Determination of the main characteristics of semi-rigid beam-to-column connections through numerical and experimental method

Transcription

1 Determination of the main characteristics of semi-rigid beam-to-column connections through numerical and experimental method K. Vértes & M. Iványi Budapest University of Technology and Economics, Department of Structural Engineering Abstract Connections play an essential role in steel structures which is why it is necessary to know the behaviour of these structural elements. This study provides a FEM model for the determination of the main characteristics of a semi-rigid joint. Although this joint form is very economical, it still not widely used in practice. The main reason for this is that its characteristics are hard to determine. In this study an overview is provided about the handling of such connections by introducing Eurocode 3 [1] and some numerical and experimental methods and results. 1 Introduction The main characteristics of a joint are its strength, stiffness and rotation capacity. The most often appearing problems of using semi-rigid connections hide firstly in the modelling of the connection, then in the determination of their stiffness and at last in the handling of the softening part of the moment-rotation curve [2]. Three ways are known for the determination of the joint characteristics. These are the following: Experimental method accurate but expensive and inconvenient FE analysis its accuracy depends on the model Analytical method EC 3 offering This study discusses the finite element modelling of steel semi-rigid connections by demonstrating the finite element model of welded and bolted beam-to-column connections.

2 678 High Performance Structures and Materials II 2 Basic information on steel beam-to column connections 2.1 Joint classification There are several classification systems. Here we just mention the one according to Eurocode 3. Based on overall studies, EC3 has introduced its classification system. The new idea of this classification is to consider the joint as a part of a structure. It means that not only the joint-type influences the structure behaviour, but the structure-type (braced, or unbraced) has influence on the joint behaviour as well. According to this phenomenon the following joint classes can be distinguished: classification by rigidity for elastic analysis (nominally pinned connections; rigid connections; semi-rigid connections) and classification by strength for plastic analysis (nominally pinned connections; full-strength connections; partial strength connections) [4]. 2.2 Main parameters influencing a joint s characteristics Joints usually have quite a complex behaviour. It is because a lot of parameters influence it. The flexibility sources of a joint have a major effect on the joint characteristics. These flexibility sources of a joint are the following: Connection flexibility, which consists of the deformation of its components (plates, cleats, T-stubs, etc.), the slip between its components (if bolted) and its fastener deformation (bolt and rivet elongation). Localised deformation of the column (plastification, flanges deformation, web buckling, shear deformation of the panel zone and elongation and shortening in the tension and compression regions of the panel zone). Localised deformation of the beam. (Less important than the two previous ones). The parameters that can affect these flexibility sources and consequently influence the joint behaviour can be the connection types (web cleats, flange cleats end plates etc.) and details and the environment of the connection (the column axis to that the connection is fastened, the connection location, the type of the fasteners, the joint loading type, the material) [3]. 2.3 The moment-rotation curve of a joint The moment-rotation curve describes the behaviour of a joint. It is a non-linear curve. However this non-linearity is hard-to-handle in everyday practice. In most cases simplifications of the curve can be done without causing relevant inaccuracy. Such simplifications can be bi-linear law multi-linear low or the non-linear low can be used for an elastic-plastic calculation too. According to Eurocode 3, the main parameters of a bended joint are the moment resistance and the initial elastic stiffness of the joint. These two parameters provide the whole moment-rotation curve (fig. 1)

3 High Performance Structures and Materials II 679 Figure 1: Non-linear M-Φ curve according to EC3 Annex. If the rotation capacity (Φ Cd ) is not limited, this curve has three parts. Up to 66% of the moment resistance (M Rd ), the curve is linear, and the stiffness of this part is the so-called initial stiffness. From 2/3 M j,rd up to M Rd the curve is non-linear and after the moment have reached the yielding limit, only the rotation increases. The non-linear curve between 2/3 M j,rd and M j,rd : S j, = 1.5M M where Ψ=2,7 for end-plate and welded joints and 3,1 for flange cleat joints. 2.4 Eurocode 3 s component method [4] S j For determining a joint s characteristics, EC3 provides the component method. Its main idea is to handle a joint as a set of individual basic components, where each of these possesses its own strength. During the calculation process the building components of the joint have to be identified, then the stiffness and resistance of the basic components have to be calculated and finally these components have to be put together in a statically appropriate way. In case of a general bolted end-plate connection in bending, the following components can be distinguished: Compression zone: Column web in compression Beam flange and web in compression Tension zone: Column web in tension Column flange in bending Bolts in tension End-plate in bending Beam web in tension Rd ini Sd Ψ (1)

