Ductile Behavior of Timber Structures under Strong Dynamic Loads

Due to their comparatively low mass that implies reduced horizontal dynamic loads even during strong earthquakes, wood-made buildings might be a good choice in seismic prone regions. To meet the modern design philosophy requirements, however, such structures should be able to behave in a ductile way under exceptional events. By presenting a brief review of the latest developments in the field, this chapter investigates on when and to what extent historical and modern timber buildings may exhibit a ductile and dissipative behavior. A special focus is given to the crucial role of connections and to the difficulties involved by their mechanical model when carrying out codebased non-linear dynamic analyses. Although a ductile behavior is typically required under strong earthquakes, it is to note that a well-designed ductile structure may also be able to withstand other exceptional events as, for instance, tornadoes or blasts.


Introduction
To be able to exhibit a ductile behavior is a bonus that a structure can exploit when exposed to extreme and unpredictable actions like those applied by earthquakes, hurricanes, snowstorms, fire or explosions. In fact, it would be uneconomical to design structures that withstand such infrequent events still deforming in the elastic range. In addition to cost-effective reasons, a significant advantage of the ductile behavior is the great amounts of input energy that can be dissipated during the plastic motion, considerably higher than what could be dissipated in the elastic range. Further advantages are the beneficial redistribution of stress within statically undetermined systems and the warning that large deformations may give to inhabitants in case of exceptional loads. Aimed by these reasons, the seismic codes of practice typically require that buildings survive earthquakes of moderate severity deforming in the elastic range whilst they behave in a dissipative ductile way, even getting damaged severely but without collapsing, during strong seismic events. Local curvature ductility and strength hierarchy requirements ensure such extreme performance of buildings with the final goal of life safety.
Based on this well-established design philosophy, a lot of experimental data, numerical procedures and code provisions are in fact available to design earthquake-resistant buildings made by steel or reinforced concrete [1][2][3]. On the contrary, a lack of sufficient research results and detailed code requirements still affect the design of wood structures in high seismicity areas, despite the growing interest in natural and renewable materials. Light weight as they typically are timber structures might possibly resist earthquakes better than other kind of structures. Being proportional to the building masses, in fact, the horizontal loads acting on light structures during a given earthquake are lower than those acting on heavier structures, so that reducing the building active mass may be even a strategy for seismic stress control [4,5].
On the other hand, to meet the modern design philosophy, timber structures are expected to exhibit a ductile and dissipative behavior-besides adequate strength and stiffness-under strong earthquakes. Ductility is in fact the capability to undergo large inelastic displacements without significant reduction in strength. On the other hand, high values of ductility usually imply large amount of energy dissipated during the dynamic motion, being the energy dissipated in each cycle related to the hysteresis area of the load-displacement diagram.
With the aim of investigating on the dynamic behavior of timber structures under extreme conditions, this survey focuses on the post-elastic behavior of wood constructions. The chapter is composed of two main parts. The first one deals with the ductile behavior of historical buildings (Section 2). A brief review on the performance of existing wood-made buildings under past events is presented in Section 2.1 while experimental data on the ductile and dissipative behavior of ancient timber buildings, as available from the literature, are provided in Section 2.2. The remarks listed in Section 2.3 close the first part of the chapter. The second part refers to the ductile and dissipative behavior of modern timber constructions (Section 3).
The key role of metallic connections is addressed in Section 3.1, whereas some practical aspects to be taken into account before carrying out a code-based non-linear dynamic analysis of a timber structure are highlighted in Section 3.2. Some brief conclusive notes are provided in section 3.3.

Ductile and dissipative behavior of ancient timber buildings
Until the advent of reinforced concrete, wood buildings have been popular for centuries in many seismic areas like China, Japan, Greece, Turkey and Balkan countries. In other geographical areas prone to earthquakes or tornados (North America), wood-frame single-family houses and low-rise multi-family dwellings never stopped to be built since colonial times. Timber constructions are today still very common in countries where wood is in good supply (USA, Canada, North Europe and New Zealand), but a growing interest is developing even in regions where adobe and masonry have been the most typical construction materials for centuries (e.g. Mediterranean countries). Assessing the performance of timber structures during past severe natural events may be thus of great interest not only to preserve the architectural heritage but also to improve the design of new buildings.

