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Analytical expressions for preliminary design of dissipative bracing systems in steel frames
Abstract
In this paper a direct displacement-based design (DDBD) method for seismic design of steel frames equipped with dissipative braces is proposed. Attention is focused on concentric braced steel frames with pinned beam-to-column joints in which the bracing system (with viscoelastic or elastoplastic dissipative devices) is the main seismic resistant component. The proposed design method uses an equivalent continuous model where flexural deformability and shear deformability are related respectively to columns and diagonals of the bracing system. In this way, analytical expressions of the required flexural and shear stiffness distributions are obtained. These expressions are quite simple and can be conveniently used in preliminary design of dissipative diagonal braces and columns. Examples are shown for steel frames with dissipative braces based on elastomeric dampers (viscoelastic devices) and steel frames with buckling-restrained braces (elastoplastic devices). Results of time history analyses are illustrated and discussed in order to evaluate the effectiveness of the proposed DDBD procedure.
... However, also steel structures designed before the publication of modern regulations (e.g., AISC 341-16 [17], ASCE 7-16 [18], EN 1993-1-1 [19], EN 1998-1 [20]) have been reported to suffer local and global collapses as a consequence of earthquakes [21][22][23][24][25][26][27]. Braces equipped with energy dissipation devices have proved to be effective in reducing the seismic demand for both RC [6][7][8][9][10][11][12]15] and steel structures [26][27][28][29][30][31][32][33][34][35][36][37][38][39], and the most updated codes (e.g., [17,18,20]) have incorporated general guidelines for the design of dissipative braces in new constructions, with the goals of limiting the lateral displacement and dissipating most of the seismic energy in auxiliary devices, avoiding any damage to the gravity-load resistant system [33,[39][40][41][42]. ...
... However, also steel structures designed before the publication of modern regulations (e.g., AISC 341-16 [17], ASCE 7-16 [18], EN 1993-1-1 [19], EN 1998-1 [20]) have been reported to suffer local and global collapses as a consequence of earthquakes [21][22][23][24][25][26][27]. Braces equipped with energy dissipation devices have proved to be effective in reducing the seismic demand for both RC [6][7][8][9][10][11][12]15] and steel structures [26][27][28][29][30][31][32][33][34][35][36][37][38][39], and the most updated codes (e.g., [17,18,20]) have incorporated general guidelines for the design of dissipative braces in new constructions, with the goals of limiting the lateral displacement and dissipating most of the seismic energy in auxiliary devices, avoiding any damage to the gravity-load resistant system [33,[39][40][41][42]. ...
... Most of the procedures proposed in the literature [6][7][8][9][10][11]39,[43][44][45] for dimensioning dissipative braces are based on the Direct Displacement-Based Design (DDBD) method [45], in which a "substitute" single degree of freedom (SDOF) model is used to replace the real multi-degree of freedom (MDOF) structure. The design of the dissipating system is performed to achieve, for a given seismic intensity level, a specified performance objective, expressed for example as a specific target displacement [11]. ...
Supplementary energy dissipation has proved to be an effective way of protecting structures from the disastrous effects of earthquakes and has been used in the last decades both in new and in existing constructions. In this regard, various procedures for the design of the damping system for the seismic retrofit of buildings have been formulated over the years, mainly focused on reinforced concrete (RC) constructions, which represent the largest part of the existing stock in many seismic-prone countries. The study deals with the assessment of a displacement-based design procedure for proportioning the damping system recently proposed in the literature for RC framed buildings, with the goal of establishing a good practice for the application of the procedure to steel buildings as well. The method was applied to three case-study frames, regular in plan and in elevation, which were assumed as being representative of old structures designed without consideration of seismic requirements. The retrofit was performed by using chevron braces equipped with dampers with an elastic-perfectly plastic behavior. The method aimed at defining the properties of the dampers to achieve a target performance in terms of the maximum lateral deflection for a specific level of seismic intensity. The effectiveness and reliability of the proposed procedure was eventually assessed by evaluating the seismic performance of the upgraded steel structures in static and dynamic non-linear analyses.
... To simultaneously consider both characteristics in the design process, the capacity curve of the structure can be compared to the ductility-reduced (e.g., inelastic) demand spectrum in the Acceleration-Displacement Response Spectrum (ADRS) plane, as previously done by several other authors (e.g., 17,18). Several design methods have been developed for newly designed BRBFs and for the retrofitting of existing structures with BRBs (e.g., [19][20][21][22]. The present study uses a design procedure aligned with the one developed by Ragni et al., 20 as it allows to directly calibrate strength, stiffness and ductility of the BRBs in order to meet specific design objectives. ...
... Several design methods have been developed for newly designed BRBFs and for the retrofitting of existing structures with BRBs (e.g., [19][20][21][22]. The present study uses a design procedure aligned with the one developed by Ragni et al., 20 as it allows to directly calibrate strength, stiffness and ductility of the BRBs in order to meet specific design objectives. Nonetheless, prioritising either strength or deformation capacity may allow simultaneously reaching other performance objectives. ...
... The design of the retrofitted structures considers a dual system configuration, in which the existing MRF and the BRBF work in parallel. The design procedure for the BRBs is similar to the approach used by previous authors 20 and relies on an equivalent SDoF approximation. 17 The main objectives of the design procedure are: (1) to produce a controlled increase of the base shear capacity of the system, i.e., the base shear of the dissipative system when added to the base shear of the bare frame; (2) to increase strength, stiffness, and energy dissipation capacity of the structure while maintaining a proportional response per storey. ...
Buckling restrained braces (BRBs) represent an effective strategy for the seismic retrofit of existing steel moment resisting frames (MRFs), as they contribute to increasing the strength and ductility capacity of the structure. However, current design strategies do not provide recommendations on how the performance increase is achieved. Prioritising either the increase of strength or ductility capacity has an impact on the damage evolution and affects the overall performance of the structure. A low increase of strength typically requires larger exploitation of the ductility capacity (i.e., damage) of the existing structure, while a high increase of strength produces a significant increase of stiffness, which is often accompanied by an increase of the seismic demands that may limit the effectiveness of the retrofitting solution. The present study assesses the impact of these decisions on the overall performance of steel MRFs retrofitted with BRBs. For this purpose, two MRFs with several BRB retrofitting configurations are used as case study structures. Finite Element Models are built in OpenSees and assessed through Incremental Dynamic Analyses to account for the record‐to‐record variability. Fragility relationships are derived based on local Engineering Demand Parameters (EDPs) to describe structural and non‐structural damage, as well as path‐dependent damage indicators (i.e., residual drifts and cumulative ductility in BRBs). A comparison of the overall performance of the structures is carried out in terms of risk estimates for a high seismicity location.
... For this reason, the use of these devices is very effective for both new constructions and the rehabilitation of existing buildings. 7,8 The large and stable energy dissipation capacity of BRBs, proven by many experimental campaigns, 5,6 is accompanied by a low post-yielding stiffness, which may result in inter-story drift concentration 9 and large residual inter-story drifts. In addition, experimental tests demonstrated the susceptibility of BRBs to low-cycle fatigue fracture due to the limited cumulative ductility capacity. ...
... 3 This assumption is realistic only for BRBs yielding simultaneously at various stories, a condition which is usually sought in the design. 7,8,33 The Zona and Dall'Asta 3 model features both kinematic and isotropic hardening, the latter controlled by the cumulative plastic deformation. Moreover, it allows the description of the tension-compression asymmetry characteristic of the BRBs, where the maximum forces resisted in compression are typically about 10% to 15% higher than forces resisted in tension. ...
... 45 The lower bound of 5 is considered because often, such as in case of the seismic retrofit of RC frames, 8 the BRB devices are arranged in series with an elastic brace and this leads to reduced values of the ductility capacity, which can be as low as 5 for flexible braces. 7,46 Finally, in order to limit the parameters to be varied in the parametric analysis, the values for the damping factor and the post-elastic stiffness ratio of the frame are assumed constant and respectively as ξ = 5% and k fh = 5%. ...
Buckling‐restrained braces (BRBs) have proven to be very effective in improving the seismic performance of existing and new structures. They provide strength, stiffness and add energy dissipation to the structure. However, being BRBs characterized by a low post‐elastic stiffness, their use may lead to residual deformations hindering the building's reparability and to excessive cumulative ductility demand possibly compromising the residual capacity of BRBs. To overcome these drawbacks, BRB frames (BRBFs) can be coupled with moment‐resisting frames (MRFs) to form dual systems. If properly designed, MRFs acting as back‐up frames allow the control of the residual drifts and the optimization of the performance of the BRBs. The contribution of this study is to provide insights into the performance and residual capacity of BRBFs‐MRFs dual systems and to shed light on the influence of the main BRB's design parameters. To this end, a nondimensional formulation of the equation of motion is introduced for a single degree of freedom system, and an extensive parametric study is performed for a set of natural ground motion records with different characteristics and scaled to various intensity levels. This allows the investigation of a wide range of configurations, considering different levels of the relative strength and ductility demand of BRBFs and MRFs, and obtains useful information for their design. Finally, two case study frames, modeled as two‐dimensional nonlinear multi‐degree of freedom systems, are analyzed, and the results were compared to those obtained from the nondimensional formulation to show the capabilities and the limitations of the adopted methodology and of the SDOF approximation.
... For this reason, the use of these devices is very effective for both new constructions and the rehabilitation of existing buildings. 7,8 The large and stable energy dissipation capacity of BRBs, proven by many experimental campaigns, 5,6 is accompanied by a low post-yielding stiffness, which may result in inter-story drift concentration 9 and large residual inter-story drifts. In addition, experimental tests demonstrated the susceptibility of BRBs to low-cycle fatigue fracture due to the limited cumulative ductility capacity. ...
... 3 This assumption is realistic only for BRBs yielding simultaneously at various stories, a condition which is usually sought in the design. 7,8,33 The Zona and Dall'Asta 3 model features both kinematic and isotropic hardening, the latter controlled by the cumulative plastic deformation. Moreover, it allows the description of the tension-compression asymmetry characteristic of the BRBs, where the maximum forces resisted in compression are typically about 10% to 15% higher than forces resisted in tension. ...
... 45 The lower bound of 5 is considered because often, such as in case of the seismic retrofit of RC frames, 8 the BRB devices are arranged in series with an elastic brace and this leads to reduced values of the ductility capacity, which can be as low as 5 for flexible braces. 7,46 Finally, in order to limit the parameters to be varied in the parametric analysis, the values for the damping factor and the post-elastic stiffness ratio of the frame are assumed constant and respectively as ξ = 5% and k fh = 5%. ...
