Seismic spectra are fundamental tools in earthquake engineering due to their intuitive conceptual framework and broad practical applicability. However, when extended to nonlinear structural analyses, such methods often require approximations that significantly compromise result accuracy. This study presents a comprehensive evaluation of the seismic response of hysteretic nonlinear systems, focusing on the energy-based aspects of the response. The Bouc–Wen model is adopted to accurately capture the hysteretic behaviour of structures subjected to intense cyclic loading. This model effectively represents the nonlinear dynamics commonly observed in structural materials under seismic excitation. The seismic input is modelled using a stochastic approach, specifically as a time-modulated, filtered, non-stationary stochastic process. This allows for a realistic simulation of seismic events, accounting for both temporal and spectral variability. The analysis involves computing the system’s response covariance and deriving the mean values of various energy components, with a particular focus on dissipated energy. By emphasizing energy dissipation, the study investigates how structural parameters and earthquake features—such as strong motion duration and Arias intensity—affect energy absorption and dissipation mechanisms. The findings aim to inform more resilient structural designs and contribute to enhanced seismic performance.

Seismic isolation has become an effective technique for seismic protection, significantly reducing lateral forces and horizontal accelerations in buildings. Among various isolation devices, High Damping Rubber Bearings are widely used due to their cost-effectiveness, ease of application, and clear mechanical behavior during the design phase. A precise mechanical behavior model is essential for the efficient use of High Damping Rubber Bearings in practice, as it realistically mitigates seismic actions on protected structures. The design of these systems mandates a permissible displacement limit under seismic conditions, beyond which the mechanical performance and operational functionality of the bearings maybe compromised. This paper focuses on the optimal selection of mechanical behavior models for High Damping Rubber Bearings, constrained by the maximum design displacement to prevent phenomena such as pinching. The primary innovation lies in evaluating not only the accuracy but also the stability of mechanical parameters derived from standard experimental tests, as specified by construction guidelines. The research investigates the mechanical behavior within the limits of maximum design displacement, ensuring alignment with practical design scenarios and addressing relevant mechanical responses under typical service conditions. Moreover, it provides a reliable assessment approach for the assessment of the real industrial production variability of such devices, emphasizing the effect of uncertainties induced in manufacturing, and the need for robust, adaptable design models to accommodate such variability. Six established High Damping Rubber Bearings models were evaluated through experimental tests on ten samples. The analysis revealed that models with higher accuracy in reproducing the experimental behavior of a specific device might fail to represent the variability found in industrial production. This highlights the importance of balancing accuracy and robustness in the model's selection for practical applications.

Seismic isolation emerged as an efficient technology for seismic protection. It has been proven to simultaneously reduce inter-story drift demands and horizontal accelerations in buildings when properly implemented. Since the 80s, several numerical models appeared in literature to simulate the dissipative behaviour of High Damping Rubber Bearings (HDRB) devices under different acting scenarios. Despite the efforts provided by several authors to reproduce the real behaviour of such devices through the definition of efficient numerical models, the variability of laws' parameters in the mass-production series of devices should receive further investigations. This research presents the preliminary results pointed out by an identification procedure of no.2 existing literature models with an increasing level of computation effort. The reliability of the numerical outputs and the goodness of each numerical model have been demonstrated by comparing them with experimental tests obtained from the SISMALAB laboratory. Experimental data are composed of no. 5 samples of the same devices, subjected to both compression forces and horizontal displacement under sinusoidal cyclic deformation. The optimal values of each device have been obtained by performing an optimization process where the difference between experimental and numerical behaviour has been minimized. The well-known Genetic Algorithm has been chosen for this purpose.

This study deals with the parametric design and the optimization of pedestrian steel structures that are particularly significant in the field of civil engineering. Structural optimization is performed through the use of genetic algorithms. In particular, Grasshopper parametric analysis solver is used, by implementing the Galapagos algorithm. The optimization is carried out in terms of both weight and shape. Three models of simply-supported beams, with a span equal to 20 m, are considered: a truss girder, an arch with orthogonal ropes and a network arch. In the first structure, the design variables are represented by the cross-section and the geometric arrangement of the elements constituting the beam. In the case of the arch and the network beams, the design variables are the width of the arch curvature, the cross-section of the different components and the arrangement of internal ropes. In all optimization procedures the weight of the structure is assumed as the objective function and the attention is focused on hollow circular sections. The performed analyses show that the network arch represents the optimal model. In fact, it is characterized by normal and bending stresses lower than the other typologies and by the lowest weight and then cost. There is an inverse relationship between the angle of curvature of the top chord and the number of ropes. The cross section of the top chord is bigger than the one of the bottom chord, as well as diagonals are characterized by smaller cross sections, coherently with previous literature studies.

