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Comparison of nonlinear behavior of steel moment frames accompanied with RC shear walls or steel bracings Hamed Esmaeili 1 * ,† , Ali Kheyroddin 1 , Mohammad Ali Kafi 1 and Hamed Nikbakht 2 1 Faculty of Civil Engineering, Semnan University, Semnan, Iran 2 Department of Civil Engineering, Sharif University of Technology, Tehran, Iran SUMMARY In this paper, the seismic behavior of dual structural systems in forms of steel moment-resisting frames accom- panied with reinforced concrete shear walls a
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  Comparison of nonlinear behavior of steel moment framesaccompanied with RC shear walls or steel bracings Hamed Esmaeili 1 * , † , Ali Kheyroddin 1 , Mohammad Ali Ka  󿬁 1 and Hamed Nikbakht  2 1 Faculty of Civil Engineering, Semnan University, Semnan, Iran 2  Department of Civil Engineering, Sharif University of Technology, Tehran, Iran SUMMARYIn this paper, the seismic behavior of dual structural systems in forms of steel moment-resisting frames accom-panied with reinforced concrete shear walls and steel moment-resisting frames accompanied with concentricallybracedframes,havebeenstudied.Thenonlinearbehaviorofthementionedstructuralsystemshasbeenevaluatedas, in earthquakes, structures usually enter into an inelastic behavior stage and, hence, the applied energy to thestructures will be dissipated. As a result, some parameters such as ductility factor of structure ( m ), over-strengthfactor (  R s ) and response modi 󿬁 cation factor (  R ) for the mentioned structures have been under assessment. Toachieve these objectives, 30-story buildings containing such structural systems were used to perform thepushover analyses having different load patterns. Analytical results show that the steel moment-resisting framesaccompanied with reinforced concrete shear walls system has higher ductility and response modi 󿬁 cation factor than the other one, and so,it is observed to achieve suitable seismic performance; using the 󿬁 rstsystem can havemore advantages than the second one. Copyright © 2011 John Wiley & Sons, Ltd. Received 2 August 2011; Accepted 3 November 2011 KEYWORDS : dualsystem;steelmoment-resistingframe;shearwall;steelbracing;reinforcedconcrete;seismicbehavior  1. INTRODUCTIONAs extensive areas in Iran, especially the populated cities, are located on the critical seismic zones andthey have high vulnerability to destruction, the study of seismic behavior of structural systems is of great importance. Today, reinforced concrete (RC) shear walls or steel bracings are used widespread as a mainload-carrying system in tall buildings, for different reasons such as increase of energy dissipation and itsability to resist lateral displacements of tall buildings that have moment-resisting frames. Therefore, therecognition of the seismic behavior of the dual structural systems and  󿬁 guring out their advantages canbe helpful to structural engineers in selecting a proper system for structures that are being designed.Studying the behavior of building structures as subjected to severe earthquake ground motionsreveals that this type of structures can exhibit enough strength, due to the nonlinear behavior of materialsandpossibilityofsuf  󿬁 cientdeformationsofthestructures.Thesestructuresabsorbtheapplied energyandwill dissipate it via tolerating great displacements in nonlinear seismic behavior.Nonlinear time history analysis of a detailed analytical model is perhaps the best option for theestimation of deformation demands. However, because of many uncertainties associated with thesite-speci 󿬁 c excitation as well as uncertainties in the parameters of analytical models, in many cases,the effort associated with detailed modeling and analysis may not be justi 󿬁 ed and feasible (Hajirasouliha and Doostan, 2010).In current years, nonlinear static analyses have earned a great deal of research attention within theearthquake engineering community. Their main purpose is to demonstrate the nonlinear capacity of a structure when subjected to horizontal loading with a reduced computational attempt with respect  *Correspondence to: Hamed Esmaeili, Faculty of Civil Engineering, Semnan University, Semnan, Iran. † E-mail: H_Esmaeili@sun.semnan.ac.ir THE STRUCTURAL DESIGN OF TALL AND SPECIAL BUILDINGS Struct. Design Tall Spec. Build.  