INFLUENCE OF CONNECTION TYPOLOGY ON THE SEISMIC BEHAVIOUR OF MR-FRAMES
2. EXAMINED BEAM-TO-COLUMN CONNECTIONS AND THEIR MODELLING The study of semi-rigid steel joints can be carried out by means of the component
approach (Jaspart, 1991; Faella et al., 2000) which has been codified by Eurocode 3 (CEN, 2005b). With reference to beam-to-column joints, the component approach allows the prediction of the moment-rotation response, provided that all the sources of strength and deformability of the joint, i.e. all the components, are properly identified. However, Eurocode 3 provides information for evaluating only the monotonic behaviour of beam-to-column connections, but it does not give any indication concerning the modelling of the cyclic behaviour of the joint components. For this reason, a significant research activity dealing with the ultimate behaviour of the main components of beam-to-column connections under cyclic actions has been carried out (Faella et al., 1998, 2000; Kim and Engelhardt, 2002; Clemente et al., 2004; Piluso and Rizzano, 2008; Dubina et al., 2008, Hu et al., 2011). In particular, in a recent experimental program (Iannone et al., 2011) it has been pointed out that the energy dissipation provided by beam-to-column joints under cyclic loads can be obtained as the sum of the energy dissipation due to the single joint components, provided that they are properly identified and their cyclic force-displacement response is properly measured. This result is very important, because it testifies the applicability of the component approach even in the case of cyclic loading conditions.
In addition, the actual possibility of extending the component approach to the prediction of the cyclic response of beam-to-column joints has been investigated (Latour et al., 2011) leading to the definition of a mechanical model for predicting the cyclic response of bolted connections.
On the base of the component approach, it has been pointed out how the ultimate behaviour of bolted beam-to-column connections under cyclic actions can be governed by properly strengthening the components whose yielding has to be prevented (Iannone et al., 2011). Therefore, the component approach can be also regarded as an effective design tool from the seismic point of view allowing the adoption of hierarchy criteria at the component level, as soon as the dissipative zone, i.e. the weakest joint component, has been properly selected and designed.
The beam-to-column typologies herein investigated are three partial-strength connections whose structural detail has been designed by means of hierarchy criteria, based on the component approach, aiming to obtain the same flexural resistance, but changing the weakest component. Therefore, they are characterized by different locations of the weakest joint component, leading to different values of the joint rotational stiffness and of the plastic rotation supply (Iannone et al., 2011).
The reason for investigating these beam-to-column joints is related to the availability of results dealing with their cyclic rotational response, tested as structural sub-assemblages at the Materials and Structures Laboratory of Salerno University. The structural details of the connections are depicted in Fig. 1 with the analysed MR-Frame.
In order to point out how the cyclic behaviour is governed by the location of the weakest joint component, the tested specimens have been designed aiming to obtain the same flexural strength, but different values of rotational stiffness and plastic rotation supply. The joint non-dimensional resistance , given by the ratio between the joint flexural resistance and the beam plastic moment is equal to 0.76 (Iannone et al., 2011).
Specimen EEP-CYC 02 was designed aiming to obtain the aforementioned value of the non-dimensional resistance and relying on the ductility supply of the end-plate, by properly designing its thickness and bolt location (Piluso et al., 2001). The first component to be designed is the weakest component, i.e. the end-plate, whose design resistance is obtained as the ratio between the desired joint flexural resistance and the lever arm. Successively, the other components are designed to have sufficient overstrength aiming to avoid their plastic engage.
Specimen EEP-DB-CYC 03 is an extended end-plate connection, whose design is aimed at the investigation of the energy dissipation capacity of beams. However, aiming to obtain the same flexural resistance of previous specimen, the RBS (Reduced Beam Section) strategy, called also “dog bone”, has been adopted whose structural detail has been designed according to Moore et al. (1999).