Performance of timber buildings during past natural events
Somehow unexpected, the finding that many ancient wooden constructions remained nearly intact after strong earthquakes, whilst modern reinforced concrete buildings collapsed, as emblematically shown in Figure 1, gave new impetus to build timber constructions even in seismic regions. Several authors documented, in fact, a generally good performance of timber buildings during natural events as earthquakes, hurricanes, tornadoes and snowstorms [6][7][8][9][10][11][12].
Actually, most of the existing timber constructions were built according to conventional guidelines based on the empirical knowledge of the past while only the more recent ones (a little part) are engineered structures meeting modern anti-seismic standards. Mainly based on inspections made after natural disasters, best-practice rules were suggested-although not always applied-in the past [13]. It may be interesting to mention that the first European antiseismic recommendations, which were enacted in 1783, after a devastating earthquake struck Calabria and Sicily (at that time belonging to the Borbone Kingdom), prescribed to strengthen buildings by means of wood frames in filled in the masonry walls. The timber frames were recommended to be suitably connected to each other's, to the ground and to the floors, see Figure 2 [14]. Even more interesting is the fact that such an aseismic system (adopted in Italy till the twentieth century and referred to as "casa baraccata"), had actually been borrowed from the traditional little wooden single-story houses (called baracche) which were usually built near to the palaces of nobles to be used as earthquake-proof shelters [15][16][17]. Although not written, aseismic recommendations similar to-and most likely inspiring-the Borbone's ones were adopted in Lisbon a few years before, after the catastrophic earthquake and the ensuing tsunami that struck the town in 1755. Based on the knowledge collected from survived buildings, the Pombalino constructive system (imposed by the Prime Minister Marquis of Pombal) consisted in fact of a three-dimensional timber structure (called gaiola due to its cage-like structure) included in the masonry walls above the first floor of the building, see   Due to the different role given to the timber structure, the "Borbone" and the "Pombalino" constructive systems were quite dissimilar in their mechanical behavior, as discussed in Ref. [16]. Both of them are, however, examples of ancient timber-framed buildings. Although the concept of structural ductility was still very far to be introduced in building design, the role of timber frames in traditional constructions was in fact that of withstanding lateral loads by allowing large-and usually inelastic-displacements (like a sort of reinforcement skeleton), a role which cannot be played by unreinforced masonry.   Ottoman traditional timber-frame houses (see Figure 4b), that may be still found in earthquake-prone areas as Turkey, Balkan countries, Iraq, Siria and Egipt [6,9,21]. Likewise the Pombalino system, also in the Ottoman houses, the timber frames were introduced from the first floor up (for this reason they are also referred to as half-timbered frames). Further examples of timber-framed buildings (dating back even to the medieval period) may be also found in European countries as Germany, the United Kingdom, Greece, France, Spain, Poland (see e.g. the examples given in Figure 4c-f), as well as in India [22,23], the USA [24], China [25] and Peru [26]. An overview of the history of timber framed buildings may be found for instance in Ref. [32].
Different from the timber-framed systems, other wooden ancient buildings can be also broadly found (see Figure 5).
The widespread use of wood as structural material even in earthquake-prone areas highlights the awareness they had in the past of the good performance of such a material even under extreme conditions. Of course, mistakes and experience taught how to build timber structures to better withstand strong dynamic actions. The following shortcomings were typically found, in fact, to be responsible for the inefficient structural behavior of wood buildings in past natural disasters: lack of adequate foundation anchorages or inadequate foundations soil; presence of a soft-story mechanism (typically due to large openings at the ground floor of multi-story buildings); insufficient connections between major components or lacking lateral bracing, as documented, among others, in Refs. [6][7][8][9][10][11]. Other causes of failure were also detected as, for instance, failure of infill materials in timber-framed buildings, failure of chimneys, collapse of neighbor buildings, structural changes or excessive loadings given at a certain stage of the building life which caused very large inertia forces [6,9,11,27,28]. However, the main lesson drown from past events was that, to better resist to lateral loads, a timber structure should be regular, have little openings, possess effective connections, bracing elements and ground anchorages. In other words, it should eventually behave as a box-like unit.

Ductility of historical buildings
Apart from the qualitative considerations recalled in the previous section, we can ask whether and to what extent existing (and often very ancient) timber structures can be able to exhibit a ductile and dissipative behavior under extreme conditions. Unfortunately, answering this question is not an easy task, since the actual dynamic behavior of historical timber buildings is hardly predictable and it is usually documented, as far as for the past, only by empirical data. The task is even made more difficult by the different constructive techniques, wood species, kind and quality of infill materials and by the large variety of joints adopted in ancient structures. Some recent studies can be, however, exploited to have some clues.

