Nonlinear Static Analysis Research Articles

Nonlinear static analyses to improve the seismic damage assessment of monitored masonry palaces: application to the Consoli Palace of Gubbio, Italy

The conservation of the built architectural heritage in seismic-prone regions is a topical task in modern civil engineering. The ongoing diffusion of structural health monitoring systems calls for innovative and efficient methodologies for damage identification and condition assessment from field data. For this purpose, the paper proposes a novel model-based and data-informed approach relating the variation of the modal properties of the structure to increasing levels of seismic damage, looking into the outcomes of pushover analysis from a frequency-domain perspective. The direct problem is addressed through nonlinear static analyses, in which the structure is progressively damaged by applying simplified distributions of earthquake-induced horizontal forces, followed by a modal analysis at each degraded damage state. Addressing the inverse problem, starting from experimentally identified variations of the spectral properties and exploiting the simulation results, efficiently provides valuable insights into potential damage levels suffered by the structure. The forward methodology is exemplified by the application to a continuously monitored monumental masonry palace, the Consoli Palace of Gubbio, Italy, which was recently hit by a low-to-medium intensity earthquake and exhibited a slight reduction of its natural frequencies.

Seismic analysis and fragility estimate of a mixed masonry-r.c. school building

Nowadays, there is still very little scientific understanding of the seismic response of mixed masonry-r.c. structures, despite their unneglectable frequency, in particular in public building assets. This contribution presents the investigations carried out on a representative school, built at the turn of 1950s and 1960s. It is a two-storey building, characterised by central longitudinal load-bearing masonry walls, as well as transverse masonry panels, coupled with r.c. frames on major façades, and isolated columns in halls. This structural configuration is commonly found in public buildings, specifically schools. R.c. elements were exploited to build open-space environments, as well as to increase openings on façades, thus ensuring a better natural lighting.In this study, masonry components were modelled through an equivalent frame model (EFM). Half-height infills, interacting with frames, were simulated through a single-strut macro-model. To simulate the nonlinear response of the structure, lumped plasticity hinges were implemented for both load-bearing masonry and infills, while a fibre model was chosen for r.c. frames. The presence of non-seismic joints among structural units was also considered. The relative contribution of masonry and r.c. components was investigated through parametric linear dynamic analyses. Preliminary nonlinear static analyses (NLSA) were carried out to identify thresholds of damage. Moreover, the structure was analysed through nonlinear time history analyses (NLTHA) by applying a large number of natural unscaled ground motion records. Lastly, fragility curves were estimated from outcomes of NLTHA. The derived fragility model represents a key instrument in seismic risk evaluations for the analysed macro-class, being one of the few examples of fragility sets specific for mixed masonry-r.c. buildings.

Influence of spatially heterogeneous deterioration patterns on strength and ductility of corroded reinforced concrete bridge piers

This work reports on some preliminary results obtained within the framework of a wide research project aimed to study the influence of the corrosion of in Reinforced Concrete (RC) piers on the overall seismic performances of bridges. In this context, after the statistical evaluation of a large database of real structures, a consistent set of bridges and piers has been selected as a sample representative of typical bridge profiles, pier heights and cross-sections as well as of material properties. In the first part of the project, pushover analyses of isolated piers with different corrosion patterns and intensity are carried out to evaluate the residual strength and ductility of corroded piers. In the second part, nonlinear static and dynamic seismic analyses of bridges with corroded piers are carried out to evaluate the influence of the deterioration on the overall seismic performance. Due to specific environmental conditions exposure or to water percolation from the superstructures, it is often the case that corrosion is non-uniformly distributed over piers producing non-homogeneous spatial deterioration patterns. The nonlinear modeling of this type of situations represents specific challenges related to the description of the deterioration patterns and the calibration of material properties. To this end, a multi-level modeling approach based on fiber-based finite elements has been developed and implemented in a specific OpenSeesPy software that allows users to accurately model RC piers subject to arbitrary corrosion patterns, up to their ultimate limit states. In this work, a specific case study of a typical RC rectangular hollow bridge extracted from the mentioned above database subject to different corrosion intensity and patterns is studied. In particular, the influence of the corrosion-induced deterioration on residual strength and ductility are studied. Results show that depending on the intensity and on the patterns significant variations of both strength and ductility can be observed with respect to the undamaged conditions.