Buckling-restrained braces (BRBs) are energy dissipation devices which have proven to be very effective in improving the performance of existing and new building frames. However, their post-elastic stiffness may lead to excessive residual deformations in the systems to be protected, and this may cause irreparable damage and jeopardize the capability of withstanding multiple shocks. Previous studies demonstrated that buckling-restrained braced frames (BRBFs) can be used in conjunction with special moment-resisting frames to form a dual system, able to minimize the residual drifts and optimize the performances of the BRBFs. The objective of this present paper is to provide recommendations regarding the proportioning in terms of forces, stiffness and ductility of the two systems. For this purpose, an extensive parametric analysis under the single degree of freedom approximation for the dual system is carried out to shed light on the parameters that control the seismic performance and residual capacity of frames equipped with BRBs. A non-dimensional formulation of the problem allows investigating wide ranges of configurations, including the case of BRBFs and the case of BRBFs forming a dual system with moment-resisting frames. The results of this study provide useful information for the preliminary sizing and the optimal choice of the design parameters of structural systems equipped with BRBs.
... For this reason, the use of these devices is very effective for both new constructions and the rehabilitation of existing buildings. 7,8 The large and stable energy dissipation capacity of BRBs, proven by many experimental campaigns, 5,6 is accompanied by a low post-yielding stiffness, which may result in inter-story drift concentration 9 and large residual inter-story drifts. In addition, experimental tests demonstrated the susceptibility of BRBs to low-cycle fatigue fracture due to the limited cumulative ductility capacity. ...
... 3 This assumption is realistic only for BRBs yielding simultaneously at various stories, a condition which is usually sought in the design. 7,8,33 The Zona and Dall'Asta 3 model features both kinematic and isotropic hardening, the latter controlled by the cumulative plastic deformation. Moreover, it allows the description of the tension-compression asymmetry characteristic of the BRBs, where the maximum forces resisted in compression are typically about 10% to 15% higher than forces resisted in tension. ...
... 45 The lower bound of 5 is considered because often, such as in case of the seismic retrofit of RC frames, 8 the BRB devices are arranged in series with an elastic brace and this leads to reduced values of the ductility capacity, which can be as low as 5 for flexible braces. 7,46 Finally, in order to limit the parameters to be varied in the parametric analysis, the values for the damping factor and the post-elastic stiffness ratio of the frame are assumed constant and respectively as ξ = 5% and k fh = 5%. ...
Buckling-restrained braces (BRBs) have proven to be very effective devices improving the seismic performance of existing and new building frames. They provide strength, stiffness and added damping to the structure, however, due to their low lateral post-elastic stiffness, their use may lead to excessive residual deformations which may hinder the building’s reparability. Moreover, excessive cumulative ductility demand in the BRBs may compromise the capability of withstanding multiple earthquakes. To overcome these drawbacks, BRB frames (BRBFs) can be coupled with moment-resisting frames (MRFs) to form a dual system. If properly designed, the MRF acts as a back-up frame and allows to control the residual drifts and optimize the performance of the BRBs. This paper attempts to provide insights into the performance and residual capacity of this type of dual systems and to shed light on the influence of the main BRB’s design parameters. A non-dimensional formulation of the equation of motion is derived and an extensive parametric study is carried out on a single-degree-of-freedom system subjected to a set of natural records with different characteristics and scaled to various intensity levels. This allows to investigate a wide range of configurations, considering different levels of the relative strength of the BRBF and MRF and their ductility demand, and to obtain useful information for the BRBs design.
... Adaptada de [39] . 36 [81] . Tomada de [59] . ...
... Como señala Urrego [33] y Barbagallo et al. [12] , es posible ver a las estructuras equipadas con CRP's como el ensamble de dos subsistemas: el conformado por los disipadores, el cual resiste las acciones sísmicas, y el conformado por las vigas y columnas, cuya función es tomar las acciones gravitatorias. Esta consideración permite dos enfoques de diseño distintos: mientras algunos métodos se limitan a consideran únicamente la participación de los disipadores en la toma de fuerzas sísmicas [34][35][36] , hay otros que toman en cuenta también la capacidad resistente de la estructura principal [24,33] . ...
Se plantea el problema de determinar el diseño óptimo de la estructura de refuerzo conformada por disipadores de energía sísmica de tipo Contraviento Restringido al Pandeo (CRP), que permita el reajuste del desempeño sísmico de marcos de hormigón armado.
Los CRP’s son elementos conformados por un núcleo metálico confinado, capaz de plastificar tanto a tracción como a compresión, característica que les permite disipar energía sísmica por medio de ciclos histeréticos. Debido a su comportamiento estable frente a acciones cíclicas, los disipadores de tipo CRP han sido utilizados tanto en el diseño como en el reajuste de estructuras ubicadas en zonas de elevado riesgo sísmico, como Japón, EU y América Latina.
Debido al comportamiento no lineal que presenta la respuesta de estructuras equipadas con disipadores de tipo CRP, los diseños candidatos a solución han sido analizados por medio de OpenSees, que es un programa de elementos finitos enfocado a la ingeniería sísmica. El desempeño sísmico de todos los diseños ha sido evaluado por medio del método del espectro de capacidad (Capacity Spectrum Method), el cual utiliza la información de análisis estáticos no lineales (Pushover) para estimar el desplazamiento máximo que presentará la estructura bajo una demanda sísmica dada.
El proceso de optimización ha sido realizo por medio del algoritmo metaheurístico conocido como Simulated Annealing (SA), teniéndose como objetivo determinar el número, disposición y características de los disipadores. Las características geométricas del núcleo de los CRP’s y su distribución en el marco fueron consideradas como variables, mientras que los elementos estructurales del marco se mantuvieron inalterados durante el proceso. El algoritmo de SA se corrió en el programa Matlab, creándose un vínculo entre este último y OpenSees para permitir la transferencia de información durante el proceso de optimización. El uso conjunto de ambos programas se mostró eficiente en la optimización de estructuras complejas por medio de algoritmos metaheurísticos.
... The use of BRBs for seismic retrofitting has been widely investigated in the last few years through components as well as large-scale experimental tests, [8][9][10][11] extensive numerical studies, [12][13][14][15][16][17] and exploring design methods for their optimal distribution. [18][19][20][21] However, while the effect of some uncertain parameters, such as the ground motion record-to-record variability, is often investigated, only a deterministic description of the dampers' properties is usually considered. ...
... While extensive details on the methodology used for BRBs design can be found elsewhere in literature, 14,18,19 a brief outline of the design process and the parameters involved is presented herein. The primary objectives that dictate the BRBs design process comprise of (a) defining BRBs dimensions such that they produce a controlled increase of the base shear capacity of the system, that is, the base shear of the dissipative system (V d,1 ) when added to the base shear of the bare frame (V f,1 ); (b) distributing the stiffness of BRBs among the stories such that the first mode shape of the bare frame remains unchanged following the retrofit implementation. ...
Passive control systems, such as buckling‐restrained braces (BRBs), have emerged as efficient tools for seismic response control of new and existing structures by imparting strength and stiffness to buildings, while providing additional high and stable energy dissipation capacity. Systems equipped with BRBs have been widely investigated in literature; however, only a deterministic description of the BRBs’ properties is typically considered. These properties are provided by the manufacturer and are successively validated by qualification control tests according to code‐based tolerance limits. Therefore, the device properties introduced within the structure could differ from their nominal design estimates, potentially leading to an undesired seismic performance. This study proposes a probabilistic assessment framework to evaluate the influence of BRBs’ uncertainty on the seismic response of a retrofitted RC frame. For the case study, a benchmark three‐story RC moment‐resisting frame is considered where BRBs’ uncertainty is defined compatible to the standardized tolerance limits of devices’ quality control tests. This uncertainty is implemented through a two‐level factorial design strategy and Latin hypercube sampling technique. Cloud analysis and probabilistic seismic demand models are used to develop fragility functions for the bare and retrofitted frame for four damage states while also accounting for the uncertainty in the property of BRBs. Risk estimates are successively evaluated for three case study regions. The results show that, for the considered case study structure, these uncertainties could lead to an increase of fragility up to 21% and a variation in seismic risk estimates up to 56%.
... In order to design structures protected with BRBs, methods based in the control of the response have been proposed recently. Most of these methods were proposed only for BRB frames, defined as systems whose lateral resistance is only provided by BRBs while the contribution of the frame is neglected [9][10][11]. However, the contribution of the main structure may represent a significant amount of capacity and should be taken into account when designing and assessing structures equipped with BRBs. ...
... where u; _ u; and € u are the displacement, velocity and acceleration; € u g is the acceleration of the ground, n 1 and n 2 are the damping ratios of the primary and secondary parts of the dual oscillator; T is the period estimated with Eq. (9); m is the modal mass; f s1 ðu; _ uÞ and f s2 ðu; _ uÞ are the restoring forces of each part of the dual oscillator (they depend on the history of displacements, the sign of the velocity, and the yielding load capacity, which may be determined using Eqs. (11) and (12)). In this part, it should be noted that the restoring forces do not necessarily have to follow the bilinear hysteretic model presented in Fig. 1c. ...
This paper proposes a method for preliminary Performance-Based Seismic Design (PBSD) of low-rise structures protected with Buckling-Restrained Braces (BRBs). It is assumed that a frame structure protected with BRBs, termed as a dual structure, is rationally represented by a dual single-degree-of-freedom (SDOF) oscillator whose parts yield at different displacement levels. The formulation of the method is presented for SDOF structures. This simplification is validated using a case study example. A comparison of the responses between conventional and dual structures shows that, when designing dual structures, the common practice of using conventional design spectra may lead to biased designs. One of the main advantages of the method is that, during its application, information useful for preliminary and quick assessment of structures is generated, facilitating the application of the PBSD philosophy. A case study example is conducted to show its applicability and its potential for preliminary assessment of structures. Regarding its limitations, the method is valid for low-rise regular buildings with rigid in-plane diaphragms, and whose dynamic response is dominated by their fundamental mode of vibration.
... Sci. 2023, 13, 8250 3 of 35 strength raise from isotropic hardening [23]; the Bouc-Wen smooth law [24]; the modified Ramberg-Osgood smooth law with isotropic and kinematic strain hardening as well as a yield load in compression increased by 10% [25]; the Menegotto-Pinto smooth law with kinematic and isotropic hardening [26]. All uni-axial constitutive models have their own advantages and disadvantages. ...
