| Assembled rack made of cold-formed thin wall steel(CFTWS)has the advantages on its high ratio of strength to mass and convenient installation.It is widely used in the field of logistics and storage,and the most common cross-section of rack's column is ? shape,which is called ?-column.After thin-walled plate is rolled many times to form ?-column,its moment of inertia can be effectively increased in the case of section area unchanged.However,it is found that the capacity of CFTWS ?-column is usually dominated by section buckling behavior in practical examples.Compared to hot-rolled steel column,CFTWS ?-column can not only have global buckling,but also distortional and local buckling problems.At present,the direct strength method is introduced into the mainstream codes in the world,which can calculate the ultimate capacity of thin-walled members under pure compression or pure bending.As to the whole structure,finite element(FE)analysis is still needed.On one hand,when shell or solid element is used in FE analysis,the FE model can reflect the buckling behavior of section,so that the analysis accuracy is high,but it is time-consuming and difficult to be applied to engineering practice.On the other hand,when ordinary beam-column element which can not reflect section buckling behavior is used to establish FE model,although the analysis time is very short,the accuracy is poor,which brings potential danger to engineering design.In view of the contradiction above,a thin-walled beam-column element which can reflect buckling behavior is proposed based on the idea of plastic hinge method.When this element is utilized in engineering FE analysis,the precision and cost of calculation can be well balanced,which is highly practical.The main contents of this paper show as follows:(1)According to the common specifications in engineering,a large number of shell element FE models of CFTWS ?-column are established.Then,different combinations of axial force and bending moment are consiedered,and nonlinear static analysis is carried out.After that,the loaddisplacement curve is extracted,and the failure mode of ?-column is identified.Results show that most of the ?-columns in rack structure are distortional buckling failure,some of long ?-columns are global buckling failure,and no local buckling failure occurs.(2)In accordance with the principle of energy equivalence,the load-displacement curve is fitted as bilinear constitutive relationship.With the slenderness ratio of member,the length thickness ratio of rolled edge,the width thickness ratio of web plate and the combination of axial force and bending moment as independent variables,and the initial stiffness,yield stiffness and yield load as dependent variables,the correlation analysis and parametric analysis of bilinear constitutive relationship of distortional and global buckling are carried out,and fitting formulas for buckling PMM surface are proposed.The bilinear constitutive relationship can be completely described by these fitting formulas combined with the TPI-PMM ultimate capacity formula.(3)Based on the secondary development of OpenSees,the zero length link elements are set at both ends of the elastic beam-column element,and the bilinear constitutive relationship of two buckling modes is given to them,which forms ‘buckling hinge'.The thin-walled beam-column element of CFTWS ?-column is established,which can reflect the whole process from the very beginning of loading to the section buckling and finally up to its ultimate capacity.The accuracy and effectiveness of this element are verified by column compression test.(4)The thin-walled beam-column element is applied to a frame FE model for pushover analysis of the whole rack structure.Compared to the rack pushover test and ABAQUS mixed element FE model,it is found that their load-displacement curves are close,and the failure mechanism is similar.Moreover,the frame FE model with thin-walled beam-column element only costs a few seconds to analyze,which raises the calculation efficiency in the case of precison guaranteed. |
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