Displacement-based design approach to evaluate the behaviour factor for multi-storey CLT buildings

Engineering Structures 201 (2019) 109711

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Review article

Displacement-based design approach to evaluate the behaviour factor for multi-storey CLT buildings

T

⁎

Johannes Hummela, , Werner Seimb a b

EFG Beratende Ingenieure GmbH (Consulting Engineers) Ederweg 4-6, 34277 Fuldabrück, Germany Timber Engineering, University of Kassel, Kurt-Wolters-Str. 3, 34125 Kassel, Germany

A R T I C LE I N FO

A B S T R A C T

Keywords: Displacement-based seismic design Force-based seismic design Behaviour factor Force reduction factor Experimental data Cross-laminated timber Multi-storey structures

Different aspects of force-based and displacement-based design of multi-storey cross-laminated timber (CLT) structures are discussed in the context of the definition of the behaviour factor q. A review of approaches to determine the behaviour factor for force-based design will be given. A new approach to evaluate the behaviour factor based on non-linear static analyses together with a displacement-based design procedure will be discussed and demonstrated. CLT structures with two and four storeys and different types of structural models are considered for illustration and validation. Results of experimental investigations on anchoring connections will be presented. These test data are employed to derive properties of non-linear springs for structural modelling. The spring properties will be validated by comparison of analytical to experimental results on the wall level. An appropriate behaviour factor can be found based on the evaluation of 24 different structural configurations.

1. Introduction The q-factor is a force reduction factor used in force-based design. Force reduction factors are defined differently in the design codes of various countries due to differences in basic design provisions. These provisions include definitions of ductility, damping and structural overstrength. The definition of the behaviour factor q for timber structures has been discussed recently in the context of the revision of Eurocode 8 by Follesa et al. [1]. The differences between the force reduction factors throughout the codes are discussed by Tannert et al. [2] with reference to cross-laminated timber (CLT) buildings. Rodrigues et al. [3] stated that structural overstrength is not considered within the q-factor for timber structures according to Eurocode 8 [4], in contrast to steel and reinforced concrete structures. However, structural overstrength is commonly considered within the force reduction factor in other codes. Several studies have been performed aiming at the determination of the behaviour factor for CLT structures [5–7]. However, all these investigations pursue basically the same procedure which is the peak ground acceleration (PGA) approach (see Section 1.2). Fragiacomo et al. [8] performed a case study on a four-storey CLT building incorporating displacement-based design (DBD) to show the influence of the connection properties. Nevertheless, an evaluation of the behaviour factor was not included in this study. The ongoing discussion and

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research about appropriate definitions of the behaviour factor covering different cyclic behaviour of CLT structures is the motivation for a systematic evaluation using alternative assessment methods. DBD especially appears less complex here compared to the PGA approach together with a numerical time history analysis. A new evaluation procedure based on DBD will be proposed in this paper (see Section 2). Calculation methods will be presented briefly in Section 1.1 and a review of methods to determine the behaviour factor will be given in Section 1.2. 1.1. Seismic analysis methods There are basically three different design methods for buildings under earthquake impact, which are all three introduced in Eurocode 8 [4]: lateral force method, displacement-based design and design by time history analysis. A very common method for practicing engineers is the lateral force method. Here elastic response spectra are scaled by a behaviour factor q to calculate the base shear (see Fig. 1), which is equivalent to the total of seismic forces. Assessment of the fundamental period T1 as the decisive parameter characterising the dynamic behaviour of the structure is, in many cases, not trivial, as was discussed by Hummel et al. [9]. The time history analysis, on the other hand, can be assigned to be the most comprehensive calculation method. Time history analysis

Corresponding author. E-mail address: [email protected] (J. Hummel).

https://doi.org/10.1016/j.engstruct.2019.109711 Received 28 March 2017; Received in revised form 5 September 2019; Accepted 23 September 2019 0141-0296/ © 2019 Elsevier Ltd. All rights reserved.

Engineering Structures 201 (2019) 109711

J. Hummel and W. Seim

Fig. 1. Transfer of the elastic response spectrum to the design spectrum for the determination of the lateral seismic loads (schematic).

determine the behaviour factor q. The five approaches considered are: (1) (2) (3) (4) (5)

ESECMaSE stands for Enhanced Safety and Efficient Construction of Masonry Structures in Europe. Fig. 3 shows schematically the procedure of the base shear approach. Two analyses – the first one with linear-elastic behaviour and the second one with inelastic hysteretic behaviour – are carried out, each for a series of different ground motion records. The base shear Fb obtained by time history analysis assuming linear and non-linear structural behaviour are plotted for each of the ground motion records. The ratio of the base shear Fb,el for elastic behaviour and the base shear Fb,nl for non-linear dissipative behaviour defines the q-factor for each ground motion record:

Fig. 2. Basic procedure of DBD in the Sa-Sd format.

needs ground motion records of real earthquakes or artificial accelerograms, a definition of non-linear hysteretic behaviour for all structural elements and an efficient analysis software to determine the loaddisplacement response of the structure. Time history analyses need highly skilled and experienced engineers and might be applied for seismic retrofit of existing structures and for seismic design of high-risk structures, such as dams or the power plants of chemical factories. DBD can be classified to lie somehow between the lateral force method and the time history analysis in terms of effort and outcome. It incorporates the post-elastic behaviour of the specific structural components of the lateral load-resisting system. The inelastic behaviour of the structure is represented by a capacity curve which is transformed into a capacity spectrum. The seismic action is defined by inelastic or damped spectra in the Sa-Sd format [10]. The inelastic response is found if the demand spectrum and the capacity spectrum intersect at the so-called performance point (see Fig. 2).

q=

The behaviour factor accounts for the capability of structures to exhibit ductile inelastic behaviour connected with energy dissipation [11]. Different procedures to define the behaviour factor for engineering structures are used in parallel. A very general and commonly used definition is the ratio of the strength for elastic behaviour and inelastic behaviour:

Fel Finel

Fb, el Fb, nl

(2)

Ceccotti and Sandhaas [5] proposed the PGA approach for the determination of the behaviour factor of multi-storey timber structures. In a first step of this approach, the structure is designed by means of the lateral force method for elastic behaviour (q = 1) and a specific peak ground acceleration PGAdesign. Based on that, an analytical model is developed considering realistic hysteretic properties. The analytical model is subjected to a set of ground motion records by means of timehistory analyses, and the peak ground acceleration is scaled until a predefined collapse criterion is reached. This defines the near-collapse peak ground acceleration PGAu. The q-factor is then obtained with

1.2. Behaviour factor – definition

q=

The base shear approach [11]. The PGA approach [13,5]. The ESECMaSE approach [14]. The FEMA P695 approach [15] and. Displacement-based determination [16,17].

q=

PGAu . PGAdesign

(3)

The ESECMaSE approach proposed by Fehling et al. [14] incorporates analytical and experimental investigations on substructures and structural systems to evaluate the behaviour factor. The elastic stiffness of the lateral load-resisting system is derived by means of wall element tests and is applied for the time history analysis of a linear analytical model. The inelastic response is obtained by shaking table tests using the same set of ground motion records considered for the linear time history analysis. The behaviour factor is then defined as the ratio between the base shear from the linear dynamic analysis Fb,el and the base shear obtained from testing Fb,exp.

