A new Aluminium Structural Analysis and Design Methodology

Transcription

1 A new Aluminium Structural Analysis and Design Methodology Jean-Pierre RAMMANT Chief Executive Officer SCIA int l, Belgium Chris VAN LOOCK Process Manager SCIA Int l, Belgium Summary The unique properties of aluminium concerning strength, light weight, durability, ease of production and the recycling ability have lead to a growing use of aluminium in structural applications. The complex sections and the high deformability of the thin material pose a real challenge to the structural engineer. In Eurocode 9 practical design rules have been prepared. In this paper research results are reported concerning a consistent analysis and design methodology for practical aluminium structures of any complexity. The design rules for complex cross-sections and the translation to equivalent more simple design values have been examined. The HAZ (Heat Affected Zones) sectional values are incorporated in the design rules. To facilitate detailed analyses an automatic conversion of aluminium sections into finite element meshes has been developed. The methodology also accounts for connections where reinforcing elements such as steel tubes are added, which influence the overall structural stability and resistance. Comparisons with test results are validating the new design methodology. Keywords: aluminium; thin-walled sections; heat affected zone; local buckling; distortional buckling; finite element method; connections. 1. Introduction This paper reports on the results of the IWT (Flanders Research Agency) research and development project Constructief Aluminium [1]. In this project, there is investigated the possibility of implementing specific aluminium engineering design topics into a commercial software package, as is SCIA ESA Professional Technology [2]. Three main problems are explored: the buckling instability of complex-shaped sections, the definition of HAZ data for the cross section and the conversion of aluminium cross-sections into FEM models. 2. Buckling instability of complex-shaped sections 2.1 Linear profile cross sections A first way to describe a section is by building it up with linear thin plates. In order to avoid local buckling of the composing plates, the latter can be reinforced. These reinforcements include edge stiffeners and intermediate stiffeners. The different normative prescriptions (Ref. [3], [4], [5], [6]) are implemented into the cross section module of the general SCIA ESA PT program. For linear profile cross-sections and for standard shapes (I, section, channel section, angle section, ) an initial geometrical shape is introduced. The basic types of thin-walled parts are identified: flat symmetrical outstand part (SO), flat unsymmetrical outstand part (UO) or flat internal part (I). These parts can be reinforced by longitudinal stiffening ribs (RI, reinforced - internal) or edge lips (RUO, reinforced - unsymmetrical). The input is illustrated in Fig.1.

2 Fig. 1 Input of Initial geometrical shape An algorithm is set up to derive apart from the linear plate elements - the different types of reinforcements from the geometric definition as well. The engineer will quantify the influence of the reinforcements through intermediate calculations (according to the chosen material and standard) and, if required, optimise the section. When the entire section has been defined, the effective properties are calculated. The analysis is performed for different sets of internal forces. The intermediary results are shown in Fig.2, and the final results are in Fig.3. Fig. 2 Intermediary results for effective cross section properties

3 Fig. 3 Effective cross section properties 2.2 Polygonal profiles A second possibility to describe a section (of an extrusion or a rolled section) is by building it up from the sum and the difference of polygons. A graphical method is set up to determine the composing plate elements and their boundary conditions (edge stiffeners and intermediate stiffeners, cantilever plate, plate between supports ) from the general profile definition. This method contains a fast interaction method allowing for the adaptation of the interpretation. The user is able to optimise a section through intermediate calculations (according to the chosen material and standard). The method is illustrated in Fig. 4 and Fig. 5. Fig. 4 Example of sections made by polygons

4 Fig. 5 Equivalent initial shape of section made by polygons 2.3 Finite Elements Method to define the local buckling This sub-project aims at calculating the effective section properties for an arbitrary section using the finite element method. This problem is extensively described in [7] and [8]. In the general program SCIA ESA PT [2], equivalent finite element models are generated for the aluminium cross sections. These models are evaluated using the stability module (see Fig.5). The results are compared with the results given in [7]. (see Table 1). Fig. 6 First buckling mode