4 680 High Performance Structures and Materials II Shear zone: Column web panel in shear 2.5 Numerical modelling of joints Nowadays numerical models are developing because of the development of the computer capabilities. Some often-used models will be introduced here: Spring element, which incorporates the joint stiffness as the element rigidity. It consists of a rotational spring an sometimes it also contains translational springs incorporating axial and shear semi-rigidity Equivalent beam elements with a reduced stiffness assuring the M-Φ characteristics to be respected Truss model, which consists of a particular arrangement of truss elements representing the several kinds of joint flexibility [3]. 3 Results of numerical and analytical calculations compared to experiments In the following section the FEM (Ansys 5.7) [5] model of two different connection types, (a welded and an end-plate bolted connection) will be shown and compared to analytical (EC3) solutions and experimental results. The stress distributions and stress levels and the moment-rotation curves have been determined for both cases by the FEM. In order to compare the results between the Eurocode s component method and our results, the moment-rotation curves have been determined by the component method as well. 3.1 Welded joint The numerical modelling of a welded (continuous) connection is relatively easy compared to a bolted (non-continuous) one. Here a welded connection built up by IPE 100 sections has been analyzed. A monotonously increasing vertical loading was applied at the end of the beam, so the connection was bent. For the analysis a non-linear inelastic material model was used. The FE model was built up by 8node non-linear brick elements. The mesh was refined at the highly stressed areas according to the joint s basic components (such as the column web and flange and the beam flanges and web at the connection part). The stress results and the deformed shape are shown in figure 2. It is clearly visible that the stress distribution in the connection meets the assumed components according to EC3 (the tensioned and compression zones appear in the flanges and the column web in shear is visible too). The moment rotation curve also agrees with the EC assumption it is linear up to 2/3 M Rd and then non-linear, finally the yield plateau appears (Figure 3).

5 High Performance Structures and Materials II 681 Figure 2: Welded joint stress distributions (vertical normal stress left above, horizontal normal stress right above, shear stress underneath). moment (knm) rotation FE result EC3 Experiment 3.2 Bolted end-plate joint Figure 3: Moment-rotation curves. Bolted connections are not continuous so this discontinuity has to be taken into account when modelling such joints. This makes their modelling more complicated. At present example two IPE 100 sections were connected to each other with four bolts of M12. The thickness of the end-plate was taken to 10 mm.

6 682 High Performance Structures and Materials II No stiffeners were built in into the joint. The FE model was built up by 8node non-linear brick elements and the mesh was extremely fine at the bolts and also fine at the assumed components of the connection. Again, the monotonously increasing vertical load was applied at the beam end. The stress levels at each load step and the moment-rotation curve has been determined by FEM. Also in this case the moment-rotation curve has been determined by the Eurocode offering too. The main problem of the modelling of a bolted joint is to model that the bolts play the force transmission role in the connection. First of all the bolts have to be built up from solid elements and in order to simulate the complex stress state in it a quite fine mesh is required, not to mention the contact problems. For the modelling of this connection 8node non linear brick elements were used. Contact surfaces were defined between the end plate and the column flange, between the shank of the bolt and the surface of the bolthole and between the bolthead and the endplate/column flange. The material model was identical to the previously mentioned one. The results are shown in figures 4, 5, and 6. Figure 4: Bolted joint, vertical normalstress distribution. Figure 5: Bolted joint, shear stress distribution.

7 High Performance Structures and Materials II 683 Figure 6: Bolted joint, horizontal normalstress distribution. moment (knm) 3 2,5 2 1,5 1 0, ,05 0,1 0,15 rotation FE result EC3 Experiment Figure 7: Moment-rotation curve for bolted joint. The stress distributions here also show the assumed components of this connection. The column web panel in shear, the column web in tension, the bolts in tension, the end-plate and column flange, the column web in compression, the beam flange and web in compression appear in full view. Also the moment-rotation curve is near to the EC3 curve. 4 Frames with semi-rigid connections Investigations were carried out on multi-storey, multi-bay steel frames in order to study the effect of semi-rigidity on the load bearing capacity and ultimate behaviour of these structures. After the numerical analysis the results showed that the presence of semi-rigid connections significantly influences the load bearing capacity and deformations of frames. However, this influence was not clearly proportional

8 684 High Performance Structures and Materials II having frames of different numbers of bays and storeys. Primary the sequence of occurrence of plastic hinges governed the magnitude of ultimate displacements [6]. 5 Conclusions The results of the FE calculation were close to the ones calculated according to EC3 offering and the experimental results. In both cases the connection behaviour was semi-rigid. For the future spatial semi-rigid connections will be modelled and analyzed. Then a parametrical study will follow, by which the characteristics of these spatial semi-rigid joints can be determined. References [1] Eurocode 3. Design of steel structures [2] K. Vértes Overall behaviour of steel frames with semi-rigid connections, 4.th Int. Ph.D. Symposium in Civil Engineering, ed. Peter Schiessl, München, 2002, pp. Vol2., 391 [3] Wajd Atamaz Sibai (1991), Semi-rigid joint modelling for non-linear analysis of flexibly connected frames, These No. 967 Lausanne, EPFL, 1991 [4] Jaspart J.P. (1999) Semi-Rigidity in Connections of Structural Steelworks: Theory, Analysis and Design: Characterisation and Idealisation of Moment Resisting Joints, Udine, [5] Ansys Release 5.7 SAS IP Inc., [6] Miklós Iványi (1995) PECO COST C1 Technical Report, Column Base Strength and Rigidity Modelling, Budapest, 1995.