(1)

The inelastic strength Finel is the one required for the full non-linear or simplified bilinear response of a structure or a structural element under earthquake excitation [12]. The elastic strength Fel is a theoretical value, strictly speaking, since elastic behaviour is only assumed. The definition according to Eq. (1) leaves room for interpretation. Consequently, a handful of different approaches have been proposed to

q=

2

Fb, el Fb, exp

(4)

Engineering Structures 201 (2019) 109711

J. Hummel and W. Seim

Fig. 3. Procedure of the base shear approach (schematic).

spectral acceleration Sa (Tel) for full elastic behaviour can then be read from the elastic response spectrum (see Fig. 4). The spectral acceleration for inelastic response Sa (Tinel) is determined using the CSM. The performance point denotes the maximum acceleration for inelastic behaviour. The capacity spectrum represents the transformed pushover curve. In addition to the spectral acceleration, the modal mass coefficients αel and αinel are required to consider the vibration behaviour which might have changed due the inelastic response. The modal mass coefficients are obtained by using consistent rules for modal transformation (see Section 2). It must be noted here that the fundamental assumption of this approach is that only the first mode of vibration is relevant. The approaches (1) to (4) are all associated with sophisticated and time-consuming dynamic time history analyses. A displacement-based determination of q appears to be more transparent and, by using the backbone-curve, it is strongly connected to real physical behaviour. Displacement-based procedures are adapted in the following to develop a new approach to define and evaluate the behaviour factor. The methodology, together with all relevant parameters, will be explained in Section 2. The application of the procedure is documented with a case study for CLT structures with up to four storeys in Sections 3 and 4.

The fourth approach comes from FEMA P695 [15], which addresses the determination of the response modification factor R, the NorthAmerican equivalent of the q-factor. The methodology starts with the choice of a trial q-factor. The trial behaviour factor is applied to design specific archetypes of building structures. The archetypes are used to evaluate the behaviour factor chosen in terms of its acceptability. The evaluation is similar to trial and error and is based on collapse fragility curves. The fragility curves are generated by means of non-linear time history analyses considering non-linear dissipative behaviour for the archetype structure together with a series of ground motion records. If the preset behaviour factor fulfils the requirements in terms of an acceptable low failure probability, then an adequate R- resp. q-factor is found. If not, then the system must be redesigned with a lower q-value and the procedure repeated. The FEMA P695 approach has already been adapted by Seim et al. [18] to determine the behaviour factor for light-frame timber constructions. A displacement-based determination of the q-factor for masonry structures was first presented by Mistler [17]. The approach is generally a modification of the base shear approach and combines Eqs. (1) and (2) as follows:

q=

Fb, el Sa (Tel )·m ·α el Sa (Tel )·α el = = Fb, inel Sa (Tinel )·m ·αinel Sa (Tinel )·αinel

(5)

2. Methodology

The approach is based on the capacity spectrum method (CSM) [19] and is illustrated in Fig. 4. The elastic period Tel is computed using the initial stiffness. The

The procedure to evaluate q-values based on DBD is depicted in

Fig. 4. Displacement-based determination of behaviour factors (systematic). 3

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Fig. 5. Procedure for the evaluation of the behaviour factor using DBD.

together with the higher strength of the lateral load-resisting system. It should be mentioned that strength and deformation limits for each element have already been checked when the non-linear analysis is carried out determining the capacity curve of the structure.

Fig. 5. The first step of the procedure is the definition of the archetype system, which includes the dimensions of the structure, the structural elements and all connection details. Reference structures are defined for different structural configurations which represent the type of the structure sufficiently (see Section 3.5). The archetype structure must be transferred into an analytical model for linear and non-linear static analyses (see Section 3.6). The seismic action is represented by response spectra. The spectrum in the Sa-T format is used for force-based design and the spectrum in the Sa-Sd format is employed within DBD. Limits of the inter-storey drift can be predefined to account for different performance levels. In the next step, the structure is designed, and the structural model is created to perform pushover analyses. The design of the structure is conducted by means of the lateral force method using a trial behaviour factor. The principles of capacity design must be considered. Based on the design of the structure, the analytical model is created considering the inelastic characteristics of all components and connections as well as other structural characteristics, such as gravity loads. A non-linear static analysis provides the so-called push-over curve, also known as capacity curve (cf. Fig. 2 and Section 4.1). The behaviour evaluation represents the final step of the procedure. Whether the trial behaviour factor is acceptable or not can be evaluated based on the determination of the performance point (PP) using DBD. Acceptance criteria are that:

2.1. Pushover analysis and capacity diagrams Non-linear static analyses – called pushover analyses in the following – are performed to derive the inelastic capacity curve of the structure. In this context, load patterns which represent the seismic forces as external forces must be selected in a first step. The load pattern describes the distribution of the lateral loads Fi over the height of the building. Eurocode 8 [4], ATC-40 [20] and FEMA 440 [21] provide additional information regarding the distribution of these forces. The base shear Fb and the deflection on the top of the building d are recorded and plotted for increasing lateral loads (see Fig. 2). The modal parameters m* and Γ, according to Eqs. (6) and (7), are calculated depending on the horizontal displacements ui in level i

m∗ =

Γ=

∑ mi ·ϕi

m* ∑ mi ·ϕi2

with ϕi = ui / d

(6)

(7)

These parameters are used to transform the capacity curve into the capacity spectrum according to Eqs. (8) and (9).

• performance points do exist, • predefined drift limits are not violated, and • strengths and deformations of each structural component remain

Sa =

Fb m*· Γ

(8)

An acceptable behaviour factor is found if all criteria are fulfilled. Otherwise, the system must be revised, which means a lower q-value

Sd =

d Γ

(9)

within acceptable limits.