22 , 1062 – 1074 (2013)Published online 19 December 2011 in Wiley Online Library (wileyonlinelibrary.com). DOI: 10.1002/tal.751Copyright © 2011 John Wiley & Sons, Ltd.  to nonlinear dynamic analyses. Pushover methods are particularly shown for assessing existing structures(frequently not srcinally designed with seismic criteria in mind), when the employment of linear elasticmethods,typicalinnewdesignsituations,tendstobeunsuitable.Forthesegoals,manycodesandguidelines(e.g. Eurocode 8, 2005; ATC-40, 1996; FEMA-356, 2000) propose the use of nonlinear static methodolo-gies to evaluate structural behavior under seismic movement (Ferracuti  et al  ., 2009). To assess the seismicperformance of the structures, three various nonlinear static analyses are used, each of which contains a constant load pattern. These approaches are pushover analyses with load patterns proportionate to uniform and reverse triangular displacements of structures, and modal pushover analysis (MPA).2. REVIEW OF THE LATEST RESEARCHESIn general, numerous studies in forms of analytical and experimental works have been implemented onthe mentioned structural systems. Most important results of which are as follows:A series of experimental programs including two-story specimens was developed to recognize thecyclic behavior of the composite structural systems. This study shows that the lateral shear force toleratevia compressive strut of wall and shear studs (Tong, 2001).Tong  et al  . (2005) presented an experimental study on the cyclic behavior of a composite structuralsystem consisting of partially restrained steel frames with RC in 󿬁 ll walls. The one-bay, two-story test specimen was built at one-third scale. The study shows that this system has the potential to offer strength appropriate for resisting the forces from earthquakes and stiffness adequate for controllingdrift for low-rise to moderate-rise buildings located in earthquake-prone regions.As a basis of many studies, structural frames with in 󿬁 ll panels are typically providing an ef  󿬁 cient method for bracing buildings (Jung and Aref, 2005). The presence of in 󿬁 lls can also have a signi 󿬁 cant effect on the energy dissipation capacity (Decanini  et al  ., 2002).In common practice, steel bracing system is used to increase the lateral load resistance of steel struc-tures. Steel moment-resisting frame structures possess high strength and signi 󿬁 cant ductility, thus areeffective structural forms for earthquake-resistant designs. However, the load-carrying ef  󿬁 ciency of such designs is limited when an earthquake induces large story drift because of the lower structuralstiffness of the steel frames (Hsu  et al  ., 2011).Over-strength, ductility and response modi 󿬁 cation factors of buckling-restrained braced frameswere evaluated by Asgarian and Shokrgozar (2009). To do so, buildings with various stories anddifferent bracing con 󿬁 gurations including diagonal, split X and chevron (V and inverted V) bracingswere considered. In this article, seismic response modi 󿬁 cation factor for each of bracing systems hasbeen determined separately, and tentative values of 8.35 and 12 has been suggested for ultimate limit state and allowable stress design methods, respectively.The over-strength, ductility and response modi 󿬁 cation factors of special concentric braced framesand ordinary concentric braced frames were evaluated by performing pushover analysis of modelstructures with various stories and span lengths (Kim and Choi, 2005). The results were compared withthose from nonlinear incremental dynamic analyses. The results of incremental dynamic analysisgenerally matched well with those obtained from pushover analysis.A signi 󿬁 cant aspect in the design of steel braced RC frames is the level of interaction between thestrength capacities of the RC frame and the bracing system. Maheri and Ghaffarzadeh (2008)conducted an experimental and numerical investigation to evaluate the level of capacity interactionbetween the two systems. It was found that the capacity interaction is primarily due to the connectionsover-strength and also the number of braced bays and the number of frame stories recognized.3. SEISMIC BEHAVIOR OF STRUCTURES 3.1. The ductility of structures As a general rule, it is possible to replace the ideal bilinear elasto-plastic diagrams with the baseshear  – displacement curves of structures (Figure 1). The ductility factor in single degree-of-freedom  COMPARISON OF NONLINEAR BEHAVIOR OF STEEL MOMENT FRAMES 1063 Copyright © 2011 John Wiley & Sons, Ltd.  Struct. Design Tall Spec. Build.  22 , 1062 – 1074 (2013)DOI: 10.1002/tal  (SDOF) systems is a proportion of maximum lateral displacement to the yielding lateral displacement of structures. m ¼ Δ max Δ y (1)In fact, the ductility factor explains to what extent the structure enters when in nonlinear state. There isno accurate de 󿬁 nition for the ductility factor of multiple degrees-of-freedom structures. In some provi-sions, yielding is assumed to have been simultaneous, although not precise (Wakabayashi, 1986). Mean-while, the relation between the base shear and displacement is not an elastic – perfectly plastic equation.With consideration to Figure 1, an idealization in de 󿬁 nition of the ductility factor is accepted. 