Integration of joint design of steel structures using product model

Transcription

1 icccbe 2010 Nottingham University Press Proceedings of the International Conference on Computing in Civil and Building Engineering W Tizani (Editor) Integration of joint design of steel structures using product model M Heinisuo, M Laasonen & H Ronni Tampere University of Technology, Finland T Anttila Ramboll Finland Oy, Finland Abstract The component method of the recent European standard EN has large potential for the derivation of general joint design rules for practical applications including 3D effects of the joints. In this paper the generation of the finite beam element model for local 3D joint analysis is based on the component method. Component models can be generated from the geometrical models of product models. Therefore, we end up with a very generic system. The stiffnesses of the joints are automatically generated into the global structural analysis of the frame. Resistance checks of the joints including all their active components can be done after the structural analysis. The global analysis model is non-linear and includes compression-only and tension-only members that depict potential components of the joints. The active components become known after the global frame analysis model is solved. The moment resistance and the rotational stiffness of an end plate joint are demonstrated to be reliable and safe compared to the results of a continuum model. The base bolt joint is used to demonstrate the developed integrated design system. Keywords: 3D steel joints, product model, component method, integration, eurocode 1 Introduction Product models (PMs) have many uses in building projects, today, especially in the case of steel structures (Crowley and Watson, 2000; Heinisuo, 2001). In structural design of steel frames, the design of members has been solved rather completely by the integration of product models, structural analysis and resistance checks of members. There are two-way links between product modeling and structural analysis programs. Resistance checks of the members between joints are typically done with the structural analysis programs after the stress resultants of the members are known. Joint design in practical applications is not at the same general level as the design of members. The generally used product models are very generic and complete. They model steel structures with all their features. Structural analysis using the finite element method is also generic. Generic local joint analysis models are needed to bring joint design to a level with member design. The component method of the recent European standard (EN , 2005) has large potential for the derivation of general joint design rules for practical applications. The component method has been developed during the last 20 years, initially for ambient conditions (Tschemmernegg et al., 1987) and later for elevated conditions e.g. (Leston-Jones, 1997). The method of standard (EN , 2005) applies only to planar joints. Extensions and new components are being developed all the time (Vertes and Ivanyi, 2008; Del Savio et al., 2009). 3D

2 behaviour of steel joints has been examined by (Simões da Silva, 2008). (Heinisuo et al., 2009) proposed the enlargement of the component method into 3D. This study looks at the generation of a finite beam element model for local 3D joint analysis based on the component method. The goal is to have the local joint model generated automatically from the product model to the global analysis model. Here automatically means without extra work by the designer. The designer should only model the geometrical layout of the joint using the PM software. The moment resistance and rotational stiffness of an end plate joint is calculated using the method, and the result is compared to the result of a continuum model. The design of the base bolt joint is shown to demonstrate the integrated method. The stiffness and resistance properties of the components are those given in the standard (EN , 2005). In planar cases the method is fully consistent with the standard. 2 Component method in 3D, theory In the component method the joint is composed of deformable or non-deformable components. The composition is modeled using rigid links. The rigid links join the components to the member axis. Thereby, the deformations of all components are taken into account when assessing the behaviour of the entire joint. After structural analysis, the forces of all components are known and the resistance checks of the components can be done. This study deals with bolted end plate joints and their compression and tension components, e.g. shear components are excluded. Every bolt centre has one potential tension component. Bolt centres are connected by rigid links to the member axis, as in the standard. In the standard (EN , 2005) the rigid links are in one plane. In this case they are on a perpendicular plane against the member axis (see Figure 1). That means enlargement of the component method into 3D. Potential compression components are built so that all the flanges of H profiles and sides of rectangular tubular profiles connected in the joint (welded to the end plate) are divided into three equal parts. Each part is a potential compression component of the joint. The web of an H profile includes one potential compression component. The mid points of these compression components are connected to the member axis by the rigid links on the same plane as the links connecting the potential tension components. At the free ends of the rigid links, tension-only or compression-only finite elements are connected to other parts of the joint. They are perpendicular to the rigid links and complete the local joint model. The members of steel frames are frequently analyzed in 3D. To advance joint design to the same level, it is necessary to analyse joints in 3D. The component method in 3D described above offers good potential for that. The axial stiffnesses of the tension and compression-only spring elements are defined using the equations of the standard (EN , 2005). The equations needed for the resistance checks of the components originate from the same standard. Steel frames are typically statically indeterminate. Thus, the stiffness of the joints determines which potential components are active. The potential components are not known in advance. If the frame is statically determinate, we may be able to establish in advance which components are active. That is not the case typically. Application of the component method leads to the non-linear model including compression-only and tension-only members depicting potential components of joints. In large global problems this may require a lot of computing time. The components may act as a group or as individuals according to the standard (EN , 2005). This may cause additional iterations. Grouping affects both the stiffness and the resistance of a component. The linearity rule applied to frictionless contact problems (Heinisuo and Miettinen, 1989) can be used when solving the system equations for proportional loads. The assumption of no pre-forces and