4

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2.2. Displacement-based design procedure Different DBD procedures have been developed in the past [19,22–27], However, procedures which employ the response spectrum in the Sa-Sd format are more common in Europe, where the CSM [19] and the N2 method [27] are well-known. The CSM and N2 method use different definitions to convert the elastic response spectrum into the demand spectrum. The CSM applies equivalent viscous damping as a scaling parameter and the N2 method uses a reduction factor depending on ductility and period. This issue has already been discussed in different studies [10,25,27,28]. In the following, the method which is used to create the demand spectrum relates to the CSM and ATC 40 [20]. In this context, it must be stated that CSM has been critically discussed by some researchers. A summary of the advantages and drawbacks of the CSM together with recommendations on how to overcome the drawbacks can be found in FEMA 440 [21]. The main issues to be looked at critically are the accuracy of displacement estimates and the definition of effective damping representing hysteretic energy dissipation. A comprehensive study on the DBD of midrise CLT structures with up to eight storeys [25] shows that the CSM according to ATC 40 [20] leads to strength and displacement demands which are very close to the results from the non-linear time history analysis. Nevertheless, the N2 method will be used as a second method to review the results obtained by the application of the CSM for midrise CLT structures with up to four storeys. The CSM incorporates damped spectra to generate the demand spectrum. Spectral values of the damped spectra are determined by means of the damping correction factor η, see Eq. (10), according to Eurocode 8 [4]. The damping correction factor becomes 1.0 for 5% damping.

η=

10 ⩾ 0.55 with ξ = ξeff (%) 5+ξ

Fig. 6. Definition of equivalent viscous damping ξeq according to ATC 40 [18].

illustrated in Fig. 7. Damped spectra were determined for multiple spectral displacements Sd,Pi of the capacity spectrum. The points of spectral acceleration of each damped spectrum that corresponds to the spectral displacements Sd,Pi are then connected to the transition curve as shown in Fig. 7. The capacity spectrum and demand spectrum are drawn into one diagram. The intersection between the two curves defines the performance point (see Fig. 2). The N2 method is applied for comparison according to Eurocode 8 [4], Annex B. This procedure makes use of a handy relationship for the reduction factor Rµ, see Eqs. (14) and (15), derived for a stiffness-degrading hysteretic model, called Q-model, by Vidic et al. [30]. The suitability of this relationship for timber structures has been discussed critically by some researchers [8,28,31,32].

Rμ = (μ − 1) · (10)

Rμ = μ

Effective damping ξeff [20] is used to account for nominal damping ξ0 and energy dissipation due to inelastic deformations and is computed according to Eq. (11).

ξeff = ξ0 + κ·ξeq

with ξeq =

2 Sa, y·Sd, pi − Sd, y·Sa, pi · π Sa, pi·Sd, pi

Sd =

T2 ·Sae (η) 4·π 2

for T > TC

(14) (15)

The reduction factor depends on the ductility µ and the period T. The transition period is set to the “corner” period TC of the elastic response spectrum according to Eurocode 8 [4]. The ductility available is connected with the capacity curve. The application of the N2 method to CLT structures was discussed in detail by Hummel [25], including all the steps required and definitions of displacement-based design.

(11)

The modification factor κ considers hysteretic behaviour which differ from elastic perfect plastic hysteresis. In case of severely pinchedshaped hysteretic behaviour, which is true for CLT structures, ATC 40 [20] suggests reducing equivalent damping by two third (κ = 0.33). Furthermore, effective damping ξeff has to be limited to 20%. Both has been considered within this study. The spectral acceleration Sa and the spectral displacement Sd of the damped spectrum are given by the Eqs. (12) and (13).

Sa = Sae (η)

T + 1 for T ⩽ TC TC

3. Case studies Case studies will be performed on the wall and the building level to show the interdependency between structural conditions and input parameters. The input parameters required will be defined in Section 3.1 and will be determined and validated in Sections 3.2 to 3.4. The structural system will be defined in Section 3.5 considering different configurations. Seismic design and the development of three-dimensional (3D) structural models will be illustrated in Section 3.6.

(12) (13)

3.1. Definition of input parameters

The parameter Sae represents the spectral acceleration of the elastic response spectrum (cf., Fig. 1). A definition of the initial stiffness Kini, respectively, initial frequency ωini is required for the determination of the yield points Sa,y and Sd,y (see Fig. 6) regarding equivalent viscous damping. It is commonly assumed for timber structures that the deformation behaviour is fairly elastic until 40% of the maximum load-bearing capacity are reached, see, for example, ISO 21581 [29]. This approach has been used to define the initial frequency ωini, as illustrated in Fig. 7. Energy equivalency under the non-linear and the bilinear idealised capacity curve (cf., Fig. 7) was considered in the determination of the yield point. Nominal damping ξ0 is usually considered with 5% as already included in the elastic response spectrum. A transition curve was created to define the demand spectrum, as

Load-displacement characteristics of CLT wall elements are governed by the behaviour of the connections. Both, experimental investigations on connections only and on CLT wall elements with realistic boundary conditions were performed within the scope of the research project Optimberquake [33]. Data which are necessary for non-linear static (pushover) analysis will be derived from the test results of the connections and implemented into a spring model (see Section 3.2). Non-linear springs will be used to account for the load-displacement characteristics of the connections. The suitability of the spring properties will be validated on the wall level by comparing results from testing (see Section 3.3) with results from numerical simulations (see Section 3.4). The SAWS model [34] has been used to consider the non-linear 5

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Fig. 7. Determination of the demand spectrum as a transition curve; example with six sampling points [23].

calculation, does not provide the strength interaction for different loading directions for the spring element selected. Consequently, a comparatively simple approach was taken by reducing the strength in both directions (F1 and F2) by means of a constant factor α, taking into account a rectangular force interaction surface, as shown in Fig. 9. The factor α was iteratively determined by calibrating calculations on the wall level. A total of eight wall elements with different configurations were considered for the calibrating calculations. The factor α was varied in steps of 2.5% until the error in comparison to the behaviour from testing became a minimum. A ‘force interaction factor’ of α = 0.15 was found based on calibrating calculations incorporating the entire hysteretic behaviour – backbone curve and dissipated energy [25].

