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The simulation capabilities of a specifically developed phenomenological model for timber structures are described and presented through some representative case studies. This component model has been developed based on the behaviour of a single nail embedded in wood, considering the compressive behaviour of the wood and plasticization of the nail. As a result, the behaviour in cyclic conditions due to seismic actions, was modelled through a slip-type piecewise hysteretic relationship (Figure 1a), and some desirable features such as stiffness and strength degradation were included. Most of the connections employed in timber structures use nails or screws, allowing the application of the proposed framework to various types of subassemblies and to full-scale structures. In particular, this framework has been used to simulate various timber building typologies, such as light-frame, cross-laminated (Figure 1b), loghouse (Figure 1c) and moment-resisting frame structures, at different levels, from the single nail (Figure 1d) to the whole joint behaviour. Hence, a discussion on the results from non-linear static and dynamic analyses is provided, contributing to the improvement of the numerical methods adopted in literature until now.

This paper investigates the structural response and vulnerability of Blockhaus buildings under seismic loads. Blockhaus systems are widely used in daily practice for the construction of wooden houses or commercial buildings (see for example (Rubner Haus AG SpA)). Native of forested areas, they are often built also in earthquakeprone regions. Several research projects have been carried out, in order to experimentally and/or numerically assess the seismic performance of full-scale structures and small components (Branco & Araújo (2012), Piazza et al (2013), Bedon et al (2015a), Bedon et al (2015b), Bedon et al (2015c), Grossi et al (2016)). However, the seismic characterization of this construction system requires further investigations and studies, since the current standards for timber structures (e.g. Eurocode 5 (2004) and Eurocode 8 (2004)) do not provide specific recommendations for the calculation of their q-behaviour factor. In this work, based on past research contributions (Bedon et al (2015a), (2015b), (2015c)) and full-scale experimental tests (Piazza et al (2013)), Finite-Element (FE) investigations are performed on three dimensional Blockhaus buildings subjected to seismic loads by means of FE-models implemented in the ABAQUS software package (Simulia (2012)). Parametric simulations are carried out on several building archetypes, characterized by different overall geometrical properties, inter-storey floors (up to 2 levels), number and position of openings, corner joints. Design recommendations are then provided, based on the collected FE results, for a rational estimation of the corresponding q-behaviour factor.

The paper investigates the seismic response of Blockhaus shear walls under in-plane lateral loads. As known, the typical Blockhaus systems consists in a series of timber structural elements stacked horizontally once upon each other and interacting by means of traditional timber joints based on the effectiveness of carvings and contacts of multiple surfaces. Native of forested areas, Blockhaus systems are widely used in daily practice for the construction of wooden houses also in earthquake-prone regions. However, the seismic characterization of this construction system currently requires further investigations and studies. In order to assess the vulnerability of the examined structural typology, Finite-Element numerical investigation on log-haus timber walls subjected to in-plane lateral loads are performed by means of a computationally effective FE-model derived from earlier research contributions. In it, non-linear hysteretic springs implemented in ABAQUS/Standard and validated to cyclic experiments of single joints are used to describe the joint behaviour. Parametric cyclic investigations are first presented, in order to highlight the effects of multiple geometrical and mechanical aspects on the in-plane cyclic response of single log-walls. Refined non-linear dynamic analyses are then proposed for a significant set of configurations characterized by different geometrical properties and applied vertical loads, and preliminary estimations for the q-behaviour factor are presented.

This paper presents an experimental programme on Simpson Strong-Tie annular ringed shank nails, conducted at the Institute of Timber Engineering and Wood Technology, Graz University of Technology. The fastener under investigation is commonly used in cross-laminated timber (CLT) buildings to anchor typical metal connectors to the timber panels, and the understanding of its performances is of particular interest for the design of earthquake resistant timber structures. Shear tests in parallel and perpendicular direction to the face lamination of a CLT panel, and withdrawal tests, investigated the bearing capacity of a nail driven in the plane side of a CLT element. Furthermore, uniaxial tension tests and bending tests were performed on single fasteners to determine the ultimate tensile strength and the yielding moment, respectively. Mean and characteristic values of the mechanical properties were assessed in terms of strength, stiffness and ductility, and compared with the simplified calculation methods provided by the standards. Finally, a numerical model of the connection, considered as a non-linear spring with three degrees of freedom, is presented and calibrated on the experimental results. As an applicative example, the numerical model is used to simulate a shear and a tension test of a Simpson Strong-Tie AE116 angle bracket.