Recently, buckling-restrained braces (BRBs) have been widely implemented as seismic load resistance systems in buildings to enhance their response against dynamic vibration. However, during catastrophic earthquakes, the steel core in BRB devices fully yields, which causes the BRB to lose its functionality. While the incorporation of various filler materials, such as new high-performance concretes, has the potential to enhance the performance of buckling-restrained braces (BRBs), there remains a notable gap regarding comprehensive research investigating this aspect. Therefore, this study assessed the effect of implementing ultra-high-performance concrete (UHPFRC) as filler material on BRB behavior. For this purpose, the finite element model for the proposed BRB was developed and hysteresis analysis results under incremental cyclic loads were investigated. Then, the prototype of a BRB with UHPFRC concrete was cast and experimentally tested under cyclic loads by using a dynamic actuator. Based on the testing results, a new design for a BRB device named as rubber buckling-restrained brace (RBRB) was developed, implementing hyperelastic rubber components between the steel core and UHPFRC as an additional load-bearing mechanism to enhance the device vibration dissipation capacity. Subsequently, a finite element model of the newly proposed rubber buckling-restrained brace (RBRB) was developed to assess the device’s performance. The analysis results demonstrate a notable enhancement in load capacity and energy dissipation for the RBRB device compared to conventional BRBs.
... In the latter case, a bilinear hysteretic model is used for the material properties of flexural and shear cantilevers. Ragni et al. [9] proposed a displacement-based method, particularly devoted to the seismic design of steel frames equipped with dissipative braces, by using an equivalent continuous beam-like model where flexural deformability and shear deformability are related to columns and diagonals of the bracing system respectively. ...
This study presents an original inelastic beam-like model for the simulation of the nonlinear dynamic behaviour of three-dimensional buildings subjected to earthquake loadings. The proposed model is defined as a step-wise shear only cantilever beam, whose segments have the same mechanical properties of the corresponding inter-storeys of the building. The inter-storey constitutive laws are calibrated by means of the results of a static nonlinear analysis performed on the 3D FEM model of the building. An inverse nonlinear static identification procedure allows obtaining an inelastic beam-like model equivalent to the more demanding 3D FEM model, related to a specific direction and under a precise distribution of horizontal loadings. Dynamic nonlinear analyses performed on this simplified model allow a drastic reduction of the required computational effort and time with respect to the more demanding 3D FEM model. The reliability of the proposed beam-like model is validated through numerical applications on an irregular multi-storey RC frame representative of residential buildings in Catania designed to resist only gravity loadings.
... The response spectrum for a 5% probability of exceedance in 50 yrs (i.e., TR = 975 yrs) is considered for the design at the Collapse Prevention (CP) structural performance level, as required by the ASCE 41-17 [13] for buildings within Risk Category II. The retrofit design procedure used [10,14,15] aims to maximise the energy dissipation capacity of the BRBs by proportioning their stiffness to match the first mode shape of the bare frame and their strength to induce the simultaneous yielding of the devices in all storeys. The retrofit design is based on a target top storey drift of 0.275 m, which corresponds to a drift at which some of the structural elements in the MRF have overpassed the Immediate Occupancy (IO) [13], but none of the elements has overpassed the Life Safety (LS) structural performance level. ...
The behaviour of Buckling-Restrained Braces (BRBs) is characterised by steady and nearly symmetrical hysteretic loops that provide large energy dissipation capacity. However, their low post-yielding stiffness may result in large residual deformations at the end of the earthquake motion. Moreover, the cumulative ductility demand due to repeated plastic excursions can lead to low-cycle fatigue failure. These two unfavourable conditions could be exacerbated by the occurrence of subsequent earthquakes (e.g., mainshock-aftershock sequences or multiple earthquakes during the design lifetime). Therefore, their assessment requires a framework that considers ground motion (GM) sequences. In this paper, a case study structure subjected to GM sequences is analysed, considering three Engineering Demand Parameters (EDPs) relevant to the performance evaluation of the BRBs and of the frame, namely the maximum ductility demand in the BRBs, the cumulative ductility demand in the BRBs, and the residual inter-storey-drift in the frame. These EDPs are assessed both independently and simultaneously, in order to establish the risk of overpassing any capacity limit that may lead to the collapse or demolition of the structure.KeywordsBuckling-restrained bracesGround motion sequencesCumulative ductilityResidual deformationRisk assessment
... Beam-like structures have also been adopted taking into account dissipative devices. For example, Ragni et al. [21] proposed a displacement-based method, particularly devoted to seismic design steel frames equipped with dissipative braces, by using an equivalent continuous beam-like model where flexural deformability and shear deformability are related, respectively, to columns and diagonals of the bracing system. The design method is appealing since analytical expressions of the required flexural and shear stiffness distributions are obtained and conveniently adopted in the preliminary design of dissipative diagonal braces and columns of steel frames. ...
Modern computational techniques have greatly influenced the numerical analyses of structures, not only in terms of calculation speed, but also in terms of procedural approach. In particular, great importance has been given to structural modelling, that is, the process by which a structure and the actions to which it is subjected are reduced to a simplified scheme. The use of a simplified calculation scheme is necessary since the structures are, in general, considerably complex physical systems whose behaviour is influenced by a large number of variables. The definition of a structural scheme that is at the same time simple enough to be easily computable as well as sufficiently reliable in reproducing the main characteristics of the behaviour of the analysed structure is, therefore, a crucial task. In particular, with reference to multi-storey framed buildings, the extensive use of three-dimensional finite element models (FEM) has been made in recent decades by researchers and structural engineers. However, an interesting and alternative research field concerns the possibility of studying multi-storey buildings through the use of equivalent beam-like models in which the number of degrees of freedom and the required computational effort are reduced with respect to more demanding FEM models. Several researchers have proposed single or coupled continuous beams to simulate either the static or dynamic response of multi-storey buildings assuming elastic or inelastic behaviour of the constitutive material. In this paper, a review of several scientific papers proposing elastic or inelastic beam-like models for the structural analyses of framed multi-storey buildings is presented. Considerations about limits and potentialities of these models are also included.
... Thus, the response of the dual system is considered to be the addition of the MRF and BRBF responses. The procedure considered for the design of the retrofitting BRBFs is similar to the approach used by previous authors (e.g., [18,20,40]), which relies on an equivalent SDoF approximation [14]. The main objective of the design procedure is to increase the strength, stiffness and energy dissipation capacity of the structure while maintaining a proportional response per storey. ...
Buckling Restrained Braces (BRBs) represent an effective strategy for the seismic retrofit of existing steel Moment Resisting Frames (MRFs), as they contribute to increase the strength, stiffness and energy dissipation capacity of the frame. Nonetheless, the design choices made during the retrofit process have a significant impact on the performance of the structure. For example, the inclusion of ‘large’ BRBs (i.e., high yielding strength and stiffness) may contribute to limit the deformation demands in the MRF; nonetheless, it may also induce large forces in the beams and columns of the existing structure. On the other hand, the inclusion of ‘smaller’ BRBs (i.e., low yielding force and stiffness), while allowing reaching the required safety requirements, may not be able to protect the MRF from damage. Additionally, the sizing of the BRB elements has an influence on the seismic demand parameters affecting the global performance of structural and non-structural components (i.e., peak and residual drifts, as well as storey accelerations). The present study investigates the impact of the design choices in the seismic performance of a retrofitted three-storey case-study frame by considering three retrofit options. The case-study MRF for the bare frame and the three retrofit configurations are modelled and numerically investigated in Opensees by monitoring local damage states (e.g., damage in BRBs, beams, columns, panel zones). First, a comparison is made in terms of non-linear static analyses to identify the deficiencies of the structures. Then, a fragility analysis is carried out through Incremental Dynamic Analyses (IDAs) accounting for the influence of the recordto-record variability. Finally, a comparison is made in terms of local and global Engineering Demand Parameters, by developing fragility curves for the components, for storey drifts and accelerations.
... To address this problem, some studies focused on the development of design methods for the optimal distribution of device properties within the frames (e.g., Refs. [171,172]) and considered the influence of Moment Resisting Frames (MRFs) working in parallel with the BRB system (e.g., Refs. [173,174]). ...
The Sendai Framework for Disaster Risk Reduction 2015-2030 (SFDRR) highlights the importance of scientific research, supporting the ‘availability and application of science and technology to decision making’ in disaster risk reduction (DRR). Science and technology can play a crucial role in the world’s ability to reduce casualties, physical damage, and interruption to critical infrastructure due to natural hazards and their complex interactions. The SFDRR encourages better access to technological innovations combined with increased DRR investments in developing cost-effective approaches and tackling global challenges. To this aim, it is essential to link multi- and interdisciplinary research and technological innovations with policy and engineering/DRR practice. To share knowledge and promote discussion on recent advances, challenges, and future directions on ‘Innovations in Earthquake Risk Reduction for Resilience’, a group of experts from academia and industry met in London, UK, in July 2019. The workshop focused on both cutting-edge ‘soft’ (e.g., novel modelling methods/frameworks, early warning systems, disaster financing and parametric insurance) and ‘hard’ (e.g., novel structural systems/devices for new structures and retrofitting of existing structures, sensors) risk-reduction strategies for the enhancement of structural and infrastructural earthquake safety and resilience. The workshop highlighted emerging trends and lessons from recent earthquake events and pinpointed critical issues for future research and policy interventions. This paper summarises some of the key aspects identified and discussed during the workshop to inform other researchers worldwide and extend the conversation to a broader audience, with the ultimate aim of driving change in how seismic risk is quantified and mitigated.
... The steel frames consist of columns and beams whose main purpose is to support gravity loading and diagonal bracing members that resist horizontal forces. Several comprehensive references are available on the analysis and design of steel frames with bracing systems (Baradaran and Madhkhan 2019;Chaudhuri 2013;Ghaffarzadeh and Maheri 2006;Jiang et al. 2015;Kazemi et al. 2020;Maheri and Yazdani 2016;Nassani et al. 2017;Ragni et al. 2011;Semko and Prokhorenko 2013;Shamivand and Akbari 2020). (Ghowsi and Sahoo 2015) investigated the performance of chevron and split-X bracing systems under near-fault ground motions. ...
In this study, the effects of wind and seismic loads on 5, 10, and 15 story steel buildings with different bracing systems were investigated. Linear static and nonlinear dynamic analyses were performed to assess the base shear, base moment, and story drift for all bracing systems. In addition, the cost analysis was taken into consideration. Five structural configurations were used: V-bracing, inverted V-bracing, one-story X-bracing, and multistory X-bracing. One of the most important features of a building is lateral stiffness, which defines the resistance to displacement under seismic and wind loads, at the same time, the lateral stiffness has a major impact on the natural time of the structure. Reducing displacement and cost in the structures indicates that the design is safe and economical. Therefore, the purpose of this article is to find the best bracing system that causes minimum displacement, which indicates maximum lateral stiffness. From this point of view, the behavior of bracing systems exposed to wind and seismic loads in buildings with different stories was investigated. Static linear analysis results showed that the best bracing systems to reduce lateral displacement were the one-story X-bracing system for 5 and 15 story buildings and the V-bracing system for 10 story buildings. On the other hand, nonlinear dynamic analysis results showed that lateral displacement was minimum in unbraced, V-bracing, and one-story X-bracing systems for 5, 10, and 15 stories, respectively.