3.2. Connections In addition to the test results from Optimberquake [39], data from experimental investigations on connections performed by Gavric [40] and Flatscher [41] were included to cover spring properties for a wide range of detailing. Characteristics of hold-downs (HDs) and angle brackets (ABs) are required to predict the non-linear behaviour of CLT wall elements. The HDs and ABs were tested on a rigid base (steel) and an elastic base (CLT) to account for different support conditions in a CLT building. Ring shank nails (ø 4.0 × 60 mm) were used to connect the HDs and ABs to the CLT members. Furthermore, properties for screw connections are necessary to develop the 3D analytical model. The backbone curves presented (see Figs. 10 to 12) represent the first envelope curves of the cyclic

Fig. 8. SAWS hysteretic model according to Folz and Filiatrault [29].

behaviour of connections within numerical analyses. Different researchers, e.g., [25,35], demonstrated that the behaviour of connections of CLT wall elements under both cyclic and monotonic loading can be reproduced by the SAWS model. For this study, only the analytical formulation of the backbone curve is required, which is described by the parameters K0, F0, δu, r1 and r2 (see Fig. 8). Some basic considerations have to be made for the determination of spring properties. The typical connectors used for the anchoring of CLT wall elements exhibit different load-bearing capacities for the two loading directions 1 and 2 (see Section 3.2). Rinaldin and Fragiacomo [36] showed that a circular interaction surface (see Fig. 9) matches the experimental results for biaxial-loaded connections best. However, the analysis software OpenSees [37], which was used for the non-linear

Fig. 9. Force interaction of connectors; (a) definition of load-bearing capacity in loading direction 1 and 2, (b) force interaction surface.

Fig. 10. Backbone curves of angle brackets, comparison of experimental and numerical curves, loading direction 1, anchored on steel (St) and CLT (Ti). 6

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Fig. 11. Backbone curves of angle brackets, comparison of experimental and numerical curves, loading direction 2, anchored on steel (St) and CLT (Ti).

Fig. 13. Boundary conditions of the reference wall elements; vertical load and support conditions.

3.3. CLT wall elements Two monotonic tests and two cyclic tests out of a test series with 15 CLT wall elements [42] were chosen as illustrative examples for the validation of the spring properties. In the case of the cyclic tests the backbone curve (envelope curve) of the hysteresis was used. The complete validation was performed based on the test results of 12 specimens out of the test series with 15 CLT wall elements, see [25]. Two configurations of CLT wall elements were considered. One CLT wall element was connected to a rigid support (steel girder) and the other one to an elastic base (CLT), as shown in Fig. 13. A vertical load of 10 kN/m was applied. The CLT wall elements consisted of layers: three in a vertical direction and two in a horizontal direction. The board thickness was 21 mm with a strength class C 24. The CLT wall elements were anchored by hold-downs and angle brackets, which had been tested separately as single connections (see Section 3.2). The test set-up is depicted in Fig. 14. The figure illustrates where

Fig. 12. Backbone curves of hold-downs, comparison of experimental and numerical curves, loading direction 2, anchored on steel (St) and CLT (Ti).

connections. The spring properties derived for hold-downs, angle brackets and self-tapping screws are documented in Table 1. The abbreviations SCWC-0 and SC-WC-90 refer to the screw connection between perpendicular walls which relate to the connection between the slab and lower wall by means of self-tapping screws (see Section 3.6). Detailed information about the test programme, test set-up, data acquisition, test results and data processing can be found in [39,40,41].

Table 1 Spring properties derived for hold-downs, angle brackets anchored on steel (St) and CLT (Ti) and properties for self-tapping screws.

AB-St-S HD-St-S AB-St-T HD-St-T AB-Ti-S HD-Ti-S1) AB-Ti-T2) HD-Ti-T SC-WC-03) SC-WC-903) SC-WS-03) SC-WS-903) 1) 2) 3)

K0

F0

δu

r1

r2

(kN/mm)

(kN)

(mm)

(–)

(–)

5.36 2.38 14.29 9.64 3.99 2.38 11.79 14.52 2.27 1.29 1.83 1.52

23.2 3.1 9.3 21.4 10.7 3.1 6.9 22.0 7.9 5.6 7.6 5.6

15.0 31.0 16.8 26.0 15.0 31.0 3.0 50.0 23.3 32.0 23.3 31.2

0.170 0.080 0.112 0.180 0.230 0.080 0.130 0.060 0.010 0.015 0.024 0.076

−0.170 −0.170 −0.100 −0.200 −0.500 −0.170 −0.020 −0.071 −0.100 −0.100 −0.075 −0.070

same as HD-St-S assumed. based on test results from Flatscher [34]. based on test results from Gavric [33].

Fig. 14. Test set-up of CLT wall elements. 7

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Friction was also considered by means of the contact spring. A friction coefficient of µ = 0.1 was applied for the rigid support – contact between painted steel and CLT. A friction coefficient of 0.38 was taken into account in the connection between the CLT wall and the CLT slab. It is assumed that kinetic friction applies. The specifications for the contact springs were discussed in detail by Hummel [25] regarding friction and stiffness. The load-displacement curves obtained by means of the numerical simulation are compared with the backbone curves from monotonic and cyclic testing in Fig. 16. It shows that the simulation predicts the loaddisplacement characteristics for two configurations, WCLT-St-10 and WCLT-Ti-10, quite well in terms of stiffness, strength and characteristic load-displacement behaviour. The simulation provides backbone curves which lie between the backbone curves from monotonic and cyclic testing. The sufficiency of the spring properties was also validated for different conditions of the vertical load, see Hummel [25].

Fig. 15. Analysis model for CLT wall elements.

loads and displacements were applied and measured, respectively. The load-displacement curves obtained are shown in Fig. 16. Detailed information about the test set-up, data acquisition, test results and data processing are documented by Seim and Hummel [42].

3.5. Reference structures Reference structures were developed as a basis for numerical simulations on the building level. The floor plan is illustrated in Fig. 17. The reference structures were predesigned in accordance to FEMA P695 [15] considering aspects of building physics, fire safety and usage regarding gravity loads. The dimensions are oriented towards common modular dimensions in Europe. The floor plan was applied to set up a two-storey and four-storey CLT building using a storey height of 2.75 m (see Fig. 20 and Table 2). Comparatively simple and regular reference buildings have been used to show all relevant steps in structural design and the development of the model. Torsional effects have been excluded from the study for reasons of replicability.