Timber-framed buildings
Experimental researches were carried out to assess the behavior of the Borbone constructive system, [16,17,29]. Particularly remarkable are the results provided in Ref. [16], relevant to inplane cycling tests performed on two full-scale models of Borbone walls, following the UNI EN 12512:2006 protocol [30]. Experimental findings evidenced a non-linear behavior of specimens with comparatively high values of ductility. The latter was calculated as the ratio between the maximum displacement u max and the displacement at yield u y , namely The quantity defined by Eq. (1) is sometimes also referred to as the static ductility. To quantify the dissipation of energy in the plastic range, the hysteresis equivalent damping ratio was calculated in Ref. [16], as defined by Based on the Jacobsen approach [31], Eq. (2) considers the ratio between the energy dissipated for a half hysteresis cycle, namely E d , and the potential energy E p that an equivalent simple oscillator would store for the same displacement achieved in the hysteretic half-cycle (see Figure 6). The value of ξ eq was evaluated in Ref. [16] for the third cycle of each level of displacement imposed, as suggested by the UNI EN 12512:2006 protocol [30]. The cumulative dissipated energy E d_cum , obtained by summing the loop areas of successive cycles, was also calculated. The values of μ, E d_cum and ξ eq obtained in Ref. [16] for infilled and bare walls are provided in Table 1. In the infilled specimens, the energy dissipation was found to depend mostly on friction and small ruptures in the masonry. In bare specimens, the almost wholeness dissipation was found instead to be concentrated in the connections, where two mechanisms occur contemporarily: the first one is related to the compression and crushing of wood grain with the formation of a cavity due to the presence of nails (which is also responsible for the pinching effects discussed in the following); the second one concerns the inelastic deformation of the iron nails, [16,17].
The dynamic behavior of the Pombalino timber-framed buildings in Lisbon was investigated through experimental tests on specimens taken from actual sites [28] or rebuilt in laboratory [19,27,32]. All of them assessed a rather good ductile behavior of Pombalino walls. In particular, the results given in Ref. [19], relevant to real-size reconstructions of Pombalino walls under cyclic displacement sequences following the CUREE protocol [33], showed fat hysteresis loops dissipating reasonable amounts of energy (although the actual values are not given by the authors). The ductility ratio was found to be around 3. Significant pinching effects, related to gaps and residual displacements which form in the connection zones and between masonry and timber members were detected. A rather accurate non-linear hysteresis model was also developed in the same paper to capture the dynamic response of the walls. Similar experimental tests on real-size laboratory reconstructions of infilled and bare-framed Pombalino walls were carried out in Ref. [32]. The values of μ, E d_cum and ξ eq found in Ref. [32] are collected in Table 1.
Experimental tests on eight different timber frames with and without infill (brick and adobe) or cladding, all reproducing portions of the typical himis-timber-framed Ottoman constructions, were carried out in Ref. [21]. The force-displacement curves obtained for reversed cyclic in-plane lateral loading showed stable hysteretic loops with highly dissipative behavior. The authors suggested to evaluate the cumulative energy dissipation capacity through the following empirical formulas [21]: Here E d_cumW and E d_cumWO denote the cumulative energy dissipation capacity (expressed in Joule) of specimens with and without infill/cladding, respectively; while W ef f , A ef f and D max are the effective width (m), the effective area (m 2 ) and the maximum lateral top displacement (mm) of each framed wall considered in the experimental tests. The values of E d_cum as obtained by applying Eqs. (3) and (4) and of ξ eq , as defined by Eq. (2), were derived from the data given in Ref. [21] and are provided in Table 1 both for infilled and bare frames. A high ductile behavior was found to be exhibited by the considered timber-framed walls, although the actual values of the ductility ratio μ were not provided in Ref. [21]. The highly dissipative behavior detected for Ottoman walls was found to depend on the dissipative plastic behavior of nailed connections, as also confirmed by other authors [22].
The results of in-plane quasi-static cyclic tests on full-scale dhajji-dewari walls (woodenbraced frame system with masonry infill, typical of India and Pakistan) were given in Ref. [23]. The tests highlighted a very strong resilience of the dhajji-dewari system against lateral loads, which is almost totally due to the performance of the timber framework. Also in this case, a rather good ductile and dissipative behavior is found in the experimental tests. The values of μ and ξ eq obtained in Ref. [23] for infilled and bare walls are given in Table 1.
Finally, the data taken from [26] relevant to experimental tests carried out on half-scale quincha walls are also provided in Table 1. (Quincha is a Peruvian traditional timber-framed constructive system consisting of an adobe-made ground floor and upper stories built with timber frames infilled with a weave of canes and mud).
A qualitative diagram is provided in Figure 7 showing some of the typical features evidenced by the experimental cyclic tests on timber-framed walls, infilled with masonry and connected with metallic nails. The main features evidenced in Figure 7 are (a) non-linear behavior; (b) almost symmetric curves; (c) indistinct yield point; (d) lateral stiffness degradation for increasing loading cycles; (e) pinching effect after the first load cycle; (f) strength degradation at the same deformation level for increasing loading cycles; (g) strength degradation for higher deformation;(h) fat hysteresis loops which implies large amounts of energy dissipated (narrowed loop areas are generally found, however, for successive load cycles or for higher deformation levels); (i) rather high values of ductility.
The so-called "pinching effect" is due to the formation of a cavity around the fasteners due to irrecoverable crushing of wood (this effect occurs after the first loading cycle) which implies a reduced stiffness at load reversals (the connection stiffness is due, in this phase, to the sole contribution of metallic fasteners). As soon as the contact with the surrounding wood is reestablished, at increased deformation levels, the stiffness rapidly increases which leads to the typical pinched shape of curves in the load-displacement diagram. It can be noted, finally, that features very similar to those illustrated in Figure 7 and discussed before were also detected for modern timber walls (plywood shear, strand-board diaphragms), as can be inferred by examining, for instance, the experimental load-displacement curves provided in Ref. [34].

