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In this article, one of the procedures to design viscous dampers proposed in literature is applied to 3D asymmetricplan buildings, considering different distributions for the damping coefficients, which are assumed to be proportional to specific structural or response parameters. The main purpose was to investigate the effectiveness of different vertical and in-plan distributions of the damping coefficients of nonlinear viscous dampers for the seismic retrofit of existing buildings. For comparison purposes, all the distributions were applied utilizing both a simplified and an extended method for the 3D structures, where the simplified method takes into account only the translation in the seismic direction, and the extended method considers the translations along the two orthogonal directions together with the floor rotations. The proposed distributions were then applied to a typical case study involving an asymmetric-plan six-storey RC building. The effectiveness of the different distributions was examined through time-history analyses, assuming nonlinear behaviour for both the viscous dampers and the structural elements. The results of the nonlinear dynamic analyses were examined in terms of maximum and residual inter-storey drifts, peak floor accelerations and maximum damper forces.

Among the numerous intuitions and projects that have characterized Leonardo da Vinci's art and technique, the conception of architectural structures has an important role, including studies and the proposal for the project of the tiburio of the Milan Cathedral. Based on some hypotheses of reconstruction of geometries and structural systems developed in the architectural field, and formulated as an interpretation of original drawings, it was intended to test whether the solutions proposed by Leonado were also actually feasible, examining them with current structural modeling techniques, of evaluation of static functioning and definition of structural safety. Using the finite element method (FEM), two different proposals were investigated for the vaults and supporting arches of the tiburio, finding its substantial reliability even though this was hypothesized in the absence of technical verification tools that did not exist at the time.

In this research, one of the procedures proposed in literature for the design of viscous dampers is extended to 3D plan-asymmetric buildings considering different distributions of the damping coefficients. In particular, simple distribution criteria, based on specific structural or response parameters, were considered with the purpose to improve the design of the damping system in terms of cost without significant change of response. All the distributions were applied considering, for comparison, both a simplified and an extended method, by neglecting or considering, respectively, the plan-asymmetry in the design. The effectiveness of the different distributions was examined by performing time-history analyses of a case study with different configurations of dampers adopting a nonlinear behaviour both for the viscous dampers and the frame members. The dampers were dimensioned considering that the structure can exceed the elastic limit, with the only condition to satisfy the prefixed performance limit. The considered case study is a RC frames characterized by six storeys and an irregular plan configuration. The examined response parameters were maximum interstorey drifts, residual interstorey drifts and peak floor accelerations as well as maximum damper forces.

The work focuses on the application of modal identification techniques to plan-asymmetric building structures that are subjected to base excitation. The challenging problem related to the identification of high-order modes and, especially, torsional modes is taken into account for different lengths of time and directions of the applied base excitation. The evaluation of the identification accuracy was performed through a simulation approach: analytical models of plan-asymmetric RC frames, which are characterized by different structural eccentricities, were subjected to white noise base excitation. This kind of input is rather idealized for real buildings, which are generally excited by earthquake or traffic loads, but it is commonly adopted in experimental programs related to vibration-based damage detection using scaled or full-size buildings tested on shaking tables. The output-only modal identification was applied using the response time-histories only and the modal parameters, in terms of natural circular frequencies, modal damping ratios and mode shapes, were determined. These identified parameters were then compared with the true values related to the initially assumed analytical models. Firstly, the analyses were performed for one structural configuration, for a fixed direction of the applied base excitation, but considering various durations of such input. The results showed that the accuracy related to mode shapes identification was lower for the first torsional mode with respect to the second longitudinal mode, which is a higher-order mode. In addition, the identified torsional mode shape exhibited major modal complexity than the longitudinal mode, as a result of simulated noise and identification errors. Secondly, the analyses were conducted considering different structural configurations, a fixed duration of the base excitation, but different directions of the applied input. The outcomes showed that the accuracy in mode shape estimations, evaluated by calculating the Modal Assurance Criterion (MAC) between identified and analytical mode shapes, was strongly dependent on the direction of the applied input, especially for high-order modes. It was also observed that these MAC values are directly correlated with the modal participation factors of the structure, evaluated for the different directions of the base excitation. Referring to the torsional mode shapes, the results showed that the number of input directions, for which these modes can be identified, are higher for the structures with major structural eccentricities.

