Rigid Floors Research Articles

Discrete macro - models of nonlinear interlocking mechanisms in the out-of-plane failure of masonry walls

AbstractHistorical unreinforced masonry (URM) constructions are generally vulnerable to out-of-plane (OOP) failures due to the absence of rigid floors and poor connections between orthogonal walls. That leads to the activation of rocking mechanisms of external walls, whose ultimate force and displacement are affected by complex nonlinear interactions with sidewalls. These interactions are often neglected in the engineering practice, potentially leading to significant approximations, as demonstrated by experimental and numerical studies available in the literature. As a novel contribution to the field, this paper presents an upgraded discrete macro-element model (DMEM) to predict the rocking capacity of OOP loaded URM walls interacting with sidewalls. Considering both the onset and the evolution of the rocking mechanism of the front wall, interlocking effects with the sidewalls are first simulated through frictional resistances using the macro-block model (MBM) and the nonlinear kinematic approach of limit analysis. Then, the upgraded DMEM is implemented on the basis of the equivalence between the continuous distribution of these forces, introduced as a further novelty of the paper, and the discrete distribution of lateral elastic-plastic links, accounting for mechanical and geometrical nonlinearities. The results of the two models are discussed in terms of both frictional resistance-displacement and pushover curves, referring to a case study of a front wall belonging to a two-storey URM building. The wall response is also compared with the results derived from the original source of the case study and analysed by changing the number of nonlinear links to define different levels of accuracy.

A novel mode shape identification approach for structures having planes with rigid-like behavior

The identification of mode shapes of structures through Operational Modal Analysis (OMA) often requires the application of data merging techniques to compensate for the lack of information on mode shapes scaling factors, which is inherent in OMA. In this paper, we propose a novel mode shape identification approach for structures having planes with rigid-like behavior, such as steel or reinforced concrete buildings with rigid floors. The approach is based on a theoretical model that generalizes the mechanical features of the structures under considerations. We show that the mode shapes of the model can be reconstructed starting from two components, i.e., modal centers of rotation and modal rotations; modal rotations depend on scaling factors of mode shapes, while modal centers of rotation turn out to be invariant with respect to mode shape scaling. Afterwards, we develop a method for identifying modal centers of rotation and modal rotations from experimental data, and then for reconstructing mode shapes. Numerical experiments have been performed to assess the capability of the approach with respect to a structural specimen having known modal properties. Compared with classic merging techniques, our approach enables a significant simplification of the experimental setup and a deeper analysis of mode shapes.

Empirical seismic fragility of masonry buildings in historical centres accounting for structural interventions

Fragility models are widely employed to forecast seismic damage in built environments. However, the actual conditions of buildings, depending on their construction systems and transformations, are crucial for model reliability, especially in historical centres.In this paper, an empirical fragility model for residential masonry buildings from data collected within 19 historical centres struck by the 2016 Central Italy earthquake is proposed. The dataset includes both traditional unreinforced and hybrid buildings, where reinforced concrete elements were applied in the 1980s according to seismic reinforcement prescriptions for existing structures.This study acknowledges the impact of such structural modifications on the seismic performance of buildings, which can alter their vulnerability classification either improving or worsening it. The intensity measure for the fragility functions is the peak ground acceleration obtained from actual records through interpolation for each centre. Damage data and vulnerability assessment of 2134 traditional and hybrid structural units are conducted in the framework of the European Macroseismic Scale (EMS-98). The fragility functions are plotted for both structural types and EMS-98 vulnerability classes, also considering the contribution of structural interventions, and then compared to literature empirical models. Hybrid buildings achieve a behaviour similar to traditional buildings when floors are strengthened but walls are not. However, when both masonry walls and floors are strengthened, their performance significantly improved, approaching that of modern clay block buildings with rigid floors. Compared to literature models, the proposed one showed good compatibility for the most vulnerable buildings, whereas less vulnerable ones appeared even stronger thanks to interventions.