Other kinds of ancient wooden constructions
Experimental studies were carried out to assess the dynamic behavior of traditional Chinese [35][36][37] and Japanese [38][39][40] constructions. Of particular interest to the purpose of the present study are the results provided in Ref. [37]. They are relevant to scaled specimens, reproducing a prototype of a historical Chinese timber palace, subjected to cyclic lateral loading. Stable and large-area hysteretic loops were found in the tests, associated with rather high values of ductility (9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19) and energy dissipation (not quantified). The equivalent viscous damping was evaluated to reach even values of 20-30%. It is worth noting that Chinese and Japanese constructions were found able to exhibit a rather high ductile response and to dissipate large amount of energy, despite they typically avoid metallic connections. Energy dissipation was found to be due, in fact, to friction and embedding between structural elements at the contact interfaces inside the wooden joints.
Further experimental studies can be also quoted, for example [41], confirming a rather good ductile and dissipative behavior of ancient timber constructions.

Some remarks on the ductility of ancient timber constructions
Before closing the present section, the following remarks can be drawn.
i. Ductile behavior and energy dissipation are two key points of the modern aseismic strategy adopted by current standards. Experimental findings showed that historical timber buildings can generally be able to meet these modern requirements.
ii. Table 1 substantiates statement (i). With reference to the classification given by EC8 [1], recalled in Table 2, three kinds of the traditional timber structures referred to in Table 1 may be assigned to the high ductility class (DCH), namely the Borbone, the Pombalino and the quincha walls (all in the case of infilled timber frames). A low ductility class (DCL) should be assigned instead to the dhajji-dewari walls. The class of ductility of the Ottoman traditional walls cannot be assessed through the available data.
iii. Although giving an interesting portrait of the ductile and dissipative capacity of traditional timber buildings, the data collected in Table 1 should be compared with caution due to the different settings (laboratory set-ups, loading procedures, recorded data analysis, yield and ultimate deformation evaluation) adopted in the experimental studies mentioned. For instance, the total amount of energy dissipated can be strongly dependent on the load protocol, which is usually different from an experimental research to the other. In addition, it can be noted that a different ductile behavior was sometimes detected in experimental tests from positive to negative direction of load, although such an aspect has not been evidenced in Table 1 for the sake of brevity.
iv. The last column of Table 1 reports the values of the drift (in %) as given by the ratio between the maximum lateral displacement and the wall height. This is in fact a very significant parameter to be considered when large displacements are involved.
v. Despite the extreme attention paid by the authors in reproducing, as faithfully as possible, the in-situ conditions(timber species, infill materials, geometry, ground constraints, connections, and so on), the results obtained in laboratory on rebuilt models of parts of ancient constructions should be obviously used with great care to predict the actual dynamic behavior of existing whole buildings, also in view of all the aspects affecting the behavior of real structures (material degradation, efficiency of connections, internal damage, workmanship irregularities, tridimensional behavior of the building).
vi. A crucial role in the ductile behavior of ancient timber structures was found to be played by connections, since timber elements generally do not exploit their latest strength resources [21,42]. Based on this statement, some retrofitting solutions were also proposed to improve the dynamic behavior of ancient structures under dynamic loads [27,42]