The object of this paper is the study of simplified probabilistic procedures for the seismic assessment of nonlinear structures equipped with nonlinear fluid viscous dampers. The considered reference probabilistic approach is the 2000 SAC-FEMA method, which allows to obtain the probability of exceeding a specified performance level. In particular the purpose is to study the correlation between the results of the probabilistic seismic assessment method for structures without and with dampers, with emphasis on the results in terms of dispersion. To this aim a wide set of recorded ground motions has been selected and applied to the considered RC frames. The study has been performed without applying scaling factors to the earthquake records, but selecting different sets of records for increasing values of seismic intensity. All the obtained results have been examined considering different criteria for the determination of the set of time-history analyses to be used for the probabilistic evaluation and different methods to obtain the dispersion of seismic demand. Moreover, with reference to the application of the SAC-FEMA method, a sensitivity analysis has been performed considering different procedures for the interpolation of the hazard curve. From the analyses it has been possible to derive expressions to correlate the results for structure without and with dampers and suggestions for the application of the SAC-FEMA method. Finally, a direct procedure previously proposed by some of the authors for the response assessment of nonlinear structures with nonlinear viscous dampers has been applied for the probabilistic assessment of the case study as an alternative to nonlinear dynamic analyses.

The main purpose of this research is to investigate the effects of different vertical distributions of the properties of nonlinear fluid-viscous dampers for the retrofit of existing multi-storey reinforced concrete frames. In particular, the different distributions are defined on the basis of the same value of the supplemental damping ratio. Since the viscous dampers are used for the retrofit of existing buildings, they are dimensioned assuming that the structure can exceed the elastic limit, with the only condition to satisfy the prefixed performance limit. In the design phase the different vertical distributions of damper properties are compared in terms of the total sum of the damping coefficients. The effectiveness of the different distributions is then examined by performing time-history analyses of several case studies considering a nonlinear behaviour both for the viscous dampers and for the structural members. The considered case studies are five RC frames characterized by different number of storeys and different properties in terms of regularity in elevation. The results of the nonlinear dynamic analyses are examined in terms of maximum and residual interstorey drifts, peak floor accelerations and maximum damper forces.

Alla luce dei recenti sviluppi normativi e dell‟attenzione che la tematica della sicurezza sismica degli edifici ha acquisito dopo gli ultimi eventi, l'analisi e la verifica del patrimonio esistente è divenuto un indispensabile strumento di valutazione della vulnerabilità e pianificazione degli interventi. Particolare attenzione è stata dedicata agli edifici pubblici, che, in caso di calamità, rivestono un importante ruolo strategico. In tale ottica l‟Ufficio Tecnico dell‟Università di Bologna ha espresso la necessità di avviare la valutazione della vulnerabilità dei propri edifici secondo criteri di efficienza ed economicità. E‟ nata così nel 2012 la convenzione per l‟esecuzione delle verifiche tecniche delle strutture di Ateneo con il Dipartimento DICAM, struttura dotata di competenze e attrezzature tecnico-scientifiche necessarie a garantire il risultato atteso. Partendo dalla consapevolezza di andare a valutare un patrimonio architettonico complesso e disomogeneo, avendo a disposizione, al tempo stesso, una limitata conoscenza sui singoli fabbricati, si è dovuto necessariamente definire una metodologia capace di fornire risultati confrontabili al fine di facilitare la futura attività di gestione e pianificazione. L‟obiettivo del presente articolo è di descrivere il patrimonio edilizio di Ateneo, illustrando, poi, la metodologia che è stata definita nell‟ambito della convezione ed infine presentare alcuni casi esemplificativi del lavoro svolto.

The present work aims at performing an output-only modal identification starting from the dynamic responses of a plan-asymmetric RC frame structure that is subjected to a random ground motion along different directions. The main purpose is to evaluate the accuracy of the identified modal model for each direction of the exciting input, which is an unmeasured white noise signal. The Eigensystem Realization Algorithm is the applied identification method and it could be extended to the Operational Modal Analysis by adopting adequate pre-identification procedures. Two of them, which are the Natural Excitation technique and the Random decrement method, are separately applied and compared. All the identification procedures are performed on simulated data and the results show that the identification of the mode shapes of the structure is influenced by the direction of the applied ground motion; however, the main modes of the structure are always identified while some uncertainties occur for the modes at the highest frequencies, especially for the torsional ones. Notwithstanding the classical assumption of the OMA are not completely satisfied by the considered input, the obtained results, compared with the known analytical structural model, demonstrate the effectiveness of the algorithm.