... This arrangement conveniently allows the independent calibration of the stiffness (Kc i ) and strength (Fc i ) of the dissipative diagonal braces. The distribution of the stiffness Kc i at each story is designed such that the first mode shape of the bare frame stays invariant upon placement of the retrofit [32,33]. This measure helps to avoid drastic changes to the internal action distribution in the frame, at least within the range of the elastic behavior. ...
Non-ductile buildings designed without consideration of modern seismic design principles may lead to damage, incurring loss of life and property following earthquake events. Alleviation of damage due to earthquakes is accomplished utilizing structural retrofitting techniques. Among the various viable retrofit measures, the use of buckling restrained braces (BRBs) has emerged to be promising, as indicated by past researchers. These braces provide a supplemental path for the earthquake-induced lateral loads and thus enhance the seismic behavior of the frame by adding energy dissipation capacity and, in some cases, stiffness to the bare frame. Consequently, this retrofitting technique leads to reduction in seismic losses in case of a future earthquake event. A frame can be designed for various retrofit level defined as the ratio between the base shear capacity of the bracing system and the bare frame. Since the infrastructure owners and stakeholders are often restricted by economic resources; it is crucial to estimate the cost-effectiveness of different retrofit level in terms of economic metrics by considering various sources of uncertainties into consideration. A benchmark two-dimensional reinforced concrete frame with low ductility capacity is considered as a case study. The gravity load designed frame is retrofitted with BRBs for different retrofit level. The cost effectiveness of various retrofit level is conducted by a probabilistic approach where record-to-record variability of ground motions and BRB parameter uncertainty is considered to first develop seismic fragility curves of retrofitted frame for different retrofit level. Next, the fragility curves are used in conjunction with regional hazard information and repair costs data to evaluate the seismic life-cycle cost estimates of the retrofitted frame for various retrofit level. The study identifies the most viable retrofit level that result in minimum seismic life-cycle cost and consequently highest benefits in terms of retrofit implementation. The conclusions from this study aim to help infrastructure management agencies to assess investment decisions and identify the most cost-effective retrofit level for BRB design.
... The accredited finite element pattern was then applied for parametric investigations to define the results of different elements of the frame, containing column base link hardness and correction to the brace link plan, on the frame position and treatment. The construction treatment of beamcolumn hinges acts as a serious part in the seismic answer of frame constructions (Laura et al., 2011). The vulnerability of steel-framed constructions in many new incidents has incited construction engineers to comprehend their efficiency under such risk. ...
Evolutionary Structural Optimization (ESO) is one of the rules in structural engineering which has received much attention by the researchers. Today, the reduction of construction cost and weight is an important issue in the structure design. The optimization phenomenon is pursuing to fulfill this objective. Thus, presenting a design which could be both safe and economic is of special significance. Despite the valuable researches which have been conducted on optimization of steel structures, the gap of research on ESO of wind bracing connection plates and other metal connections is sensible. The purpose of the present paper is to make an optimal design of these types of connections in the frames with convergent bracing. In this study, the software of Finite Element Method (FEM) of abaqus has been used to design the concentrically (convergent) wind bracing of connection plates based on optimization principles. The Von-Mises stress distribution contour has been presented for two statuses in different angles. In the designed bracing frame, dimensions and thickness of connection plate have been defined as the design variables and the design of optimization is compared with the design of ordinary status and the past works as well. This shows a noticeable reduction in the weight of the optimal designed plate in comparison with the ordinary design.
... The accredited finite element pattern was then applied for parametric investigations to define the results of different elements of the frame, containing column base link hardness and correction to the brace link plan, on the frame position and treatment. The construction treatment of beamcolumn hinges acts as a serious part in the seismic answer of frame constructions (Laura et al., 2011). The vulnerability of steel-framed constructions in many new incidents has incited construction engineers to comprehend their efficiency under such risk. ...
Evolutionary Structural Optimization (ESO) is one of the rules in structural engineering which has received much attention by the researchers. Today, the reduction of construction cost and weight is an important issue in the structure design. The optimization phenomenon is pursuing to fulfill this objective. Thus, presenting a design which could be both safe and economic is of special significance. Despite the valuable researches which have been conducted on optimization of steel structures, the gap of research on ESO of wind bracing connection plates and other metal connections is sensible. The purpose of the present paper is to make an optimal design of these types of connections in the frames with convergent bracing. In this study, the software of Finite Element Method (FEM) of abaqus has been used to design the concentrically (convergent) wind bracing of connection plates based on optimization principles. The Von-Mises stress distribution contour has been presented for two statuses in different angles. In the designed bracing frame, dimensions and thickness of connection plate have been defined as the design variables and the design of optimization is compared with the design of ordinary status and the past works as well. This shows a noticeable reduction in the weight of the optimal designed plate in comparison with the ordinary design.
... Other models such as Bouc-Wen smooth law (Black et al., 2004), improved Ramberg-Osgood (providing good approximation for elasticplastic behavior) law having combined isotropic and kinematic strain hardenings and a model with compression yield load enhanced by 10% (Tremblay et al., 2008) are available in the literature. The Menegotto-Pinto smooth model, again in combination with kinematic and isotropic hardening, has been used to date (Ragni et al., 2011). Similarly, Zona and Dall'Asta (2012) developed both kinematic and isotropic hardening model and the associated parameters that are useful for realistic simulation of the behavior of BRBs that were tested elsewhere. ...
Hysteretic performance of buckling restrained braces (BRBs) having various core materials, namely, steel and aluminum alloy and
with various end connections are numerically investigated. As a computational tool, nonlinear finite element analyses (FEAs) are
performed to better model the hysteretic behavior. For the simulation, various aspects such as 1) stress – strain relationship including
the strain hardening effect 2) von Mises yield criterion 3) contact surface parameters between the core metal and surrounding high
strength grout and 4) friction are defined. Experimental results from near-full scale cyclic tests on two steel core BRBs having steel
casing as a restraining environment (named as BRB-SC4 and BRB-SC5) and an aluminum alloy core & aluminum alloy casing tube
(named as BRB-AC3) are used in the analyses. All cyclically tested specimens have been designed according to AISC Seismic
Provisions. Numerical results obtained from 3D models developed in ANSYS-Workbench give satisfactory response parameters
when compared with the experimental ones (e.g., hysteretic curves, dissipated energies). Further, a convergence analysis regarding
element numbers in the developed model is conducted for each BRB specimen. Finally, key issues that influence the hysteretic
modeling of BRBs are identified.
... This arrangement allows the independent calibration of the stiffness (Kc i ) and strength (Fc i ) of the dissipative diagonal braces. The distribution of the stiffness Kc i at each story is designed in order to keep the first modal shape of the bare frame unchanged after the retrofit implementation (Dall'Asta et al. 2009, Ragni et al. 2011). This avoids drastic changes to the internal action distribution in the frame, at least in the range of the elastic behavior. ...
Passive control systems, such as buckling restrained braces (BRBs), have emerged as an efficient tool for the seismic response control of new and existing structures by providing strength and stiffness to buildings, in addition to high and stable energy dissipation capacity. Systems equipped with BRBs have been widely investigated in literature, however, only deterministic description of the BRBs’ properties is usually considered. These properties are provided by the manufacturer and are successively validated by qualification control tests. The acceptance criteria specified by codal standards allows for some variation in the response of a single BRB by introducing a tolerance limit. Therefore, the ‘real’ properties of these devices could differ from the design values. This difference can affect the seismic response and potentially lead to an undesired seismic performance at the global level. This paper provides some preliminary insights on the influence of the BRBs’ uncertainty on the seismic response of a retrofitted RC frame. For the case-study, a benchmark two-dimensional RC frame is considered. A single retrofit condition is analyzed and the BRBs’ uncertainty is defined according to the tolerance limits of devices’ quality control tests. Cloud analysis and probabilistic seismic demand models are used to develop fragility functions for four different damage states. Fragility curves are defined for the bare and retrofitted frame while considering both the design and the ‘real’ values of the BRBs properties. The preliminary results show that the BRBs’ uncertainty could lead to an increase of the vulnerability up to 26.80% for the considered case-study.
... BRBs are then designed following the methodology proposed by Dall'Asta et al. (2009) that has been extended in order to account for the axial deformability of columns (Maley et al. 2010, Ragni et al. 2011). Finally, beams and columns of the BRBF, assumed pinned at the joints, are designed in overstrength, following the capacity design provisions to ensure that damage is concentrated within BRBs only. ...
Buckling-restrained braces (BRBs) are employed in new constructions and in the retrofitting of existing frames. They provide additional strength and stiffness to buildings, together with high and stable energy dissipation capacity. BRBs can fail due to excessive maximum and/or cumulative ductility demands. In addition, the use of BRBs can result in large residual drifts in the structure due to their low post-elastic hardening. Moreover, in seismic-prone regions, structures are usually subjected to mainshock-aftershocks (MS-AS) earthquake sequences, often leaving no time for repair or retrofit between events. Ductility demand accumulation and/or residual drifts induced by the MS can affect the structural performance during the following AS. The present study addressed the abovementioned issues by first investigating an optimal design procedure for steel dual systems in which conventional BRB frames are combined with moment-resisting frames. The latter are designed to behave elastically to enhance the self-centering capability of the structure and limit soft-story mechanisms. The design procedure is first presented and applied to a case-study building. The seismic performance of the latter is assessed by means of sequential Cloud Analysis. Both real and artificial MS-AS sequences are used to derive system fragility curves. Results show that the BRB’s capacity can be potentially affected by multiple earthquakes, which cause accumulation of plastic strains within the devices. However, the preliminary results show that when accounting for real MS-AS sequences, ASs do not significantly increase the cumulative ductility demands in BRBs.
... The dissipative braces considered in this paper are made by an elasto-plastic dissipative device placed in series with an elastic brace exhibiting adequate over-strength. The properties of the dissipative brace are defined on the basis of the properties of its components [33]. If K b denotes the axial stiffness of the elastic brace and K 0 , F 0 and m 0u respectively, the stiffness, yielding force and ductility capacity of the elasto-plastic device, the dissipative brace stiffness K d and ductility capacity m du are given by ...