Ductile and dissipative behavior of modern timber structures
Besides the more common single-family and low-rise houses, spectacular and daring-shaped modern timber buildings may be even encountered nowadays in many countries, as the few instances of Figure 8 let imagine. A feeling for eco-friendly and renewable materials, together with the easy of production and transportation from the past, adds new motivations to the construction of wooden buildings.
As discussed in the introductive section of this chapter, modern structures are required to be ductile and dissipative, particularly when they are built in seismic areas. While timber structures are uniquely recognized to be able to meet such requirements provided that they are   regular, hyperstatic and connected with ductile fasteners (as also confirmed by Table 2), most of the issues related to evaluating and modeling this ability are still under discussion.

Crucial role of connections
Connections in modern timber buildings are metallic devices ensuring transmission of forces between structural elements. Their design is the most strategic part of the structural project of a timber construction, since from the characteristics of the connections (type, mechanical properties, geometry, spacing, assembly techniques) may strongly depend the stiffness, the strength, the ductility and the energy dissipation of the whole structure.
Although some constructive typologies (such as moment-resisting timber frame systems, timber shear panel systems and cross-laminated panel systems) are indicated as being particularly able to ensure a ductile behavior under extreme dynamic lateral loads [43], it is the connection design that eventually decides the ductility resources of a timber structure. The same structural type may be, in fact, assigned to different ductility classes in dependence of the rotational ductility capacity of its connections, as can be inferred, for instance, by the classification done by EC8, recalled in Table 2.
The most common connections in modern timber structures are the dowel-type mechanical fasteners (nails, screws, dowels, bolts, rivets) which deeply penetrate into the wood to transfer the load by means of wood bearing and connector bending. Dowel-type connectors can be used alone or in combination with metal predrilled plates. Joints with dowel-type fasteners are expected to be ductile due to the highly nonlinear behavior of the wood under embedding stresses and the plastic behavior of the steel fasteners in bending [44]. Nevertheless, they can sometimes be affected by sudden and brittle failures like block shear or splitting [45]. Ten different types of failures (six in single shear and four in double shear) are considered by the European standards for dowel-type timber connections [46].
As a matter of fact, timber members and metallic joints play different roles in the seismic behavior of timber structures. Since the failure mechanisms of wooden elements are mostly brittle, the timber members are required to remain in the elastic range even under very strong events. The task of satisfying the demand of ductility is entrusted instead to the metallic connections which are expected to sustain large inelastic deformations while preventing collapse. The ductile behavior of connections is influenced both by metallic fasteners (which may behave in a ductile or brittle way depending on whether plasticization is attained or not) and by the strength properties of the wood surrounding the connection zone (direction of the grain with respect to the load direction).
Preventing brittle failure may guarantee an adequate ductility to the whole structure.
Complying some strength hierarchy rules can assure a ductile behavior to timber structures. In particular, it is essential to design the fasteners to be weaker than the wood members they are connecting, so that they can yield and dissipate great amount of energy.
On the other hand, the weaker the fasteners, the lower their bearing capacity. A way of ensuring both adequate ductility and sufficient bearing area is using a large number of weak fasteners. Some alternatives to improve the performance of dowel-type joints are discussed in Ref. [47].
Although the plastic properties of the steel fasteners alone are well-known and their behavior under cyclic loads easy predictable, the non-linear response of the assembly of metallic connectors and surrounding wood is rather difficult to predict, since it is not a cross-section property (as for reinforced concrete). In fact, the behavior of the timber connections depends from several factors, some well-known as the strength properties and the geometric configuration of involved materials, others affected by uncertainty as the influence of neighboring metallic fasteners or the interaction between fasteners and surrounding wood. This makes rather difficult to develop an analytical model able to reproduce the behavior of a timber connection.
Most of the features evidenced in Figure 7 and discussed in Section 2.2.1 characterize the behavior of metallic timber connections, as can be inferred from Figures 9a and 9b, which provide qualitative examples of the typical hysteretic behavior of riveted and nailed connections, respectively. In particular, two phenomena were found to be typical of the hysteretic response of steel dowel-type connections, as recalled in Ref. [43]. The first one is the pinching effect implying different hysteretic curves from the first to the subsequent load cycles (see Figure 9). The second one, referred to as the memory of material, is due to a dependence of the load-slip curve from the loading history. Both these phenomena may influence the ductile behavior of a timber structure.