Seismic response of unreinforced masonry building aggregates: Investigation on the “aggregate-effect” based on an elementary building aggregate

Masonry building aggregates constitute a significant portion of Italian and Mediterranean countries built heritage. These structures originate from the progressive transformation and interconnection of originally isolated structural units over time. Masonry aggregate seismic performance is affected by significant uncertainty arising from the lack of knowledge of their complex structural arrangement, which is also reflected in the reliability of modeling assumption adopted for the analysis and the descending outcomes. This paper presents a numerical study investigating the seismic behavior of an elementary building aggregate made of three almost identical structural units. Different boundary conditions are explored in the analysis, extracting and comparing the responses of the individual structural units modeled both in aggregate and isolated and with rigid or flexible floors. Homogenized masonry approach is implemented for the building aggregate models with 2D layered inelastic shell elements. The structural models are realized with the STKO software platform for OpenSees, enabling parallel computing to analyze large scale models. Results will highlight the extent of the so-called “aggregate effect” for the elementary aggregate building and its potential benefits to the structural units, showing also that the behavior of structural units in aggregate strongly depends on their position and the polarity of the seismic forces.

Evaluation of Seismic Demand on Nonstructural Elements Based on Shake-Table Testing of Full-Scale 2-Story Steel Moment Frame

ABSTRACT A shake table test using a full-scale 2-story steel moment frame was conducted to investigate the peak floor acceleration (PFA) and the peak component acceleration (PCA), which directly affect the seismic demand on nonstructural elements. The main focus of this study was to evaluate the effects of structural and component nonlinearity on the nonstructural seismic demand. The PFA reduction suggested by ASCE 7-22 to account for structural nonlinearity was shown to be larger than the experimental results for low-to-moderate ductility levels. The analysis on the resonant PCA showed the importance of structural nonlinearity on the elastic C AR (=PCA/PFA). The high resonant PCA around the fundamental period of the elastic test frame (7 times PFA) was effectively decreased as the test frame experienced a moderate level of ductility; PCA was lowered by 36% and 25% on the 2nd and roof floors, respectively. The effect of component yielding on the PCA was evaluated based on the test results of steel racks mounted on flexible and rigid access floors. The PCA reduction depending on the component ductility level was less than the relevant provisions of ASCE 7-22, and the reason was discussed from the perspective of the pinched hysteretic behavior of the tested specimens.

Development of expeditious methods for seismic assessment of pre‐code masonry buildings in Portugal

AbstractAlthough Portugal has not been hit by high‐magnitude earthquakes in recent years, its history is marked by tragic seismic events and it remains susceptible due to its geographical location. The Portuguese building stock is constituted approximately by 45% masonry residential buildings and most were built before the enforcement of the first seismic code in 1958. For several years, structural interventions in these buildings were allowed without the need to assess their seismic vulnerability. In 2019, a new law was approved to regulate the rehabilitation interventions to provide safety and comfort of existing buildings. The seismic assessment of existing buildings became mandatory and based on the procedures and requirements included in NP EN 1998–3: 2017 (Portuguese version of Eurocode 8 – part 3), which establishes the performance requirements and compliance criteria for existing buildings subjected to a certain level of seismic action. According to this normative requirements, analytical seismic vulnerability assessment and reliability‐based analyses were carried out on a large set of masonry buildings representative of the Portuguese housing stock, leading to the development of surrogate and expeditious method for seismic assessment in compliance with the reference method defined in the European standard. The method allows the seismic assessment of masonry buildings with rigid and flexible floors, without explicit numerical analyses, using only geometric parameters and the material properties. Compliance of results assessed by the proposed method and the corresponding values obtained by the code were carried out by confidence tests.