The paper illustrates a probabilistic methodology for assessing the vulnerability of existing reinforced concrete (RC) buildings with limited ductility capacity retrofitted by means of dissipative braces. The aim is to highlight the most important parameters controlling the capacity of these coupled systems and specific aspects concerning the response uncertainties. The proposed methodology is based on the use of local engineering demand parameters for monitoring the seismic response and on the development of component and system fragility curves before and after the retrofit. In the first part of the paper, the methodology is illustrated by highlighting its advantages with respect to the existing approaches. Then, its capability and effectiveness are tested by considering a benchmark two-dimensional RC frame designed for gravity-loads only. The frame is retrofitted by introducing elasto-plastic dissipative braces designed for different levels of base shear capacity. The obtained results show the effectiveness of the methodology in describing the changes in the response and in the failure modalities before and after the retrofit, for different retrofit levels. Moreover, the retrofit effectiveness is evaluated by introducing proper synthetic parameters describing the fragility curves and by stressing the importance of employing local engineering demand parameters (EDPs) rather than global EDPs in the seismic risk evaluation of coupled systems consisting in low-ductility RC frames and dissipative braces.
... The parameter 0 is varied in a range In some situations, such as the seismic retrofit of RC frames (Freddi et al. 2013), the BRB device is arranged in series with an elastic brace exhibiting adequate over-strength. This leads to reduced values of the ductility capacity which may attain the lower bound of 5 for a very flexible elastic brace (Ragni et al. 2011). The value of 2% is assumed for the damping factor in this study. ...
Buckling-restrained braces (BRBs) are often employed for the seismic retrofit of existing systems and the design of new systems given their significant contribution in terms of stiffness and added damping. However, since BRBs are characterized by a low lateral post-elastic stiffness, their use may lead to excessive residual deformations that may jeopardize the reparability of the building. Moreover, accumulation of plastic deformations in the BRBs may endanger the capability of withstanding multiple earthquakes and aftershocks. The objective of this paper is to provide insight into the performance and residual capacity of dual systems made of BRB frames coupled with moment-resisting frames. This study considers a simplified single degree of freedom model which permits to investigate a wide range of configurations. A non-dimensional formulation of the equation of motion is introduced, the statistic of the normalized peak and residual displacements and cumulative ductility of the system is evaluated under a set of ground motion records. Different values of the BRB target maximum ductility and different coupled frame properties are considered. The results of this study provide useful information for the preliminary design of dual systems made of BRB frames coupled with moment-resisting frames.
... In some situations, such as the seismic retrofit of RC frames [6], the BRB device is arranged in series with an elastic brace exhibiting adequate over-strength. This leads to reduced values of the ductility capacity which may attain the lower bound of 5 for a very flexible elastic brace [12]. The value of 2% is assumed for the damping factor . ...
Buckling-restrained braces (BRBs) are often employed for the seismic retrofit of existing build-ings and the design of new structures, given their significant contribution in terms of stiffness and added damping. However, BRBs are characterized by a low lateral post-elastic stiffness, leading to excessive residual deformations that may compromise reparability. Moreover, accumulation of plastic deformations in the BRBs may compromise the capability of withstanding multiple earth-quakes and aftershocks. The objective of this paper is to provide insight into the performance and residual capacity of dual systems made of BRB frames coupled with moment-resisting frames, through a simplified single-degree-of-freedom model. A non-dimensional formulation of the equation of motion is introduced, the statistic of the normalized peak, residual displacements and cumulated ductility of the system is evaluated for a set of ground motion records. Different values of the BRB target maximum ductility and coupled frame properties are considered.
... Several recent experimental tests and numerical simulations (e.g. [7,8,9,10,11] among many others) have shown that multi-storey framed building structures may be efficiently retrofitted by using unbonded or buckling restrained braces (BRBs). A typical BRB consists of a steel ductile core designed to yield both in tension and compression. ...
... Interstorey height h = 3.4 m is constant between adjacent floors; columns are continuous with pinned beam-tocolumn connections and hinge restraints at the base. Four V-bracing systems (BRBs) for each direction are the only seismic resistant components (Figure 1a), their preliminary design was based on the procedure described in [15]. Masses from vertical live and superimposed dead loads are 1200 kNs 2 /m for each floor. ...
... In such a case, the yielding takes place only at a limited number of storeys and the ductile elements should be designed to guarantee the global ductility, e.g. [9][10] [11]. ...
... In the latest decade many studies have been centred on seismic design and behavior of BRBs. Ragni et al. (2011) have proposed a direct displacement-based design (DDBD) method for seismic design of dissipative bracing systems in steel frames. In particular, an equivalent continuous model where flexural deformability and shear deformability are related respectively to columns and diagonals of the bracing system is used. ...
... More specifically, two alternative approaches have been followed: (a) the force-based design (FBD) approach combined with required deformation target verification (e.g. see (Ponzo et al. 2012;Ragni et al. 2011) or (Kim et al. 2003), referring to hysteretic (HY) or viscous (VS) dampers, respectively); (b) the displacement-based design (DBD) approach, in which the design starts from a target deformation (e.g. see Vulcano 2008a,b, 2013), in the case of HY dampers; (Mazza and Vulcano 2013) and (Kim and Choi 2006) in the case of VE dampers) of an equivalent elastic (linear) system with effective properties (i.e. ...
... But, they tested the dampers added to a moment resisting frame in the usual configuration as a supplemental energy dissipation device. In reference [12], Ragni et al. presented a numerical investigation of a SFRS similar to the one proposed in this paper together with a displacement-based design method. We present a similar SFRS that was developed about the same time as the previous reference but the proposed study is different in two ways: a different, more practical, design procedure is proposed and, as opposed with the previous study, the proposed design procedure is validated experimentally and reliability of the system is shown with shake table tests on a reduced scale structures and full scale reversed cyclic loading tests. ...
This paper presents an innovative use of natural rubber pads for seismic control of multistory low- and medium-rise steel braced frames. Such pads have always been used as supplemental energy dissipation devices in structures that already have their own and independent seismic force resisting system. This paper investigates the use of such devices in series with chevron braces as an autonomous seismic force resisting system, which provides not only additional damping to the structure but also a period shift. The damping and isolation material is a fiber reinforced natural rubber exhibiting strong nonlinear dependence with respect to strain. First, a design procedure based on numerical studies is illustrated for a typical one-story building. Pseudo-linear models of the structures are used for the final evaluation of the seismic response. Cyclic tests on a full scale frame were conducted to calibrate the models and showed the reliability of the autonomous rubber-based system under full loading and real assembly conditions. Then a 1/3-scale 3-story chevron braced steel frame with and without rubber devices was used to evaluate the seismic performances of the system. The application was studied numerically and experimentally through shake table tests of the 1/3 reduced-scale model at different seismic intensities. Results show the efficiency of the system to significantly reduce linear seismic forces induced on the structure without devices. Control of displacements is also achieved but is highly dependant on the initial value of damping in the structure without devices.
... Examples of application of the derived response sensitivities with respect to the BRB constitutive model parameters and relevant numerical validation are illustrated using as benchmark problem a 4-storey steel V-bracing system with BRBs as depicted in Fig. 2a. Such bracing system is one of the four equal bracing systems that are the only seismic resistant components for each direction in a realistic 4-storey steel frame described in [35,48] and designed using the elastic spectrum type 1 of Eurocode 8 [49] for ground type B with design ground acceleration a g = 0.35 g as seismic input. The considered benchmark bracing system is connected to a side column representing the gravity-resisting steel frame pertinent to the bracing system with equivalent stiffness, mass, and loads. ...
... The dissipative braces considered in this paper are made by an elasto-plastic dissipative device placed in series with an elastic brace exhibiting adequate over-strength. The properties of the dissipative brace are defined on the basis of the properties of its components [33]. If K b denotes the axial stiffness of the elastic brace and K 0 , F 0 and m 0u respectively, the stiffness, yielding force and ductility capacity of the elasto-plastic device, the dissipative brace stiffness K d and ductility capacity m du are given by ...
The paper illustrates a probabilistic methodology for assessing the vulnerability of existing r.c. buildings with limited ductility capacity and retrofitted by means of dissipative braces. The methodology is based on the development of single component and system fragility curves before and after the retrofit. The proposed approach allows to highlight the possible changes in the most significant collapse modalities before and after the retrofit and to evaluate the effectiveness of the retrofit by taking into account the probabilistic properties of the seismic behaviour of the considered systems. A benchmark 2-dimensional reinforced concrete frame with low ductility capacity is considered as case study. The frame is designed for gravity-loads only and does not comply with modern anti-seismic code requirements. It is retrofitted by introducing elasto-plastic dissipative braces designed for different levels of their target base-shear capacity, following a design method involving the pushover analysis of the system before and after retrofit. The obtained results show that the use of braces yields a significant increase in the seismic capacity, though an increased dispersion of the behaviour is observed in the retrofitted system.
... More specifically, two alternative approaches have been followed: (a) the force-based design (FBD) approach combined with required deformation target verification (e.g. see (Ponzo et al. 2012;Ragni et al. 2011) or (Kim et al. 2003), referring to hysteretic (HY) or viscous (VS) dampers, respectively); (b) the displacement-based design (DBD) approach, in which the design starts from a target deformation (e.g. see Vulcano 2008a,b, 2013), in the case of HY dampers; (Mazza and Vulcano 2013) and (Kim and Choi 2006) in the case of VE dampers) of an equivalent elastic (linear) system with effective properties (i.e. ...
A displacement-based design (DBD) procedure aiming to proportion hysteretic
damped braces (HYDBs) in order to attain, for a specific level of seismic intensity, a designated
performance level of a structure is proposed for the retrofitting of framed buildings. A
key step for the reliability of the DBD procedure is the selection of the equivalent viscous
damping in order to account for the energy dissipated by the damped braced frame. In this
paper, expressions of the equivalent damping are obtained considering the energy dissipated
by the HYDBs and the framed structure. To this end, dynamic analyses of an equivalent single
degree of freedom system, whose response is idealized by a trilinear model, are carried
out considering real accelerograms matching, on the average, Eurocode 8 (EC8) response
spectrum for a medium subsoil class. Then, a three-storey reinforced concrete (r.c.) framed
structure of a school building, designed in a medium-risk seismic region according to the
Italian code in force in 1975, is supposed as retrofitted as if in a high-risk seismic region
of the current seismic code (NTC08) by the insertion of HYDBs. Nonlinear static analyses
are carried out to evaluate the vulnerability of the primary structure, characterized by the
lack of interior girders along the floor slab direction, and to select optimal properties of
the HYDBs. The effectiveness of the retrofitting solutions is checked referring to nonlinear
dynamic analyses, considering artificially generated accelerograms whose response spectra
match those adopted by NTC08 for the earthquake design levels corresponding to the
serviceability and ultimate limit states.
