Including Social Nash Equilibria in Abstract Economies

We consider quasi-variational problems (variational problems having constraint sets depending on their own solutions) which appear in concrete economic models such as social and economic networks, financial derivative models, transportation network congestion and traffic equilibrium. First, using an extension of the classical Minty lemma, we show that new upper stability results can be obtained for parametric quasi-variational and linearized quasi-variational problems, while lower stability, which plays a fundamental role in the investigation of hierarchical problems, cannot be achieved in general, even on very restrictive conditions. Then, regularized problems are considered allowing to introduce approximate solutions for the above problems and to investigate their lower and upper stability properties. We stress that the class of quasi-variational problems include social Nash equilibrium problems in abstract economies, so results about approximate Nash equilibria can be easily deduced.quasi-variational, social Nash equilibria, approximate solution, closed map, lower semicontinuous map, upper stability, lower stability

Simplified Modeling of Rectangular Concrete Cross-Sections Confined by External FRP Wrapping

The goal of this research project is to model the effect of confinement by means of fiber reinforced polymer (FRP) externally bonded wrapping, hence to provide a simplified closed form solution to determine directly the ultimate confined concrete strength. Common cross-section shapes for reinforced concrete (RC) columns are considered herein, namely square and rectangular. The simplified model is derived from a more refined iterative confinement model proposed by the same authors to evaluate the entire stress-strain relationship of confined concrete. Based on a detailed analysis of the stress state through Mohr's circle, a simplified closed form solution is proposed to account for the non-uniformly confined concrete performance exhibited in non-axisymmetric sections. The non-uniform confining stress field exhibited in such cross-sections is explicitly considered by means of the mean value integral of the pointwise variable stress state over the cross-section. The key aspect of the proposed methodology is the evaluation of the effective equivalent pressure to be inserted in any triaxial confinement model, to account for the peculiarities of square and rectangular cross-sections. Experimental data, available in the literature and representative of a wide stock of applications, were compared to the results of the theoretical simplified model to validate the proposed approach, and satisfactory results were found

Comparison of Two Parameters Models for clay brick masonry confinement

Masonry elements are often strengthened in order to improve their structural capacity. Generalized methods to assess the behavior of confined masonry columns are not available in the technical literature. They have been usually derived from concrete confinement models. However, concrete and masonry present several crucial differences due to their physical and mechanical properties. In fact, generalized models to assess the axial capacity of masonry columns were limited by the strong variability and heterogeneity of physical and mechanical properties. However, the recent scientific researches provided relevant information on the experimental behavior of confined masonry columns. In this paper, a confinement model has been proposed to assess the axial capacity of clay brick masonry strengthened using several strengthening systems. The model has been validated by means of comparisons with experimental results. In order to assess the potential of the proposed model, the comparison was carried out also with other available mechanical models

RC deck - stiffened arch existing bridges: simulated design and structural analysis

The 20th century is known as the age that gave birth to the largest reinforced concrete structures. Many applications of this new material were realized at that time, both from a theoretical and practical point of view. With reference to bridges, the engineer Robert Maillart achieved a new concept of arched bridges, characterized by very stiff deck beams and slender and wide vaults, i.e., the "Deck-Stiffened Arch". The paper deals with the study of such bridge typology, particularly widespread in Italy around the 50s of the 20th century. While, nowadays, calculation tools allow developing very refined structural modelling, in the past very simple structural schemes were adopted in the design phase in order to simplify the calculation effort. The study starts from a "simulated design" of such a bridge typology adopting a reliable geometry and following the design rules and the simplified structural schemes of the time and, then, by means of a refined three-dimensional model, the performance of a typical "Maillart-Type Arch" bridge is analysed

Simplified Model for Strengthening Design of Beam–Column Internal Joints in Reinforced Concrete Frames

The beam-column joints are very restricted areas in which the internal forces, generated by boundary elements, act on the concrete core and reinforcing bars with a very high gradient. They are the link between horizontal and vertical structural elements, and therefore, they are directly involved in the transfer of seismic forces. Thus, they are crucial to study the seismic behavior of reinforced concrete (RC) structures. To fully understand the seismic performances and failure modes of beam-column joints in RC buildings, a simplified analytical model of joint behavior is proposed and theoretical simulations are performed. The aim of the model, focusing on internal perimetric joints, is to identify the strength hierarchy in terms of capacity for different failure modes (namely failure of cracked joint, bond failure of passing through bars, flexural/shear failures of columns or beams). It could represent a tool for the designers of new joints to quantify the performance of new structures, but also as a tool for the designers of external strengthening of existing joints in order to calculate the benefits of the retrofit and pushing the initial failure to a more desirable failure mode. Further, some experimental results of tests available in the scientific literature are reported, analyzed and compared