On the seismic response of rack structures affected by pinching

The nonlinear static and dynamic behavior of rack structures affected by joint pinching are studied using a simplified single-degree-of-freedom system. Since the joints of steel rack structures play a crucial role in the capacity design methodology, as they are the main source of energy dissipation, their behavior is widely studied in the literature, highlighting their reduced hysteresis loop. However, no systematic study investigates and associates these characteristics with a possible increase in displacement demand. Using a single-degree-of-freedom system focuses attention on the type of cyclic behavior and allows a comparison of linear and nonlinear responses, the latter evaluated using both elastic-plastic and pinching laws. At prescribed ductility, the elastic-plastic and pinching responses can be compared with the prescriptions of Italian and European building codes. This simplified method was also applied to case studies of experimental pushover tests on racks found in the literature. Results showed that neglecting the joint pinching behavior for a rack structure can lead to an underestimation of the displacement demand in the case of the application of the nonlinear static seismic analysis method and hence to the overestimation of the q-factor for the application of linear seismic analysis methods.

Survey on non-linear cyclic responses of Unreinforced Masonry buildings by means of commercial finite-element codes

This work presents a comparison about the nonlinear cyclic response of unreinforced masonry structures obtained by using commercial calculation codes and on the base of the type of modeling approaches currently available. In particular, several elasto-plastic modeling methodologies are considered, representative of a good part of the state of the art for this type of construction: mechanical-based concentrated plasticity macro-element (Tremuri), macro-element with diffuse fiber-based plasticity for flexure and concentrated springs for shear (SeismoStruct) and macro-element with phenomenological-based concentrated plasticity (NextFEM Designer). The purpose of the present research is to evaluate the ability of the different codes to represent the proper hysteretic response of masonry structures. To this aim, several experimental tests from literature are analyzed and compared; two different masonry panels, characterized by different resistant mechanisms, and an entire perforated wall have been studied through nonlinear cyclic static analyses. The reported comparison, mainly focused on the numerical cyclic behaviour exhibited by each computer program, is conducted on the basis of the path of the cycles obtained and on the amount of dissipated energy.

ОБОСНОВАНИЕ ФОРМУЛЫ ДЛЯ КОЛИЧЕСТВЕННОЙ ОЦЕНКИ ДЕФИЦИТА СЕЙСМОСТОЙКОСТИ ЗДАНИЙ НЕЛИНЕЙНЫМ СТАТИЧЕСКИМ МЕТОДОМ В SAP2000

The article is a continuation of research previously published in the Bulletin (2021, vol. 21, no. 2). Au-thor offers explanations and clarifications of a formula proposed to assess insufficient earthquake resistance shortage (hereinafter Id) of buildings using calculation procedures of nonlinear static Pushover analysis in SAP2000. An idea was implemented to graphically justify the mathematical expression used to determine Id with building age adjustments per building age. It was assumed that under certain conditions a change in service life-span (hereinafter referred to as Tst) of a building will lead to changes in the calculated acceleration of vibrations in proportion to the cube root of Tst. It was also assumed that at the end of a building's service life an earthquakes, can cause severe structural damage (or destruction) of its members, can occur. Change of a building age by estimation time of Id value was assumed to be distributed accord-ing to an exponential law. A value corresponding to the end of the building's service life Tst was taken an objectivity compliance criteria for the proposed formula for estimating of Id. Obtained an Id value should be confirmed by technical survey of buildings in seismic areas. Relationship curves of Id (Tst) were plotted according to a refined formula for the considered territory tremor values and earthquake waiting time. The obtained results can be applied to fulfill the re-quirements of term 6.19.11 of Seismic Design Building Code SP 14.13330.2018 and to be used as a supplement the cal-culation provisions laid out in the Assessment Procedure for Survey of Standard Buildings to Determine their Earth-quake Resistance and Need for Seismic Retrofitting (Kamchatgrazhdanproekt, 2009).