Real physical events, such as earthquakes, sea waves, and wind, are often random in nature and can be defined as a realization of a stochastic process. The simplest way to model them is to use stationary processes. However, in some cases, it’s necessary to consider their evolutionary nature over time to properly account for their non-stationary nature, as in the case of seismic records. In such circumstances, it’s common to assume the process as a non-stationary separable process modulated by a deterministic function that can represent the time variation of the physical event. Solving this problem is a complex task, and there are a few numerical approaches proposed with this aim. In this paper, the case of the dynamic structural response of a linear multi-degree-of-freedom system subject to non-stationary random Gaussian dynamic actions is analyzed. In the case of non-stationary inputs, the evaluation of second-order spectral moments requires the solution of a Lyapunov matrix differential equation. In this work, numerical schemes for its resolution are proposed. The numerical computational effort is minimized by taking into account the symmetry characteristic of the state space covariance matrix. As an application of the proposed method, a multi-storey building is analyzed to determine the reliability of ensuring that the maximum inter-storey drift does not exceed a specified acceptable limit.

Structural optimization is an active research branch in engineering, especially dealing with complex and concomitant aspects likewise in seismic design. Capacity design criteria for seismic design and detailing must be respected, e.g. according to the "strong-column weak-beam" principle. In steel structures, the choice of a specific beam-column joint typology may strongly affect its behavior under horizontal actions. In this study, the authors investigated the role of beam-column joint stiffness within an optimization paradigm related to steel structure frames. Specifically, the authors adopted simplified modeling assumptions for analysis under lateral loads in the Python environment and Computer and Structures inc. SAP2000 finite element software. Indeed, the main focus hitherto is oriented toward the problem definition accounting for geometric constraints and beam-column rotational stiffness capacity. Future investigations will adopt more realistic modeling procedures accounting for the typical non-linearities involved during strong dynamic actions.

Fluid-viscous dampers played a crucial role in the protection of new or existing buildings against external actions as earthquakes and winds. In the last decade, several investigations have been conducted aiming to develop accurate numerical models. However, none has been focused on a comprehensive comparison between the most used fluid-viscous damper models considering the variability of their parameters in a mass-production series. In this paper, an identification procedure has been performed by comparing nine different existing literature models with the objective of evaluating their ability to match experimental loops of mass-produced fluid-viscous devices, both in terms of accuracy and robustness. Indeed, the model that is most effective for reproducing the characteristic of a specific specimen may not be representative (i.e., showing larger parameters variability) of the mass production of the same device type. For this purpose, dynamic tests have been developed in the laboratory and the experimental outputs have been adopted as the target function of the procedure. The identification scheme has been designed by implementing an optimization procedure via Genetic Algorithm. Results demonstrate how differential laws better fit the experimental cycles with respect to algebraic ones, and also show how few models in the series can offer a high level of both accuracy and robustness.

Monitoring and evaluating the deterioration of structures is one of the most pressing challenges of the last decades. Bridges and overpasses represent a significant percentage of infrastructures requiring ongoing maintenance and monitoring. In this scenario, a typical static solution used in the last century is the Gerber half-joint, obtained by reducing the cross-section of a beam end, supported by the nib of the adjacent beam or abutment. The particular geometry gives many benefits. However, at the same time, it is the origin of damages and failure due to the difficulty to access for inspections, and the proneness to corrosion phenomena. This study estimates the effect of corrosion on the capacity and ductility of two case studies: a half-joint tested by Desnerk et al. used for model calibration and a real-case half-joint. The author simulated an increasing level of corrosion in the two case studies by reducing the cross-section of the re-bars and modifying the ductility of steel. The analyses showed different behaviour in the two case studies. While the first exhibited a significant reduction of capacity and ductility, the real-case half joint did not show a manifest capacity reduction, still, accompanied by minor embrittlement of the response.

