Keywords: finite element analysis, rectangular hollow section, space-truss, plastic deformation, flattened edges, model verification.

The steel space-truss systems are applicable very wide range in the practice of structural engineering. The joint set-up of the Hungarian TOP-SYSTEM space-truss system, which was developed by DUNAFERR Iron Work Company, requires special edge shape of the bars. The edges of the rectangular hollow members are formed with the help of excessive plastic deformations to the flattened shape. In this paper the behaviour of the rectangular hollow members under the formation procedure is studied. The deformation of the plate elements of the members and the development of the plate buckling state are analyzed. The special "flattening" process is described. Using an appropriate finite element model and analysis, the "flattening" process is modelled, and the results of the finite element analysis are compared to the results of the manufacturing process.

The bars of the DUNAFERR TOP-SYSTEM space-truss roof-system [1] is examined. The examined truss is a so-called N-type system, which means the upper and the lower layer grids are rectangular, and are connected by diagonal bars. The theoretical lengths of the grid bars and diagonals are uniform, thus this space-truss system can be generated by connecting pyramids.

The special procedure for the formation of the edges involves a four stages process to ensure the sufficient shape of bars, which is connected to a gusset plate with bolts. This procedure is often applied in Hungary. The procedure is done in a hydraulic ram applying different tools for the different stages.

The first stage is the splitting, where the members are pulled over onto a prod and cut by the ram. The second stage is the pressing, where the split members are pulled over onto a gusset plate in the pressing tool. The cross section is pressed in the vertical direction pressing the half deformed shape of the member. Then the members are pulled out, rotated upside down and pulled back to the tool pressing the final shape of the edge. The third stage of the formation procedure is the punching the holes of bolts into the members. The punching is made in hydraulic ram by a tool with shaped supporting and guiding plate. Finally in the last stage reinforcing plates are welded into the flattened edges of the member ensuring the sufficient load bearing capacity of the bolted connections.

In order to simulate the formation process (second stage) numerical model is developed, and analysed by ABAQUS finite element program, the pre- and post- processing are made by MSC Patran 2000 r2 program.

It is decided to model only a part near the flattened end and only the quarter of the hollow section and the half of the pressing tool due to the symmetry of the members and the formation process.

For modelling the members a 4-node thick shell element, modelling the pressing tool a 4-node rigid body element is used (ABAQUS program library [2]).

The steel material is supposed to be elastoplastic with isotropic hardening. This material is defined according to the ABAQUS program library [2] applying *ELASTIC and *PLASTIC keywords and the adequate parameters. The yield surface follows the Von-Mises criterion. Stabilized nonlinear static analysis was applied with frontal linear equation solution, described in ABAQUS program library [2]. In order to handle the contact conditions, an appropriate algorithm was used by ABAQUS [2].

During the analyses several results are monitored, such the deformations (displacements, rotations), the reaction forces at the supports and between the connected surfaces. Furthermore the stresses, elastic and plastic strains in the bar are checked. The maximal reaction force according to the analysis is approximately 60 kN, while the pressing force at the manufactory is between 58 and 64 kN.

The maximum plastic strains and stresses are at the inner edge and the inner corner of the deformed shape. It is interesting to notice the significant stresses remain after the formation procedure.

The numerical analysis followed the pressing stage of the real manufacturing process, and we obtained the maximum pressing force within tolerance.

The following work will be the numerical analysis of the buckling modes of this flattened ends member, as compressed bar. For this reason we will apply a rigid plate at the end of the member and will apply a longitudinal displacement along the z-direction. Because of the possible non-symmetric buckling modes, half- and whole models will be applied instead of the above presented quarter model.

1

"TOP-SYSTEM DUNAFERR. Space-Truss Roof- and Structure System" (in Hungarian), Design Manual S-45, Budapest: Gyorsjelentés Kiadó Kft. 1997.

2

Hibbitt, Karlsson & Sorensen, Inc. ABAQUS/Standard User's Manual Version 6.3

3

DUNAFERR Sheet-forming Ltd. (DLA Ltd.), Cold bent steel sections, (in Hungarian), Dunaújváros, Hungary, 1996.

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