Optimizing Seismic Capacity of Existing Masonry Buildings by Retrofitting Timber Floors: Wood-Based Solutions as a Dissipative Alternative to Rigid Concrete Diaphragms

The inadequate seismic performance of existing masonry buildings is often linked to the excessively low in-plane stiffness of timber diaphragms and the poor quality of their connections to the walls. However, relevant past studies and seismic events have also shown that rigid diaphragms could be detrimental for existing buildings and do not necessarily lead to an increase in their seismic performance. Therefore, this work explores the opportunity of optimizing the retrofitting of existing timber floors by means of a dissipative strengthening option, consisting of a plywood panel overlay. On the basis of past experimental tests and previously formulated analytical and numerical models for simulating the in-plane response of these retrofitted diaphragms, in this work nonlinear incremental dynamic analyses were performed on three case–study buildings. For each structure three configurations were analyzed: an as-built one, one having floors retrofitted with concrete slabs and one having dissipative diaphragms strengthened with plywood panels. The results showed that the additional beneficial hysteretic energy dissipation of the optimized diaphragms is relevant and can largely increase the seismic performance of the analyzed buildings, while rigid floors only localize the dissipation in the walls. These outcomes can contribute to an efficient seismic retrofitting of existing masonry buildings, demonstrating once more the great potential of wood-based techniques in comparison to the use of reinforced concrete for creating rigid diaphragms.

Discrete-element analysis of floor influence on seismic response of masonry structures

Traditional masonry buildings are highly vulnerable to earthquake loading and their dynamic response is strongly influenced by the in-plane deformability of the timber floors and the quality of the wall-to-floor connections. Understanding the behaviour of timber floors and roofs and their interaction with masonry walls is therefore fundamental for the protection of historical buildings. In a previous research project, different timber-based dry-connected strengthening solutions for timber floors were tested under in-plane loading. The experimental results showed a significant increase in shear strength and stiffness. In the current study, the discrete-element method (DEM) was used to model a simple masonry structure and evaluate the effectiveness of strengthening solutions to avoid triggering first-mode mechanisms, namely out-of-plane collapse of masonry walls. The structure was stressed by seismic ground accelerations. The unreinforced and reinforced floors were modelled with non-linear springs that reproduced their experimental hysteretic response. Parametric analyses were performed, changing the geometry of the structure and the masonry wall thickness. The comparison highlighted the effectiveness of the proposed wood-based strengthening solutions for reducing out-of-plane displacements of masonry walls, potentially matching the performance of rigid floors.

Adaptive Vibration Control for an Active Mass Damper of a High-Rise Building

As a kind of large flexible structure, high-rise buildings need to consider wind-resistant and anti-seismic problems for the safety of occupants and properties, especially in coastal areas. This article proposes an infinite dimensional model and an adaptive boundary control law for an active mass damper (AMD) on this question. The dynamic model of the high-rise building is a combination of some storeys which have flexible walls and rigid floors under a series of physical conditions. Then the adaptive boundary controller is acted on an AMD which is equipped on the top floor, in order to suppress the vibration of every floor and guarantee the comfort of residents. Moreover, simulations and experiments are carried out on a two-floor flexible building to illustrate the effectiveness of the proposed control strategy.

Development and validation of simplified mechanics-based capacity curves for scenario-based risk assessment of school buildings in Basel

This paper deals with the development of nonlinear static models for the calculation of capacity curves that are subsequently applied in a scenario-based assessment of school buildings. The investigated building types include unreinforced masonry buildings with rigid floors and reinforced concrete buildings with slender shear walls, both of which are typical in central Europe. The curves were established by means of simplified mechanics-based models of the structures together with the expected failure mechanisms of the structural members, from which bilinear capacity curves were calculated. These capacity curves were used to derive fragility curves for a number of predefined earthquake scenarios in Basel, Switzerland. This application revealed that with the initial capacity curves developed in this project, the damage in the earthquake scenarios was largely overestimated compared to that predicted from empirical intensity-based vulnerability models. The initial curves had been determined with models that made use of code recommendations for the assessment of existing structures together with experimental mean material characteristics. Modifications to the modelling procedure, including revised assumptions concerning the failure modes and changes to the assumed initial stiffness based on vibration measurements, led to revised curves which featured, in particular, increased ductility. With these updated and validated capacity curves, results closer to the empirical intensity-based models were obtained. While the type of modelling used herein has its limitations due to simplicity, it was still possible to account for the influence of typical characteristics (such as the detailing of RC walls) on the relative behaviour and response of the buildings, thus justifying the use of analytical capacity and fragility functions, as opposed to empirical intensity-based models, in the final risk assessment.