5 Table 1 Comparison of critical loads CSS N cr FE N u FE N u Exp N cr PT Class (-) A eff (mm²) fo (N/mm²) N cr EC9 RHS RHS RHS RHS RHS RHS US US US US In Table 1, we find the values N cr FE (initial buckling load FE analysis according to ref.[7] Tab B4), N u FE (failure load FE analysis according to ref.[7] Tab B4), N u Exp (failure load experimental according to ref.[7] Tab B4), N cr PT (critical load according to linear stability analysis in SCIA ESA PT), the section classification according to EC9, A eff (effective cross section according to EC9), f o (the characteristic value of 0.2 % proof strength for aluminium material) and N cr EC9 (A eff x f o ). The SCIA ESA PT stability module does not calculate the ultimate failure load, because the nonlinear elastic-plastic material behaviour and imposed mesh imperfections are not taken into account. 3. The definition of HAZ data When designing welded aluminium constructions, the decrease of the strength properties acting in the proximity of the welds must be taken into account. The affected area extends in the immediate vicinity of the weld. The extent and the extensiveness of this area are, amongst others, associated with the chosen aluminium material, the weld type (fillet weld, butt weld) and the welding method. Therefore, the welding spot and method must be indicated in the profile section, as shown in Fig.7. This HAZ ('Heat Affected Zone') data are integrated in the analysis of the effective section properties (see Fig. 8). Fig. 7 Introduction of the HAZ data

6 Fig. 8 Effective section properties, inclusive the HAZ data 4. The conversion of aluminium cross-sections into FEM models. To dimension the section by means of the local stresses, the graphic section is converted into a finite element model. The sections and beam segments (linear or polygonal) are converted into a new calculation project through a finite element model. In this way, the influence of a tensile force (of a screwed bolt) on the local stresses in the section can be analysed (Fig. 9) Fig. 9 Shear stress distribution in the FEM model of the cross section.

7 The conversion of aluminium connections into a finite element model, is investigated in collaboration with a student thesis project Eindige Elementenmodellering van verbindingen in aluminiumconstructies (FEM for aluminium connections) [9]. The thesis deals with the conversion of some connections to a 3D Finite Element model. More specific, it encloses the comparison between two finite element models. One model is made with Ansys (3D- volumetric elements), the other model with SCIA ESA PT (2D-plate elements). Two types of aluminium connections are investigated : the connection at the ridge in aluminium tent construction (see Fig.10) and the connection in an aluminium façade construction (see Fig.11). By comparing the FEM models (see Fig.12), interesting conclusions are taken in the field of feasible accuracy with 2Delements, restrictions linked to the use of 2D-elements, internal tensions, critical points in the connections, Fig. 10 Connection at the ridge in a tent structure Fig. 11 Connection in a façade construction Fig. 12 Rendered FEM model of the ridge connection A method is in development to automatically explode the selected detail from the linear member model to obtain a new calculation model with 3D elements (shells). The internal forces of the member model are taken into account as loads on the finite element model. After the application of the boundary conditions, the model is calculated. The stress distribution and the stress concentrations will be calculated, visualised and checked. Modifications to the model will be

8 possible, thus enabling improvements of the design. One of the remaining issues, is the use of contact elements. In Ansys these elements are used to model the contact between the different parts of the connections. Discussion and Conclusions The conversion of the research-results, the design rules and the design methodology in a userfriendly (SCIA ESA PT) software results in a new design tool available for the structural engineers and leads to a more reliable design-process for aluminium cross sections in real life structures. For the aim of FEM modelling in the field of advanced aluminium analysis, the SCIA ESA PT program needs to be extended with non-linear elastic-plastic material behaviour, imposed mesh imperfections and contact elements. 5. References [1] SCIA GROUP nv, Constructief Aluminium, IWT Project , 2004 [2] SCIA GROUP nv, Program Guide SCIA ESA PT, 2006 [3] CEN (2004), Eurocode 9: Design of aluminium structures, Part 1-1 : General structural rules, pren :2004, Brussels, Belgium [4] HOGLUND T., Design of Members, Talat Lecture 2301, EAA, 1999 [5] MAZZOLANI F.M., GHERSI A., LANDOLFO R., Design of metallic cold-formed thinwalled members, Spon Press, 2002 [6] VALTINAT F., Aluminium im Konstruktiven Ingenieurbau, Ernst & Sohn, Berlin, 2003 [7] MENNINK J., Cross-sectional stability of aluminium extrusions, PhD Thesis, The Netherlands, 2002 [8] KIM Y., PEKOZ T., Behaviour and design of aluminium members in bending, Research Project Sponsored by The U. S. Department of Energy and The Aluminium Association, Cornell University, 2003 [9] DEURINCK G., ROELSTRATE K., Eindige Elementenmodellering van verbindingen in aluminiumconstructies, Thesis (in preparation), KU Leuven, 2006