Masonry spandrels affect in-plane seismic performance of masonry walls in existing unreinforced masonry buildings, as they guarantee an effective coupling between adjacent masonry piers. In this work some results achieved in experimental tests carried out to investigate the structural response of unreinforced masonry spandrels under cyclic loads are presented. Three full-scale spandrel specimens were considered: two made of masonry bricks and one made of sandstone. The effectiveness of two strengthening techniques was investigated: CFRP strips glued horizontally on the spandrel surface and a horizontal steel angle fixed to the spandrel through injected dowels. Based on the above experimental results, a schematization of the resisting mechanism was developed and an analytical model to assess the capacity of spandrels was carried out.

Steel-concrete composite framed buildings are highly efficient structural systems due to their stiffness, strength and ductility. Such systems allow also adequate seismic performance nevertheless their application in seismic area is prevented by the lack of experimental information and design rules, especially about joints. The present work focuses on the seismic design and assessment of a typical steel and concrete composite multi-story moment-resisting frame, with 4 stories. The provisions implemented in European standards and guidelines are applied and discussed especially when uncertainties about their application come out; in fact a number of such provisions are not straightforward and/or reliable and further improvements are deemed necessary. After the frame has been designed by a linear analysis, a series of non-linear pushover analyses are performed by a lumped plasticity model introducing different models for the beam-column joint and plastic hinge length. In particular, since the definition of the plastic rotation capacity is not univocally defined, the formulations available for steel or reinforced concrete structures are discussed and evaluated also. The results are synthesized in terms of q-factor in order to assess the values suggests by the international codes.