This paper deals with the parameters which influence the probability of reaching the near collapse limit state of RC frame structures equipped with nonlinear fluid viscous dampers. The study can be divided into two steps. The first, aims to assess how the median and the dispersion of seismic demand can vary in the RC frame structures equipped with nonlinear fluid viscous dampers, considering a wide set of ground motions; these parameters have been compared with those obtained for RC structures without dampers. The second step evaluates the expression in closed form, given in the 2000 SAC/FEMA method to assess the annual probability of failure of RC structures. This calculation has been performed using the parameters obtained in the previous step. The annual probability of failure has been estimated in the RC frame structures, with and without dampers, considering a wide set of ground motions and different methods to approximate the hazard curve. The adopted case study is a frame configuration characterized by three bays and six floors. The analyses have allowed to evaluate the variability and the influence of the terms in the expression proposed in the 2000 SAC/FEMA method, as the dispersion of seismic demand.

The purpose of this paper is to propose a simplified probabilistic procedure for the seismic assessment of nonlinear structures equipped with nonlinear fluid viscous dampers. The considered reference probabilistic approach is the 2000 SAC-FEMA method, which allows to obtain the probability of exceeding a specified performance level. Within this method, in general, the probabilistic seismic demand analysis is performed in terms of incremental dynamic analysis (IDA) by considering several earthquake records. This approach has been followed with reference to a set of case studies, characterized by RC frames with and without added dampers. The main characteristics of the proposed simplified approach are: the application of a direct procedure previously proposed by the authors for the response assessment of structures with dampers as an alternative to nonlinear incremental dynamic analyses; the study of the relation between the dispersion of seismic demand of structures with dampers with that of structures without dampers. The latter, in fact, can be estimated also on the basis of several available literature data. In this paper the direct procedure previously proposed by the authors has been applied to the case studies for increasing values of seismic intensity. The results of such applications have been then compared with those of the IDA analyses in terms of the relation between the roof displacement demand and the seismic intensity. The results of the IDA analyses have been also examined in order to determine the correlation between the dispersion of demand of structures with dampers with that of structures without dampers. Finally the values of probability obtained with the proposed simplified approach has been compared with those of the 2000 SAC-FEMA method based on IDA analyses.

The insertion of fluid viscous dampers in building structures is an innovative technology that can improve significantly the seismic response. These devices could be very useful also in the retrofit of existing buildings. The effect of this typology of damping system is usually identified with an equivalent supplemental damping ratio, which depends on the maximum displacement of the structure, so that iterative procedures are required. In this paper, a simplified direct assessment method for nonlinear structures equipped with nonlinear fluid viscous dampers is proposed. The method proposed in this study is composed by two steps. The first one yields the direct estimate of the supplemental damping ratio provided by nonlinear viscous dampers in presence of a linear elastic structural response. The second step extends the procedure to structures with nonlinear behavior. Both graphical and analytical approaches have been developed. The proposed method has then been verified through several applications and comparisons with nonlinear dynamic analyses. Moreover, an investigation has been performed with regard to the influence of the relations that define the damping reduction factor and the hysteretic damping.

The main purpose of this research is to investigate the effects of different vertical distributions of the properties of nonlinear fluid-viscous dampers for the retrofit of existing multi-storey reinforced concrete frames. In particular, the different distributions are defined on the basis of the same value of the supplemental damping ratio. Since the viscous dampers are used for the retrofit of existing buildings, they are dimensioned assuming that the structure can exceed the elastic limit, with the only condition to satisfy the prefixed performance limit. In the design phase the different vertical distributions of damper properties are compared in terms of the total sum of the damping coefficients. The effectiveness of the different distributions is then examined by performing time-history analysis of several case studies considering a nonlinear behaviour both for the viscous dampers and for the structural members. The results of the nonlinear dynamic analyses are examined in terms of interstorey drifts and dampers forces. The considered case studies are five RC frames characterized by different number of storeys (3, 6 and 9 storeys) and also by different properties in terms of regularity in elevation. In this way it is also possible to investigate the effect of the vertical distribution of the damper properties for regular and irregular frames.

This research focuses on the different modelling approaches for the simulation of the seismic response of structures with friction pendulum isolation systems. The behaviour of such systems is strongly affected by several parameters, as for example the friction coefficient and the axial load. The latter has a particular importance in presence of seismic actions characterized by the simultaneous presence of high horizontal and vertical accelerations. In many recent seismic events, as for example L’Aquila (2009) and Emilia (2012) in Italy, the vertical seismic component has been characterized by very high values of acceleration and has played a crucial role in damaging the buildings. To study these aspects, several nonlinear dynamic analyses have been performed considering a two degree of freedom model isolated at the base and subjected to recorded horizontal and vertical ground motions. The response of the isolation systems has been studied through different models, starting by the more simple ones based on constant friction coefficient to the more complex ones based on a friction coefficient varying as a function of sliding velocity and axial force. The analyses have been performed considering a set of ground motions with near field records that present different values of the ratio between the peak vertical and horizontal accelerations. The records have been also applied considering increasing values of intensity, in order to determine the collapse acceleration. The results have allowed to compare the different models and to study the effect of the vertical seismic component on the response of the isolators.

