Available online at ScienceDirect. Procedia Engineering 160 (2016 )

Transcription

1 Available online at ScienceDirect Procedia Engineering 16 (216 ) XVIII International Colloquium on Mechanical Fatigue of Metals (ICMFM XVIII) Characterization of the cyclic behavior of the web components in end-plate beam-to-column joints Hugo Augusto a *, José Miguel Castro b, Carlos Rebelo a, Luís Simões da Silva a a (ISISE)University of Coimbra, Department of Civil Engineering, Polo II, Rua Luís Reis Santos, Coimbra , Portugal b University of Porto, Department of Civil Engineering, Rua Dr. Roberto Frias, s/n, Porto , Portugal Abstract Mechanical models have the potential to characterize the behavior of complex steel joints, using for that the isolated behavior of its components, assembled according to their geometry. However, the mechanical models implemented in the current design codes are not prepared to deal with cyclically loaded joints, due to the complexity associated to load reversal. To overcome this difficulty this work makes to use of detailed finite elements models, to extract the needed force-displacement components response. The FE models are capable of representing the various connections components and the several sources of nonlinearity associated to them and are validated against existing experimental data. The discretized nature of the FE models is able to provide all the relevant information of any element, and even provide data that is typically unavailable from experimental tests, such as the contact or friction forces. Several models of bolted end plate beam-to column joints, with partial-strength classification in relation to the connected beam, have been developed using the ABAQUS FE package. A methodology to extract the needed force-displacement relationships of the column web components of the joint is presented and applied to the joints, through integration of stress and displacement fields. The results, presented in this paper, allow setting the base for a component-based model to simulate the dissipative behavior of steel connections subjected to cyclic loading conditions. 216 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license 216 The Authors. Published by Elsevier Ltd. ( Peer-review Peer-review under under responsibility responsibility of the of University the University of Oviedo of Oviedo. Keywords: Finite elements method; joints; cyclic behavior; component method; end plate. * Corresponding author. Tel.: ; fax: address: hugo.augusto@dec.uc.pt The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license ( Peer-review under responsibility of the University of Oviedo doi:1.116/j.proeng

2 12 Hugo Augusto et al. / Procedia Engineering 16 ( 216 ) Introduction In steel moment resisting frame structures, although allowed in current codes of practice, the use of bolted endplate beam-to-column joints in seismic regions implies the full characterization of their behavior, especially if they are classified as partial-strength joints. In that case joints became the main dissipative element in the structure, and a proper cyclic characterization of the joints is crucial for a rational analysis and design of the structure and joints. The component method currently implemented in Eurocode 3 [1] allows for the assessment of the stiffness, strength and rotation capacity, when a joint is subjected to monotonic loading conditions. The method consists of a mechanical model based on the assemblage of a series of springs, representing the various components of the joint, each one with an associated value of stiffness and strength. This allows the determination of the joint s properties. The extension of this methodology to joints subjected to cyclic loading requires additional information regarding the characterization of each component, namely the description of the behaviour under unloading and reloading conditions, the stiffness and/or strength degradation rules, the potential for pinching, among other effects. It is therefore clear the increased complexity of the mechanical model. Typically, the characterization of the behaviour of each component, defined by a force-deformation curve, is obtained either from experimental tests or from numerical or analytical models. There have been already few attempts in the past to extend the component method to the cyclic behaviour of joints. Madas and Elnashai [2] characterized the cyclic behaviour of beam-to-column joints using a component approach in which the components behaviour was obtained from mechanics principles. Few years later, Calado and Ferreira [3] considered the monotonic behaviour of each component to assess the cyclic response of a beam-column joint. However, the procedure adopted by the authors had some limitations as it was unable to account for pinching and also for stiffness and strength degradation. Calado [4] also proposed a model for top and seat web angle for steel beam to-column connections with damage accumulation, considered in the stress-strain relationship of the material, and including also the behaviour of the bolts in cyclic shear, taking into account the slip between the connected elements, disregarding although the ovalization of the hole and the changes in preloading force. This paper aims to contribute to the mechanical characterization of components in end-plate beam-to-column joints using a numerical model developed in ABAQUS [5] and were validated with experimental data available in the literature. The model applies to end-plate beam-to-column joints and considers a three dimensional detailed representation of the various connection components taking into account the several phenomena involved in the connection behaviour, namely the nonlinearities related to the geometry, contact, slip and material properties. To deal with cyclic loading, a combined isotropic and kinematic material-hardening model is also included in order to characterize the connection behaviour under load reversal. Using the validated FE models a detailed procedure is described to isolate column web components, namely the column web panel in shear and the column web in transverse compression or tension, and to identify their mechanical behaviour analysing the stress and deformation fields in the FE models. 2. Development and validation of the numerical models The numerical model developed in ABAQUS [5] consists of sub-assemblages of a column and a beam connected to each other by means of an end-plate welded to the beam and bolted to the column flange and are representative of an external node of a moment-resisting framed structure with double-extended end plate joints. The lengths of the beam and the column are established according to the experimental tests setup used in the validation of the FE models. The FE models and the finite elements modelling options were already object of a detailed description and validation in [6] and [7], in here a small remainder of the model is described. The models are composed of solid (mainly C3D8RH) finite elements in the joint region. Beam elements (B31) are used in the adjacent regions of the joint, i.e., in the beam and column segments, aiming at reducing the computational time. The kinematic relations being transferred from the solid to the beam elements by multi-point constraint equations. The model and its parts are illustrated in Fig. 1, with the corresponding adopted mesh, namely the wire columns, the wire beam, the solid column with or without stiffeners and with the bolt holes in the flange, the solid