2011/2012 Il lavoro di ricerca svolto ha avuto per oggetto lo studio e la definizione di modelli di calcolo e di verifica non lineari per strutture in muratura e legno. Lo studio ha riguardato principalmente la modellazione fenomenologica del comportamento non lineare di pannelli murari e connettori metallici per legno, e la conseguente implementazione delle leggi isteretiche analizzate in molle utente in diversi solutori commerciali/open-source (ABAQUS e OpenSees). In particolare il lavoro svolto si è articolato nei seguenti punti: 1. strutture in muratura: a. studio del comportamento meccanico del materiale muratura e raccolta dati di letteratura b. studio di modelli isteretici fenomenologici adatti alla rappresentazione degli edifici in muratura c. scrittura di routine in Fortran per implementare il modello fenomenologico studiato (modello di Tomazevic) nel programma ABAQUS d. analisi non lineare di edifici in muratura già studiati in letteratura ai fini della validazione del modello proposto e. studio di metodi semplificati per il calcolo sismico di edifici a schiera e scrittura di programma autonomo per l’analisi di pushover con il metodo RigStripTS f. prove di laboratorio sul comportamento di fasce murarie g. studio del modello in mesoscala incluso nel programma ADAPTIC e costruzione di modelli per la simulazione di test sperimentali tramite un meshatore sviluppato ad-hoc. 2. strutture in legno: a. studio del comportamento meccanico dei connettori metallici per le costruzioni in legno lamellare incrociato (X-lam) e a telaio leggero e raccolta dati di letteratura b. studio del comportamento ortotropo del materiale e scrittura routine per materiale utente per la sua rappresentazione in campo elastico c. formulazione di legame isteretico fenomenologico per connettori metallici (squadrette, hold-down e unioni con viti/chiodi) d. scrittura di routine in Fortran per implementare il modello fenomenologico proposto nei programmi ABAQUS e OpenSees e. studio di prove sperimentali su connettori singoli e analisi e implementazione di un metodo di taratura adatto al modello utilizzato, implementato in un programma scritto ad-hoc f. analisi di modelli non-lineari di test di laboratorio eseguiti su pareti in X-lam e a telaio leggero e di test pseudo-dinamici su edifici in X-lam monopiano, condotte con il modello sviluppato g. estensione del modello ad altre tipologie di edifici con struttura lignea. Entrambe le tipologie strutturali sono state trattate con modelli fenomenologici in modo da fornire uno strumento di calcolo non lineare per analisi statiche e dinamiche compatibile con le capacità di calcolo attuali; è stata indagata inoltre la possibilità di distribuire l’onere computazionale a più computer parallelizzando l’analisi strutturale. Particolare attenzione è stata riservata inoltre alla capacità sismica delle strutture analizzate, stimando in modo rigoroso l’energia dissipata in ogni analisi. A tal fine è stato eseguito anche uno studio sui modelli isteretici più comuni atto a verificare l’attendibilità di metodi di verifica globale in campo statico non lineare, come il metodo N2 introdotto da Fajfar e il metodo dello spettro sovra-smorzato proposto dalla norma ATC-40 statunitense. Tale studio è stato condotto tramite la scrittura di un programma ad-hoc per il calcolo di spettri inelastici a partire da record sismici di qualsiasi natura (registrati, artificiali o generati). I risultati ottenuti con tale strumento sono stati utilizzati per validare i metodi sopracitati e verificare la loro attendibilità al variare del periodo strutturale e della capacità dissipativa delle diverse tipologie strutturali. Strutture in muratura La necessità di uno strumento di calcolo flessibile ma potente ha indotto lo sviluppo di un elemento molla che implementasse un ciclo isteretico rappresentativo del comportamento del materiale. È stato scelto dalla letteratura disponibile la legge proposta da Tomazevic e Lutman nel 1996 formulata sulla scorta di numerose prove sperimentali condotte su maschi murari. Tale legge lineare a tratti si compone di una curva scheletro trilineare e di percorsi di scarico/ricarico, oltre che gli opportuni degradi di rigidezza e resistenza necessari per poter caratterizzare correttamente il comportamento del materiale muratura vicino alle condizioni di collasso. La routine implementata utilizza un set di parametri che regolano le rigidezze del sistema e l’ampiezza dei cicli, mentre la resistenza di ciascun elemento molla è calcolata automaticamente sulla base del valore di sforzo normale letto durante l’analisi. Tale operazione è svolta in modo disaccoppiato (cioè è riferita allo sforzo assiale letto al passo precedente durante l’analisi) e il valore resistente cambia sulla base del meccanismo di rottura, che il modello seleziona automaticamente. Tale strumento è stato utilizzato con successo per l’analisi statica non lineare della Parete D, facente parte del progetto Catania, progetto nato con l’intento di valutare la vulnerabilità sismica di edifici storici, poi con analisi dinamiche incrementali sulla parete stessa e su altre testate da Magenes a Pavia, che hanno dimostrato tutta la potenza del modello sviluppato, permettendo di stimare correttamente la capacità di dissipazione isteretica. Il metodo è stato esteso anche alle fasce di piano. Infine, il lavoro sul lato della modellazione fenomenologica è culminato con la formulazione di un macro-elemento, non ancora implementato, che permette di condensare le diverse molle utilizzate per ogni pannello in un solo elemento asta. I risultati con tali strumenti avanzati sono poi stati traslati in metodi e modelli per l’applicazione professionale, come il metodo RigStripTS (Amadio et al.) per il push-over di edifici in muratura e il metodo delle celle per lo studio sismico semplificato di edifici a schiera. L’analisi è stata approfondita con l’utilizzo del un modello a mesoscala per la modellazione dei pannelli murari, sviluppato all’Imperial College e disponibile nel software ADAPTIC (Macorini e Izzuddin). Tramite un meshatore sviluppato ad-hoc per la scrittura dei modelli, sono stati studiati diversi modelli in regime monotono. Strutture in legno Lo studio delle strutture in legno si è concentrato prevalentemente sul Cross-Lam (X-lam) e sul telaio leggero, mancando nelle normative internazionali delle linee guida per il calcolo sismico di tali strutture. Con lo scopo di stimare il comportamento strutturale in campo elastico e plastico e partendo dall’ipotesi, già documentata in letteratura, che tale tipologia costruttiva dissipa energia per i soli connettori, è stato formulato e implementato un modello isteretico lineare a tratti che rappresenta il comportamento ciclico in condizioni statiche e dinamiche di connettori metallici per pannelli in X-lam e per pareti a telaio leggero. Tale legame è stato implementato in elementi multi-molla per rappresentare ogni grado di libertà associato al connettore. Caratteristiche come degrado di resistenza, di rigidezza, effetto di attrito e dominio di resistenza sono state proposte e implementate. Tale modello necessita di una taratura preliminare da svolgersi su prove di laboratorio cicliche di connettori singoli; è stata proposta una metodologia per la taratura ciclica e implementata in un software autonomo sviluppato ad-hoc. Con tale strumento sono stati riprodotti fedelmente test ciclici di laboratorio condotti su singole pareti in X-lam in diverse configurazioni, giungendo poi alla validazione tridimensionale del modello eseguita sull’edificio monopiano testato pseudo-dinamicamente dal CNR-IVALSA a Trento. È stato sviluppato un programma per la meshatura automatica di modelli tridimensionali in X-lam. Analogo approccio è stato adottato per la tipologia a telaio leggero. Infine, è stata sviluppata una routine per il materiale legno che utilizza il modello ortotropo. La routine lavora in campo elastico ma può essere estesa al campo plastico mediante l’aggiunta del dominio resistente di Tsai e Wu, che è stato studiato si dimostra particolarmente adatto al materiale legno. XXV Ciclo 1984