3.4. Validation on the wall level A two-dimensional model of the CLT wall was developed by means of the numerical software package OpenSees [37], incorporating different support conditions. The analytical model consists of shell elements with isotropic material properties and discrete springs, as illustrated in Fig. 15. An effective young modulus of 6600 N/mm2 accounts for the layered crosssection of the CLT element [25]. The application of effective isotropic material properties for CLT elements is described, for example, by Blaß and Fellmoser [38]. The Poisson’s ratio was set to 0.3, referring to Pozza et al. [6]. The non-linear behaviour is attributed to the discrete springs, which are denoted in Fig. 15. Springs for hold-downs and angle brackets are described by the parameters in Table 1 using the SAWS model [34]. The quantities K0 and F0 were modified by the ‘force interaction factor’ α of 0.15, according to Eq. (16).

Q mod = (1 − α )·Q

3.6. Design and structural model The number of connectors – hold-downs, angle brackets and screws – which are required was determined by means of force-based design and using a trial behaviour factor (cf., Sections 1.1 and 1.2). This factor was increased stepwise from 2.0 to 3.0 and 4.0. The acceptance check of the trial values is discussed in Section 4. The response spectrum type 1, soil class B [4] and a ground acceleration of ag = 0.25 g were taken to compute the equivalent lateral seismic forces Fi (see Figs. 1 and 19). The structural period T1 was estimated by an empirical formula, as proposed in Eurocode 8 [4] in the initial step. This assumption was always checked by calculating the first period of the 3D model (see Fig. 20) using full modal analysis. The design of the structure was refined until the difference in the structural period between analysis and predesign was less than 5%. The location of the structural periods T1 in the response spectrum is depicted in

(16)

‘Contact springs’ were implemented to allow uplift under tensile forces. The contact stiffness Kc was set to 103 kN/mm for the rigid support. The contact stiffness was adopted to obtain approximately the same deformation in the compression zone as that measured in the test. The elastic contact stiffness Kc was found to be 70 kN/mm.

Fig. 16. Backbone curves from testing of CLT wall elements, monotonic (m) and cyclic (c), compared with results from numerical simulations.

Fig. 17. Floor plan of the reference structure. 8

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one given in the design brochure [45]. In addition, it was considered that also hold-downs have a resistance for shear loading (direction 1). The design value of the shear resistance of the hold-down Fhd,1,Rd is based on test results (see Section 3.2). The characteristic resistance of the screw connection SC-WS was determined according to Eurocode 5 [44] and Blaß et al. [46] for screws with a diameter d of 10 mm and an embedment length lef of 122 mm. The rope effect was taken into account for screws and ring shank nails. The wood density ρ was 350 kg/ m3. Components and connections which exhibit a non-ductile behaviour or should remain elastic were designed with overstrength. Fig. 17 illustrates the design process for the screw connection between the slab and wall. According to the recommendations of Follesa et al. [1], the screw connection between the slab and wall was designed with an overstrength factor of γRd = 1.3. It can be noticed from Fig. 19 that the structural period increases with increasing behaviour factors. This effect is more pronounced for the four-storey structure. As a result, the number of connectors required for each shear wall decreases, especially in the case of the hold-downs (see Table 4). It must be noted that the number of the connectors which were obtained for a q-factor of 4 appears unrealistic. However, it shows the impact of both parameters. The structural model was implemented with shell elements and discrete spring elements, as described in Section 3.4. Shells elements for wall and slab structures and spring elements for connections (see Fig. 20). The thickness of the slab was fixed at 138 mm – with two layers in the X-direction each 21 mm and three layers in the Y-direction each 32 mm (32-21-32-21-32 mm) – based on service limit state provisions. An elastic orthotropic material model was applied to consider the different load bearing behaviour of the slab in the X- and Y-direction. The material properties listed in Table 5 are effective material values and were determined by a ‘back-calculation’ from effective bending and shear stiffness of the layered cross-section for out-of-plane bending according to Thiel [43]. Two configurations of the structure (see Fig. 20a) – ‘shear wall type’ (SWT) and ‘box type’ (BT) – were taken into account within the nonlinear static analysis. The SWT means that perpendicular walls are not connected to each other. In the BT model, perpendicular walls at the wall corner are joined together. Perpendicular walls were connected by self-tapping screws with a spacing of 250 mm in the case of the BT model. The assembling of shells and discrete springs is illustrated in Fig. 20. The connection of the walls to the bottom is the same as that described in Section 3.4. In addition, a linear-elastic spring was considered to prevent the out-of-plane movement of the shear wall at the bottom. A comparatively low stiffness with 1 kN/mm2 was applied here. The parameters documented in Table 1 were applied for the screw connections. Consistent with the springs for anchoring, the spring properties K0 and F0 for the screw connection are modified according to Eq. (16). The stiffness in tension and compression of the connection between the slab and lower wall was considered by an additional spring with non-symmetric elastic behaviour. The compression stiffness Kn accounts for the contact (see Section 3.4). The tensile stiffness Kt is the withdrawal stiffness of a self-tapping screw. The withdrawal stiffness was determined according to Blaß et al. [46] using the same parameters as those for the determination of the resistance (see above). The mean value of 420 kg/m3 was applied as wood density ρ.

Table 2 Data of the reference structures. Length in X-direction Length in Y-direction Storey height Number of Walls × wall length in X-direction in Y-direction Gravity loads Dead load Live load Dead load walls

12.50 m 7.50 m 2.75 m 6× 4× Roof slab 1.0 –

2.50 m 2.50 m Floor slab 3.0 kN/m2 1.5 kN/m2 1.5 kN/m2

Fig. 19.

Fb = Sa (T1)·m ·λ

(17)

The spectral acceleration Sa follows from the response spectrum (Fig. 19), depending on the period and the behaviour factor. The parameter m stands for the total mass of the structure as the sum of the lumped masses in each floor (see Table 6). The modal correction factor λ is 1.0 for the two-storey structure and 0.85 for the four-storey structure, according to Eurocode 8 [4]. The lateral seismic forces Fi were determined by distributing the base shear Fb, calculated according to Eq. (17), proportional to the mass and the height of the structure, see Eq. (22). The lateral load for each shear wall Fj in each level was obtained by Table 7.

Fj =

Fi nw

(18)

assuming equal lateral stiffness of all shear walls in the direction considered. The number of walls nw is six in the X-direction and four in the Y-direction, as illustrated in Fig. 15. The shear force V and the tensile force Z (cf., Fig. 17) were calculated from the lateral loads in each level to design the connections. It should be noted that the vertical load p from the dead load was considered in the determination of the tensile forces. Design values for the resistance of the connectors were used to determine the number of connectors. FRd was determined according to Eq. (19), with a modification factor of kmod = 1.1 and a partial factor of γM = 1.0, as defined in Eurocode 5 [44], for a very short load-duration and the accidental combination, respectively.

