Nonlinear analysis of space roof trusses under monotonically increasing vertical loading

Space grid trusses, especially with MERO joint systems, are widely used systems for roof structures that have large areas and aesthetic forms, by the help of their light self-weight, high stiffness, lower cost and flexibity. Moreover, easy manufacture and assembly of these systems makes them preferred systems as well. However, space grid trusses are very sensitive to load accumulation conditions and manufacture and design faults. The main objective of these thesis is to investigate the behaviour of space roof trusses for the cases which are fourfold: load accumulation, initial imperfection, slenderness ratio and bolt effect. To observe the effect of slenderness ratio, two sample roof structures were taken into consideration, which have different tube sections while their shapes are totally same. Also, initial imperfection and bolt effects were introduced into the material models of tube elements rather than explicity taking into account. Space trusses were modeled by using OpenSEES (Open System for Earthquake Engineering Simulation) Software and they were subjected to nonlinear pushover analysis in vertical direction under three load accumulation forms which are covering a full, a half and a quarter of the roof area. According to the results of analyses, load-displacement curves were discussed and some inferences and recommendations were given. This thesis which its outline is given above, consists of five main parts. In the first chapter of this study, the topic and aim of the thesis are given, following methodology is defined brieflly. Afterwards, literature review about the subject is appended. The second chapter of the thesis contains general definition of the space grid trusses and using elements. Frame elements and MERO joint which includes bolt, nut, pin, and sphere, are introduced briefly. In the third chapter of this study, two space roof trusses, denoted ModelA and Model B, were modeled. The considered double layer grid systems span is 15mx15m and have 5 square modules in both X and Y direction. Module of size is 3mx3m while height of the roof 1.5m. The roof was simply supported at four corner nodes of the bottom layer. Truss members were round hollow structural section. All bottom layer, top layer and diagonal members were connected with MERO system at joint nodes. Design of the Model A was carried out with FrameCad software used for space grid system design in the industry. According to the TS648 "Building Code for Steel Structures" and FrameCAD Software assumptions, design of the truss members are explained for two case; under tension loading and under compression loading. Bolts are designed only for tension loading while nuts are designed only for compression loading. FramedCad initially assigns random truss members and performs elastic analysis by using matrix displacement methods iteratively under design criteria such as load carrying capacity of the members. All members were reassigned at each step until attaining optimum design taking lightweight and serviceability limitations into consideration. Deflection of the system is checked manually. After that, Model B was designed by restricting slenderness ratio of compression members with 80. New members were reassigned manually and system was checked by SAP2000 software under strength and serviceability conditions. In the fourth section, initially, tube elements were modeled with OpenSEES and reversal cyclic loading applied on tube members to obtain the behavior of the brace members. Brace elements was modeled using nonlinear beam-column element which is defined in OpenSEES manual. Fiber sections with uniaxial Menegotto-Pinto steel material were used to characterize cross sections of the elements. Initial imperfection was introduced at mid and quarter spans of the tubes. Spheres and bolts were located at the ends of the braces. Bolt material was defined with hysteretic material definition which reflects the bolt characteristics in tension and the nut characteristics in compression simultaneously, depending on the assumption that there is no compression failure in nut elements before buckling of tube elements. Furthermore, corotational transformation was used to take the second-order geometry effects into account. Members which have tube, bolt and nut combinations were analyzed under reversal cyclic loading to obtain force-displacement relations of the members. Cyclic loading analysis were performed in according to the ATC-24 (Guidelines for Cyclic Seismic Testing of Components of Steel Structures) loading protocole, correspondingly target displacements of each step were evaluated depending on ATC-24. After all, utility of this model was checked by comparing force-displacement curves of elements with plastic hinge description given in FEMA356 (Prestandard and Commentary for the Seismic Rehabilitation of Buildings). Space grid systems were modeled in OpenSEES to perform pushover analysis in vertical direction. Brace member was modeled by nonlinearBeamcolumn element is well suited for spread plasticity along the element with five integration points along length of the element. Cross sections of braces were modeled using fiber sections and dimensions of the cross sections were assigned depending on elastic analysis results. All members were assumed to have pinned connection at their ends. To account for the rotational releases at the ends of the braces, zeroLengthelement was used at the ends. Rotations were characterized by elastic material with low young modulus to allow rotational movements, while translational movements were constrained by using equalDOF command. Behavioral models of tube members were derived from result of the cyclic analyses performed in the previous subchapter, for each individual tube including, nut and bolts. By following to analysis flowchart for OpenSEES, which is prepared in this section, OpenSEES data files were generated by the help of Matlab (Matrix Laboratory) Software. To conduct pushover analyses in vertical direction, an incremental concentrated vertical loads were applied on top layer nodes in accordance with three load patterns, which represent the load accumulation conditions. Initial imperfection ratios of L/300 and L/500 and bolt effects were also introduced into the material models. Pushover analyses were performed for 24 cases using displacement-control procedure at middle joint node of the system. Then, force-displacement curves were obtained for each cases. In the last section, some inferences obtained from comparison of the analysis' results were mentioned. According to these, in Model A which was designed by using optimum tube sections, member failure due to the buckling was resulted in a sudden collapse, while in Model B collapse behaviour was determined by yielding of tension members. Hence, Model A is more brittle than Model B which had limited slenderness ratio on its elements. Also, results were discussed in terms of initial imperfection, bolt definition and load accumulation effects.