The purpose of this research was to propose an extension of the displacement-based approach for the assessment of the seismic response of infilled RC frames. In order to evaluate the behaviour of these structures, it was fundamental to define an appropriate analytical model. In this study the equivalent strut model for monotonic loading proposed by Al-Chaar was considered. This model was extended to the case of cyclic loading by calibrating the degradation of strength and stiffness, the residual strength and the loading and unloading branches through comparisons with available experimental results. The model was then applied for investigating the seismic response of infilled RC frames: pushover and nonlinear dynamic analyses were carried out for obtaining the response in terms of base shear-top displacement and for estimating the configuration of collapse. On the basis of the results of these analyses, a displacement-based method for the assessment of infilled frames was proposed. The method is based in particular on simplified criteria for the estimate of the equivalent damping and of the collapse displacement profile of infilled RC frames. The effectiveness of the method was verified through comparison between the displacement demand estimated with the proposed procedure and the one obtained from nonlinear dynamic analyses.

This research focuses on the different modeling approaches for the simulation of the seismic response of structures with friction pendulum isolation systems. The behavior of such systems is strongly affected by several parameters, as for example the friction coefficient and the axial load. The latter has a particular importance in presence of seismic actions characterized by the simultaneous presence of high horizontal and vertical accelerations. In many recent seismic events, in fact, the vertical seismic component has been characterized by very large values of acceleration and has played a fundamental role in damaging the buildings. For example it is possible to mention the recent events in Italy, as the ones of L’Aquila in 2009 and Emilia in 2012. Therefore another important object of this research is the study of the effect of the vertical seismic component on the behaviour of friction pendulum isolation systems. To study all the mentioned aspect several nonlinear dynamic analyses have been performed considering a two degree of freedom model isolated at the base. The response of the isolation systems have been studied through different models, starting by the more simple ones based on constant friction coefficient to the more complex ones based on a friction coefficient varying as a function of the sliding velocity and of the axial force. The analyses have been performed considering a set of ground motion with near field records characterized by different values of the ratio between the peak vertical and horizontal accelerations. Several structural models have been analyzed by varying the following paramateres: mass of the structure, horizontal and vertical stiffness of the structure and of the isolation system. All the records have been applied to such models two times: the first with the horizontal component alone, the second with the horizontal and vertical component. The records have been also applied considering increasing values of intensity, in order to determine the collapse acceleration of the structures and of the isolation systems. The results have allowed to compare the different models and to study the effect of the vertical component on the response of the isolation system.

The insertion of fluid viscous dampers in building structures is an innovative technology which can improve significantly the seismic response. These devices could be very useful also in the retrofit of existing buildings. This paper proposes a simplified and direct procedure for the assessment of the nonlinear seismic response of a given structure equipped with given nonlinear viscous dampers. The effect of this typology of damping system is usually identified with an equivalent supplemental damping ratio which depends on the maximum displacement of the structure, so that iterative procedures are required. The method proposed in this study is composed by two steps. The first one requires the direct estimate of the supplemental damping ratio under elastic conditions. In this step a particular procedure based on a new dimensionless parameter, called damper index, is employed. The second step extends the procedure to structures with nonlinear behaviour and requires the definition of two functions: the constant design acceleration curve and the constant supplemental damping ratio curve. The intersection of these two functions provides directly the effective damping ratio and the ductility demand required to the structure. Both graphical and analytical approaches have been developed to determine the solution. The direct method has then been applied to a set of different RC frames. Its effectiveness has been studied through comparisons with several nonlinear dynamic analyses. Moreover, an investigation has been performed with regard to the influence of the relations which define the damping reduction factor and the hysteretic damping.