Seismic vulnerability of masonry buildings: Numerical insight on damage causes for residential buildings by the 2016 central Italy seismic sequence and evaluation of strengthening techniques

This study aims at investigating the causes of damage and collapse of several residential masonry structures during the devastating seismic sequence that hit Central Italy in 2016. After analyzing the structural features of affected buildings, an extensive series of numerical analyses is performed for a sample two-story masonry building to better understand its seismic vulnerability and suggest valuable hints for the reconstruction of historical city centers. Each analysis is carried out by adopting realistic hypotheses concerning material properties, connection among multi-leaf walls, different roofing systems (e.g., use of RC slabs at the top of the buildings), and the presence of rigid or flexible floors. Numerical analyses consist of modal and non-linear dynamic analyses, the latter using input accelerograms recorded during the main shocks of 2016 by the permanent accelerometric station of Amatrice (one of the most affected municipalities). For non-linear dynamic analyses, an elasto-plastic constitutive law with reasonable damage parameters in tension is adopted. Numerical results highlight good correspondence with observed behavior of residential low-rise buildings after the main seismic events in Amatrice, demonstrating the validity of the numerical approach. Moreover, the poor quality of the constitutive masonry material and the insufficient rigidity of floors and roofing systems are identified as the main causes of seismic vulnerability and, consequently, of collapse mechanisms. It is found that high quality masonry and well-connected walls play a crucial role in limiting damage formation and reducing global seismic vulnerability.

Equivalent Timoshenko linear beam model for the static and dynamic analysis of tower buildings

• Development of a general framework for evaluation of the equivalent beam stiffness . • Proposal of an innovative, constitutive linear law for the equivalent model. • Identification of a measure for the flexural-to-shear ratio in building deformation. • Derivation of motion equations generalizing the classic 3D Timoshenko model. • Easy-to-use procedure to regain deformation and stress state on the single element. A continuous Timoshenko linear beam model immersed in a three-dimensional space is introduced to study the static and dynamic behavior of tower buildings. A schematization of the building as a periodic system with rigid floors connected by deformable elements (columns and shear walls) is considered. The rigid floors are endowed with six degrees of freedom (three displacements and three rotations). The constitutive equations of the equivalent beam (coarse model) are identified from a discrete model of the three-dimensional frame (fine model) via a homogenization procedure. A complete linear constitutive law is obtained, with axial force coupled with bending and shear force coupled with torsion. The first aim is to investigate the relative importance of the macro-shear and macro-bending contributions to the deformation of the building. Then, the ability of the coarse model to reproduce the local stress distribution of the fine model is checked. Finally, the representativeness of the coarse model for the detection of the natural frequencies of the fine model is analyzed.

Determination of the quality of coarse aggregates for the elaboration of concrete mixes from 3 water sources in the City of Cucuta-Colombia

A comparative analysis was performed on the mineral material extracted from 3 water sources in the city of Cucuta, from the rivers Tachira, Pamplonita and Zulia to determine the viability of their incorporation in the concrete mixtures for the construction of rigid floors. There were visits to the companies Preconcretos Trituradora la Roca y Concretos, and Tirurados, in charge of the material extractions, where samples of the crushed material “coarse aggregate” from each of the water sources were taken respectively. The granulometry of the coarse aggregate was performed according to the arranged parameters in the NCT 174 whose results were determinant for the conclusions. The trial of degradation to abrasion to each of the samples was executed, taking as guide the indications described by the Colombian INV-218-13 standard. The results obtained in the trial were analyzed and compared with the parameters stipulated by the INV standard described for the % of the degradation limit allowed for coarse aggregate for its usage as concrete material in the construction of rigid floors. It was concluded that each of the extracted materials from the water sources were viable according to the data obtained from their comparison.