3 Hugo Augusto et al. / Procedia Engineering 16 ( 216 ) beam with the corresponding fillet welds, the end plate with the bolt holes and the bolts composed by the shank, head and nut. The various parts interact with each other by constraints or interactions, to form the beam-to-column endplate joint mechanism. Fig. 1. Finite element model and global response comparison under cyclic loading. 3. Characterization of the cyclic behavior of the column web components 3.1. Description of the methodology In this section an extension to the methodology presented in [6] is described to deal also with reversal load conditions. For the extraction of the column web panel components behaviour, due to the load-introduction effect and the shear effect. This methodology is also fully based on the results provided by the FE models and allows the derivation of force-displacement and shear-distortion curves of the components. It was developed using numerical integration of the stress fields obtained from FE models in order to characterize the component column web panel in shear and the component column web in transverse compression/tension, and it is illustrated in Fig. 2 and 3. The forces are obtained by integration of the stress field according to Eqs. (1) and (2) due to the load-introduction effect and from Eq. (3) due to the shear effect. In these equations, 33 (or zz) is the normal horizontal stress in the column web along path P1, integrated over the lengths h c for compression and h t for tension (Eq. (1)), 23 (or yz) is the shear stress in the column web along path P3, integrated over the corresponding lengths (Eq. (2)), t fc and t wc are the column flange and web thicknesses, respectively, and t 1 is the thickness according to the shear area defined in Fig. 2. To determine the shear force, the stress field is evaluated at a cross section in the middle of the column length, path P3, where the stresses reach their maximum values, also using the middle elements of the web to extract the shear stresses. The elongation and rotation corresponding to the load-introduction effect and shear effect, respectively, are obtained from the displacement fields. In the case of the load-introduction effect, the displacements are extracted from paths P1 and P2, and the elongation is determined as the difference between them. In the case of the shear rotation, the displacements are extracted from the predefined nodes indicated in Error! Reference source not found.. To account for the additional shear strength provided by the frame formed by the column flanges and the transverse stiffeners aligned with the beam flanges, a plastic mechanism is idealised considering that the plastic hinges will occur in the column flanges due to the higher stiffness of the stiffeners. The stresses are extracted at a section near the flanges maxima normal stresses, 22, as depicted in Fig. 3. Subsequently, Eq. (3) is used to determine the bending moment in the flanges, and Eq. (4) is used to obtain the additional shear strength V c. For simplification it is considered that the stresses are uniform along the width of the column flanges, so the integration of the stress along each path results in a single force at that thickness level.

