Seismic evaluation of reduced beam section frames considering connection flexibility M. Ghassemieh and J. Kiani* ,† School of Civil Engineering, University of Tehran, Tehran, Iran SUMMARY In the present article, the seismic performance of frames with reduced beam section (RBS) connections is evaluated. A key purpose of this study is the inclusion of connections flexibility in the seismic performance of RBS frames. Almost in every research projects carried out on seismic performance and design of
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  Seismic evaluation of reduced beam section frames consideringconnection  󿬂 exibility M. Ghassemieh and J. Kiani* , † School of Civil Engineering, University of Tehran, Tehran, Iran SUMMARYIn the present article, the seismic performance of frames with reduced beam section (RBS) connections isevaluated. A key purpose of this study is the inclusion of connections  󿬂 exibility in the seismic performanceof RBS frames. Almost in every research projects carried out on seismic performance and design of RBSframes, the beam-to-column connection is typically assumed as fully rigid. The results of nonlinear   󿬁 niteelement analysis performed on investigating the local performance of RBS connection reveal that theyare within the American Institute of Steel Construction-de 󿬁 ned semirigid connections. Three buildingframes, including 4, 8 and 16 stories considering the semirigid connection as well as fully rigid connection,are considered. A numerical study of the overall seismic response of the building frames subjected to near aswell as far   󿬁 eld earthquake ground motions using nonlinear static and/or nonlinear dynamic analysis ispresented. Results in terms of inter-story drifts, total drifts, story shears and shear deformation in panel zoneindicate that overlooking the  󿬂 exibility of beam-to-column connections may lead to erroneous conclusionsand unsafe seismic behavior that subsequently become signi 󿬁 cant in some cases. Copyright © 2012 JohnWiley & Sons, Ltd. Received 25 September 2011; Revised 18 December 2011; Accepted 28 December 2011 KEYWORDS : reduced beam section connection; RBS frames;  󿬂 exibly connected frames; rigidly connectedframes; connection  󿬂 exibility 1. INTRODUCTIONSteel moment-resisting frames (SMRFs) as conventional lateral systems are assemblage of beams andcolumns in which beams and columns are connected rigidly. Lateral loads are resisted by  󿬂 exuralaction of beam-to-column connection in moment-resisting steel frames, and therefore, beam-to-columnconnection plays an important role. Before the Northridge earthquake, rigid connection with fullpenetration welds attained status as an almost ideal connection in moment-resisting frames. However,the Northridge earthquake has demonstrated that this connection is prone to brittle fracture near thebeam-to-column  󿬂 ange groove welds. To investigate damages that occurred in the beam-to-columnconnection and to develop solutions, the SAC Joint Venture was formed, and many research on theseismic behavior of steel moment connections were performed. Overstrength of the beam material,stress concentration caused by the backing bar and tri-axial forces at the column face were recognizedas potential causes for the brittle fractures in pre-Northridge connections (Yang and Popov, 1995;Kaufmann  et al  ., 1997). Reinforcing the connection with items such as cover plate, ribs, side platesand haunches and/or weakening the beam at the area away from column face were introduced asremedies to improve connection performance (Federal Emergency Management Agency (FEMA)350, 2000a). All those mentioned strategies in the connection design showed suitable performanceby displacing the plastic hinge away from the column face. Weakening the beam instead of reinforcingthe connection has shown to be more economical since trimming beam   󿬂 anges result in reducing *Correspondence to: Jalal Kiani, School of Civil Engineering, Tehran University. † E-mail: THE STRUCTURAL DESIGN OF TALL AND SPECIAL BUILDINGS Struct. Design Tall Spec. Build.  22 , 1248 – 1269 (2013)Published online 17 January 2012 in Wiley Online Library ( DOI: 10.1002/tal.1003Copyright © 2012 John Wiley & Sons, Ltd.  the demand in panel zone and achievement of strong column and weak beam requirements.Reduced beam section (RBS) connection is a practical approach for the latter strategy in which a region in the beam at short distance away from the column face is intentionally weakened byremoving material from the beam   󿬂 anges. Removing a section of beam   󿬂 ange, different con 󿬁 gu-ration has been proposed (constant, tapered and radius cut), among which tapered and radius cutsdisplay better performance since they approximately follow seismic moment gradient (Engelhardt  et al  ., 1996; Plumier, 1997). The results of experimental and numerical analyses on assessing thebehavior of RBS connection have shown a superb performance of this type of connection(Engelhardt   et al  ., 1998; Chen  et al  ., 1996; Popov  et al  ., 1998; Zekioglu  et al  ., 1997). Despitegood performance of RBS connection, web and  󿬂 ange local buckling turn out to be demerits for ordinary RBS connection. Accordion Web RBS (AW-RBS) connection has been