## GIULIO AUGUSTO TROPEA

Dottore di ricerca**ciclo**: XXXVI

**supervisore**: Prof. Fabrizio Mollaioli

**Titolo della tesi:**ENERGY BASED CAPACITY CHARACTERIZATION OF REINFORCED CONCRETE STRUCTURES

In the field of seismic and structural engineering, the advent of the performance-based approach - Performance-Based Earthquake Engineering (PBEE) - marked a turning point in the methodology of evaluation and design of structures subjected to seismic motion. This work would like to give a contribution in this innovative context by proposing a methodical and in-depth characterization of structural capacity based on the energy approach. The research is structured on a theoretical-practical level, to investigate the validity and effectiveness of a new methodology aimed at characterizing the structural response, based on a physical and quantifiable representation of the state of damage in terms of energy. This method was developed starting from the premise that damage can be described in a measurable space, simultaneously considering internal energy and internal power, going beyond the simple quantification of energy dissipation, also including the velocity with which energy is imparted to the structure.
In recent years, there has been a growing interest in using numerical indices to measure damage limit states. In particular, methods using energy concepts have proven effective in identifying the collapse point of structures. However, these damage indices, generally based on statistical analyses, often do not offer a clear explanation of structural capacity in physical terms. Furthermore, current definitions of damage tend to ignore how energy is absorbed and dissipated. This study introduces a new approach to analyze the seismic damage, based on a physical representation of structural resistance that links together the amount of energy dissipated and the rate at which it is applied, i.e. the internal power. Using these observations, the nonlinear behaviour of a simple structural system (SDOF) is described through two new parameters: one to quantify the damage, D, and the other to measure the internal energy variations, I.
The parameter D (damage) is instrumental in recognizing the most substantial changes and thus the internal damage denoted by the energy dissipation. On the other hand, the parameter I (intensity) is pivotal in assessing the rapidity of energy fluctuations. These metrics are integrated into a function that elucidates the hysteretic behaviour more clearly than a simple hysteresis loop. This function allows for the quantification of hysteretic energy dissipated over a number of cycles, in relation to the system's maximum internal energy. The primary shifts in hysteretic energy, significant in marking a specific damage level, are determined through the derivative of this function's backbone. In conjunction with defining specific limit states—undamaged elasticity, significant damage, and collapse—the methodology offers a thorough analysis of a structure's seismic response. The elastic limit state is defined for computing the hysteretic energy, and the collapse limit state is essential to establish the system's operational bounds. Thus, we derive a function that facilitates both qualitative and quantitative identification of the inelastic behaviour limits and all principal variations preceding the collapse, valuable for diverse load types and material histories
The theory was subsequently verified on a sample of experimental tests pursuing a dual objective: to verify the validity of a proposed methodology in the case of a large sample of extracted reinforced concrete columns from the PEER Database and ascertain which form of energy associated with the hysteretic behaviour of materials is most suitable for characterizing the damage state of the system. A series of useful approaches are proposed to identify damage states, with a particular focus on collapse, a fundamental limit for the design of structural elements.
The proposed methodology is then applied to MDOF systems by analyzing and reproducing a series of tests conducted on shaking tables on reinforced concrete buildings, both with and without infill walls. The objective of these tests was to verify the effectiveness of the proposed methodology in the dynamic field, with real structures subjected to simulated dynamic motions. In this way, it was possible to check damage states at both global and local levels. At this stage, a crucial element of the research was the realistic reproduction of the experimental tests through the use of OpenSees software and the STKO (Scientific ToolKit for OpenSees), a Graphical User Interface (GUI), widely recognized in the field of earthquake engineering for its ability to model complex structural behaviours.
OpenSees has been enhanced to monitor and calculate the energy dissipated through hysteresis in various structural materials such as reinforced concrete, steel, and regular masonry, in addition to infill walls. This comprehensive approach enables a nuanced assessment of each material's contribution to the overall seismic resilience, addressing a broader spectrum of elements that significantly impact structural behaviour during earthquakes.
Another innovative aspect of the work was the distinction between the contribution of steel and concrete in the seismic response of the structures. Through careful analysis, it was possible to develop to precisely quantify how much each material contributes to reaching a certain state of damage. This approach has allowed a deeper understanding of the damage mechanisms in reinforced concrete structures, providing important insights for more resilient future designs. The proposed collapse criteria were then tested on the models of the buildings analysed, confirming their validity and applicability in the real context. The methodology has proven effective in predicting and describing the different stages of damage and collapse of the structures under examination.
Finally, the work is further enriched with the introduction of an evaluation of the seismic demand. This was obtained through the development of an instrument similar to the response spectrum, but built as a function of the normalized internal energy. This approach allows direct compatibility with the proposed energy methodology, offering a more complete and coherent vision of the behaviour of reinforced concrete structures under seismic stress,
The holistic approach that integrates energetic, experimental and computational analyses, seeks to overcome traditional methodologies based on forces and displacements, with the aim of obtaining greater accuracy in the evaluation of damage and collapse, including the evaluation of the cumulative nature of the effects of response, but also opens new perspectives for the design approach, aiming for optimized structural resilience in seismic contexts by trying to provide a unified vision for all types of seismic events that can potentially affect a building.

**Produzione scientifica**

11573/1690912 - 2023 -

**New Energy Based Metrics to Evaluate Building Seismic Capacity**Tropea, G. A.; Angelucci, G.; Bernardini, D.; Quaranta, G.; Mollaioli, F. - 04b Atto di convegno in volume

**congresso:**2 International Workshop on Energy-Based Seismic Engineering (Oporto , Portogallo)

**libro:**Energy-Based Seismic Engineering. IWEBSE 2023 - (978-3-031-36561-4; 978-3-031-36562-1)

11573/1702386 - 2023 -

**New Energy Based Metrics to Evaluate Building Seismic Capacity**Tropea, G. A.; Angelucci, G.; Bernardini, D.; Quaranta, G.; Mollaioli, F. - 04b Atto di convegno in volume

**congresso:**2 International Workshop on Energy-Based Seismic Engineering (Oporto, Portugal)

**libro:**Proceedings of the 2 International Workshop on Energy-Based Seismic Engineering, Oporto 3-6 July 2023, Energy-Based Seismic Engineering. IWEBSE 2023. Lecture Notes in Civil Engineering, vol 236. Springer, Cham - (978-3-031-36561-4; 978-3-031-36562-1)

11573/1690918 - 2023 -

**Structural Damage Characterization via Energy-Based Limit State Definition**Tropea, G. A.; Angelucci, G.; Quaranta, G.; Mollaioli, F. - 04b Atto di convegno in volume

**congresso:**2nd Eurasian OpenSees Days (Torino)

**libro:**Proceedings 2nd Eurasian OpenSees Days - (978-3-031-30124-7; 978-3-031-30125-4)

11573/1619593 - 2020 -

**La vela e il dragone**Bulian, Giovanni; Tropea, Giulio Augusto - 01a Articolo in rivista

**rivista:**TERRITORI DELLA CULTURA (Ravello (SA) : CUEBC Centro Universitario Europeo per i Beni Culturali) pp. 56-91 - issn: 2280-9376 - wos: (0) - scopus: (0)