In the world of structural design, in most cases, there is a need to control the shape of structural elements and-at the same time-the performance that each one can achieve. With the evolution of structural analysis tools, nowadays it is possible not only to have an immediate investigation of the structure's performance, but also to search for the best shape by imposing geometric constraints. The aim of this paper is to present an innovative methodology called the performative structural design optimization (PSDO) method, based on the use of algorithm-aided design (AAD). The proposed approach deals with an emptied voided beam; starting from the parameterization of a large-span beam, the search method for the most performing shape is accomplished by multi-objective evolutionary algorithms (MOEAs). The obtained results are characterized by a double optimization: the structure achieved by the hypervolume estimation algorithm for multi-objective optimization (HypE Reduction) (OCTOPUS) represents the starting shape for the application of form-finding, giving so the possibility to obtain different feasible solutions from a single study and to choose the best one in terms of structural behavior.

Multiple Tuned Mass Dampers (MTMD) is one of the simplest and most reliable solution to control the vibrations of a structure, e.g. allowing to deal with a wide distribution of structural natural frequencies and usually showing inherent stability. Nevertheless, uncertainties in the behavior of structures under random dynamic input may induce implications on the MTMD effectiveness, e.g. detuning or amplifications. Typically, uncertainties in the input are exclusively considered, while uncertainties affect as much also the mechanical parameters. This paper proposes a robust optimum design of the MTMD, considering uncertainties both in the structural parameters and in the earthquake input. At this aim, a random vibration analysis of the response is adopted, and a direct linear perturbation method is applied on the uncertain parameters. Results show that a deterministic optimization is inappropriate for sensible systems as TMDs, while a robust optimization aims to better control the response with low computational efforts. Furthermore, the selection of the objective functions significantly affects the optimal design parameters, as the number of TMDs influences the robust designs.

Many classes of engineering problems focus on the process of calibrating mathematical models using observed data. The enormous progress of scientific computation and data-mining techniques has allowed the search for accurate mathematical models from experimental data using algorithms. Among them, the evolutionary polynomial regression (EPR) is an artificial intelligence (AI) technique that merges genetic algorithms (GAs) and regression techniques such as ordinary least square (OLS). This paper presents a robust and well-conditioned EPR technique to remove potential outliers and leverage points included in any biased data set. This hybrid approach combines bisquare, Huber, and Cauchy robust multivariate techniques with GAs and the Akaike weight-based method to assess the optimal polynomial model while limiting the impact of the data bias. The robust techniques will define the parameters, the GAs will determine the exponents, and the Akaike weight-based method will evaluate the relative importance of each observed variable of the proposed model. As a case study, a shear strength data set of RC beams without stirrups is used to compare the standard EPR algorithm with the new proposed hybrid methodology. Furthermore, the optimal robust model is compared with different benchmark formulations to highlight its accuracy and consistency. The proposed hybrid technique can be adopted as a mathematical tool for many engineering problems, providing an unbiased prediction of the observed variable. Furthermore, the shear strength equation that provides the best compromise between accuracy and complexity allows its potential use in many engineering practices and building codes.

fib Conceptual Design of Structures - Attisholz-Areal- Switzerland (2021) – Proceedings PDF fib Proceedings No. 55. Conceptual Design of Structures. - Proceedings of the International fib Symposium - 16-18 September 2021 - Attisholz-Areal, Switzerland PDF format

The use of in situ strain measurements to reconstruct the deformed shape of structures is a key technology for real-time monitoring. A particularly promising, versatile and computationally efficient method is the inverse finite element method (iFEM), which can be used to reconstruct the displacement field of beam elements, plate and shell structures from some discrete strain measurements. The iFEM does not require the knowledge of the material properties. Nevertheless, it has always been applied to structures with linear material constitutive behavior. In the present work, advances are proposed to use the method also for concrete structures in civil engineering field such as bridges normally characterized by material nonlinearities due to the behavior of both steel and concrete. The effectiveness of iFEM, for simply supported reinforced concrete beam and continuous beams with load conditions that determine the yielding of reinforcing steel, is studied. In order to assess the influence on displacements and strains reconstructions, different measurement stations and mesh configurations are considered. Hybrid procedures employing iFEM analysis supported by bending moment-curvature relationship are proposed in case of lack of input data in plastic zones. The reliability of the results obtained is tested and commented on to highlight the effectiveness of the approach.