Influence of the pinching effect on the ductile behavior of connections
The pinching effect is a very typical feature of the hysteretic behavior of dowel-type connections affecting both historical and modern timber constructions. The mechanical causes of it have been discussed in Section 2.2.1. This effect has been documented by many authors, as for instance [48][49][50][51][52]. It was found, in particular, that for a given displacement level, the highest resistance and widest hysteresis loop was attained at the first load cycle, whilst the subsequent cycles were narrowed and achieved lower resistance, stabilizing after about three cycles (see Figures 9a and 9b). Stabilization of the pinched curve after three cycles is also referred to in UNI EN 12512:2006 [30]. Due to the reduction of the area of the hysteresis loop, the pinching effect may be actually responsible for a reduced amount of energy dissipation, although connections are still able to exhibit high values of ductility. In modeling the mechanical behavior of a steel dowel-type connection for numerical analysis purposes, the pinching effect should be considered. A discussion on how this can be done may be found in Ref. [34], even if standard models comprehensive of the pinching effect and of the strength and stiffness degradation are not yet available, neither suggested by codes of practice.

Influence of the load history on the ductile behavior of connections
From the results available in the literature, it is clear that the hysteretic behavior of timber connections may strongly depend on the type of experimental test carried out (dynamic, static, cyclic, monotonic) as well as on the testing protocol adopted. On the other hand, while different protocols are available to carry out cyclic loading tests on timber structures, for example, EN 12512 [30], CUREE-Caltech standard [33], UBC protocol [11], a consensus on the best protocol to be assumed as standard has not been yet reached [48]. Many experimental findings proved, however, the influence of the load history on the final results.
It was shown in Ref. [48] that a connection usually reaches its maximum load at a lower deformation under cyclic loads than under monotonic loading. In Ref. [50], it was found that the ductility ratio of timber shear walls may be much higher when measured under static monotonic tests than when measured under dynamic tests. These experimental findings indicate that results from monotonic tests tend to overestimate the load-deformation behavior of connections with respect to cyclic loading tests, and therefore should be avoided when determining the seismic performance of timber buildings [48]. Dynamic tests are surely the best choice to capture the behavior of timber structures under seismic or wind loads, also in view of the fact that the failure modes may be very different in static and dynamic conditions [50]. The hysteresis loops obtained from dynamic tests were, however, found to be very sensitive to the protocol adopted [11,53].
The dependence of the connection ductility from the experimental test may be also inferred from Table 3, where are collected the ductility ratios experimentally obtained for different timber connections [44,48,[51][52]54]. Table 3 may be quite convenient to have an idea of the ductile capacity of timber connections, although the data herein provided should be compared with care, owing to the different specimens, test setups and loading protocols involved in the tests (the reader is referred to the papers quoted in the table for any detail).
Analogously, the ductility ratios of modern timber walls are given in Table 4, as derived from Refs. [50,55,56]. The data collected in Table 4 highlight the good ductility which may be exhibited by modern timber constructions, although comparing the data collected in Table 4 needs again caution. It can be also noted, finally, that the hysteresis curves obtained by testing modern timber walls with nailed connections evidenced features similar to those of Figure 7, as can be inferred for instance from diagrams provided in Ref. [50-51, 55, 57].