4 14 Hugo Augusto et al. / Procedia Engineering 16 ( 216 ) ht(1st) F t P P1 h 5 t(2nd) F t 4 F c h c(2nd) h t(2nd) F t F c h c(2nd) 2 h t(1st) F t 1 h F c (N/mm 2 ) F c h c(1st) 23 (N/mm 2 ) h c(1st) -4 P3 V n (-) h shc V n (+) 1 2 h shc (mm) r twc fc rc hwc h shc rc t fc /2 Fig. 2. Procedure to assess the components: column web in transverse tension/ compression, and column web panel in shear. F V c n h h c t i dy t or F 33 wc t i dy t,, 33 wc (1) 2t 2 3 fc 3r fc back h t r wc front 23dz t 1 23dz twc 23dz t 1 (2) da P5 P7 P4.1 M fc P4 P6 P4.2 P4.3 z t fc Fig. 3. Determination of the bending moment in the flanges by the stress integration. t fc M z 22dA (3) fc V c fc( P4) M fc( P5) M fc( P6) M M fc( P7) (4) d b

5 Hugo Augusto et al. / Procedia Engineering 16 ( 216 ) Application to the joints Introduction The methodology described above was applied to some variants of the original test specimens, Fig.1, used in the validation of the model, considering or not the column web continuity stiffeners, J1_1_pv1_tp18_ts2 and, J1_1_pv1_tp18_ts, respectively. The force-deformation (F-) and shear-distortion (V-) relationships of the column web panel components were determined for use in a mechanical model capable of characterizing the contribution of these components to the joint cyclic rotation. For the steel mechanical properties adopted in the analyses, of the joints based on the J1.1, the nominal values in Eurocode 3 part 1-1 [8] were used (E = 2.1E 5 N/mm 2 ; f y = 355 N/mm 2 ; f u = 49 N/mm 2 ) Load-introduction effect Two components, defined in the Eurocode 3 part 1-8 [1], can be directly associated to the load-introduction effect: column web in transverse tension and column web in transverse compression. The introduction of the loads in the column web carried by the beam is different in tension and in compression, tension is transferred by the bolt rows and the compression is transferred directly from the contact of the beam flanges to the column web. To overcome this problem in here the bolt row 1 and 2 will be grouped and analysed together. For the joints in study the stress and deformation fields are represented in Fig. 4. By analysing the stress fields in the joints, it can be concluded that the stress distribution is very similar in tension and in compression, in the joints without continuity stiffeners, although with a more careful analysis of the results some differences can be detected in the stress distribution in tension and in compression, a fact more notorious in the stiffened joints. 7 Row Row 2 4 Row 3 2 Row 4 1 J1_1_pv1_tp18_ts (N/mm 2 ) 7 Row 1 6 Row Row 3 2 Row 4 1 J1_1_pv1_tp18_ts Web elongation (mm) 7 Row Row 2 4 Row 3 2 Row 4 1 J1_1_pv1_tp18_ts (N/mm2) 7 Row Row 2 4 Row 3 2 Row 4 1 J1_1_pv1_tp18_ts Web elongation (mm) Fig. 4. Stress fields, and elongation fields, for increasing levels of bending moment.

6 16 Hugo Augusto et al. / Procedia Engineering 16 ( 216 ) By applying the methodology described before it is possible to obtain the numerical F- results. The results are presented in Fig. 5. The procedure is able to capture the behaviour of the column web under tension and compression, both for groups of bolts and for isolated bolt rows. The direct comparison of the behaviour of the joints, with and without stiffeners, allows to conclude that the presence of continuity stiffeners have major influence in the amplitude and shape of the force-displacement relationships. Also in terms of tension and compression the differences are notorious this is due to the fact that the compression are being transmitted to column web in a more direct and incisive manner than in tension that is distributed for several bolts. Fig. 5. F- behaviour for the components due to the load-introduction effect considering the group of bolts around the beam flanges Shear effect Similarly to the previous sub-section by applying the methodology described before it is possible to obtain the shear-distortion (V-) relationship. The stress fields for the joints with and without column web stiffeners are quite similar, as shown in Fig. 6. Although in the presence of the continuity stiffeners the shear stress is confined by the stiffeners and the flanges, and more distributed in the case of the bare column web. Also in Fig. 6 is depicted the derived relationships and compared the results with and without continuity column web stiffeners. 35 J1_1_pv1_tp18_ts 35 J1_1_pv1_tp18_ts (N/mm 2 ) (N/mm 2 ) h shc (mm) -35 h shc (mm)

