2014 Research Reports No R943-R951

Abstract
Insect-borne plant diseases recur commonly in wild plants and in agricultural crops, and are responsible for severe losses in terms of produce yield and monetary return. Mathematical models of insect-borne plant diseases are therefore an essential tool to help predicting the progression of an epidemic disease and aid in decision making when control strategies are to be implemented in the field. While retaining a generalized applicability of the proposed model to plant epidemics vectored by insects, we specifically investigated the epidemics of Flavescence dorée phytoplasma (FD) in grapevine plant Vitis vinifera specifically transmitted by the leafhopper Scaphoideus titanus. The epidemiological model accounted for life-cycle stage of S. titanus, FD pathogen cycle within S. titanus and V. vinifera, vineyard setting, and agronomic practices. The model was comprehensively tested against biological S. titanus life cycle and FD epidemics data collected in various research sites in Piemonte, Italy, over multiple years. The work presented here represents a unique suite of governing equations tested on existing independent data and sets the basis for further modelling advances and possible applications to investigate effectiveness of real-case epidemics control strategies and scenarios.

Keywords
Insect-borne plant disease, Flavescence dorée, Scaphoideus titanus, Vitis vinifera, epidemiological modeling

Abstract
This report presents a comprehensive parametric study on the ultimate strength of perforated cold-formed steel columns using the Finite Element package ABAQUS. FE models were first developed for columns predisposed to local (L), distortional (D) and global (G) buckling failures respectively. Modelling issues such as boundary conditions, meshing, initial imperfections, material models, and non-linear solution controls in FEA were addressed. The FE models were validated against documented experiments and also theoretical solutions.

The parametric study involved five cross-section types (i.e. C, stiffened C, Z, rack, and hat sections), five widths of holes, four lengths of holes, four spacings of holes, three material properties, and three buckling modes (i.e. L, D, and G) and all the possible interactions between them (i.e. LD, LG, DG, and LDG). Ultimate strengths, as well as failure modes, were obtained from the analyses and are plotted against the current codified DSM in AS/NZS 4600:2005. Significant discrepancies between the numerical results and the DSMpredicted strengths were observed due to the influence of holes, and more severely, the interaction of buckling modes, and occasionally, the inherent limitations of the DSM itself. The effects of column length, material properties, centroid shift due to perforation were also discussed. A data pool including 146207 column ultimate strengths was obtained which was used to formulate new design equations for perforated thin-walled columns based on the Direct Strength Method, as presented in another report (Yao and Rasmussen 2014).

Keywords
Cold-formed, Thin-walled, Columns, Perforations, Parametric study, Finite element modelling, Interactive buckling, Direct Strength Method

Abstract
The strength database from the parametric study presented in (Yao and Rasmussen 2014) was used to evaluate an overall number of 19 design methods based on the DSM for non-perforated and perforated thin-walled steel columns with the Ramberg-Osgood material model defined by n=20. These methods included the current codified DSM, the design options proposed by Moen and Schafer (2011), the methods based on simple modifications to these aforementioned methods, the methods considering buckling interactions (in addition to LG interaction), and the methods based on regression analyses.

A concerted effort was made to compare the 19 DSM methods by presenting the detailed statistics of the predictions for each section type and failure mode, as well as figures illustrating the corresponding simulation to predicted ratios. This led to the best-performing method proposed for the design of perforated cold-formed carbon steel columns. This method was based on modifying the Option 4 method proposed by Moen and Schafer (2011) such that (i) DG interaction was included, (ii) Pcr-l-nh and Pcr-d-nh based on gross section were used, and (iii) a factor based on a regression analysis was added to improve the final design strength.

The proposed method was based on a reliability analysis with a target reliability index of 2.5, carried out on 60132 data points. A linear regression equation was taken to calculate the additional factor in the method. Two sets of best-fit constants were proposed for the regression equation, one for general section types including C, Z, Hat, Rack, and Stiffened C sections, the other for Stiffened C section only. When calculating the design strength of a perforated column as per the proposed method, the major effort will be calculating the elastic local and distortional buckling loads Pcr-l-nh and Pcr-d-nh based on the gross section (which can be readily calculated by a SAFSM software such as THIN-WALL or CUFSM), and the elastic global buckling load Pcr-e-h including the influence of hole(s).

Keywords
Cold-formed, Thin-walled, Columns, Perforations, Design, Interactive buckling, Direct Strength Method, Reliability analysis, Resistance factor

Abstract
The buckling and strength capacities of channel members depend on the geometry of the whole section. For channel sections, the shear buckling modes occur mainly in the web. The structural efficiency of the sections in shear can be improved by adding intermediate stiffeners cold-formed longitudinally in the web. Recently, the Direct Strength Method (DSM) of design of cold-formed sections has been extended in the North American Specification for Cold-Formed Steel Structural Members-NAS S100:2012 to include shear. The two new features of the DSM rules for shear researched are the effect of full-section shear buckling as opposed to web-only shear buckling and Tension Field Action (TFA). The prequalified sections in the rules include sections with flat webs and webs with small intermediate longitudinal stiffeners. In order to extend the range to larger intermediate stiffeners as occurs in practice, a series of fourteen shear tests have been performed at the University of Sydney for C-sections with rectangular stiffeners of varying sizes. Six different types of stiffeners were tested with an additional preferred plain section. Each type of sections was tested twice to ensure accuracy. As the web stiffener sizes increase, the shear buckling and strength of the sections are expected to improve accordingly. However, the tests show that the shear ultimate strengths only increase slightly in association with the respective increase of stiffener sizes. The test results are compared with the DSM design rules for shear and found to be lower than those predicted by the DSM curve for shear with TFA. The test failures were observed mainly due to the combined bending and shear modes. The effect of the bending is therefore significant and starts to govern when the shear capacity is significantly strengthened by adding the large longitudinal web stiffener. The test results are subsequently plotted against the DSM interaction curves between bending and shear where the interaction is found to be significant. Modifications and recommendations for prequalified sections with longitudinally stiffened web channels in shear are proposed in the report.

Keywords
Cold-formed sections; High strength steel; Longitudinal web stiffener; Shear strength; Complex channel sections; Direct strength method.

Abstract
Thin-walled sections under localised loading may lead to web crippling of the sections. This report develops the Semi-Analytical Finite Strip Method (SAFSM) for thin-walled sections subject to localised loading to investigate web crippling phenomena. The method is benchmarked against analytical solutions, Finite Element Method (FEM) solutions, as well as Spline Finite Strip Method (SFSM) solutions.

The report summarises the SAFSM theory then applies it to the buckling of plates, and channel sections under localised loading. Multiple series terms in the longitudinal direction are used to compute the prebuckling stresses in the plates and sections, and to perform the buckling analyses using these stresses. Solution convergence with increasing numbers of series terms is provided in the report. The more localised the loading and buckling mode, the more series terms are required for accurate solutions.

Keywords
Thin-walled sections; Localised loading; Buckling analysis; Semi-analytical finite strip method; Spline finite strip method.