... The dissipative braces considered in this paper are made by an elasto-plastic dissipative device placed in series with an elastic brace exhibiting adequate over-strength. The properties of the dissipative brace are defined on the basis of the properties of its components [33]. If K b denotes the axial stiffness of the elastic brace and K 0 , F 0 and m 0u respectively, the stiffness, yielding force and ductility capacity of the elasto-plastic device, the dissipative brace stiffness K d and ductility capacity m du are given by ...
The paper illustrates a probabilistic methodology for assessing the vulnerability of existing reinforced concrete (RC) buildings with limited ductility capacity retrofitted by means of dissipative braces. The aim is to highlight the most important parameters controlling the capacity of these coupled systems and specific aspects concerning the response uncertainties. The proposed methodology is based on the use of local engineering demand parameters for monitoring the seismic response and on the development of omponent and system fragility curves before and after the retrofit. In the first part of the paper, the methodology is illustrated by highlighting its advantages with respect to the existing approaches. Then, its capability and effectiveness are tested by considering a benchmark two-dimensional RC frame designed for gravity-loads only. The frame is retrofitted by introducing elasto-plastic dissipative braces designed for different levels of base shear capacity. The obtained results show the effectiveness of the methodology in describing the changes in the response and in the failure modalities before and after the retrofit, for different retrofit levels. Moreover, the retrofit effectiveness is evaluated by introducing proper synthetic parameters describing the fragility curves and by stressing the importance of employing local engineering demand parameters (EDPs) rather than global EDPs in the seismic risk evaluation of coupled systems consisting in low-ductility RC frames and dissipative braces.
... Various cyclic models have been proposed to represent the BRB behaviour in numerical studies using truss finite elements: bilinear elastoplastic model with brace axial compressive strength set to 110% of the tensile counterpart and post-yield stiffness conservatively set to zero [8] [9]; bilinear force-deformation relationship with post-yield stiffness ratio of 0.05 [10]; trilinear force-deformation analytical model (obtained with two inelastic truss elements in parallel) with representation of the strength increase of BRBs that comes from isotropic hardening [11][12][13]; Bouc-Wen smooth law [14]; modified Ramberg-Osgood smooth law with isotropic and kinematic strain hardening as well as a yield load in compression increased by 10% [15]; Menegotto-Pinto smooth law with kinematic and isotropic hardening [16]. Each of these uniaxial constitutive models has benefits and limitations. ...
Buckling-restrained braces (BRBs) permit exploiting the hysteretic properties of their core material both in tension and compression. However, the global behaviour of the BRB does not fully replicate the local behaviour of the core material and important differences have been observed in experimental tests, such as a higher bearing capacity in compression and a significant role of isotropic hardening. These observations have thus promoted the use of specific constitutive models for BRBs. Besides a proper description of behavioural aspects, a BRB model should include some highly desired requirements: explicit computation of the plastic component of the deformation as required in BRB capacity models, smoothness of the elastic-plastic transition to improve convergence rate, simple implementation and limited number of input data parameters to facilitate its implementation and use. In order to address the above behavioural and modelling issues, an elastoplastic model for steel BRBs is presented in this paper following a consistent approach based on a rheological scheme that leads to a quite simple constitutive law involving only one internal variable. The adopted formulation allows a straightforward physical interpretation and identification of the constitutive parameters of the model as well as explicit computation of response quantities related to failure and dissipated energy. Response results obtained using the proposed model are compared to the outcomes of experimental tests available in the literature and involving different BRBs under various strain histories, showing good predictions of the experimental behaviour. © 2011 Elsevier Ltd.
... Masses from vertical live and superimposed dead loads are 1200 kNs 2 /m for each floor. A preliminary design of the bracing frames was carried out using a displacement-based design (DBD) procedure [34] based on the first vibration mode, with maximum interstorey drift equal to the 1% of the storey height as design objective and the elastic spectrum type 1 of Eurocode 8 [3] for ground type B with design ground acceleration a g = 0.35g as seismic input. The global structural ductility values estimated by the DBD procedure are 4.78 and 2.9 for the 4-floor and the 8-floor frames, respectively. ...
In this paper, a novel hysteretic friction damper, called Prestressed LEad Damper with Straight Shaft (or PS-LED), is presented as a viable solution for the seismic rehabilitation of existing RC framed buildings. The PS-LED is characterized by high stiffness and damping capability combined with a compact design, and low manufacturing cost, which make it suitable for social housing. The constitutive behavior of the PS-LED, assessed experimentally in cyclic tests at different speeds, is formulated in the OpenSees framework through a simple rheological model comprising a parallel of a non-linear spring and a viscous model.
To explore the viability of the PS-LED for seismic upgrade of existing buildings, a numerical investigation is performed by considering a RC frame structure, paradigmatic of a category of Italian buildings designed according to outdated codes. The case-study structure retrofit is designed considering two possible damage targets: (i) in the first case, the upgrade is performed in order to achieve elastic response of the structure under the basic design earthquake; (ii) in the second case, a partially dissipative behavior of the RC frame is conceived, with activation of plastic hinges to a repairable level. Non-linear static and Non-linear dynamic analyses are performed, showing a satisfactory agreement between the seismic performance and the design targets.
As final stage, a comparison between two retrofit solutions with either the PS-LED or with a conventional steel hysteretic damper (SHD) is performed, demonstrating that the PS-LED, thanks to its high damping capacity, is able to control the increase in internal forces that usually affects frames upgraded with SHDs.
Structural vibration is a widespread issue occurred in the field of civil engineering. The passive energy dissipation devices are being increasingly popular for protecting structures from external excitations due to their high performance and no need for external energy. They can be divided into displacement-dependent dampers and velocity-dependent dampers, among which the metallic yielding dampers (MYDs) and fluid viscous dampers (FVDs) are the most representative. This paper presents an overview of the MYD and FVD, aiming to reveal their defects and provide suggestions for future development. The basic concept, the mechanical models, the design approaches, and the applications in civil engineering of the two dampers are reviewed. In particular, the obstacles in application and preference in research of these two dampers are summarized, and their merits and drawbacks are further discussed. Emphatically, the strategies for improvement and future development trends are explored.
An adaptive version of the capacity spectrum method for displacement-based seismic assessment of steel frames is presented. The procedure can improve the efficiency of estimation of seismic demand and avoids the problems of no convergence and multiple solutions because it is non-iterative. Reliability of the procedure is verified by means of nonlinear dynamic analysis on structures subjected to earthquake records. The results are finally compared with the seismic response estimated with nonlinear static procedures proposed in FEMA 440-ATC-55.
Is archaeology a social science? Most archaeologists would probably agree that the goal of our discipline is to learn about the people, societies and cultures of the past. Thus there should be little objection to labelling archaeology a ‘social’ field of study. We study both people and society, but what about the ‘science’ part? This label is more controversial. Many archaeologists reject the notion that archaeology is, can be or should be a science. Others assume that archaeology is indeed a science and get on with their work, not worrying much about epistemology or definitions of science. Still others pursue decidedly non-scientific goals yet borrow scientific techniques from other disciplines and call it ‘archaeological science’.
Numerical simulation is an important measure to study the seismic performance of buckling-restrained braced frames (BRBFs). Practically, some simplified models, such as the elastic–plastic with kinematic hardening model and the elastic perfectly-plastic model, are used to simulate the behavior of buckling-restrained brace (BRBs). To provide structural engineers the reference of errors when simplified models are used, this paper comparatively evaluates the effect of the BRB model on seismic structural responses using the OpenSees software. A comparison is made on six-storey and 16-storey BRBFs with rigid beam-to-column connections; these are designed according to Chinese seismic design code. Moreover, the effects of the post-yielding stiffness ratio of frame α and the stiffness ratio of BRB to frame β on the errors are specifically investigated through a parametric study of both BRBFs. The results show that the seismic response average errors of the simplified models are mostly less than 5%, which satisfies the engineering requirements.
This book helps designers and manufacturers to select and develop the most suitable and competitive steel structures, which are safe, fit for production and economic. An optimum design system is used to find the best characteristics of structural models, which guarantee the fulfilment of design and fabrication requirements and minimize the cost function. Realistic numerical models are used as main components of industrial steel structures. Chapter 1 containts some experiences with the optimum design of steel structures Chapter 2 treats some newer mathematical optimization methods. Chapter 3 gives formulae for fabrication times and costs. Chapters 4 deals with beams and columns. Summarizes the Eurocode rules for design. Chapter 5 deals with the design of tubular trusses. Chapter 6 gives the design of frame structures and fire-resistant design rules for a frame. In Chapters 7 some minimum cost design problems of stiffened and cellular plates and shells are worked out for cases of different stiffenings and oads. Chapter 8 gives a cost comparison of cylindrical and conical shells. The book contains a large collection of literatures and a subject list and a name index. © Springer-Verlag Berlin Heidelberg 2013. All rights are reserved.
Abstract - The Internet Site for European Strong-Motion Data (ISESD) provides
unlimited free access to over 2,000 strong-motion records of earthquakes from
Europe, the Mediterranean and the Middle East (EMME). Four mirror sites of
ISESD have been operating since 26th March 2002. The URLs of these sites are:
www.isesd.cv.ic.ac.uk, smbase.itsak.gr, seismo.univ.trieste.it and www.isesd.hi.is.
ISESD provides a basis for improved dissemination of strong-motion data in
EMME. There are a number of future improvements to ISESD which would
improve its usefulness to seismologists, earthquake engineers and insurance
specialists.