Non-linear dynamic analysis to predict the seismic response of timber structures
The non-linear time-history analysis (NLTHA) is the most comprehensive procedure allowed by seismic codes to design earthquake-resistant structures. It involves a complete time-history investigation under different spectrum-compatible ground motions. Despite its potential, the NLTHA is still underused, likely due to the difficulties it indubitably involves and even to some inadequacies of the current codes of practice [58]. Such an analysis is, however, the better way to predict the actual seismic performance of structures composed of elastic and inelastic parts. Current codes of practice allow non-linear analyses for the calculation of the internal forces in the members of timber structures, provided that they are able to redistribute the internal forces via connections of adequate ductility [46].
When implementing a NLTHA, an efficient approach to model the structure is that of separating the critical zones where the NLTHA ductile behavior may be exhibited from the other Slotted-in steel plates with nails [54] glulam members Monotonic (parallel to grain) 11.9-31.9 Note: XLam, cross-laminated.  structural parts which are expected to deform elastically even at the ultimate state. This is a typical procedure followed, for example, in reinforced concrete frames where plastic hinges are usually lumped at either end of columns and beams, while preventive plasticization of beams is guaranteed by some code-based strength hierarchy rules. An analogous procedure can be exploited for timber structures, by assuming timber members as purely elastic elements and connections as nonlinear links. To comply with the modern philosophy of the capacity design, the timber elements should be overdesigned to ensure their brittle failure will follow plasticization of connections (strength hierarchy rule).

Modeling timber connections
Exploiting experimental data is often the best way to obtain the mechanical behavior of a timber connection under dynamic loads. Several empirical models were proposed in the literature, which commonly involve parameters calibrated to experimental data, see for example [34,43,59,60]. It should be noted, however, that extracting a general model from the experimental load-displacement curves needs caution owing to the possible dependence on both the loading history and the test set-up [34,61,62], as already discussed in Section 3.1.2.
More detailed micro-models were also proposed by other authors, for example [62][63][64], which investigated the non-linear response of metallic fasteners and surrounding wood through three-dimensional finite element dynamic analyses. Still requiring some empirical adjustments of parameters, such sophisticated models usually imply a significant aggravation of the computational effort, which may become unsustainable for purposes other than those of advanced researches.
As already observed in Section 3.1, the behavior of timber connections depends from several factors, some of which are not easily predictable. This makes rather difficult to develop an analytical model able to reproduce the behavior of a timber connection. However difficult it may be, finding a suitable model for the hysteretic behavior of connections is essential to study the dynamic response of a timber structure, at least when a non-linear analysis has to be performed.
Commercial packages for structural analysis usually allow choosing between different mechanical models to implement the behavior of nonlinear links. For instance, the pivot hysteretic model provided by the widely used SAP2000 for nonlinear links (NLLINK) is depicted in Figure 10. To adopt a model like this, a set of parameters have to be properly assigned to reproduce all the typical phenomena experimentally detected in timber connections such as stiffness and strength degradation as well as pinching effects.

Concluding notes on the ductile behavior of modern timber structures
When appraising the ductile behavior of modern timber structures, the following aspects can be eventually addressed.
i. In-situ inspections, laboratory investigations and analytical models available in the literature converge to the statement that modern timber structures may be ductile and dissipative, provided that their metallic connections are well designed and detailed. Data collected in Tables 3 and 4 show that timber constructions own a rather high-and sometimes excellent-ductility capacity. However, the actual ductility of a timber construction is not always univocally established. Different definitions of the ductility ratio are, in fact, proposed by authors and by codes of practice, as extensively discussed in Refs. [65][66][67].
ii. A decisive step to evaluate the ductility ratio, in its more classical definition, is the determination of both the deformation at yield and the ultimate deformation from the experimental load-deformation curve. Different conventional methods are available to this purpose as discussed in Refs. [66,67], but adopting one method or another may lead to substantial differences in the calculation of the ductility ratio (even up to 100%), as evidenced in Ref. [66].
iii. The value of the ductility ratio alone cannot be sufficiently representative of the performance under strong dynamic loads. Not always, in fact, to higher values of ductility corresponds a greater amount of energy dissipated. This was addressed, for instance, in Ref. [55].
iv. To carry out a NLTHA of a timber structure nonlinear links should be located where plasticization is expected to occur, that is, at connections (plastic hinges). The mechanical model of the plastic hinges is generally difficult to be defined by the designer due to (a) insufficient support given by codes of practice; (b) difficulty in finding the experimental data relevant to the specific connection adopted; (c) uncertainty in the correct extraction of the required parameters from the experimental curves. These difficulties may eventually