Seismic vulnerability analysis and structural rehabilitation of a historical masonry tower

This paper presents the results of the structural performance assessment of an existing masonry tower and the subsequent repair and strengthening intervention. The study deals with an Italian architectural heritage building in the Cilento National Park (Southern Italy): the bell tower in Torre Orsaia. The tower has been the subject of on-site diagnostic investigations including geometrical surveys, laser scanning surveys, flat jack tests, endoscopic tests, sonic pulse velocity tests, geognostic surveys, and tie-rods tests. The multilevel assessment path proposed by the Italian Guidelines for the assessment and mitigation of the seismic risk of the cultural heritage is followed and the corresponding results are discussed. The global inelastic behavior of the masonry tower is studied through a macro-model approach using the nonlinear static (pushover) analysis. The local collapse mechanisms are studied through a kinematic limit analysis based on rigid block rotation. The repair and strengthening interventions have shown their effectiveness to close the existing cracks, preventing damage to the belfry, and improving the seismic performance of the tower. Both the compatibility, durability, and reversibility of the interventions and their reliability and monitoring are finally highlighted since the bell tower of Torre Orsaia is a historical heritage building.

Seismic vulnerability assessment of RC frame structures subjected to seismic excitation: A review

Because of their unpredictable nature and high damage-causing ability, earthquakes pose a significant threat to buildings. As a result, loss of lives and significant loss of economy became a primary concern in many parts of the world. Damage to structures is one of the many reasons to examine their seismic behavior when subjected to seismic forces. The seismic vulnerability of a structure can also be defined as its vulnerability to damage caused by ground shaking of a certain intensity. A building fragility analysis is performed to assess its vulnerability. The analysis of structural fragility provides a better understanding of the response of structural and non-structural systems during seismic events. It also helps to reduce damage and the risk of loss of life. Fragility curves indicate the likelihood of failure when a building is subjected to earthquakes of varying magnitudes. This paper provides an overview of the studies published in the field of seismic vulnerability assessment of RC buildings using fragility curves. The adopted methods within the past studies were nonlinear static pushover analysis, nonlinear time history analysis, incremental dynamic analysis etc. This review study discusses the effects of aging, soil structure interaction, set back irregularities, effects of infill, effect of strong column and weak beam, soft story, construction quality etc. on the vulnerability of RC frame structures.

Empirical modelling of the cyclic response of reinforced concrete columns with deformed bars

In this paper, the results of the cyclic experimental tests performed on ductile rectangular reinforced concrete columns with deformed bars are processed to define characteristic points of the lateral base moment – chord rotation response envelope. Four characteristic points are determined: yielding, maximum, conventional ultimate, and collapse. The value of base moment corresponding to these points can be determined based on mechanical principles or is intrinsic to the definition itself of the characteristic points of the response. On the other hand, based on the processed experimental data, empirical equations are derived for calculating chord rotation values corresponding to the four characteristic points. The proposed cyclic response envelope can be implemented in OpenSees by adopting Pinching4 Material model, which also allows modeling the cyclic degradation of unloading stiffness, reloading stiffness, and the pinching effect. Based on the processed experimental data, the hysteretic parameters that should be adopted to model these phenomena are calibrated. The proposed model can be adopted for nonlinear static and dynamic analyses for the seismic assessment of new and existing buildings.