The damages produced by earthquakes on historical unreinforced masonry buildings have shown that out-of-plane collapses of the external walls are frequent and very dangerous even in terms of loss of human lives. Different approaches have been proposed to study such mechanisms, like static, kinematic or dynamic analyses, but the experimental tests are still relatively few and have been concentrated on the simplest failure modes because of their simpler reproducibility and interpretation (parapet wall or simply supported wall). Recently some analytical and experimental studies highlighted the necessity of dynamic analysis in order to understand the real behaviour of walls in out-of-plane bending and to assess, without an over conservative approach, the vulnerability against earthquake action. They pointed out the fact that out-of-plane failures of walls are caused essentially by an excessive displacement demand rather than force or acceleration demand. Quite all the past works considered simplified hypotheses about the interaction of the wall with the rest of the building, assuming diaphragms as rigid and reducing therefore the complexity of the dynamic problem and the number of the degrees of freedom. When the diaphragms cannot be considered as rigid, like in most historical buildings, the inputs to the out-of-plane walls at adjacent floors have different amplitude, phase and frequency content. In this case it is necessary to consider multiple-degrees-of-freedom instead of the usual single-degree model. In this work a simplified two-degrees-of-freedom model is proposed to model the wall, idealized as an assemblage of two rigid bodies connected by an intermediate hinge and restrained at the top by a spring, that simulates a flexible diaphragm. The influence of diaphragms flexibility on the displacement capacity and demand of walls in out-of-plane bending has been studied by means of dynamic analyses, varying the values of the spring stiffness. Damping has been introduced through the coefficient of restitution, that concentrates energy dissipation at every impact at the base of the wall. The equations of motion of the 2-DOF system have been derived and integrated in the time domain through a numerical algorithm: a set of walls with different properties has been subjected to Gaussian pulse and natural recorded inputs. Comparisons between the cases with rigid and flexible diaphragms, in terms of displacement capacity and demand have then been performed.

The existing buildings in several countries are characterized by numerous examples of RC frames with masonry infills. Various studies showed how the presence of masonry infills may alter the overall behaviour of structures when subjected to seismic action. The presence of the masonry infills can produce positive or negative effects. In the first case it can increase the strength and the dissipative capacity of the structure, in the second case it can produce unexpected distributions of forces and consequent local phenomena of collapse. The objective of this paper is the assessment of the seismic vulnerability of existing infilled RC frames. In order to evaluate the behaviour of these structures, it is fundamental to define an appropriate analytical model which could take into account the presence of the infills. Several models have been proposed in literature for the masonry infills. In this study the equivalent strut model is considered. The study starts from the model for monotonic loading proposed by Al-Chaar. This model is extended to the case of cyclic loading by calibrating the degradation of strength and stiffness, the residual strength and the loading and unloading branches. The model is then applied for investigating the seismic response of infilled RC frames: pushover and nonlinear dynamic analyses are carried out for obtaining the response in terms of base shear-top displacement and for estimating the configuration of collapse. In particular the lateral displacement profile at collapse and the plastic hinge distribution are examined. A proposal for the extension of the Displacement-Based Assessment to infilled frames is then presented and verified. In this assessment procedure it is implemented a simplified method proposed by the authors for the prediction of the displacement profile of infilled frames at the yield and collapse conditions. This method is applied together with specific ductility damping relationships derived by the authors in previous studies. The proposed assessment procedure is then applied to the considered cases of study and its effectiveness is verified through comparisons with the results of the nonlinear dynamic analyses.

In the design of viscous dampers to be inserted in existing structures the supplemental damping is often defined a priori, as the value is fixed before the execution of the seismic analysis. This way of proceeding simplifies the design, but it does not give any information about the real need of supplemental damping. In particular the calibration of this value requires to perform iterations. This work proposes, instead, a direct and simple procedure to determine the minimum supplemental damping ratio to be provided by the dampers for the rehabilitation of a structure for a given seismic action. The purpose is the calculation of the required supplemental damping ratio by knowing the capacity of the buildings in terms of lateral strength and ductility. The procedure proposed in this work has been developed according to both analytical and graphical approaches. The graphical formulation is based on the construction of “constant design acceleration curves” or “constant design displacement curves”, which can be obtained from the response spectrum. These curves are determined for a given level of structure yield acceleration and allow to define the required effective damping ratio as a function of the effective period of the equivalent single degree of freedom system associated to the structure. These curves are very useful since they are not specific for a single building but they are valid for all structures. Their construction is then very simple and requires to know only the expressions which define the response spectrum and the damping reduction factor. The effective period is calculated on the basis of the secant stiffness at maximum displacement. The supplemental damping ratio is then obtained by using “constant ductility curves” which establish such value in relation to the available ductility and the damper class. These curves allow also to evaluate the maximum improvement of the building which can be reached with the application of the maximum supplemental damping from code provisions. The proposed method has been applied by carrying out nonlinear static analyses considering a set of RC plane frames. The effectiveness of the method has been verified through the comparison with the results of a series of nonlinear dynamic analyses performed considering recorded ground motions. Finally, the proposed methodology has been applied to a case study regarding an existing building located in Italy and designed without considering the earthquake action.