3 no initial gaps should be valid, too. The linearity rule holds if the stiffness of tension and compression components is linear. That is a hypothesis of this study, which means that the joints behave linearly in the global analysis model. According to the standard (EN , 2005), the linear rotational joint stiffness, S ini /η, can be used for the whole range of the moment resistance of the joint. The non-linear stiffnesses of the components are known (Del Savio et al., 2009), but are not used in this study. The linearity rule means that the active components remain the same if the loading increases proportionally. 3 Component method in 3D, example Consider the idealized extended end plate joint presented in Figure 1. The beam part of the joint is the same as in fire tests (Wang et al, 2009, Test 5). This study focuses only on ambient conditions. The support is supposed to be rigid and its resistance infinite. Bolt elongation length is supposed to be 44 mm for all bolts. The deformations of the tension components consist of the end plate bending and the bolt elongation derived from the equations of the standard (EN , 2005). According to the standard, no deformations are supposed to occur in the compression components. The resistances of all components should nevertheless be checked including compression components (one thirds of the flanges and the web, if compressed), welds and tension component of the web. Figure 1 presents all potential components of the joint and the resistance values of the active tension components in one load case: moment around the weak axis of the joint. The compression components are not critical in this case. The resistances of the components are calculated using the equations of (EN , 2005). The details of the calculations are given in (Ojala, 2010). Figure 1. End plate joint and all its potential components and active components in one load case. The moment resistance around the weak axis is according to Figure 1: M z =79 mm*( ) kn=8.5 knm. The corresponding rotational initial stiffness is 2.3 knm/mrad. If half of the flange is taken for the compression component then the values are 7.5 knm and 1.8 knm/mrad. The values are calculated ignoring the effects of welds. In this case the pure moment around the weak axis causes also the rotation around the strong axis due to non-symmetry of the joint, as shown in Fig. 2. To demonstrate the accuracy of the results of the component method, the finite element method software, ABAQUS Standard 6.9, and its non-linear modules were used to model the joint. Material and geometrical non-linear options were used. The non-linear material model of steel (EN , 2006) was used for all parts. The finite element model was constructed applying the rules of [Yu et al., 2008]. Brick elements C3D8R with hour class controls were used. The parts were connected using TIE options. The contacts between the rigid foundation and the end plate, as well between bolt heads

4 and end plates, were modelled using surface to surface option of the program. Small friction (0.1) was used and normal direction behaviour was modelled using hard contact option. The constraint enforcement method was augmented Lagrange. The rigid support was modelled as a steel plate with the elastic modulus 1000 times that of steel. The FEM model is shown in Figure 2. Moment in weak direction - Rotation in weak direction Joint: Wang et al, Test 5 18,0 16,0 14,0 12,0 M [knm] 10,0 8,0 6,0 4,0 2,0 0,0 FEM ABAQUS EN 1/3 of flange in compression EN 1/2 of flange in compression FEM Rotation in strong direction φ [mrad] Figure 2. Comparison between FEM and component method. The rotations were calculated from the FEM results as weighted averages of the end plate displacements at the lines where the flanges and the web are connected to the end plate. It can be seen in Fig 2. that the initial rotational stiffness using the component method for weak axis bending fits well to the FEM results. It can be seen, also, that the moment resistance using the component method is well below the moment resistance of the FEM result, as required. 4 Product model integration, base bolt joint The integration of the 3D component method to the product modeling software was done for the designing the base bolt joints that exist in almost every steel building. The rules for generating component-based local joint analysis models are defined in programmed macros of the PM software. They allow downloading the stiffness of the joints to the global analysis model. The resistance checks of the joints including all active components can be done after the structural analysis. The checks of joint resistances are done using another macro of the PM software. The macros were written using C# language and.net interface of Tekla Structures product modeling software. The structural analysis program used in this study was Autodesk Robot. There are two-way links between these programs, and they were used as they are.