FRd = k mod ·

FRk γM

(19)

The characteristic and design values of the connector resistance required for the seismic design of the structure are summarised in Table 3. The resistance of the connectors depends on the load-bearing capacity of the ring shank nails. The characteristic shear resistance of a ring shank nail (ø 4.0 × 60 mm) was calculated according to Eurocode 5 [44]. According to the manufacturer’s information [45], the steel plates are considered as thick. It should be noted that the resulting characteristic resistance FRk of the connectors is slightly higher than the Table 3 Characteristic and design values of resistance of the connector. nf (wall / slab) AB-St AB-Ti HD-St HD-Ti SC-WS 1) 2) 3)

14 nails/2 14 nails/7 17 nails/1 17 nails/1 1 screw

1)

bolts nails bolt1) bolt1)

F1,Rk

F2,Rk

F1,Rd

F2,Rd

(kN)

(kN)

(kN)

(kN)

– – 32.82) 32.82) –

29.7 14.9 5.0 5.0 5.0

– – 36.1 36.1 –

2)

27.0 13.52) – – 4.53)

Kt = 234·(ρ ·d )0.2 ·lef0.4

(20)

It must be noted that friction was not taken into account for the simulations on the building level. Structural masses were concentrated to the centre of the slab, which is also the point where horizontal loads have been applied in each level (see Fig. 18), for the determination of capacity curves and capacity

Bolts provide sufficient overstrength. According to Eurocode 5 [37], rope effect considered. According to Blaß et al. [39], rope effect considered. 9

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J. Hummel and W. Seim

Table 4 Number of connectors for each shear wall and different trial behaviour factors of the four storey SWT structure. q = 2.0

Final period T1 (s) Spectral value Sa (m/s2) Base shear Fb (kN) Connectors in level 4 3 2 1

q = 4.0

X

Y

X

Y

0.58 3.17 384.7

0.68 2.72 329.6

0.78 1.18 143.0

0.85 1.08 131.2

1 2 2 2

1 2 2 2

1 1 1 1

AB, 2 × 1 HD ABs, 2 × 1 HD ABs, 2 × 3 HDs ABs, 2 × 4 HDs

AB, 2 × 1 HD ABs, 2 × 2 HDs ABs, 2 × 4 HDs ABs, 2 × 5 HDs

AB, AB, AB, AB,

2×1 2×1 2×1 2×1

HD HD HD HD

1 1 1 1

AB, AB, AB, AB,

2×1 2×1 2×1 2×2

HD HD HD HDs

HD – hold-downs located at the ends of the wall. AB – angle brackets uniformly distributed between hold-downs along the wall length. Table 5 Material properties for the slab. Ex

Ey

Ez

Gxy

Gyz

Gzx

vxy

vyz

(N/mm2) 1540

9460

11,000

vzx

(–) 70

70

150

0.3

0.3

0.3

Table 6 Lumped masses mi. Level of

Roof slab

Floor slab

mi (ton)

14.9

42.6

Table 7 Performance point check. Type

X-direction SWT BT Y-direction SWT BT

Fig. 19. Elastic response spectrum, design spectra and periods of the shear wall type structure.

q = 2.0

q = 3.0

q = 4.0

2S

4S

2S

4S

2S

4S

Pass Pass

Pass Pass

Pass Pass

Pass Pass

Fail Fail*

Fail Fail*

Pass Pass

Pass Pass

Pass Pass

Pass Pass

Fail Fail

Fail Fail

spectra (see Section 4.1). The masses of the walls were added to the mass of the slab. The quasi-permanent gravity loads were applied to determine the mass m according to Eq. (21).

m = (Gk + ψE ·Qk ) / g

with ψE = φ ·ψ2 = 0.8·0.3

(21)

Gk and Qk stand for the dead load and live load, respectively (see Table 2). The gravity constant g was taken into account at 9.81 m/s2. The combination coefficients φ and ψ2 were chosen in accordance with Eurocode 8 [4] and Eurocode 0 [47], respectively. The resulting lumped

* Performance point coincides with the drift limit.

Fig. 18. Action and reactions on the wall level and capacity design of the screw connection between wall and slab. 10

Engineering Structures 201 (2019) 109711

J. Hummel and W. Seim

Fig. 20. Three-dimensional model; (a) implementation of the two-storey structural model, (b) four-storey model (schematic).

the BT. Connecting perpendicular walls leads to an increase of the lateral resistance and even the deformation capacity under lateral action. It can also be observed by means of the capacity curves that the design with increasing q-factors leads not only to a decrease of the lateral resistance, but also to a reduction of the deformation capacity considering the point of the ultimate load. The latter might contradict what is expected. Nevertheless, the loss of deformation capacity can be traced back to the lower number of connectors, the contributions to the overall deformation and three-dimensional effects. The required number of connectors decrease with increasing q-factors, as illustrated in Table 4, which leads to a loss of deformation capacity due to threedimensional wall-slab interaction. The point where the inter-storey drift of 2% was reached is denoted in Figs. 21 and 22. This value was defined as an acceptance criterion for the evaluation of the behaviour factor (see Section 2).

masses are summarized in Table 6. 4. Results from DBD and evaluation 4.1. Capacity and performance points A linear distribution of the lateral forces was applied for the following calculations of the capacity curve. The load pattern is proportional to mass mi and height zi:

Fi = Fb·

z i · mi ∑ z j · mj

(22)

However, it must be noted that load patterns different from the linear distribution should also be considered for design purposes. It was demonstrated by Hummel [25] that the linear pattern yields reasonable results if the height of the CLT structure does not exceed four storeys. It was found that the uniform load pattern – constant distribution of the lateral loads – reflects the distribution of inertia forces of the CLT structure with eight storeys more sufficiently. The capacity curves and capacity spectra of the two-storey and fourstorey structure are shown in Figs. 21 and 22. The capacity curves are obviously different between the SWT and

4.1.1. Performance point Examples of the graphical determination of the performance point are illustrated for three structural configurations in Fig. 23. It can be observed that different performance points were found depending on the presumed q-factor applied for seismic design with the lateral force method. Performance points were obtained even for q = 4.0. On the

Fig. 21. Capacity curves for the X-direction for different levels of the trial behaviour factor, shear wall type (SWT) and box type (BT); (a) two-storey structure, (b) four-storey structure. 11

Engineering Structures 201 (2019) 109711

J. Hummel and W. Seim

Fig. 22. Capacity spectra for the X-direction for different levels of the trial behaviour factor, SWT and BT; (a) two-storey structure, (b) four-storey structure.