Masonry walls retrofitted with natural fibers under tsunami loads

AbstractIn the last decades, several tsunamis hit international coasts and engaged scientific awareness to the retrofit of coastal buildings against tsunami loads. Structural design under tsunami loads is difficult due to the high uncertainties of the phenomenon. Local collapse mechanisms of masonry walls, like as out of plane mechanisms, have an high probability due to flexural actions; a higher flexural capacity can be reached using specific retrofit systems; in particular, this paper aims to deepen the behavior of masonry walls retrofitted with innovative retrofit systems like as natural fibers applied with inorganic mortar matrices. The retrofit of structures under tsunami actions could be an innovative research topic for international research community dealing with coastal buildings located in areas characterized by a high tsunami risk. Recent engineering applications demonstrated the innovative strengthening systems to be effective for the retrofit of existing masonry buildings. These strengthening systems are of great interest in the practical applications due to the low costs and their sustainability. In fact, the lower costs compared to the synthetic fibers allow their diffusion in emerging countries. In a first part the impact of constituents on the structural capacity of masonry elements strengthened with natural systems has been discussed. Important results have been provided in order to improve the knowledge and encourage the development of these systems in many engineering applications. Finally, the effects of retrofit systems on masonry walls under tsunami loads will be discussed in terms of critical inundation depth variations before and after the interventions

DETECT-AGING blind prediction contest: a benchmark for structural health monitoring of masonry buildings

The installation of monitoring systems on buildings allows analyzing variations in structural parameters over time, creating room for detection of damage. Structural Health Monitoring (SHM) systems have the potential to support pro-active risk management, where structural interventions are planned if specific thresholds related to target performance losses are achieved. DETECT-AGING is a research project of relevant national interest that was funded by the Italian Ministry of University and Research (MUR) through the PRIN 2017 programme. The project started in September 2019 and involves the universities of Bologna, Genova, Napoli Federico II, and Perugia. The main goal of the project is to develop a new analytical-instrumental approach aimed at the quantitative assessment of the effects of aging and material degradation on structural safety of cultural heritage, with special focus on masonry structures. Based on a combined use of structural models and health monitoring systems, indications and operational tools will be provided for the identification and quantification of structural damage, supporting the management of built cultural heritage. To this purpose, a two-storey masonry building, having a single room with a vault at the first floor and a timber roof, was built with the aim of being monitored and progressively and will be damaged during the project. It is equipped with a hybrid SHM system managed by the University of Perugia, which is based on both vibration and strain measurements. The present paper illustrates the main features of the case-study building and presents the results of the experimental program aimed at characterizing the mechanical properties of masonry the materials used. The final part of the paper presents a blind prediction contest based on prediction of modal features of the building in different damaged configurations

Repair of composite-to-masonry bond using flexible matrix

The paper presents an experimental investigation on an innovative repair method, in which composite reinforcements, after debonding, are re-bonded to the substrate using a highly deformable polymer. In order to assess the effectiveness of this solution, shear bond tests were carried out on brick and masonry substrates within two Round Robin Test series organized within the RILEM TC 250-CSM: Composites for Sustainable strengthening of Masonry. Five laboratories from Italy, Poland and Portugal were involved. The shear bond performance of the reinforcement systems before and after repair were compared in terms of ultimate loads, load-displacement curves and strain distributions. The results showed that the proposed repair method may provide higher strength and ductility than stiff epoxy resins, making it an effective and cost efficient technique for several perspective structural applications

Low unit strength masonry: computational modelling approaches

Masonry is characterized by the large variability of its components. Parameters like strength, bond and workmanship defects strongly influence the performance of the overall structure. The applicability of different computational modelling approaches to assess the structural behaviour of masonry has been studied. Two of the most relevant computational modelling approaches have been considered namely: finite element method (FEM) and distinct element method (DEM). In order to validate the numerical outcomes, comparisons with the experimental results have been undertaken. The aim of this paper is to contribute to the knowledge and selection of a suitable modelling approach for modelling low unit strength masonry structures. The results showed that in the case of low unit strength masonry, FEM is a more suitable approach to use. In fact, since in the considered case, the block is the weak component, it is not possible to assume the brick units as a rigid block. Therefore an accurate plasticity and cracking model for the brick is required

Shear strengthening of concrete members with TRM jackets: Effect of shear span-to-depth ratio, material and amount of external reinforcement

An experimental work on reinforced concrete (RC) rectangular beams strengthened in shear with textile reinforced mortar (TRM) jackets is presented in this paper, with focus on the following investigated parameters: (a) the amount of external TRM reinforcement ratio, ρf, by means of using different number of textile layers and different types of textile fibre materials (carbon, glass, basalt); (b) the textile geometry, and (c) the shear span-to-depth ratio, a/d. In total, 22 tests were conducted on simply supported rectangular RC beams under (three-point bending) monotonic loading. The experimental results revealed that: (1) TRM is very effective when the failure is attributed to debonding of the TRM jacket from the concrete substrate; (2) the trend of effective strains for carbon, glass and basalt TRM jackets is descending for increasing values of the TRM reinforcement ratio, ρf, when failure is associated to debonding of the jacket; (3) the effect of textile geometry is significant only for low values of ρf, resulting in variances in the capacity enhancement and the failure modes, and (4) the shear span-to-depth ratio has practically no effect to the failure mode nor to the TRM jacket contribution to the total shear resistance of the RC beams