introduced toresolve these problems in which rather than removing section of beam   󿬂 anges, corrugated steelplates are used in beam web (Mirghaderi  et al  ., 2010). In addition to experimental and  󿬁 niteelement analyses that were conducted on assessing the micro-behavior of RBS connection, a number of research projects were undertaken to investigate the seismic performance of SMRFs withRBS connections. Kitjasateanphun  et al  . (2001) have proposed two RBS model for nonlinear analysis of RBS frames and have shown that the seismic response of steel frames with RBS is verysensitive to the RBS model. The overall performance of frames with RBS connections in terms of plastic deformation, inelastic drift ratio and strength demand were examined by Shen  et al  . (2000).They have shown that   󿬂 ange reduction is of great importance in seismic response of structure, asinelastic drift does not increase noticeably in frames with moderate reduction in the RBS from theunmodi 󿬁 ed SMRF. The nonlinear behavior of multi-story RBS frames for two hazard levels(immediate occupancy and collapse prevention) was investigated by Jin (2002) and Jin andEl-Tawil (2005). They con 󿬁 rmed that frames with RBS connection can provide goodperformance in the previously mentioned hazard levels. Kildashti and Mirghaderi (2009) evaluatedthe seismic response of SMRFs with RBS connections by means of mixed-based state spaceapproach and have shown that the panel zone participation in the inter-story drift for frames withRBS connections considerably declines besides that the permanent displacements of RBS framesdiminishes against frames without RBS connections.As reported, a large number of research projects show excellent performance of frames withRBS connections, but a full investigation of all those studies proves that the in 󿬂 uence of the beam-to-column connection  󿬂 exibility on the seismic behavior of RBS frames has not been thoroughlyexamined. In other words, the  󿬂 exibility of beam-to-column connection is not considered in thestructural analysis. From the design point of view, it is desirable to assume a connection as fully rigid,but in reality, it is merely an idealization of precise behavior. Most connections, together with the so-called fully rigid connections, exhibit some degrees of   󿬂 exibility. As stated in AISC (2010) provision,if a connection has adequate strength and stiffness, it can be assumed as a fully rigid connection, andthus, it is not mandatory to include the connection elements as part of the structural system analysis.Otherwise, for the semirigid connection,  󿬂 exibility must be estimated and included in the structuralanalysis. The presence of semirigid connections in a frame produces signi 󿬁 cant effects on the behavior and strength of individual elements of frame as well as on the overall frame response (Ang and Morris,1984; Maison  et al  ., 2002). A major concern about   󿬂 exibly connected frames is P- Δ loads on columnscreated by undesirable drifts in these frames (McMullin and Astaneh-Asl, 2003). If the P- Δ  effectsbecome signi 󿬁 cant, using partially restrained connections can trigger dynamic instability (Maison et al  ., 2002). The assumption of rigid joints for frames with semirigid connections will underestimatethe drift of the frame and may leads to an inaccurate prediction of critical member forces (Ang andMorris, 1984). Despite some of those notable shortcomings for   󿬂 exibly jointed frames, applicationof semirigid connections as an alternative to fully rigid connections in structures against seismic forcecan increase the ductility of structures. Nader and Astaneh (1991) have shown that a proper perform-ance of   󿬂 exibly connected frames with well-proportioned semirigid connections can be achieved.Awkar and Lui (1999) have shown that the connection  󿬂 exibility tends to reduce frame stiffness andhence augment vibration periods, especially in lower modes. If it is appropriately designed, steelframes with semirigid connections are very ef  󿬁 cient against resisting forces generated from groundmotion thanks to their ability to dissipate seismic energy through large inelastic deformation and SEISMIC EVALUATION OF REDUCED BEAM SECTION FRAMES 1249 Copyright © 2012 John Wiley & Sons, Ltd.  Struct. Design Tall Spec. Build.  22 , 1248 – 1269 (2013)DOI: 10.1002/tal  damping. Natural period and base shear in the frames with semirigid connection can be controlled(McMullin and Astaneh-Asl, 2003; Awkar and Lui (1999). So presence of the  󿬂 exibility in beam-to-column connection can be ef  󿬁 cient if the structure is properly designed; otherwise, it increasesthe inter-story drift and bring about dynamic instability of structures.This study sought to investigate the in 󿬂 uence of unintentional  󿬂 exibility of beam-to-columnconnection on the macro-behavior of RBS frames. To reach the purpose, we computed the  󿬂 exibilityof beam-to-column connection by  󿬁 nite element method and beam line analysis. By comparing theacquired stiffness with the required stiffness for a fully rigid connection, it can be suggested whether RBS connection can be assumed as fully rigid connection or not. As previously stated, if RBS connec-tion does not act as fully rigid connection, the  󿬂 