Fig. 23. Performance points for reference structures in the X-direction; (a) two-storey SWT structure, (b) two-storey BT structure and (c) four-storey SWT structure. 12

Engineering Structures 201 (2019) 109711

J. Hummel and W. Seim

Fig. 24. Performance points for SWT structure in the X-direction; comparison of CSM and N2 method.

Both methods (CSM and N2) appear to be applicable for the assessment of q-values, at least for CLT structures up to four storeys as considered in this study. Nevertheless, in this study, results from the CSM are taken to check the trial behaviour factors for their acceptance.

other hand, the structure appears to be considerably overdesigned if a behaviour factor of 2.0 is applied. The two DBD procedures, the CSM and N2 method, can be compared with reference to the performance points. Fig. 24 shows that the performance points of both methods are very close. The N2 method provides slightly higher spectral displacements than the CSM in only a few cases. The spectral accelerations differ little overall. 13

Engineering Structures 201 (2019) 109711

J. Hummel and W. Seim

the methodology proposed. Based on the results of the study, it must be stated that a behaviour factor higher than 3.0 can hardly be reached for CLT structures with up to four storeys and this might apply even for taller CLT buildings. However, the behaviour might be completely different for CLT structures with multiple stories due higher-mode and overstrength effects. The study does not consider different dimensions of walls, especially longer walls, and torsional deformable buildings, which clearly affect the behaviour factor. However, the behaviour factor found in this study defines some sort of an upper bound value, since the effects mentioned above lead more to a decrease than increase of the behaviour factor.

4.2. Derivation of behaviour factors Performance points were determined for a total of 24 different structural configurations – two- and four-storey SWT and BT structures in the X- and Y-direction (see Table 6). These performance points are now used to check the trial behaviour factors for their acceptance. Therefore, a performance level needs to be defined regarding performance-based seismic design. The definition used in this study is the limitation of the inter-storey drift, which was set to 2% of the storey height to satisfy damage limitation requirements and to exclude P-Δeffects according to Eurocode 8 [4]. This drift limit is marked in Figs. 21 to 23. All performance points which provide smaller spectral displacement than the drift limit satisfy the performance point check. Table 6 documents the assessment of all performance points. The performance points fulfil the requirements of the inter-storey drift in two-thirds of cases. In the case of q = 4.0, the performance point check failed for all structural configurations. However, the performance points coincide with the drift limit for the BT structure in the X-direction. This is exemplarily shown in Fig. 23b. A behaviour factor of 4.0 obviously does not appear to be sufficient for seismic design of CLT structures regarding force-based design. However, a behaviour factor of 3.0 could be confirmed by means of this procedure.

Declaration of Competing Interest The authors declared that there is no conflict of interest. References [1] Follesa M, Fragiacomo M, Lauriola MP. A proposal for revision of the current timber part (section 8) of Eurocode 8 Part 1. Alghero, Italy: CIB W18 Meeting 44; 2011. [2] Tannert T, Follesa M, Fragiacomo M, Gonzalez P, Isoda H, Moroder D, et al. Seismic design of cross-laminated timber buildings. Wood Fiber Sci 2018;3–26. [3] Rodrigues LG, Branco JM, Neves LA, Barbosa AR. Seismic assessment of a heavytimber frame structure with ring-doweled moment-resisting connections. Bull Earthq Eng 2018;1341:1371–416. [4] EN 1998-1. Eurocode 8: design of structures for earthquake resistance – Part 1: general rules, seismic actions and rules for buildings. Brussels: European Committee for Standardization; 2010. [5] Ceccotti A, Sandhaas C. A proposal for a standard procedure to establish the seismic behaviour factor q of timber buildings. Trentino, Italy: Proceedings of the 11th World Conference on Timber Engineering; 2010. [6] Pozza L, Scotta R, Vitaliani R. A non linear numerical model for the assessment of the seismic behaviour and ductility factor of X-lam timber structures. ,. Istanbul, Turkey: Proceeding of international Symposium on Timber Structures; 2009. [7] Pozza L, Scotta R, Trutalli D, Polastri A. Behaviour factor for innovative massive timber shear walls. Bull Earthqu Eng 2015;13:3449–69. [8] Fragiacomo M, Dujic B, Sustersic I. Elastic and ductile design of multi-storey crosslam massive wooden buildings under seismic actions. Eng Struct 2011;33:3043–53. [9] Hummel J, Seim W. Assessment of dynamic characteristics of multi-storey timber buildings. Vienna, Austria: Proceedings of the 14th World Conference on Timber Engineering; 2016. [10] Hummel J, Seim W. Performance-based seismic design of light-frame structures – proposed values for equivalent hysteretic damping. Croatia: INTER meeting Šibenik; 2015. [11] Popovski M, Karacabeyli E, Ceccotti A. CLT handbook – cross laminated timber. Chapter: Seismic performance of cross-laminated timber buildings. FPInnovations; 2011. [12] Kappos A. Evaluation of behaviour factors on the basis of ductility and overstrength studies. Eng Struct 1999;21:823–35. [13] Salvitti L, Elnashai A. Evaluation of behaviour factors for RC buildings by nonlinear dynamic analysis. Acapulco, Mexico: 11th World Conference on Earthquake Engineering; 1996. [14] Fehling E, Stürz J, Aldoghaim E. Identification of suitable behaviour factors for masonry members under earthquake loads (deliverable 7.3). Technical report of the collective research project: Enhanced Safety and Efficient Construction of Masonry Structures in Europe (ESECMaSE). University of Kassel, Institute of Structural Engineering, Chair of Structural Concrete; 2008. [15] FEMA. P695. Quantification of building seismic performance factors. Washington, DC: Federal Emergency Management Agency, FEMA; 2009. [16] Krawinkler H, Seneviratna G. Pros and cons of a pushover analysis of seismic performance evaluation. Eng Struct 1997;20:452–64. [17] Mistler M. Verformungsbasiertes seismisches Bemessungskonzept für Mauerwerksbauten. Dissertation. Technischen Hochschule Aachen 2006. [18] Seim W, Kramar M, Pazlar T, Vogt T. OSB and GFB as sheathing materials for timber-framed shear walls: comparative study of seismic resistance. J Struct Eng 2015:1–14. [19] Freeman SA. The capacity spectrum method as a tool for seismic design. Proceedings of the 11th European conference on earthquake engineering; 1998. p. 6–11. [20] ATC-40. Seismic evaluation and retrofit of concrete buildings. Applied Technology Council Volume 1. California Seismic Safety Commission; 1996. [21] FEMA. 440. Improvement of nonlinear static seismic analysis procedures. Redwood City: Federal Emergency Management Agency, FEMA; 2009. [22] Priestley M. Performance based seismic design. Bull NZ Soc Earthqu Eng 2000;33:325–46. [23] Priestley M, Calvi G, Kowalsky M. Direct displacement-based seismic design of structures. 2007 NZSEE Conference; 2007. [24] Filiatrault A, Folz B. Performance-based seismic design of wood framed buildings. J Struct Eng 2002;128:39–47.