Comparative Analysis of Multistorey RCC and Semi-Rigid Steel Frame with Cross Bracings Subjected to Mainshock and Aftershock Earthquake Sequence

Strong Ground Motions have a significant impact on structural analysis and design. Seismic evaluation is deemed necessary for the quality, reliability, and feasibility of existing and developing structures. Earthquakes are even more disastrous when a mainshock is succeeded and preceded by aftershocks of higher magnitude. Most of the time, these aftershocks are ignored during analysis. In the last few decades, steel buildings have been crucial to the construction sector. On the other hand, RCC frames are commonly designed structures for commercial purposes and cost-effectiveness. IS 1893 (Part:1)-2002 Criteria for Earthquake Resistant Design of Structures and IS 13920-2016 Ductile Detailing of RC Structures Subjected to Seismic Reactions are majorly used for Seismic Analysis. Steel bracings in the structural system increase the ductility and stiffness of the frame structure. That can be arranged in a variety of ways, such as X, diagonally, alternatively, V, inverted V, K, etc. Cross bracings are used in this paper for the design of a typical multi-story (G+9) semi-rigid steel frame and a typical RCC frame is designed of the same dimensions. Both the frames are modelled and compared using ETABS software and a static nonlinear Time History analysis is executed to examine the performance of both the frames under the Mainshock and Aftershock of Chamoli earthquake. The Mainshock and Aftershock results of the Chamoli earthquake are extracted from the Centre for Engineering Strong Motion Research Ground Motion Database. Base shear, joint displacement, kinetic energy, and story displacement are a few of the variables of Time History Analysis that affect how well a building performs during mainshock and aftershock earthquakes. When analysing the outcomes, it is important to take into account that each of these factors significantly affects how a building responds to seismic loads.

Effectiveness of traditional strengthening measures on historic masonry buildings: the seismic performance of Palazzo Comunale in Camerino after 2016-2017 seismic sequence

The implementation of seismic strengthening measures on monumental buildings requires a balance between the need to preserve its original configuration and the need to guarantee adequate safety levels. The paper presents the analysis of the performance of a heritage building in Camerino, a small town in central Italy, after the 2016-2017 seismic sequence.The building is called Palazzo Comunale, a medieval building, used as town hall. Due to the previous earthquake occurred in 1997, the Palazzo Comunale suffered extensive damage; repairs and strengthening measures were designed and realized starting from 1999. In particular, traditional strengthening techniques were adopted: the mechanical characteristics of the walls were improved by means of grout injections, the original wooden floors were either replaced or stiffened, and several steel tie rods were introduced.In situ surveys allowed to detect the damage caused by the 2016 seismic sequence and to evaluate the effectiveness of the strengthening measures in improving the seismic behavior of the Palazzo Comunale. Furthermore, the seismic vulnerabilities of the buildings are herein discussed through global non-linear static analyses and local kinematic analyses.

Development and rapid visual screening analysis of an Italian masonry building portfolio using post-earthquake damage observations

The damage observed during the seismic events occurred in Italy over the years have highlighted the seismic vulnerability of the existing masonry buildings. A significant percentage of the Italian masonry building heritage was built before the introduction of seismic provisions and their design was essentially based on the experience of professionals. Depending on the main characteristics of these buildings, both local and global damage mechanisms were observed during the post-earthquake inspections following the seismic events that occurred in Italy in the last 50 years, which have been cataloged by the Italian Civil Protection Department in the Da.D.O. platform (Observed Damage Database - Observed Damage Database). Using the data available in the Da.D.O. platform, this paper processes the main characteristics of the masonry buildings damaged by the 2009 L'Aquila earthquake to develop a representative masonry building portfolio. Such masonry buildings were then evaluated through nonlinear static analyses to identify the main sources of structural weakness and to develop or calibrate a simplified rapid visual screening (RVS) procedure. For this purpose, various RVS methods were applied to a number of buildings of the portfolio, obtaining different vulnerability indices to be scrutinized and compared with those obtained through FEM analytical methods. This ultimate goal is to identify the most seismically vulnerable buildings, with a view to prioritization, and to assist decision makers in implementing seismic risk reduction strategies.