The concept of designing structures to achieve a specified performance limit state defined by strain or drift limits was first introduced, in New Zealand, in 1993. Over the following years, and in particular the past five years, an intense coordinated research effort has been underway in Europe and the USA to develop the concept to the stage where it is a viable and logical alternative to current force-based code approaches. Different structural systems including frames, cantilever and coupled walls, dual systems, bridges, wharves, timber structures and seismically isolated structures have been considered in a series of coordinated research programs. Aspects relating to characterization of seismic input for displacement-based design, and to structural representation for design verification using time-history analysis have also received special attention. This paper summarizes the general design approach, the background research, and some of the more controversial issues identified in a book, currently in press, summarizing the design procedure. perceived in terms of simple mass-proportional lateral forces, resisted by elastic structural action. In the 1940's and 50's the influence of structural period in modifying the intensity of the inertia forces started to be incorporated into structural design, but structural analysis was still based on elastic structural response. Ductility considerations were introduced in the 1960's and 70's as a consequence of the experimental and empirical evidence that well- detailed structures could survive levels of ground shaking capable of inducing inertia forces many times larger than those predicted by elastic analysis. Predicted performance came to be assessed by ultimate strength considerations, using force levels reduced from the elastic values by somewhat arbitrary force-reduction factors, that differed markedly between the design codes of different seismically-active countries. Gradually this lead to a further realization, in the 1980's and 90's that strength was important, but only in that it helped to reduce displacements or strains, which can be directly related to damage potential, and that the proper definition of structural vulnerability should hence be related to deformations, not strength. This realization has lead to the development of a large number of alternative seismic design philosophies based more on deformation capacity than strength. These are generally termed " performance-based" design philosophies. The scope of these can vary from comparatively narrow structural design approaches, intended to produce safe structures with uniform risk of damage under specified seismicity levels, to more ambitious approaches that seek to also combine financial data associated with loss-of-usage, repair, and a client-based approach (rather than a code-specified approach) to acceptable risk. This paper does not attempt to provide such ambitious guidance as implied by the latter approach. In fact, it is our view that such a broad-based probability approach is more appropriate to assessment of designed structures than to the design of new structures. The
Frame finite-element models permit obtaining, at moderate computational cost, significant information on the dynamic response behavior of steel–concrete composite SCC frame structures. As an extension of conventional monolithic beam models, composite beams with deformable shear connection were specifically introduced and adopted for the analysis of SCC beams, in which the flexible shear connection allows development of partial composite action influencing structural deformation and distribution of stresses. The use of beams with deformable shear connection in the analysis of frame structures raises very specific modeling issues, such as the characterization of the cyclic behavior of the deformable shear connection and the assembly of composite beam elements with conven-tional beam–column elements. In addition, the effects on the dynamic response of SCC frame structures of various factors, such as the shear connection boundary conditions and the mass distribution between the two components of the composite beam, are still not clear and deserve more investigation. The object of this paper is to provide deeper insight into the natural vibration properties and nonlinear seismic response behavior of SCC frame structures and how they are influenced by various modeling assumptions. For this purpose, a materially nonlinear-only finite-element formulation is used for static and dynamic response analyses of steel–concrete frame structures using composite beam elements with deformable shear connection. Realistic uniaxial cyclic constitutive laws are adopted for the steel and concrete materials of the beams and columns and for the shear connection. The resulting finite-element model for a benchmark problem is validated using experimental test results from the literature for quasi-static cyclic tests. The paper then focuses on the numerical simulation, based on various modeling assumptions, of the eigenproperties and seismic response of a realistic two-dimensional five-story two-bay moment resisting frame made of steel columns and SCC beams and designed according to the Eurocode. It is found that the inclusion of the deformability of the shear connection in the finite-element model has a significant effect on the global dynamic response of SCC frame structures. In modeling this type of structures by using frame elements with deformable shear connection, a proper representation of the shear connection boundary conditions for all composite beams is crucial for accurate response simulation.
In code-based seismic design and assessment it is often allowed the use of real records as an input for nonlinear dynamic
analysis. On the other hand, international seismic guidelines, concerning this issue, have been found hardly applicable by
practitioners. This is related to both the difficulty in rationally relating the ground motions to the hazard at the site
and the required selection criteria, which do not favor the use of real records, but rather various types of spectrum matching
signals. To overcome some of these obstacles a software tool for code-based real records selection was developed. REXEL, freely
available at the website of the Italian network of earthquake engineering university labs (http://www.reluis.it/index_eng.html), allows to search for suites of waveforms, currently from the European Strong-motion Database, compatible to reference spectra
being either user-defined or automatically generated according to Eurocode 8 and the recently released new Italian seismic
code. The selection reflects the provisions of the considered codes and others found to be important by recent research on
the topic. In the paper, record selection criteria are briefly reviewed first, and then the algorithms implemented in the
software are discussed. Finally, via some examples, it is shown how REXEL can effectively be a contribution to code-based
real records selection for seismic structural analysis.
KeywordsEurocode 8-Hazard-Seismic design-Response spectrum
In this study, a direct displacement design procedure for steel frames with buckling-restrained braces (BRBs) is presented. The proposed structure system is composed of a hinge-connected main structure, which is designed to remain elastic under seismic load, and BRBs resisting all lateral loads. At seismic event, the BRBs dissipate dynamic energy through stable hysteretic behavior. A displacement-based seismic design procedure is applied to model structures to check the applicability of the design procedure. Two artificial earthquake records are generated from a design spectrum, and the response spectra constructed based on the earthquake records are utilized in the design process. Time-history analyses are carried out to confirm that the maximum displacements coincide with the target displacements. The results show that the seismic performance of the 3- and 5-story model structures designed in accordance with the proposed method coincide well with the given design objectives.
Some results are highlighted in this paper from a research effort being undertaken to identify ground motion and structural characteristics that control the earthquake response of concentrically braced steel frames and to identify improved design procedures and code provisions. The focus of this paper is on the seismic response of three and six story concentrically braced frames utilizing buckling-restrained braces. A brief discussion is provided regarding the mechanical properties of such braces and the benefits of their use. Results of detailed nonlinear dynamic analyses are then examined for specific cases as well as statistically for several suites of ground motions in order to characterize the effect on key response parameters of various structural configurations and proportions.
By means of a graphical procedure, the capacity spectrum method compares the capacity of a structure with the demands of earthquake ground motion on it. In the present version of the method, highly damped elastic spectra have been used to determine seismic demand. A more straightforward approach for the determination of seismic demand is based on the use of the inelastic strength and displacement spectra which can be obtained directly by time‐history analyses of inelastic SDOF systems, or indirectly from elastic spectra. The advantages of the two approaches (i.e. the visual representation of the capacity spectrum method and the superior physical basis of inelastic demand spectra) can be combined. In this paper, the idea of using inelastic demand spectra within the capacity spectrum method has been elaborated and is presented in an easy to use format. The approach represents the so‐called N2 method formulated in the format of the capacity spectrum method. By reversing the procedure, a direct displacement‐based design can be performed. The application of the modified capacity spectrum method is illustrated by means of two examples. Copyright © 1999 John Wiley & Sons, Ltd.
Based on the conclusion that the primary barrier to widespread seismic rehabilitation of buildings in the United States was the lack of a consensus-backed, nationally applicable, professionally accepted rehabilitation standard, the Federal Emergency Management Agency supported the development of the NEHRP Guidelines and Commentary for the Seismic Rehabilitation of Buildings (FEMA 273 and 274). A six-year effort by a team of experienced professional practitioners and university researchers who were motivated to produce a standard that specifically addressed the differences in designing for seismic resistance in new buildings, as opposed to existing buildings, resulted in the NEHRP Guidelines and Commentary for the Seismic Rehabilitation of Buildings. These NEHRP Guidelines will provide the tools for design professionals of varying expertise in seismic design to design economical and appropriate seismic rehabilitation for buildings of essentially any size, commonly used building material and configuration.
Supplemental damping or energy dissipation hardware are being employed in the United States to provide enhanced protection for new and retrofit building and bridge construction. Such hardware includes displacement- and velocity-dependent dampers. The types of dampers being implemented in the United States at this time are presented in the paper. Guidelines and commentary to aid in the implementation of passive supplemental dampers in existing construction are included in the new resource documents FEMA 273 and 274: Guidelines for the Seismic Rehabilitation of Buildings (FEMA, 1997). This paper introduces the FEMA 273 analysis procedures and outlines the modeling and analysis procedures developed for implementing supplemental dampers. The 2000 NEHRP Recommended Provisions for damping systems for new construction are also introduced in the paper. The key assumptions made in the development of the Provisions are described.
Equivalent lateral force and modal analysis procedures for yielding build-ings with damping systems were developed, validated, and incorporated in the 2000 NEHRP Provisions. The technical basis for each procedure is de-scribed in the paper together with the simplifications adopted for inclusion in the Provisions. Procedures for calculating the effective damping and effective period and higher mode damping ratios for buildings equipped with yielding, viscoelastic, linear viscous, and nonlinear viscous damping devices are presented.
Displacement-Based Seismic Design of Structures is a book primarily directed towards practicing structural designers who are interested in applying performance-based concepts to seismic design. Since much of the material presented in the book has not been published elsewhere, it will also be of considerable interest to researchers, and to graduate and upper-level undergraduate students of earthquake engineering who wish to develop a deeper understanding of how design can be used to control seismic response.
The design philosophy is based on determination of the optimum structural strength to achieve a given performance limit state, related to a defined level of damage, under a specified level of seismic intensity. Emphasis is also placed on how this strength is distributed through the structure. This takes two forms: methods of structural analysis and capacity design. It is shown that equilibrium considerations frequently lead to a more advantageous distribution of strength than that resulting from stiffness considerations. Capacity design considerations have been re-examined, and new and more realistic design approaches are presented to insure against undesirable modes of inelastic deformation.
The book considers a wide range of structural types, including separate chapters on frame buildings, wall buildings, dual wall/frame buildings, masonry buildings, timber structures, bridges, structures with isolation or added damping devices, and wharves. These are preceded by introductory chapters discussing conceptual problems with current force-based design, seismic input for displacement-based design, fundamentals of direct displacement-based design, and analytical tools appropriate for displacement-based design. The final two chapters adapt the principles of displacement-based seismic design to assessment of existing structures, and present the previously developed design information in the form of a draft building code.
The text is illustrated by copious worked design examples (39 in all), and analysis aids are provided in the form of a CD containing three computer programs covering moment-curvature analysis (Cumbia), linear-element-based inelastic time-history analysis (Ruaumoko), and a general fibre-element dynamic analysis program (SeismoStruct).
The design procedure developed in this book is based on a secant-stiffness (rather than initial stiffness) representation of structural response, using a level of damping equivalent to the combined effects of elastic and hysteretic damping. The approach has been fully verified by extensive inelastic time history analyses, which are extensively reported in the text. The design method is extremely simple to apply, and very successful in providing dependable and predictable seismic response.
A seismic chart as design aid for simple structures is proposed. It is suitable to be used in the environment of the Performance-Based Earthquake Engineering together with the Non-linear Static Procedure (NSP) or pushover analysis. The chart utilizes the inelastic response spectra of 10% kinematic hardening SDOF system. The performance parameters to include strength, hysteretic energy and damage, as function of numbers of independent variables such as the intensity & duration of the input motions, site characteristic, ductility, with constraint on displacement, are discussed. The random variables involved and their uncertainties can be taken into account explicitly, enabling simple incorporation of the information on the Seismic Hazard Analysis, when available. Comparison with the experimental data confirms the prediction.
Equivalent lateral force and modal analysis procedures for yielding buildings with damping systems were developed, validated, and incorporated in the 2000 NEHRP Provisions. Key to the implementation of the procedures was the validation process that demonstrated the accuracy of the proposed procedures. The procedures for implementing yielding, viscoelastic, linear viscous, and nonlinear viscous dampers were tested using the results of nonlinear response-history analysis on sample three- and six-story frames and were found to be robust.