exibility of beam-to-column connection must beincluded in the structural analysis. In the present study, the seismic performance of three buildingframes, including 4, 8 and 16 stories, are evaluated by including as well as excluding the connectionelements as part of the structural system analysis. In this direction, the nonlinear static analysis(pushover) and nonlinear dynamic analysis are performed for two hazard levels, namely, 2% probabilityofexceedancein50yearsand50%probabilityin50years.Specialpurposeelementsareemployedfortheneedsofthisstudy,andthevalidityoftheusedelementmodelsisdemonstratedthroughcomparisonswithexperimental andnumerical data reported inliterature. The in 󿬂 uence ofbeam-to-column 󿬂 exibility on theoverallperformanceofRBSframesisdiscussedbycomparingtheresultsofstaticanddynamicanalysisinterms of inter-story drifts, total drifts, story shears and shear deformation in panel zone.2. MICRO-BEHAVIOR OF REDUCED BEAM SECTION CONNECTION 2.1. Connections classi  󿬁 cation Connections are classi 󿬁 ed as rigid, semirigid and pinned with respect to their stiffness (AISC, 2010).When it comes to strength, connections can be classi 󿬁 ed as full or partial. Concerning their rotationalcapacity of the connections, they can be categorized as ductile or brittle. In order to classify beam-to-column connections, the stiffness, strength and rotation capacity of connection can be obtained from moment  – rotation (  M   –  θ ) curve of the connection, which is the most signi 󿬁 cant characteristic of theconnection. As shown in Figure 1, several methods have been proposed so as to determine the connec-tion stiffness. They are as follows: initial stiffness of the connection (  R ki ), secant stiffness at serviceload (  R ks ), secant stiffness at   θ y  (  R y ) in which  θ y  corresponds to the rotation at yield moment (  M  y )and,  󿬁 nally, secant stiffness that corresponds to a rotation of 0.01rad (  R 10 ). Because many connectiontypes do not exhibit a reliable initial stiffness, secant stiffness at service load (  R ks ) has shown to be a realistic response in regard to other methods (AISC, 2010). Here, in this study, the beam line analysis,proposed by Batho and Lash (1936), is used to establish the secant stiffness provided by connection ki R ks R  y R 10 R y M u M F M F θ  y θ  10 Rotation     M   o   m   e   n    t lineBeam s θ s M Figure 1. Typical moment  – rotation curve and de 󿬁 nition of stiffness and beam line method. 1250 M. GHASSEMIEH AND J. KIANI Copyright © 2012 John Wiley & Sons, Ltd.  Struct. Design Tall Spec. Build.  22 , 1248 – 1269 (2013)DOI: 10.1002/tal  using the actual moment  – rotation curve. In this method, the beam line connects the two ends in themoment  – rotation curve, being the rigidly  󿬁 xed end moment and the simply supported end rotation( θ F ) of the beam at service load as shown in Figure 1. Secant stiffness in the beam line method iseffective stiffness of the connection based on the expected moment and rotation at service load, whichis calculated from Eq. (1) as follows:  R ks ¼  M  S θ S (1)where  M  S  and  θ S  are the moment and rotation at service loads, respectively, as illustrated inFigure 1. For classi 󿬁 cation of the beam-to-column connections pertaining to their stiffness, thestiffness parameter,  m , was de 󿬁 ned as the ratio of the stiffness of the connection to the elasticstiffness of the beam: m ¼  R connEl  L    beam  (2)In Eq. (2),  L   and (EI) are the length and  󿬂 exural rigidity of the beam, respectively.  R conn  is thestiffness of connection calculated, based on previously mentioned methods. AISC (2010) categorizesconnections into three groups. According to this reference, if   m ≥ 20, then it is acceptable to consider theconnectiontobefullyrestrained,anditisnot necessarytoincludeconnectionasanindividualelement inthe analysis. If   m ≤ 2, it is acceptable to consider the connection tobe simple. For values between thesetwo limits, behavior of connection is considered to be semirigid or partially restrained connection.In this study, in order to investigate the real physical behavior of the connection and estimate thestiffness of RBS connection, the moment  – rotation curve of 10 different RBS specimens are obtainedby  󿬁 nite element method analysis. For classi 󿬁 cation purposes, using the beam line method, their stiff-ness are calculated, and therefore, the category of the connection is determined. 2.2. Reduced beam section specimens used in the analytical study The RBS specimens used in this study are beam-to-column connections that are going to be implemen-ted in building frames with different story level in which their overall performance is evaluated. Inchoosing the subframes, it is assumed that in 󿬂 ection points are located in the middle of beams andcolumns. Thus, the top and bottom of the column are pinned in the model in order to simulate thepractical conditions as depicted in Figure 2. The RBS connections used in this study with the radiusFigure 2. Schematic detail of RBS connection. SEISMIC EVALUATION OF REDUCED BEAM SECTION FRAMES 1251 Copyright © 2012 John Wiley & Sons, Ltd.  Struct. Design Tall Spec. Build.  22 , 1248 – 1269 (2013)DOI: 10.1002/tal

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