Last specimen, TS-CYC 04, is a partial-strength joint with a couple of T-stubs bolted to the beam flanges and to the column flanges and designed to be the main source of plastic deformation capacity. The design goal is to avoid the plastic engage of the components related to the column web panel, the column web in compression/ tension and the panel zone in shear. The main advantage of double split tee connections is due to their easy repair. In fact, if the panel zone is designed with adequate overstrength, it is possible to substitute only the end T-stubs after a seismic event. Also in this case the same flexural resistance of the other joints was imposed requiring, in addition, a plastic rotation supply of about 0.08 rad. The plastic deformation supply of the T-stub components has been predicted as suggested by Piluso et al. (2001).
In order to assess the seismic performance of steel moment resisting frames with partial-strength joints, it is preliminarily needed to set up an appropriate model to accurately represent the cyclic rotational behaviour of connections. In fact, the rotational behaviour of connections under cyclic actions is complicated by the development of strength and stiffness degradation and by pinching phenomena as the number of cycles increases.
25.20 N/m
IPE270 IPE270 IPE270
HEB200 HEB200 HEB200
600 600 600
320 HEB220
25.20 N/m
IPE270 IPE270 IPE270
HEB200 HEB200 HEB200 HEB220
25.20 N/m
IPE270 IPE270 IPE270
HEB200 HEB200 HEB200 HEB220
25.20 N/m
IPE270 IPE270 IPE270
HEB200 HEB200 HEB200 HEB220
25.20 N/m
IPE270 IPE270 IPE270
HEB200 HEB200 HEB200 HEB220
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IPE270 IPE270 IPE270
HEB200 HEB200 HEB200 HEB220 320 320 320 320 350 30 9430 41 13 4 126 13 4 41 474 154 170 25 120 25 20 0 HE200B IPE270 53 400
EEP-CYC 02
bolt M20 (10.9) t = 20 mmep t = 10 mmwp t = 10 mmcpConnections in Steel Structures VII / Timisoara, Romania / May 30 - June 2, 2012 137 138 Connections in Steel Structures VII / Timisoara, Romania / May 30 - June 2, 2012 70 180 22 22 35 93 167 93 35 423 35 9435 164 HE200B IPE270 bolt M24 (10.9) t = 25 mmep t = 10 mmwp t = 10 mmcp 400 RBS 25 120 25 200 53 R1 95
EEP-DB-CYC 03
252 177 40 257 81 81 40 40 40 54 2 75 30 135 30 73 60 60 60 40 293 170 25 120 25 200 25 HE200B IPE270 bolt M20 (10.9) t = 10 mm t = 10 mmcp 400 wp t = 25 mmep 30 9430 154 TS-CYC 04Figure 1. Analysed MR-Frame with structural details of examined connections The rules describing these phenomena cannot be deduced by means of theoretical approaches; therefore, it is necessary to have sufficient experimental data aiming to develop adequately accurate semi-analytical models, in which the monotonic envelope is predicted by means of the use of mechanical models based on the component method, while the degradation rules are empirically derived by means of the available experimental results (Latour et al., 2011). As testified by the developed experimental tests, the cyclic response of connections in terms of shape of hysteresis loops, their stiffness and strength degradation and the resulting dissipation capacity are directly related to the components involved in plastic range, mainly the weakest component.
In this work, aiming to investigate the influence of the beam-to-column joint structural detail on the seismic response of MR-Frames, the non-linear cyclic rotational response of beam-to-column joints has been modelled by means of the spring elements included in IDARC 2D (Version 6.0) software. In particular, the rotational inelastic spring elements are located at the ends of the beams. The cyclic moment- rotation curve of such spring elements has been properly calibrated on the base of available experimental results to account for both stiffness and strength degradation and for pinching phenomenon. In order to derive the parameters governing the cyclic response of the spring elements, a cyclic push-over analysis under displacement control has been carried out with reference to a structural scheme, depicted in the top left corner of Fig. 2, whose feature is that its structural response is dependent on the cyclic response of the spring elements only. Therefore, it is possible to apply to such structural model a displacement time-history exactly reproducing that adopted in testing beam-to-column joint sub-assemblages and to compare the cyclic moment- rotation response of the spring element with the one obtained from experimental tests. Therefore, by properly modifying the parameters modelling strength and stiffness degradation and pinching phenomena, it has been possible to select, for each tested specimen, the connection model leading to the best fitting between the analytical model and the experimental test results.
