contact forces as a function of loading, [PERSON] [36] proposed an analytical model that can be used for solving the Z-shaped and C-shaped purlins for both gravity and uplift loading. Design codes like EC3 [37] also provided this approach to get the real rotational stiffness of the purlin. [PERSON] and [PERSON] [38; 39] both provided a more precise semi-analytical model to calculate the rotational stiffness of the purlin. For the effect of the restraint effect on the pre-buckling, buckling, or post-buckling behavior of the purlins, [PERSON] et al. [40; 41] studied the influence of diaphragm restraints on the bending, local, and distortion buckling behavior of roof purlins. [PERSON] [42; 43; 44; 45; 46] proposed a series of models to predict pre-buckling stress and buckling types such as local, distortion, and global buckling ability of the partially restrained C-section and Z-section purlins subjected to uplift loadings. [PERSON] and [PERSON] [47; 48; 49] also conducted some tests on the behavior of purlins and applied the GBT theory into the research of purlin-sheeting systems. After [PERSON] [50] had studied the effect of the sag rods on the buckling limit of the purlins, [PERSON] and [PERSON] [51; 52; 53; 54; 55] proposed a theory to analysis the stress and lateral buckling problem of purlins with the top flange horizontally restrained and with one anti-sag bar at middle span sections. [PERSON] and [PERSON] [56] extended the Direct Strength Method into the purlin design. Due to the flexibility of the rotational stiffness, they proposed the rotational stiffness as zero, which induced a result that the method was too conservative.