Influence of bond-slip on numerical fragility curves of RC structural columns

In this paper results obtained from monotonic nonlinear static analyses performed on Reinforced Concrete (RC) columns are shown. Bond-slip phenomenon between steel longitudinal bars and surrounding concrete is also taken into account in order to predict the numerical response under lateral actions of the RC columns investigated.The study is addressed, through parametric models and Monte Carlo simulations, to propose preliminary fragility curves for different damage states of the RC columns, including materials inherent uncertainties. Finally, the paper concludes comparing the proposed fragility curves with other similar ones published in the literature.

A macro-element approach for the seismic analysis of monumental buildings

The structural assessment under earthquake of ancient masonry churches remains a challenging task due to their intrinsic characteristics, i.e. the complexity of their geometry, the strong non-linear behaviour of the masonry material, the high computational burden related to the three-dimensional models adopted for the analyses, etc. The Italian Standard suggests to study the seismic behaviour of such a type of structures analysing separately the global response to seismic loads and the local behavior of a-priori defined portion of the building involved into collapse mechanism. In this work, the authors try to establish a link between the global behavior of the church and the assessment of the local mechanism by performing a two steps procedure based on: i) the detection of the main vibration modes of the whole building with the identification of the structural macro-elements responsible for the overall seismic vulnerability and ii) the definition of the failure patterns due to earthquake by carrying out a series of finite element non-linear static analyses on the previously-identified macro-elements.The procedure will be applied to a case of study: the church of St. Martino dei Gualdesi in Castelsangelo on the Nera river (Italy).

Composite Reinforced Mortar (CRM) and Fiber-Reinforced Cementitious Matrix (FRCM) for the seismic protection of masonry vaults

Composite Reinforced Mortar (CRM) and Fiber-Reinforced Cementitious Matrix (FRCM) are two modern strengthening techniques for existing masonry, based on the coupling of fiber-based grids and inorganic matrices, applied on the masonry surface. They typically differ for the thickness of the coating (20-40 mm in the former, 8-15 mm in the latter) and the type of embedded reinforcement (pre-coated meshes with wide pitch or dry fabrics with a closer yarns spacing, respectively). To prove their effectiveness in the seismic protection of historical masonry vaulted ceilings, experimental cyclic tests were performed on full-scale thin barrel vault samples subjected to a distributed transversal load. The results are analysed and discussed in the paper: it emerged a good effectiveness of both the strengthening solutions, with significant benefits in both resistance and displacement capacities. Moreover, a key aspect for the reinforcement effectiveness is found in the connection of the composite systems with the abutments. Numerical non-linear static analyses based on a simplified multi-layer approach developed in the OOFEM code allow to analyse the resisting mechanisms and investigate on the reinforcement effectiveness.

Analytical prediction of the seismic resistance of masonry buildings retrofitted by Steel Fiber Reinforced Mortar coatings

An extensive experimental program has been performed in the last years at the University of Brescia to show the effectiveness of the in-plane seismic strengthening or repairing of existing masonry buildings by Steel Fiber Reinforced Mortar (SFRM) coatings. In particular, the tests on a full-scale hollow clay block masonry building showed the applicability of the retrofitting technique on the external surface of the structure only.An analytical model already developed and validated is briefly presented in this article and applied to the building experimentally tested. Particular attention is paid to the simplified schematization of the masonry piers based on the fracture lines expected before and after retrofitting. The effectiveness of the analytical model in predicting the seismic resistance of the building is assessed by comparing the analytical results with those obtained from the experimental test.Finally, the analytical model is applied to a real two-story residential building made of concrete hollow units to perform the seismic verification of the structure. The analytical prediction of the global seismic resistance of the building is compared with that obtained from a non-linear static analysis carried out with the finite element program Midas FEA. The results of the comparison will further prove the reliability of the proposed analytical model.