3.2. Response modi  󿬁 cation factor  Seismic codes consider a reduction in design loads, taking advantage of the fact that the structurespossess signi 󿬁 cant reserve strength (over-strength) and capacity to dissipate energy (ductility). Theover-strength and the ductility are incorporated in structural design through a force reduction or a response modi 󿬁 cation factor. This factor represents ratio of maximum seismic force on a structureduring speci 󿬁 ed ground motion if it was to remain elastic to the design seismic force. Thus, actualseismic forces are reduced by the factor   ‘  R ’  to obtain design forces. The basic  󿬂 aw in code proceduresis that they use linear methods but rely on nonlinear behavior (Kim and Choi, 2005).As it is shown in Figure 1, usually, real nonlinear behavior is idealized by a bilinear elasto – perfectlyplastic relation. The yield force of structure is shown by  V  y  and the yield displacement is  Δ y . In this 󿬁 gure  V  e  or   V  max  correspond to the elastic response strength of the structure. The maximum base shear in an elasto perfectly behavior is  V  y  (Uang, 1991). The ratio of maximum base shear considering elasticbehavior   V  e  to maximum base shear in elasto perfectly behavior V y  is called force reduction factor,  R m  ¼ V  e V  y (2)The over-strength factor is de 󿬁 ned as the ratio of maximum base shear in actual behavior   V  y  to the 󿬁 rst signi 󿬁 cant yield strength in structure  V  s ,  R S  ¼ V  y V  s (3)To design for allowable stress method, the design codes decrease design loads from   V  s  to  V  w . Thisdecrease is done by allowable stress factor, which is de 󿬁 ned as (Asgarian and Shokrgozar, 2009):Figure 1. General structure response (Uang, 1991). 1064 H. ESMAEILI  ET AL. Copyright © 2011 John Wiley & Sons, Ltd.  Struct. Design Tall Spec. Build.  22 , 1062 – 1074 (2013)DOI: 10.1002/tal  Y   ¼ V  S V  W (4)The responsemodi 󿬁 cationfactor, therefore,accounts forthe ductilityandover-strengthofthestructureand for the difference in the level of stresses considered in its design. It is generally expressed in thefollowing form, taking into accounts the aforementioned conceptions (Asgarian and Shokrgozar, 2009),  R ¼ V  e V  W ¼ V  e V  y  V  y V  S  V  S V  W ¼  R m   R S  Y   (5) 3.3. The relation between the force reduction factor, the ductility factor and the period of structure The force reduction factor (  R m ) is related to many parameters of which many are correlated to character-istics of the structural system and some of them are independent from the structure and are related to theother parameters suchasrespectedloading (the time history ofearthquake).  R m will becorrelated toaset of factors, especially the ductility factor of structure and its performance characteristics in the nonlinear state, if we consider a speci 󿬁 c earthquake for a particular place. Therefore, the  󿬁 rst step in determiningforce reduction factor is specifying the relation between it and the capacity of the ductility of structure.Multiplefactors are knownthat af  󿬂 uence ontherelation between  R m  and m , suchasmaterials,periodof system, damping,  P  Δ effects, the load – deformation model in the hysteresis loops and type of the soilthat exists in the site. If we consider this assumption that the ductility in the structures with short period isthe same as those that have longer periods, then smaller   R m  is obtained. Also, New Mark and Hall (1982)suggested the following equations for calculation of the force reduction factor of structures:  R m  ¼ 1  T   <  0 : 125 s(6)  R m  ¼  ffiffiffiffiffiffiffiffiffiffiffiffiffiffi  2 m  1 p   0 : 125 s  <  T   <  0 : 5 s (7)  R m  ¼ m  0 : 5 s  <  T  (8) 3.4. The conversion coef   󿬁 cient of linear to nonlinear displacement (C  d )It  ’ s clear that the structural damages are normally originated from excessive deformations of thestructure. Therefore, with regard to the effective parameters on seismic design of a structure, thediscussion about assessment and accurate prediction of displacement and monitoring of them are themost important aims in seismic design of a structure. The  C  d  coef  󿬁 cient can be calculated as follows: C  d  ¼ Δ max Δ S ¼ Δ max Δ y  Δ y Δ s ¼ m   R s  (9)4. DESIGN OF THE STRUCTURAL MODELS IN THIS STUDYIn this study, two structural models are used for specifying the trend of this research, de 󿬁 nesas follows: COMPARISON OF NONLINEAR BEHAVIOR OF STEEL MOMENT FRAMES 1065 Copyright © 2011 John Wiley & Sons, Ltd.  Struct. Design Tall Spec. Build.  22 , 1062 – 1074 (2013)DOI: 10.1002/tal
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