This paper presents research on seismic design of steel special moment resisting frames (SMRFs) with supplemental elastomeric dampers. The SMRF properties and damper design criteria are varied to illustrate their effects on the supplemental damper design. The SMRFs are based on current seismic design practices, and the supplemental dampers are designed using a simplified design procedure (SDP). The SDP allows the structure with dampers to be designed for specified performance objectives, where the structure is intended to reach selected performance levels, defined in terms of story drift and member response, at specified seismic input levels. Nonlinear dynamic time history analyses show that SMRFs with dampers designed using the SDP achieve the specified seismic performance objectives, and that elastomeric dampers are more effective when used in a more flexible SMRF. The SDP permits various seismic performance objectives and corresponding design criteria to be specified. Criteria that allow some inelastic behavior (R=2), but limit the story drift to 1.5% under the design basis earthquake are shown to lead to the most effective damper design.
This paper presents a summary of current practice and recent developments in the application of passive energy dissipation systems for seismic protection of structures. The emphasis is on the application of passive energy dissipation systems within the framing of building structures. Major topics that are presented include basic principles of energy dissipation systems, descriptions of the mechanical behavior and mathematical modeling of selected passive energy dissipation devices, advantages and disadvantages of these devices, development of guidelines and design philosophy for analysis and design of structures employing energy dissipation devices, and design considerations that are unique to structures with energy dissipation devices. A selection of recent applications of passive energy dissipation systems is also presented.
As buckling-restrained braced frames (BRBFs) have been used increasingly in the United States, the need for knowledge about BRBF behavior has grown. In particular, large-scale experimental evaluations of BRBFs are necessary to demonstrate the seismic performance of the system. Although tests of buckling-restrained braces (BRBs) have demonstrated their ability to withstand significant ductility demands, large-scale BRBF tests have exhibited poor performance at story drifts between 0.02 and 0.025 rad. These tests indicate that the large stiffness of the typical beam-column-brace connection detail leads to large flexural demands that cause undesirable failure modes. As part of a research program composed of numerical and experimental simulations, a large-scale BRBF with improved connection details was tested at the ATLSS Center, Lehigh University. During multiple earthquake simulations, which were conducted using a hybrid pseudodynamic testing method, the test frame sustained story drifts of close to 0.05 rad and BRB maximum ductility demands of over 25 with minimal damage and no stiffness or strength degradation. The testing program demonstrated that a properly detailed BRBF can withstand severe seismic input and maintain its full load-carrying capacity.
This paper proposes a simplified theory to predict and compare the seismic performance of viscoelastical (VE)- and elastoplastical (EP)- damped passive control systems, and to demonstrate their ability to protect structures during a major seismic event. Closed-form expressions for "equivalent period" and "equivalent damping" of these systems are proposed by idealizing them as linear single-degree-of-freedom (SDOF) systems. The expressions are used to clarify and compare the structural parameters, seismic drift, and force for the systems, based on a common high-damping linear spectrum. By extending the SDOF theory, a seismically deficient 14-story steel moment resisting frame (MRF) is upgraded by inserting VE or EP dampers. Extensive three-dimensional multi-degree-of-freedom nonlinear dynamic analyses are performed for the MRF, VE system, and EP system using earthquakes of various intensities. The 14-story VE and EP systems responded as predicted by the SDOF theory. They show much smaller drifts than the original MRF, keep frame members elastic, and protect nonstructural components, even against major earthquakes.
In recent years, considerable attention has been paid to research and development of structural control devices, with particular emphasis on alleviation of wind and seismic response of buildings and bridges. In both areas, serious efforts have been undertaken to develop the structural control concept into a workable technology, and today we have many such devices installed in a wide variety of structures. The focus of this state-of-the-art paper is on passive and active structural control systems. Passive systems encompass a range of materials and devices for enhancing structural damping, stiffness and strength. Active systems, which include active, hybrid and semi-active systems, employ controllable force devices integrated with sensors, controllers and real-time information processing. This paper includes a brief historical outline of their development and an assessment of the state-of-the-art and state-of-the-practice of this exciting, and still evolving, technology. Also included in the discussion are their advantages and limitations in the context of seismic design and retrofit of civil engineering structures.
High damping rubber (HDR) consists of natural rubber to which black carbon filler is added to increase its damping properties. The use of HDR as a dissipating device in structural systems is very promising in terms of controlling the response under live actions like wind or earthquake. The use of HDR does however entail some problems because its dynamic behaviour is not completely understood and the few HDR models that exist are not completely satisfactory for seismic analysis of structures equipped with HDR-base dissipation devices. Experimental tests were performed to obtain more accurate information about the behaviour of the material under cyclic shear paths with different strain rate and strain amplitude. A nonlinear viscoelastic damage model was proposed to describe the behaviour of rubber under cyclic loads.
Dual systems can offer an attractive lateral force-resisting solution, combining individual systems in a complementary manner. A displacement based-design (DBD) method is proposed for steel dual systems incorporating moment-resisting frames (MRFs) and buckling-restrained braces (BRBs). The validity of the method is established through a verification study considering theoretical designs of 6-, 9-, 12-, and 18-story buildings and nonlinear time-history analysis (NTHA) using ten spectrum compatible accelerograms. The results show that the DBD method provides good control of displacements and drifts for the structures, although higher mode effects tend to become significant for the taller case studies. In addition to controlling peak deformations, the article illustrates how the inclusion of the MRFs in parallel to BRB systems can be an effective means of limiting residual deformations.
By means of a graphical procedure, the capacity spectrum method compares the capacity of a structure with the demands of earthquake ground motion on it. In the present version of the method, highly damped elastic spectra have been used to determine seismic demand. A more straightforward approach for the determination of seismic demand is based on the use of the inelastic strength and displacement spectra which can be obtained directly by time-history analyses of inelastic SDOF systems, or indirectly from elastic spectra. The advantages of the two approaches (i.e. the visual representation of the capacity spectrum method and the superior physical basis of inelastic demand spectra) can be combined. In this paper, the idea of using inelastic demand spectra within the capacity spectrum method has been elaborated and is presented in an easy to use format. The approach represents the so-called N2 method formulated in the format of the capacity spectrum method. By reversing the procedure, a direct displacement-based design can be performed. The application of the modified capacity spectrum method is illustrated by means of two examples. Copyright © 1999 John Wiley & Sons, Ltd.
Large-scale experimental studies of buckling-restrained braced frames (BRBFs) have shown that although they display good overall seismic performance, they may have limitations due to connection failure modes that do not allow the braces to realize their full ductility capacity. These experimental results motivate further investigation of BRBF connection behavior. In this study, nonlinear finite element models are used to study BRBF beam–column–brace connections. The models focus on a one-story subassembly extracted from a previously-tested, four-story BRBF. After the baseline finite element analysis results are verified with experimental data, parametric studies varying the connection configuration are used to assess the key factors influencing performance. Connection configuration is shown to have a significant impact on global system response and localized connection demands.
A simplified design procedure (SDP) for preliminary seismic design of frame buildings with structural dampers is presented. The SDP uses elastic-static analysis and is applicable to structural dampers made from viscoelastic (VE) or high-damping elastomeric materials. The behaviour of typical VE materials and high-damping elastomeric materials is often non-linear, and the SDP idealizes these materials as linear VE materials. With this idealization, structures with VE or high-damping elastomeric dampers can be designed and analysed using methods based on linear VE theory. As an example, a retrofit design for a typical non-ductile reinforced concrete (RC) frame building using high-damping elastomeric dampers is developed using the SDP. To validate the SDP, results from non-linear dynamic time history analyses (NDTHA) are presented. Results from NDTHA demonstrate that the SDP estimates the seismic response with sufficient accuracy for design. It is shown that a non-ductile RC frame building can be retrofit with high-damping elastomeric dampers to remain essentially elastic under the design basis earthquake (DBE). Copyright © 2005 John Wiley & Sons, Ltd.
High damping rubber (HDR) shows a quite complex constitutive behaviour, which is nonlinear with respect to strain and is dependent on the strain rate. In addition, it exhibits a transient response during which the material properties change (scragging or more generally the Mullins effect). A number of recent works were dedicated to analysing and modelling material behaviour. This paper studies the nonlinear dynamics of systems with restoring force produced by HDR-based devices in order to propose a procedure to define equivalent linear models considering both transient and stationary behaviours. The reliability of these linear models is tested by evaluating the upper and lower bounds of the seismic response of a structural system equipped with HDR-based devices (structural system with dissipative bracings and isolated systems). Copyright © 2008 John Wiley & Sons, Ltd.
As part of a national research programme an experimental campaign was carried out on a real scale mock-up consisting of a steel–concrete composite frame equipped with dissipative bracings, based on high damping rubber (HDR) devices. Free vibration tests, followed by force-controlled and displacement-controlled cyclic tests were performed. The experimental tests were aimed at studying the dynamic response of the coupled system in order to demonstrate the effectiveness of HDR devices in increasing the stiffness and dissipation capacity of the frame and investigating the ability of the constitutive HDR model proposed by the authors to predict the dynamic response of the coupled system. Copyright © 2009 John Wiley & Sons, Ltd.
Buckling-restrained braced frames (BRBFs) have been shown to exhibit very favorable energy-dissipating characteristics. Nevertheless, low post-yield stiffness of the braces leave the system vulnerable to unfavorable behavioral characteristics such as large permanent drift. This paper presents results of a study conducted to investigate the potential benefit of using buckling-restrained braces in a dual system to minimize permanent deformations. Results from nonlinear time-history analyses demonstrate significant improvements in reducing residual story drifts using the dual system.
This paper presents a seismic displacement-based design method for new and regular buildings equipped with passive energy dissipation systems (EDS). Using the substitute structure approach for the building structure and simulating the mechanical properties of the passive energy dissipation devices (EDD) by the effective stiffness and effective viscous damping ratio, a rational linear iteration method is proposed. A target displacement is at first specified and then the corresponding design force, strength and stiffness are obtained. Comprehensive procedures for displacement-based design of several buildings with passive energy dissipation systems are presented. The results are verified by dynamic inelastic time history analysis. Based on the study, it is found that the proposed displacement-based design method is straightforward and can accurately predict the nonlinear behavior of buildings equipped with passive energy dissipation systems.
The aim of this paper is to investigate how the dynamic response of an existing r.c. single storey frame may be upgraded by using different types of steel bracing dissipating system.The dissipating bracing system is composed of steel braces in series with an energy dissipation device that is either a high damping rubber pad (HDRD) or a shape memory alloy wire assemblage (SMAD), both characterised by a hysteretic behaviour.Many tests have been performed by the authors, both in free and in forced vibration, to completely understand the behaviour of the equipped systems by the use of simple testing techniques in a wide range of frequency and displacement amplitude, in order to simulate the frequency content of an earthquake excitation.
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