5 The first macro includes all the rules of the standard (EN , 2005) dealing with the stiffness of the required components. The stiffness properties can be calculated based on the geometrical properties of the joint including all the features. All the features of the joints are available in the product model. The most difficult stiffness property was the end plate bending stiffness of the tension component. Many possible yield line mechanisms and end plate support conditions need to be checked. A rather good algorithm was developed for that purpose (Lehtimäki, 2009). The second macro searches the forces of the active components from the results of the structural analysis and checks the resistances of the components according to the equations of the standard. All the properties of the joints needed for the resistance checks are available in the product model. The method is described in Figure 3. Product model (Tekla Structures) Entities Members Joints (macro including component model) Loads Joint resistances (macro) Model Model with updated members Stress resultants Analysis model (Autodesk Robot) D FEM, Bernoulli-Euler beam elements Members: OK Joints: OK (stiffness, eccentricities) Loads: OK Run analysis Member resistances Figure 3. Developed method (new features bolded) and test case, an industrial building frame. The joint macro for the generation of the local analysis model includes options for the designer. Based on his/her experience the designer may incorporate into the local analysis model one of the following: hinge, rigid, TUT-linear and TUT-non-linear. The linear model (TUT-linear) depicts the rotational stiffness of the joint without the effect of the axial load. The stiffness is calculated as a mean of the rotational stiffness of +/- moments. Unfortunately, some design quantities of the final frame fall then on the safe side while some do not, as shown in (Laine, 2008). The linear model can be used for preliminary design in the case of large problems. TUT-non-linear, as shown in this study, should be used in the final design. In fact, that is the only extra information the designer should give when creating the joint model compared to the design without this integrated method. New macros were written to test the ideas presented above for the design of the base bolt joints. The related theoretical background is given in (Laine, 2008) and the details of the macros in (Lehtimäki, 2009). The tests (see Figure 3, right) showed that the design process of base bolt joints improved considerably as a result. The power of this application lies in that the interface of the product modeling program allows using known programming languages. Moreover, all the model objects of the PM are available for the programs. Similar macros can be developed for almost all kinds of structural steel joints, provided that the behaviours of the components are known. Behaviour refers to: stiffness, ductility and resistance. 5 Conclusions The developed integrated design method of structural steel joints has large potential for improving the design process. Joint design is often seen as a bottleneck in design. In the developed method three very generic methods are combined: product modeling, the finite element method and the component

6 method. When using the component method in 3D, the developed method can be considered highly general and used for the design of many kinds of joints. The non-linearity of the global problem is the drawback of the method. Tests results from bolted joints in 3D are badly needed both in ambient and fire conditions and other accidental events. So far, we have been able to compare the results against the results of comprehensive finite element simulations. In planar cases the method is fully consistent with the standard (EN , 2005). If joint macros similar to the ones of this study are available, a lot of time is saved by the designers, because the calculation of the stiffnesses of joints involves a lot of work. An important factor is that when using the developed method, the behaviour of the joints in the global model adheres strictly (within the range of the standard) to the behaviour of all features of the joints. The fabrication and analysis of the structures use the same PM. That increases safety and lowers the risks related to steel structures. More cases in ambient and fire conditions will be considered in future studies. Pilot macros are now being written and the related experiences are available for future projects. References CROWLEY, A. J. AND WATSON, A. S., CIMsteel Integration Standards, Release 2. The Steel Construction Institute, Ascot. DEL SAVIO, A. A., NETHERCOT, D. A., VELLASCO, P. C. G. S., ANDRADE, S. A. L., MARTHA, L. F., Generalized component-based model for beam-to-column connections including axial versus moment interaction, Journal of Constructional Steel Research 65, pp EN , Eurocode 3: Design of steel structures, Part 1-8: Design of joints, CEN, Brussels. EN , Eurocode 3: Design of steel structures, Part 1-5: Plated structural elements, CEN, Brussels. HEINISUO, M., Product Modeling of Steel Structures for Data Exchange between Organizations. In: MÄKELÄINEN, P., KESTI, J., JUTILA, A., KAITILA, O., eds. 9th Nordic Steel Construction Conference, Helsinki, pp HEINISUO, M., LAINE, V., LEHTIMÄKI, E., Enlargement of the component method into 3D. In: Proceedings Nordic Steel Construction Conference, Malmö, Sweden, September 2-4, Publication 181, LUT & SBI, pp HEINISUO, M., MIETTINEN, A., Linear contact between plates and unilateral elastic supports, Mechanics of Structures and Machines, 17(3), pp LAINE, V., Teräsrungon liitosten jouston huomioon ottaminen integroidussa suunnittelujärjestelmässä, MSc Thesis, Tampere University of Technology. (in Finnish) LEHTIMÄKI, E., Peruspulttiliitoksen jouston huomioon ottavan laskentamallin muodostaminen ohjelmallisesti liitoksen tietomallista, BSc Thesis, Tampere University of Technology. (in Finnish) LESTON-JONES, L., The influence of semi-rigid connections on the performance of steel framed structures in fire, PhD Thesis, University of Sheffield. OJALA, A., Modelling of extended end plate connection in ambient temperatures and fire by SAFIR, MSc Thesis, Tampere University of Technology. (in press) SIMÕES DA SILVA, L., Towards a consistent design approach for steel joints under generalized loading, Journal of Constructional Steel Research 64. pp TSCHEMMERNEGG, F., TAUTSCHNIG, A., KLEIN, H., BRAUN, Ch. and HUMER, Ch., Zur Nachgiebigkeit von Rahmen-knoten Teil 1, Stahlbau 5, Heft 10, pp VERTES, K. AND IVANYI, M., Calculation of the Stiffness and Resistance of Minor Axis and 3D Connections. In: JARMAI, K., FARKAS, J., eds. Design, Fabrication and Economy of Welded Structures. Chichester, UK: Horwood Publishing, pp WANG, Y. C., DAI, X. H., BAILEY, C. G., An experimental study of structural fire behaviour and robustness of different types of steel joint in restrained steel frames (under review). YU, H., BURGESS I., DAVISON, J., PLANK, R., Numerical simulation of bolted steel connections in fire using explicit dynamic analysis, Journal of Constructional Steel Research 64. pp