Figure 2. Comparison between the cyclic moment-rotation response of the spring elements and the experimental test results
The parameters of the trilinear envelope of the moment-rotation curve of the spring element, adopted in IDARC 2D model, are delivered in Table 1. In addition, the damage phenomena occurring under cyclic loading conditions have been accounted for by calibrating the corresponding parameters by imposing the equivalence in terms of dissipated energy between experimental test results and the IDARC 2D spring element response.
Table 1. Parameters of the spring elements adopted for connection modelling in IDARC 2D
Connection Initial Rotational Stiffness [kNmm/rad] First Yielding Moment [kNmm] Plastic Moment [kNmm] Yield Rotation [rad] Ultimate Rotation [rad] Post Yield stiffness ratio as % of elastic
[EI] [PCP] [PYP] [UYP] [UUP] [EI3P]
EEP-CYC 02 41411466 +116463/- 130074 +157000/-173000 +0.01/-0.01 +0.1/-0.1 +3.07/-3.52 EEP-DB- CYC 03 43420000 +119200/-136667 +180000/- 190000 +0.011/-0.011 +0.1/-0.1 +1.3/-0.8 TS-CYC 04 23196000 +89817/- 88344 +140000/-140000 +0.022/-0.022 +0.1/-0.1 +4/-5
Connections in Steel Structures VII / Timisoara, Romania / May 30 - June 2, 2012 139 140 Connections in Steel Structures VII / Timisoara, Romania / May 30 - June 2, 2012
In particular, the adopted hysteretic model is the Polygonal Hysteretic Model (PHM), available in the library of IDARC 2D program, which can be combined with three different hysteretic rules: the Yield Oriented Model, the Bilinear Model and the Vertex Oriented Model.
The PHM is an extension of three-parameter Park model, while the hysteretic rules allow to account for the stiffness and strength degradation and for pinching. The parameters characterizing the cyclic hysteretic behaviour of the tested beam- to-column connections are reported in Table 2.
In particular, the stiffness degradation is defined by means of the parameter HC which locates the pivot point (HC = 200 corresponds to a stiffness degradation equal to zero); the strength degradation is defined by the parameters HBD and HBE which represent the measure of strength degradation related to ductility and to energy, respectively (HBD = 0.01 and HBE = 0.01 correspond to a strength degradation equal to zero); finally, the parameter HS defines the pinching (HS = 1.0 corresponds to the absence of pinching).
The general meaning of the parameters can be synthesized as follows: an increase in HC delays the amount of stiffness degradation; an increase in HBD and HBE accelerates the strength deterioration; an increase in HS reduces the amount of slip.
Table 2. Hysteretic parameters of spring elements for IDARC 2D input
CONNECTIONS CYCLIC MODEL HC HBD HBE HS
EEP-CYC 02 PHM-Vertex Oriented 5 0.01 0.01 1
EEP-DB-CYC 03 PHM-Yield Oriented 15 0.01 0.10 1
TS-CYC 04 PHM-Vertex Oriented 200 0.01 0.01 1
The comparison between the cyclic moment-rotation curve of the tested connections, depicted in Fig. 1, and the corresponding rotational response, predicted by means of the IDARC 2D structural model with the spring element modelling parameters given in Tables 1 and 2, is provided in Fig. 2. From these figures, a satisfactory degree of accuracy in the modelling of the beam-to-column joint cyclic behaviour can be observed.