7 Hugo Augusto et al. / Procedia Engineering 16 ( 216 ) Fig. 6. Shear stress fields for increasing levels of bending moment for the unstiffened column web and for the stiffened web. Fig. 7. V- behaviour for the shear load. The additional shear resistance provided by the stiffeners is achieved by the frame action developed by the column flanges and the stiffeners, as the bare column web shear resistance is similar with or without stiffeners, only the rotation achieved is different. 4. Conclusions This paper describes the development of a finite element model capable of representing the cyclic behaviour of extended end-plate joints classified as partial or equal-strength according to Eurocode 3. The model developed in ABAQUS uses solid (or continuum) elements in the connection zone. The model considers non-linear material and geometrical behaviour, non-linear contacts, re-contacts and slip. A material model combining both isotropic and kinematic hardening was employed. The model was calibrated against experimental tests carried out at the University of Coimbra on double extended end-plate beam-to-column joints It is intended in this paper to contribute to the development of a component based methodology capable of characterize the cyclic behaviour of the joints in a mechanical model resulting from the assembly of the isolated components behaviour. For that a procedure developed to assess the contribution of the several mechanisms that are involved in the connection deformation, and a procedure at the level of the individual components, namely the ones developed in the column web panel. This methodology uses the integration of stress fields from the FE models of the joints, namely the column web panel in shear and the column web in transverse compression/tension components. It is worth noting that the accuracy of the methodology depends of the column web element size and the number of stress fields analysed from the available load increments. It is also important to refer that this methodology should be systematized, otherwise can be time consuming, but if well applied, the resulting force-displacement relationships can be easily used in mechanical models. Bolted end plate joints, with and without continuity column web stiffeners, were analysed and used to assess the proposed methodology. The results allowed to conclude that the procedure is able to capture the behaviour of the column web under tension and compression. The direct comparison of the behaviour of the joints, with and without stiffeners, allows to conclude that the presence of continuity stiffeners have major influence in the amplitude and shape of the force-displacement relationships. Similarly to the transverse components the procedure is also able to characterize the shear-rotation relationship, including the additional shear resistance provided by the stiffeners and achieved by the frame action developed by the

8 18 Hugo Augusto et al. / Procedia Engineering 16 ( 216 ) column flanges and the stiffeners. Concluding that the stress fields for the joints with and without column web stiffeners are quite similar, the difference in the response is the additional shear resistance provided by the stiffeners. Acknowledgements This work was partly financed by FEDER funds through the Operational Competitiveness Programme COMPETE and by national funds though FCT Foundation for the Science and Technology within the scope of the project POCI FEDER-7633 and also within QREN - POPH - Typology 4.1 Advanced Education, reimbursed by the European Social Fund and Portuguese national funds MEC, under contract grants SFRH/BD/91167/ 212, for Hugo Augusto, is gratefully acknowledged. References [1] CEN, Eurocode 3: Design of steel structures part 1-8: Design of joints, EN , European Committee for Standardization, Brussels, 25. [2] P.J. Madas, A.S. Elnashai, A component-based model for beam-to-column connections, Proc. 1th World Conference on Earthquake Engineering, July, Vol. 8, Madrid, Spain, [3] L. Calado, J. Ferreira, A numerical model for predicting the cyclic behaviour of steel beam-to-column joints, Proc. 1th European Conference on Earthquake Engineering, Vienna, Austria, [4] L. Calado, Non-linear cyclic model of top and seat with web angle for steel beam-to-column conections, Engineering Structures. 25 (23) [5] ABAQUS User s, Theory and Scripting manuals. ABAQUS, Inc., Dassault Systèmes Simulia Corp., Providence, USA. [6] H. Augusto, L. Simões da Silva, C. Rebelo, J.M. Castro, Characterization of web panel components in double-extended bolted end-plate steel joints, J. of Constructional Steel Research 116 (216) [7] H. Augusto, J.M. Castro, C. Rebelo, L. Simões da Silva, Numerical Simulation of Partial-Strength Steel Beam-to-Column Connections under Monotonic and Cyclic Loading, Proc. of Congress on Numerical Methods in Engineering, CMN, Bilbao, Spain, 213, pp [8] CEN, EN Eurocode 3: Design of steel structures part 1-1: General rules and rules for buildings, May, European Committee for Standardization, Brussels, 25.