In-plane deformability of RC floors: assessment of the main parameters and influence on dynamic behaviour

In-plane floor deformability is an important issue for the correct assessment of the behaviour of Reinforced Concrete (RC) structures subjected to seismic loads. Several studies have demonstrated that in-plane floor deformability is often not negligible in structures with RC walls as vertical resistant elements, since it mainly depends on the relative stiffness of floor and vertical elements. In this paper, approximately 700 simple buildings constructed with RC walls were simulated in finite element models considering both two-dimensional and one-dimensional modelling strategies. First, the reliability of the simplified modelling strategy was evaluated. Then, the simplified model was used to assess the effects of building shape and number of walls on the in-plane floor deformability. The differences between the behaviour of the buildings under the assumption of deformable and rigid floors were examined in terms of both floor displacements, based on static analyses, and the main vibration periods of the building, based on linear dynamic analyses. Finally, based on the collected numerical results, reliable regression curves for both the maximum displacements and the periods evaluated under the assumption of deformable and rigid floors were obtained as function of a parameter significant of floor and walls stiffness. The curves may provide a tool for evaluating the error related to an incorrect assumption about the in-plane floor deformability.

Development and implementation of a control system for the dynamic mitigation of 3-D masonry structures with feedback on the drifts in the horizontal plane

In the paper, the response of a typical 3-D masonry building subject to dynamic disturbance is considered, with the purpose to identify control strategies able to mitigate the effects of the excitation. The structure is made of vertical planar elements (the walls) firmly jointed at the wall crosses and horizontally connected by rigid floors. The structural control of the building is realized through the introduction of a suitable dissipative action, which is operated through active, semi-active, or even passive devices. The control action is ruled by suitable algorithms that are optimally designed with the purpose to optimize the balance between the reduction of the oscillations of the floors, and consequently of the ductility demand to the walls on one side, and the intensity of the control force on the other side. The system behaves in dependency of the single-wall shear displacement in-plane constitutive law that can be identified on the basis of the no-tension model with shear friction strain modes. The behaviour of the whole is ruled by the relevant non-linear history-dependent equations. The control strategy is developed for non-linear systems and then specialized and tested for the presented application to seismic protection of masonry buildings.

Flexural torsional buckling of uniformly compressed beam-like structures

A Timoshenko beam model embedded in a 3D space is introduced for buckling analysis of multi-store buildings, made by rigid floors connected by elastic columns. The beam model is developed via a direct approach, and the constitutive law, accounting for prestress forces, is deduced via a suitable homogenization procedure. The bifurcation analysis for the case of uniformly compressed buildings is then addressed, and numerical results concerning the Timoshenko model are compared with 3D finite element analyses. Finally, some conclusions and perspectives are drawn.

Evaluation of the seismic retrofitting of an unreinforced masonry building using numerical modeling and ambient vibration measurements