Fragility curves of a gravity load designed r.c. hospital building: a case study

The awareness of the vulnerability of strategic structures such as hospitals is of primary importance as local governments have the necessity of a global overview of the seismic performance of these facilities, to decide how to best allocate funds for restorations. From this point of view, the fragility curves of a building represent a powerful tool that allows to assess the probability of exceeding a damage threshold (or a limit state). Such information is useful for the assessment of the structure, and for investigating the possibility to maintain functions during and immediately after earthquakes.In this paper the case study of an hospital facility is presented. The structure was analysed and verified by means of non-linear static analyses (Pushover) and incremental non-linear dynamic analyses (IDA). Furthermore, the fragility curves for four different damage levels (null, slight, moderate and severe) and two different seismic intensity measures were obtained.

Seismic response and damage evaluation for anchored and unanchored cylindrical above ground steel tanks

This paper aims to first present a review of studies on numerical modeling and seismic response analysis of above ground steel liquid storage tanks. On that basis, a procedure for estimating dynamic parameters associated with simplified models for anchored and unanchored conditions together with calculation methods of seismic responses and damage states of tanks are presented. In which, the nonlinear behavior of the bottom plate in the case of unanchored conditions caused by sliding and uplift phenomena is properly modeled based on the nonlinear static pushover analysis on a 3D finite element model. Finally, an example of the numerical modeling and seismic response analysis of a water tank is presented. The seismic responses and damage of both anchored and unanchored conditions are compared and evaluated in detail.

Exploration Study on Energy Dissipation in Beam and Column Joint with Semi Rigid Connection

Abstract: The earthquake reconnaissance reports reveal that the failure of beam column joint has contributed to partial or complete collapse of reinforced buildings. The failure of a beam causes only localized effect whereas the failure of a beamcolumn joint causes instability of the whole building under seismic loading. This results in significant economic impact and loss of life. Hence it is essential to avoid failure of beam-column joint. The serious damage to the major structures during recent earthquakes is mainly attributed to lack of ductility in beam-column joint. In the present work, experimental investigation is carried out to study the effect of semi rigid connection in RCC beam column joints of reinforced concrete multi storey buildings. The effectiveness of semi rigid connection and effective positioning (stability approach) is analytically investigated for a typical four-bay four-storey and five-bay seven-storey RC frame with different percentage of joint connections by nonlinear static (pushover) and nonlinear dynamic (time-history) analyses. Poor performance was noted in rigid frame during the prediction of structural damage, lateralstrength and storey drift. The semi rigid connection isprovided in different places and it is found that performance of the structure enhanced in the stability approach. The stability approach exhibited improved performance in terms of roof displacement, for and semi-rigid connection.

JUSTIFICATION OF THE DESIGN AND PARAMETERS OF THE WHEELS DURING THE DESIGN PROCESS OF THE CHASSIS OF A ROBOTIC PLATFORM USING SOLIDWORKS SIMULATION

The design of robotic platform for close reconnaissance of territories is a topical scientific and engineering task, that obviously has a dual purpose – both civilian and military. Despite the fact that leading global companies are engaged in the development of such technical systems, it is important to ensure operation in difficult conditions, in particular in the conditions of the need for increased passability that requires the development of an improved design of wheels and a scientifically based choice of their parameters – which was an aim of the paper. The problem was solved by calculating the strength of the design proposed in the work, that for plastic parts requires to conduct a non-linear static analysis, determination of the forces acting on the wheels in case of its falling from a certain height. It was established that the safety factor is sufficient according to the criterion of maximum normal stresses. The developed new design of wheels for a robotic machine differs from existing designs by an increased diameter and the presence of a tread that significantly increases the passability compared to known prototypes. As a result of the conducted research, it is shown that the cellular structure of the wheel generally increases the strength and rigidity of the wheels. It was also established that despite the increase in the mass of the wheels to ensure the increased passability of the robotic vehicle, the stress value during impact (falling from a height) is reduced due to the proposed rational design of the wheels, while the minimum safety factor according to the criterion of maximum normal stresses is increased. The design is implemented as a computer 3D model and was manufactured using a 3D printer.