This paper presents an efficient strategy to minimize the volume of a large span multi-domain variable section beam considering the geometric shape parameters as mathematical constraints.The shape optimization of the beam element has been conducted through an imposed geometry to find the best shape between the design-decision making and the structural efficiency.The study, based on the kinematic hypothesis of Timoshenko, focuses on a test case retrieved from the project designed by P. M. da Rocha and the engineer S. Mitsutani developed for the Japan World Exposition, Osaka, 1970 (Osaka's Expo '70).The structural component has been remodeled and optimized through different approaches that generate comparative numerical models joining the combinations of Computational Design and Algorithm-Aided Design.Even though very abundant knowledge and literature on structural optimization already exists, this study aims not only to study the certain structural element undergone to a specific emptying function but to compute and chart the results to be used for empirical purposes.The results of the study show, in the search of the architectural optimal solutions, advantages regarding the performance of the structures and the control of the shape of the architectural component giving -at the same time -the possibility to join the needs of architectural narratives with the stability and efficiency of an optimized and correctly designed structure.

Over the last decade, the topic of regional resilience has drawn the attention of public authorities due to the increasing number of natural disasters. The absence of a practical and concrete methodology makes it extremely difficult to evaluate resilience at the regional scale, which involves several concepts such as economics, social sciences, environment, etc. This paper proposes an indicator-based approach to assess the resilience assessment of Italian regions. A set of twelve indicators has been selected among publicly available census data. A time window of ten years was considered in the analysis. Three different resilience indexes were calculated for each region. The first is an overall measure of resilience, while the other two represent resilience during the emergency and the restoration phase following a disaster. Results highlight fundamental aspects that have a higher impact on regional resilience and can be used by decision-makers to effectively allocate resources. The procedure has also been extended to evaluate the regional epidemic risk which can be used as a preliminary tool to develop risk mitigation strategies against biological hazards.

In seismic codes, elastic response spectra are usually defined by adopting a conventional value for the damping ratio equal to 5%. Damping Reduction Factors (DRFs) are then introduced to account for the effect of damping values higher than the nominal 5%. In this framework, the main aim of the present study is to explore a new definition of DRF. The concept of stochastic response spectrum is used for predicting the earthquake response of a structural system by adopting the random vibration theory for nonstationary processes. The peak theory is finally used to determine the DRF.

Aunque el arco surgió como sistema estructural hace más de dos mil años, esta tipología estructural todavía no está muy difundida y se adopta principalmente cuando hay que cubrir grandes luces. La eficiencia de los arcos depende principalmente de la explotación óptima del material, es decir, de la minimización de la excentricidad del estrés, que reduce el volumen y el peso del material estructural. Una estructura eficiente, en estos términos, implica andamios simples y ligeros, contribuyendo así a minimizar los costes de construcción. Aunque hay muchos conocimientos y literatura sobre arcos, todavía hay margen para la optimización del diseño. El presente estudio se enmarca en este contexto y se ocupa del análisis estructural de los arcos circulares planos empotrados bajo una carga vertical distribuida uniformemente y un peso propio. En el primer paso, la solución analítica del comportamiento estático y cinemático de los arcos se estudia por el método de la fuerza. En el segundo paso, se optimiza la forma del arco, asumiendo el volumen del arco, y por lo tanto el peso, como función objetiva. Finalmente se calculan los mínimos de la función objetiva (es decir, los parámetros óptimos de la forma geométrica) para poder utilizarlos con fines prácticos..

The increasing need for assessment and renovation of existing constructions yields the necessity to develop new approaches for old materials and products that are consistent with the requirements of current codes of practice. In this scenario this article focuses on two topics very common in old R.C. structures: the effect of low ribbing and of low concrete cover thickness on the anchorage length of bars. The aim of this article is to develop new formulations that are also consistent with the approach included in the forthcoming second generation of Eurocodes.

The use of wood in the construction of bridges has increased in recent decades thanks to the characteristics of this material, i.e., environmentally-friendly and suitability within natural landscapes. Nevertheless, timber constructions may be affected by degrading effects due to biological and/or abiotic agents, and may be exposed to impacts or vibrations due to external forces such as wind, earthquakes or walking pedestrians. Consequently, bridge performance with respect to these aspects should be assessed from the early design stage. Within this context, in this study, some shape, structural and durability strategies dealing with the design of timber bridges for pedestrians are investigated in order to extend the service life of these constructions. More precisely, a methodology consisting of three steps, to be applied at the early conceptual design stage, is proposed. The three fundamental steps to be considered in the preliminary design of timber bridges are: (i) main boundary constraints and load-bearing system; (ii) durability; (iii) vibration levels. In the study, the presented methodology is applied and described for the design of a pedestrian and cyclist timber bridge over the Gravina torrent, in Apulia (Italy).