The usual seismic design of buildings, based on current codes of practice, does not account for the occurrence of seismic sequences. Structures are designed to resist one single earthquake and then it is supposed that, before the following event, there is enough time to retrofit the damaged construction. This paper investigates the effects of seismic swarms on single storey Concentric X-Braced steel Frames, a very common construction system for industrial buildings. The selected seismic sequences have been chosen so that the first event is considered as the mainshock, and following events have a similar or greater PGA (Peak Ground Motion). The sequences can represent a swarm or a sequence of earthquakes spaced over time, occurring before the structures are retrofitted. The investigation of the effects on steel frames has been conducted in a simplified way through the analysis of Single Degree Of Freedom (SDOF) systems with a behaviour calibrated on the response of Multi-Degree Of Freedom (MDOF) real Concentrically Braced Frames (CBFs). One of the main focuses of this work is on the additional ductility to be used in the seismic design to account for the effects of seismic sequences. For this purpose, the 95th percentile of the required ductility ratio has been calculated in the typical fundamental frequency range of single storey concentric braced steel frames, as to estimate the increase of ductility or strength to be adopted in design. As a result, a reduction of behaviour factor up to 37% has been found.

Dalla sua concezione a metà degli anni novanta, il legno lamellare a strati incrociati, anche noto come CLT o X-Lam, ha raggiunto grande popolarità tra i materiali da costruzione grazie alle numerose innate qualità, gli sforzi a livello mondiale per costruire strutture affidabili in zone a rischio sismico e la necessità di costruire un ambiente più eco-sostenibile. Molti test sono stati fatti negli ultimi 15 anni, volti a comprendere meglio il comportamento delle connessioni in edifici in CLT, di parti strutturali o di intere strutture in CLT, in modo da fornire regole affidabili per i progettisti per progettare strutture in CLT sotto ogni condizione di carico. Sulla base di questi test, molti sono stati i modelli numerici che sono stati suggeriti negli anni. Questi rappresentano uno strumento fondamentale per la progettazione di strutture in CLT quando insorgono specifiche problematiche ed un approccio analitico da solo non è sufficiente. Nonostante i molti anni di sforzi, non esistono ancora affidabili metodologie di progetto nella quasi totalità dei codici a livello mondiale e ancora molte sono le incognite relative al comportamento delle strutture in CLT a molti livelli (connessioni, parti strutturali, strutture). Questa tesi riassume tre anni di ricerche numeriche, le quali hanno affrontato diversi problemi relativi al comportamento di elementi strutturali e strutture in CLT sotto azioni dinamiche. Durante la prima parte di questo percorso l’attenzione è stata posta sulla continuazione di un precedente studio, portato avanti durante la tesi di laurea magistrale, il quale era incentrato sulla formulazione di un metodo semplificato per la costruzione di un dominio resistente sforzo normale-momento flettente per pannelli in CLT connessi alla base da connessioni tipo hold-down e angle bracket. In mancanza di risultati di test di interesse, la concentrazione è stata rivolta ancora alla formulazione di metodi semplificati per la progettazione di elementi strutturali in CLT. È stato analizzato il problema delle connessioni pannello-pannello all’interno di una stessa parete. In particolare, è stata studiata la rigidezza di queste connessioni in relazione al comportamento ribaltante di pareti a due pannelli attraverso l’analisi di test a scala reale indipendenti e analisi numeriche agli elementi finiti. Una formula per il calcolo di queste connessioni è stata dapprima proposta e poi, dopo ulteriori analisi, rivista e corretta. Per estendere l’analisi e considerare elementi strutturali più complessi, è stata investigata, a livello di analisi numerica, l’influenza del solaio e delle connessioni parete-solaio superiore sul comportamento ribaltante delle pareti, prendendo in considerazione configurazioni con e senza solaio, variando diversi parametri di modo da ottenere risultati statisticamente significativi. Nell’estate del 2017 il candidato ha partecipato attivamente al NHERI TallWood Project, una ricerca statunitense intesa a testare strutture in CLT per fornire regole di progettazione per tali strutture nei futuri codici nazionali. Sponsorizzato dalla Colorado State University, nella persona del Prof. John W. van de Lindt, il candidato ha collaborato alla preparazione di un edificio con due orizzontamenti fuori terra testato sulla tavola vibrante della UCSD a San Diego (California) Per valutare il più corretto valore di smorzamento per strutture in CLT sotto l’azione di eventi sismici di bassa intensità, sono stati riprodotti numericamente ed analizzati i test su tavola