Seismic displacements and behaviour factors assessment of an innovative steel and concrete hybrid coupled shear wall system
Introduction
Recent researches have illustrated that the post-earthquake rehabilitation of buildings is costly and time consuming. Therefore, the current investigations are more than ever oriented towards constructing economical and easily repairable buildings. Hybrid steel and concrete coupled shear wall is one of these promising structures which has attracted attention over the past decades [1], [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16]. Recently, a new representation of the hybrid coupled wall (HCW) system is provided within a European research project [17]. This system consists of a RC shear wall coupled to two steel side columns using steel links, as shown in Fig. 1. The main objective of this method is to keep RC wall in elastic mode up to the design basis earthquake where the seismic damage is concentrated only to the replaceable steel links. This system can attain high flexural capacity. Hence, the frame of the structure can be constructed using pinned connections. Furthermore, the damaged links can be easily replaced after earthquakes. Subsequently, the proposed system not only facilitates the construction process of the whole structure but also attains a very high recovery of the community in post-earthquake repair phase. The innovative hybrid coupled wall system can attain lower damage in the concrete wall than the conventional HCW system since it is subjected to bending moment only without additional alternative traction-compression forces. Moreover, a reduced mass is achieved thanks to the reduction in RC elements which also attains a smaller horizontal dimension in plan without losing flexural capacity of the system. The new proposed system will be referred to as Inn-HCW in this study in order to be differentiated from (HCW) conventional hybrid coupled wall system. A design procedure of this system is presented by Zona et al. [18]. It provides a good agreement with the main goal of the system creation.
Das et al. [19] presented a modification of the design method by using shear critical links which indicate better performance. A computationally efficient finite element model using Opensees platform [20] is presented and validated by Zona et al. [21] for the Inn-HCW system. A development of two component-based models of steel links of the Inn-HCW system is presented by Morelli et al. [22]. The seismic design and behaviour of a steel embedded connection of Inn-HCW system were also investigated by Das et al. [23]. They have found a good dissipating ability without obvious damages to the concrete wall.
Salameh et al. [24] recommended using embedded steel sections in inner wall and nonuniform links distribution for CR = 0.6 and CR = 0.4 with shear critical links in order to minimise damage in inner wall, where CR value is defined as the ratio of the moment resisted by the two lateral steel columns over the whole resisted moment (Fig. 1).
All these researches have discussed the performance and efficiency of the novel system. However, the Inn-HCW system still needs substantial investigations concerning its design and direct assessment of nonlinear behaviour. The Inn-HCW system is characterized by low-cost materials, high lateral capacity, high seismic energy dissipation, easy construction, easy and fast repair after earthquakes without violating the investment of structure; and the most important one is easy design, where the Zona et al. [18] design procedure can be easily used in combination with the lateral force method stated in codes. The system with uniform links will be subjected to uniform rotation demand in links along the height of structure [21], [24]. Accordingly, the material volume of elements is perfectly exploited without any extra requirements in the design process. However, using nonuniform links method will cause a variation in links rotation along the height. On the other side, it can efficiently delay wall first yielding.
The objective of this study is to make the Inn-HCW system design easier and more predictable, especially in the nonlinear phase of behaviour, so that design process needs minimised number of iterations. In such regard, the behaviour factor q is a very important criterion to be considered and thoroughly investigated. The q parameter is a reduction factor through which the elastic design spectrum is reduced. On the basis of this reduced elastic spectral, lateral forces are obtained and used in structure design. It is directly associated with structure capability to dissipate ground motion energy. q behaviour factors (or strength reduction factors R) [25] are usually estimated by the seismic codes as constant numbers, aiming to satisfy life safety performance of the structural systems. Where the life safety limit state can be defined when the maximum interstorey drift ratio (IDRmax) of the structure does not exceed a predefined value stated in codes due to structure type; implementing a particular q value during the design process can restrict IDRmax to this allowed value. The q factor refers to the first local yield point thus pushover analysis is not required, which enables a rapid seismic assessment of Inn-HCW structures. Because of the significant lack of investigations, the current q factor adopted for Inn-HCW system inaccurately equals 3.3 relying on EC8 value for composite or concrete walls coupled by steel or composite beams systems as recommended by Dall’Asta et al. [17]. The nonlinear displacements assessment is also critical in the design process since it dominates the damage in nonstructural elements (such as windows and cladding). In such regard, the ductility μ is a critical response parameter defined as a ratio between nonlinear displacement and the corresponding displacement when first yielding occurs. It represents the system capacity to dissipate energy. The higher the ductility, the lower the design seismic forces. Various types of ductility are defined in literature such as local ductility, storey ductility and global ductility. Numerical investigation regarding ductility evaluation of steel buildings with moment resisting steel frames is conducted by Llanes-Tizoc et al. [26]. They concluded that ductility values may vary significantly with the strong motion, the ductility definition, the structural element, the story number, the type of analysis, and the structural model. Reyes-Salazar et al. [27] proposed a value of 1/3 for the ratio of global to local ductility for steel buildings. Su et al. [28] established analytically simple relationships for the global and local ductility demands based on the pushover analysis for quick seismic assessments of low-rise regular masonry-infilled RC buildings with soft storey failure mechanism. However, the ductility and behaviour factor are related together by the equal-displacement rule proposed by Eurocode 8, so that the inelastic deformations of structures can be obtained by multiplying elastic deformations by behaviour factor. Ruiz‐García et al. [29] and Chopra et al. [30] declared that the equal-displacement rule is only valid when T1 period is larger than the characteristic period of the ground motion Tc (the period at the transition point between the constant-acceleration and the constant-velocity portion of the elastic response spectrum). Shimazaki et al.[31] determined the range of q and T1 values where the equal-displacement rule is accurate. Lepage [32] has refined the equal-displacement rule in order to estimate seismic drift demands, especially for buildings with periods within constant acceleration range of elastic response spectrum. Later, many investigations have confirmed that equal-displacement rule considerably overestimates displacement demands of structures [33], [34], [35], [36], [37], [38], [39], [40], [41].