Ambient vibration measurements and 3-D nonlinear time-history numerical modeling are used to assess the retrofitting measures conducted in a 6-story unreinforced masonry building (URM) built in the end of the 19th century in Switzerland. Retrofitting measures were taken in order to improve the soundproofing and possibly the seismic performance of the building. Reinforced concrete (RC) footings were added under the walls and horizontal steel beams were added to link the walls together with a RC slab at each floor, though the wooden beams were left in place. Several ambient vibration recordings were performed before, during and after the retrofitting work in order to monitor the evolution of the dynamic behavior of the structure. Moreover, numerical models representing the state of the building before and after the retrofit work have been developed to perform nonlinear dynamic analyses using various ground motion records. The change in the modal vibration frequencies, mode shapes, and failure mechanism are presented and discussed in further details. According to ambient vibration measurements, the performed retrofitting resulted in an increase of about 25% of the fundamental frequency. From the results of both the numerical modeling and the ambient vibration measurements, it is confirmed that the in-plane behavior of the slabs evolved from non-rigid floors with in-plane deformation to rigid floors with diaphragm effects. The ambient vibration measurements show that the new stiff slabs could lead to torsion behavior in the building as the result of the diaphragm effect and to higher seismic demand. However, the numerical models show that the displacement capacity of the building increases as a result of those new stiff slabs. Consequently, higher deformation capacity, indicated by the inter-story drift values, on average, are observed for all the damage grades in the post-retrofit state of the building. Finally, the overall seismic safety was only slightly improved.

Realistic behavior of infilled steel frames in seismic events: experimental and analytical study

An experimental and analytical study is carried out to investigate the effects of lateral loading type on the behavior of masonry infilled steel frames. During earthquake the lateral load is applied as distributed loading to the top beams and columns through rigid floors; however, in most available experimental studies the lateral loading is applied as concentrated loading. In this study, two identical specimens are tested and their behavior is compared under distributed and concentrated lateral loadings. Finite element models of the specimens are also developed and validated against the experimental results. To have a better view, the influence of loading type is studied on another experimental specimen having concentrated loading. A parametric study is also conducted on the influence of loading type in multi-span frames and infills with different aspect ratios. The obtained experimental results show that the distributed loading results in 18.5 and 29% increase in the strength and stiffness of Infilled frames, compared to the case with concentrated loading. Less strength and stiffness in specimens subjected to concentrated loading is a result of stress concentration at the infill corner near the loading point which leads to premature corner crushing. Therefore, it is believed that the codes’ formulas, mostly based on specimens with concentrated loading, are conservative, underestimating the real ultimate strength and stiffness of masonry infilled steel frames.

Direct Linear System Identification Method for Multistory Three-dimensional Building Structure with General Eccentricity

A method of physical-parameter system identification is proposed here for three-dimensional (3D) building structures with in-plane rigid floors in which the stiffness and damping coefficients of each structural frame in the 3D building structure are identified from the measured floor horizontal accelerations. A batch processing least-squares estimation method for many discrete time-domain measured data is proposed for the direct identification of the stiffness and damping coefficients of each structural frame. While previous researches on the system identification of 3D building structures are limited to a class of structures with regular eccentricity, the present paper removes this limitation. Advantageous features of the proposed identification method are that it is unnecessary to specify the stiffness eccentricities (location of center of stiffness) before identification and the identification of all stiffness and damping parameters can be performed simultaneously. The reliability and accuracy of the proposed method are demonstrated by numerical simulations.

Who Is Ahead in the Labor Queue? Institutions’ and Employers’ Perspective on Overeducation, Undereducation, and Horizontal Mismatches

Using vignettes, this study compares employers’ assessments of matched and mismatched job applicants in England and the Netherlands. It contributes to the overeducation literature in several ways. First, matching is measured from the perspective of employers, who are better informed about job requirements than employees. Second, overeducated applicants are compared to matched applicants competing for the same job opening. This shift in focus toward applicant pools is necessary to properly test whether overeducation is rewarded during the hiring process, the central tenet of job competition theory. Third, vertical and horizontal mismatches are analyzed jointly: This more fine-grained differentiation refines sociological perspectives on credentialism and reveals the complex ways in which employers assign applicants to jobs. Results show that Dutch employers apply more rigid hiring floors and more strongly penalize horizontal mismatches: Compared to England, in the Netherlands, overeducation cannot compensate for the lack of occupation-specific training.