vibrante del progetto SOFIE a 0,15 g. Ulteriori considerazioni sono state fatte sul ruolo dell’attrito su questo tipo di strutture e sul problema delle analisi lineari per strutture in CLT (risposta non simmetrica di connessioni caricate in tensione-compressione). Since its conception in the mid 90’s, cross-laminated timber, known also as CLT or X-Lam, has achieved a great popularity as construction material thanks to its numerous intrinsic qualities, worldwide effort to build reliable structures in seismic-prone areas and necessity to build a more eco-friendly environment. Many tests have been carried out in the last 15 years, aimed to better understand the behavior of connections in CLT buildings, CLT assemblies and CLT structures in order to provide reliable rules for designers to design structures made of CLT in any loading condition. Based on these tests, many numerical models have been suggested through the years. They represent a fundamental tool for the design of CLT structures when specific design problems arise. Despite many years of efforts, reliable design rules are still missing in almost every code worldwide and many are still the unknown related to CLT structures behavior at many levels (connections, assemblies, structures). This thesis summarizes three years of numerical investigations, which have faced different problems related to the comprehension of CLT assemblies and structures behavior under dynamic loading conditions. The first part of this path focused on the continuation of a previous study made within the Master Degree thesis, which was the formulation of a simplified method to obtain an axial-load/bending moment limit domain for a CLT panel connected to the supporting surface through hold-down and angle bracket connections. Without test results of interest, the focus of the study returned to be the formulation of simple methods for CLT assemblies design. The problem of panel-to-panel connections was investigated. In particular, the stiffness of such connections related to the rocking behavior of 2-panel wall assemblies was studied through full-scale tests and FE numerical analyses. A formula for the design of these connections was firstly suggested and then, after further analyses, revised and corrected. In order to extend the analyses and consider more complex assemblies, the influence of diaphragm and wall-to-diaphragm connections stiffness on the rocking behavior of wall assemblies was numerically investigated, taking into account configuration with and without diaphragm, varying several parameters to obtain statistically significant results. In the summer of 2017 the candidate actively participated to the NHERI TallWood Project, an American research project intended to test CLT structures in order to provide design rules for these structures in the future US codes. Sponsored by the Colorado State University, in the person of Professor John W. van de Lindt, the candidate collaborated to the setup of a 2-story CLT building that was tested on the UCSD shaking table located in San Diego (California). In order to assess the most proper value of damping for CLT structures under low-intensity seismic events and to better investigate the potential of the component approach for the modelling of CLT structures, the 0,15 g shaking table tests of the 3-story building within the SOFIE Project were reproduced and analyzed. Further considerations on the role of friction for this type of structure have been made together with the problem of linear analyses for CLT structures (non-symmetric response for tension-compression loaded connections).

The seismic behaviour of masonry structures is, as well-known, strongly influenced by axial stresses. During a seismic event, variations in axial loading cause in fact a change, that can be substantial, in the response in the lateral resistance capacity of masonry panels. Moreover, the axial stress can be modified by the vertical component of the seismic input during an event, which can amplify the strength variations, in particular if there is a near-fault excitation. In general, such vertical component is neglected in a traditional design. In this work, the influence of the vertical component of a seismic event is evaluated by measuring the lateral resistance of masonry piers. Such influence is estimated through a cyclic phenomenological model which calculates in an analytical way the lateral strength of a masonry panel on the base of the actual axial loading, reached step-by-step during a non-linear analysis. This model is used to simulate the cyclic behaviour of an unreinforced masonry facade made of 3 piers, having the same section for 2 floors and connected by rigid spandrels. The wall, representative of a typical masonry facade, is subjected to a series of earthquake records, with and without the vertical component of the seismic input. The differences in the responses are quantified through the use of seismic reduction factors, in such a way to satisfy the checking of the piers adopting the current design codes.