Lots of studies have been devoted to improve and facilitate the current design approaches of concrete, steel and steel–concrete structures by proposing direct relations to estimate ductility demands, displacements and q behaviour factors [35], [39], [42], [43], [44], [45], [46], [47], [48], [49]; from which the inspiration is drawn to go more in depth with the seismic behaviour of Inn-HCW system and improving an efficient approach based on simple formulae providing a direct estimation of: fundamental periods of vibration T1, seismic displacements, ductility demands and behaviour factors q for both designed and undesigned Inn-HCW structures at different limit states involving steel first yielding of internal wall, various target IDRmax and links maximum rotations values. To this end, a group of 120 Inn-HCW systems subjected to a set of 100 far-field ground motions are selected. 420,000 dynamic nonlinear time histories are carried out in order to generate a databank of specified response quantities. Subsequently, nonlinear regression analyses are conducted and the formulae of the following response quantities are presented: (1) yield displacements Uy, (2) lateral displacements at steel first yielding in inner wall Uwy, (3) Maximum displacement profiles Ui with respect to a predefined IDRmax (4) μr,IDR maximum roof displacement ductility for a specified IDRmax (5) μr,θ maximum roof displacement ductility for a specified maximum target rotation in shear links (6) behaviour factor with respect to occurrence of first yielding in inner wall qwy (7) behaviour factor q relation as being a function of roof ductility (q-μr relation). As a result of the aforementioned relations, q factor can be estimated for different IDRmax values expressing various limit states of the structure performance. The Inn-HCW systems used in this extensive parametric study are selected in order to cover a wide range of structural characteristics and satisfy the constructional requirements and the best seismic performance recommendations have stated in the literature so far (especially Salameh et al. [24]). As a consequence, the influence of the following parameters on the structural response is investigated in detail: (1) number of storeys ns, (2) coupling ratio CR, (3) steel area ratio in boundary element ρ%, (4) uniformity status of shear links US. (5) Length of links LL. To this end, the following parameters are adopted: five cases of storeys numbers: 3, 6, 9, 12 and 15. Two CR values: 0.4 and 0.6. Three levels of steel ratio in the boundary element: medium reinforcement ratio referred to as MR, high reinforcement ratio referred to as HR, and very high steel ratio provided by using steel profiles referred to as SP. Two types of uniformity status: uniform and nonuniform (NU). Two values of links’ length: low and high.
Section snippets
Characteristics and design
A parametric study with a group of 120 case studies is performed. They are designed in order to cover a wide range of structural characteristics of Inn-HCW systems. The Inn-HCW system is connected with a gravity frame as portrayed in Fig. 2a. The structures have storeys number equals 3, 6, 9, 12 and 15 as indicated in Fig. 2b. A similar trend of components’ characteristics as that used by Salameh et al. [24] is adopted here (see Salameh et al. [24] for unmentioned characteristics). The
Finite element modelling
The finite element model proposed by Zona et al. [21] is proposed here to represent the Inn-HCW system. The force-based distributed-plasticity fibre frame element available in Opensees [20] is utilized to describe the flexural behaviour of the inner wall elements of the Inn-HCW system. The shear behaviour of the RC wall is modelled as linear elastic zero-length elements aggregated to the wall elements since the latter are dominated by flexural behaviour and do not suffer from shear yielding.
Accelerograms and response databank
NGA database [52] is used to select a set of 100 (far-field type) accelerograms on the basis of the elastic spectrum of 0.2 g ground acceleration and ground type B of Eurocode 8 [50] as depicted in Fig. 5. The response databank of the 120 Inn-HCW systems previously described is produced using 420,000 dynamic nonlinear time histories relying on the incremental dynamic analysis (IDA) (Vamvatsikos and Cornell [53]).
The results of the nonlinear dynamic analyses have been processed with a view to
Seismic response of Inn-HCWs
In this section, simple mathematical formulas are utilized in order to evaluate the seismic response of the Inn-HCW system taking advantage of similar relevant studies [35], [37], [38], [39], [40], [41], [43], [55], [56]. A nonlinear regression analysis (Levenberg–Marquardt algorithm) is utilized in order to find explicit values of the equations’ constants.
The arguments which take part in these equations are: number of storeys ns, order of floor i, coupling ratio CR, ρ parameter which expresses
Conclusions
This paper puts forward an ensemble of simple mathematical formulae of innovative steel and concrete hybrid coupled wall seismic behaviour through an extensive parametric study conducted on the basis of nonlinear dynamic response databank. These formulae can offer a direct seismic assessment of the most important response quantities i.e. yield displacements, inelastic displacements with respect to steel first yielding and predefined IDRmax, roof ductility demands for a target IDRmax and maximum
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
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