Stability analysis and modelling of a structure with corrugated roof

Abstract: Corrugated galvanized iron (CGI), or corrugated sheet metal, is a lightweight roofing material that was invented in the early 1800s. The corrugation gives the steel an increased flexural strength in its installed direction and thus increases the amount of load the CGI-plate is able to carry and the span it can be effective at. Thanks to its light weight, corrugated sheet is one of the most commonly used roofing materials for warehouses and other large premises in Sweden as of today. When the CGI-plate is installed as the roof, it is typically screwed to the top-chord of a roof truss. When installed, the sheeting is stiff, but its in-plane stiffness decreases when deformation occurs, due to second-order effects. Since it is connected to the top chord, its in-plane stiffness is also dependent of the top-chords deformation. Consequently, this will affect its stabilizing capabilities in a negative way and the rigidity may not be sufficient to prevent buckling of the trusses’ compressed parts. To counteract this phenomenon, it is usually recommended to either use a thicker profile for the CGI-sheets or to use some type of horizontal bracing in the plane of the roof. To examine how the buckling of the top chord would affect a structure like this, a model of a part of a typical warehouse was designed in the program ROBOT to decide the dimensions of the structural components. The model included three roof truss beams on supports, and the CGIroof placed on top of the truss beams. When all building elements were designed, the same part of the warehouse was modelled in the program Abaqus. Apart from analyzing the buckling behavior, another important objective was to gain more knowledge about how a roof of this type should be modelled in Abaqus and how much the CGI-thickness and the flexibility of the connectors used to fasten the roof would affect the results. The simulation made in Abaqus consisted of: first order (small displacement) linear analysis, large displacement non-linear analysis, linear buckling analysis and a non-linear buckling analysis. The linear buckling analysis showed that, for the most relevant load cases, it is in fact not the top-chord of the truss that will buckle, but instead the bottom-chord of the middle-truss. The buckling load found represents a load of approximately 5,5 times a design load case. Three different models of the roof were tested, one where the roof was modelled with a large number of CGI-plates, one with only two large CGI plates and one with only one big CGI plate. The aim was to examine if there was any difference in the result between the different modelling approaches. The different analyses showed that the configuration of the CGI-sheets did not have any major impact on the result. The buckling load and the deformation pattern of the structure changes with the connector stiffness since the load distribution changes with it. With rigid connections the applied distributed load on the roof was distributed to the three main trusses as 20/60/20%. More flexible connectors changed the distribution to 25/50/25% instead, with marked changes of the deformation pattern. The buckling load also changes with the connector stiffness, since lesser load is distributed to the middle truss with more flexible connectors. The more flexible connectors allow the elements to move which makes them a bit more flexible which also increases the buckling load. When the sheeting thickness was increased the result showed that the load distribution was changed to resemble a 33/33/33% distribution. This changed the deformation of the structure, but it could be concluded that the deformation decreases everywhere except on the outer topchord, because of the change in load distribution. The buckling load increased with thicker CGI-sheets. With a four times thicker CGI-plates the buckling load increased with 8,5%, which is not much considering the cost for the extra material. The results from the thesis are based on ideal conditions and should be considered as indicator for how it would behave in the real world with imperfections, horizontal loads, different spans and profiles. However, it is concluded that the bottom-chord rather than the top chord is of concern as regards the risk of buckling and should be braced when designing structures of this kind.