In this paper, experimental tests and numerical analyses conducted on an innovative angle bracket for Cross-Laminated Timber (CLT) structures subjected to tension and shear loads are presented. Such angle bracket represents an improvement of the available angle brackets manufactured by Rotho Blaas and was designed to increase the tensile capacity by adding inclined fully-threaded screws. Results of experimental tests carried out at Laboratory of Earthquake and Dynamic Engineering (LEDA) of the Enna Kore University are presented in terms of force-displacement curves. All the experimental tests are then simulated fusing a numerical model implemented in the FE solver ABAQUS. The influence of the mechanical behaviour of screws and nails on the angle bracket performance was then investigated, considering stiffnesses and strengths from both experimental programmes and codes of practice, and evaluating the importance of the Group Effect. The obtained force-displacement curve is compared with the experimental curves, showing a good accuracy of the proposed FE model. Experimental tests confirmed that fully-threaded screws increased the tensile capacity of the angle bracket.

In this work, the seismic behaviour of UnReinforced Masonry (URM) structures under repeated earthquakes is investigated. Such analysis is carried-out by using a purposely-developed non-linear software that describes the hysteretic behaviour of a masonry panel through an appropriate phenomenological law. First, results obtained from a series of non-linear dynamic analyses on a single degree of freedom (SDOF) system, which represents the typical cyclic response of an unreinforced masonry structure, are presented. The seismic sequences adopted for the analysis are taken from international databases and are selected on the base of the Peak Ground Acceleration (PGA) of the events following the mainshock. The selected aftershocks have a PGA equal or almost similar to the mainshock, in such a way to significantly influence of the required ductility for the analysed system and, consequently, on the damage index used to quantify the structural degradation. The obtained results are presented in terms of inelastic response at constant ductility or strength. On the base of the collected results, modifications on the behaviour factors commonly adopted in seismic design are proposed. Finally, a SDOF system representing a typical masonry structure subjected to the seismic sequence of Central Italy (2016) has been analysed with the aim to highlight the damage evolution.

Repeated seismic events strongly affect the building capacity in earthquake-prone regions, as its resilience, intended as the capacity of a system to quickly revert to a fully operational state after a damage due to a significant event, depends on the ability to withstand cumulated damage. This paper investigates the effects of repeated seismic sequences on structures characterized by different hysteretic behaviour. To this aim, non-linear single-degree-of-freedom (SDOF) systems were subjected to ten recorded seismic sequences taken from literature. The elasto-plastic and pivot hysteresis rules were analysed first, considering both hardening and softening behaviour. From each analysis, the inelastic spectrum of the seismic sequence was computed for different ductility levels, and the ductility demand was calculated and compared with the values for an only seismic event. It was shown that the effect of seismic sequences is quite significant, and a reduction of the behaviour factor from 15% for bilinear with hardening and pivot hysteretic rules to 35% for elasto-plastic systems with high ductility should be adopted in design to increase the seismic resilience. The use of linear and non-linear viscous dampers was also analysed in SDOF systems subjected to seismic sequences, demonstrating the effectiveness of this mitigation measure. Nonlinear viscous dampers with an initial friction force were found to dramatically reduce the acceleration and displacement demand, although it cannot avoid residual displacements at the end of the seismic events, and can be recommended for structures with short vibration periods. Nonlinear and linear dampers have the advantage of allowing full recentring of the structure at the end of the seismic events, thus significantly improving resilience.

Timber buildings in earthquake prone regions must be designed to withstand the seismic actions. The N2 method, already employed in the Eurocode 8 to check the seismic resistance of a building employing its capacity curve, uses inelastic spectra calculated on the basis of the system ductility. Such a procedure was extensively used for the design of steel and reinforced concrete structures. Timber structures, however, have a different and more complex hysteretic behaviour characterized by significant pinching, strength degradation and softening. Consequently, the current version of the N2 proposed spectrum may be inadequate for the design of timber systems. This paper investigates the accuracy of the N2 spectrum for timber structures by calculating the ‘rigorous’ inelastic spectra for natural seismic records selected to match, with their average, a chosen design elastic spectrum. A purposely developed software has been used to obtain the inelastic spectra for a Single Degree of Freedom (SDOF) system characterized by a slip-type hysteretic relationship with pinching typical of timber structures. Two different sets of records have been considered: the former is consistent, on average, with a given design spectrum from Eurocode 8, the latter is taken from a strong motion database by selecting the records having soil class A and PGA within a chosen range. Non-linear dynamic analyses have been carried out by varying the level of ductility and the natural vibration period of the SDOF systems. The effects of hardening or softening of the system behaviour have also been analysed. Two analysis procedures have been used with the aim to have a further confirmation of the achieved results. The comparisons between the rigorous and the approximated N2 spectrum demonstrate that, in general, the N2 method always give fairly good results in estimating the inelastic spectra even for timber structures.

In this paper, a simplified non-linear procedure for seismic design of CLT (cross−laminated timber) wall systems is presented. The proposed method considers both axial force and bending moment applied on the wall systems as result of applied loads. Timber is modelled as an elastic-brittle material, whereas metal connections (hold-downs and angle brackets) are modelled with an elastic-plastic behaviour. The reaction force in each connection is iteratively calculated by varying the position of the neutral axis at the base of the wall using a simple algorithm that has been implemented in a purposely-developed software. This method is based on the evaluation of five different failure mechanisms at ultimate limit state similarly to reinforced concrete (RC) rectangular section design. By setting the mechanical properties of timber and metal connections, and the geometry of the CLT panel, the algorithm calculates,for every possible axial load, the position of the neutral axis and the ultimate resisting moment of the system. Furthermore, this method also allows the designer to have an indication on the failure mechanism of the wall.

The mechanical behaviour of steel-to-timber joints with annular-ringed shank nails is investigated using numerical modelling and a component approach. These joints are used in Cross-Laminated Timber (CLT) buildings to anchor metal connectors such as hold-downs and angle brackets to the timber panels. At first, a general hysteresis model is introduced, where a single fastener joint is schematized as an elasto-plastic beam embedded in a non-linear medium with a compression-only behaviour. A second hysteresis model is then presented, where the mechanical behaviour of the joint is simulated by a non-linear spring with three degrees of freedom. Both models are calibrated on the design rules prescribed by the reference standards. Moreover, average strength capacities are determined from the corresponding characteristic values assuming a standard normal distribution and suitable coefficients of variation. As first applicative examples of the proposed models, shear tests are simulated on single steel-to-timber joints with annular-ringed shank nails and on a connection made of an angle bracket and sixty nails. The scatter of mechanical properties in steel-to-timber joints is also taken into account in the simulations and a stochastic approach is proposed, demonstrating acceptable accuracy.

In this paper, an extensive parametric study was carried out to evaluate the dynamic response of single degree of freedom (SDOF) systems with elasto-plastic and flag-shape hysteretic behaviour for three different dissipation capacities. Three sets of natural accelerograms were used, each one composed by at least 7 records which are on average spectrum-consistent in pseudo-acceleration, spectral displacement or both of them. All sets were also employed to draw the inelastic spectra for different ductility values. Such rigorous spectra were then compared with the approximated curves calculated using the N2 method and the Equivalent Linearization Procedure (ELP) based on the use of overdamped elastic spectra. The analyses demonstrate a general accuracy of the N2 method, which is mostly based on the ductility of the system, even for the hysteretic behaviour characterised by reduced energy dissipation. Larger discrepancies were found for systems with lower damping ratios and reduced fundamental periods. The ELP, which mainly depends upon the dissipated energy, led instead to overall slightly larger discrepancies than the N2 method, particularly for not dissipative and ductile systems, whereas the approximation is generally acceptable for elasto-plastic systems.

The paper investigates the structural response and vulnerability of Blockhaus buildings under seismic loads. The typical Blockhaus systems consists of a series of linear timber members stacked horizontally one upon another and interacting by means of traditional timber joints based on the effectiveness of carvings and contacts of multiple surfaces. Native of forested areas, Blockhaus systems are widely used in daily practice for the construction of wooden houses or commercial buildings also in earthquake-prone regions. However, no design provisions are given in the Eurocode 8. In this work, a Finite-Element (FE) numerical investigation is performed on full three-dimensional Blockhaus timber buildings subjected to seismic loads. A computationally effective FE-model developed in a previous research is implemented in ABAQUS. In this model, a key role is played by nonlinear hysteretic springs used to schematize the cyclic behaviour of the joints between perpendicular linear members and validated on cyclic experiments of single joints. Nonlinear dynamic analyses are carried out for some building configurations of technical interest. Preliminary estimations of the corresponding q-behaviour factor are also presented.

In this paper, a non−linear methodology for the design of the metal connectors in cross−laminated (XLam) timber walls subjected to bending and axial force is presented. The wall is regarded as rigid, and an elastic−perfectly plastic response is considered for each metal connector (hold−down, angle brackets) at the base of the wall. The wood is conservatively modelled with an elastic−brittle behaviour in compression at the interface with the foundation or with the supporting timber floor panel. The force distribution in the metal connectors is obtained by iteratively calculating the neutral axis position at the base of the wall using a simple purposely developed Excel spreadsheet. Five different failure mechanisms at Ultimate Limit States have been identified, starting from the fully tensioned wall to the fully compressed one. The required input parameters are the strength class of timber and the ultimate displacement, the elastic stiffness and the ultimate strength of the metal connectors used. As a result, the algorithm calculates, for every axial load value, the ultimate resisting moment of the entire wall. This procedure, of simple and straightforward implementation, allows the designers to perform a manual evaluation of the rocking resistance of XLam walls in seismic analyses.

Blockhaus structural systems are obtained by assembling multiple timber logs able to interact with each other by means of simple mechanisms (e.g. contacts, tongues and grooves, and carpentry joints, also referred to as ‘corner’ joints). Although these systems have ancient origins, the structural behaviour of Blockhaus systems under well-defined loading and boundary conditions is still complex to predict. The paper focuses on the assessment of the typical buckling behaviour and resistance of in-plane compressed timber log-walls. The effects of various mechanical and geometrical aspects such as in-plane rigid inter-storey floors, load eccentricities, different types of lateral restraints, openings (e.g. doors or windows) or additional metal stiffeners, are investigated by means of full-scale buckling experiments. Results are then critically discussed and preliminarily assessed via analytical formulations taken from classical theory of plate buckling and column buckling. Although further advanced studies are required for the development of a generalized buckling design method, it is shown that several mechanical and geometrical aspects should be properly taken into account to correctly predict the structural capacity of Blockhaus systems under in-plane compression.

This paper investigates the non-linear modelling of the cyclic behaviour of Blockhaus timber log-walls under in-plane lateral loads. The structural behaviour of Blockhaus log-walls in the examined loading condition strictly depends on the geometry – thus on the deformability and ultimate resistance – of the adopted corner joint, namely the joint between perpendicular log-walls. The presence of metal fasteners is in fact minimized and the structural interaction between the basic timber components is provided by simple mechanisms such as notches, tongues and grooves, multiple surfaces in contact. In this paper, a computationally effective FE-model is developed, in order to predict the cyclic behaviour of an entire Blockhaus log-wall once the cyclic behaviour of the adopted corner joint is known. The model uses non-linear hysteretic springs to describe the joint behaviour, where all typical features such as pinching behaviour, strength and stiffness degradation can be considered. By comparing the numerical and the experimental predictions of the cyclic response of full-scale Blockhaus log-walls, a general good agreement is found. Simulations confirmed the high flexibility of the studied structural systems, as well as the significant effect of possible openings such as doors and windows on their global resistance to in-plane lateral loads. In conclusion, the presented study confirmed that the proposed modelling approach can be used to estimate the load-carrying capacity and vulnerability to seismic events of Blockhaus shear walls, and that the same model could be extended to full Blockhaus buildings.

In this work, an effective modelling strategy for describing the non-linear behaviour of unreinforced masonry (URM) structures is presented. The approach uses the equivalent frame modelling and represents each masonry wall with macroelements, which are formed by zero-length multi-spring elements connected each other via elastic links. Each macroelement has two rotational springs, one at both ends and a shear spring in the middle of the length. Two specific hysteretic rules are used in the springs, describing the shear and the rotational hysteretic cycles. The employed laws account for stiffness and strength degradation, and the strength of each panel is calculated on the base of the axial load detected in the wall. Some numerical-experimental comparisons are presented to demonstrate the potential and the accuracy of the actual modelling.