5. Summary and outlook A DBD based procedure for the evaluation of the behaviour factor q for multi-storey CLT buildings has been presented. Therefore, CLT structures with two and four storeys were considered. The influence of different structural configurations on the seismic performance was studied by means of SWT and BT structures. It could be demonstrated that the BT structure exhibits a higher load-bearing and deformation capacity compared with the SWT structure. Performance points were determined for the different CLT structures by means of the DBD using the CSM and N2 method by comparison. The structures were designed for trial behaviour factors of 2.0, 3.0 and 4.0. The successful detection of a performance points and a predefined drift limit of 2% of the storey height were taken as acceptance criteria. A behaviour factor of 3.0 could be confirmed for all CLT structures considered in this study. The limitations of the CSM as stated by different researchers were addressed (see Section 2). However, it was found that the results using the CSM and the N2 method by comparison are very close. The procedure appears to be transparent and might be customised or extended: different types of elastic response spectra, for example, can be applied depending on national and international regulations. Even spectra from real earthquake records can be incorporated. Thus, the variability of ground motion records can be considered in the evaluation process comparatively easily. Furthermore, other DBD procedures, such as the N2 method according to EC 8 or methods according to FEMA 440 [21], might be applied to determine the performance point. Even dynamic effects, such as higher mode contribution, can be included in this way. Moreover, other performance levels in terms of inter-storey drift limit can be considered to evaluate the behaviour factor. Furthermore, it is expected that the procedure can also be employed for other types of lateral load-resisting systems, such as light-frame shear walls and other structural configurations. Various ways of coupling between lateral load resisting systems and diaphragms and different gravity load resisting systems might be incorporated by defining the system (see Fig. 5). Further influences which were not discussed in this paper, such as friction, should be considered in future studies on the evaluation of the behaviour factor of multi-storey CLT buildings. It was demonstrated in this paper that reasonable behaviour factors can be found by means of 14

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software framework. Version 2.4.6. http://opensees.berkeley.edu/. [38] Blaß HJ, Fellmoser P. Design of solid wood panels with cross layers. Lahti, Finland: Proceedings of the 8th World Conference on Timber Engineering; 2004. [39] Seim W, Hummel J, Vogt T. Optimberquake Deliverable 2C: Anchoring units – monotonic and cyclic testing. Department of Structural Engineering, Building Rehabilitation and Timber Engineering, University of Kassel; 2013. [40] Gavric I, Fragiacomo M, Ceccotti A. Cyclic behaviour of typical metal connectors for cross-laminated (CLT) structures. Mat Struct 2015;48:1841–57. [41] Flatscher G, Schickhofer G. Verbindungstechnik in BSP bei monotone und zyklischer Beanspruchung. Statusbericht TU Graz. Graz, Austria: Proceedings of the 9th Grazer Holzbau-Fachtagung; 2011. [42] Seim W, Hummel J. Optimberquake Deliverable 2D: CLT wall elements – monotonic and cyclic testing. Department of Structural Engineering, Building Rehabilitation and Timber Engineering, University of Kassel; 2013. [43] Thiel A. ULS and SLS design of CLT and its implementation in the CLT designer. Graz, Austria: The state-of-the-art in CLT research. COST Action FP1004: Focus Solid Timber Solutions – European Conference on Cross Laminated Timber (CLT); 2013. [44] EN 1995-1-1. Eurocode 5: Design of timber structures – Part 1-1: General – Common rules and rules for buildings. Brussels: European Committee for Standardization; 2010. [45] Simpson Strong Tie. Profilkatalog – Qualitätsverbinder für Holzkonstruktionen 2014. [46] Blaß HJ, Bejtka I, Uibel T. Tragfähigkeit von Verbindungen mit selbstbohrenden Holzschrauben mit Vollgewinde. Technical report. University of Karlsruhe; 2006. [47] EN 1990. Eurocode 0 – basis of structural design. Brussels: European Committee for Standardization; 2002.

[25] Hummel J. Displacement-based seismic design for multi-storey cross laminated timber buildings. Dissertation. University of Kassel; 2017. [26] Fajfar P. A nonlinear analysis method for performance-based seismic design. Earthq Spectra 2000;16:573–92. [27] Fajfar P. Capacity spectrum method based on inelastic spectra. Earthquake Eng Struct Dynam 1999;28:979–93. [28] Amadio C, Rinaldin G, Fragiacomo G. Investigation on the accuracy of the N2 method and the equivalent linearization procedure for different hysteretic models. Soil Dyn Earthq Eng 2016;83:69–80. [29] ISO 21581. Timber structures – Static and cyclic lateral load test method for shear walls 2010. [30] Vidic T, Fajfar P, Fischinger M. Consistent inelastic design spectra: strength and displacement. Earthqu. Eng. Struct. Dyn. 1994;23:507–21. [31] Hummel J, Seim W. N2 method – adaption to CLT structures. Seoul, South Korea: Proceedings of the 15th World Conference on Timber Engineering; 2018. [32] Mergos P, Beyer K. Displacement based seismic design of symmetric single-storey wood-frame buildings with the aid of N2 method. Front. Built Environ. 2015;1. [33] Optimberquake. Optimization of timber multi-storey buildings against earthquake impact. http://www.optimberquake.eu. [34] Folz B, Filiatrault A. Seismic analysis of woodframe structures. I: Model formulation. J Struct Eng 2004;130:1353–60. [35] Aranha C, Branco JM, Lourenco PB, Flatscher G, Schickhofer G. Finite element modelling of the cyclic behaviour of CLT connectors and walls. Vienna, Austria: Proceedings of the 14th World Conference on Timber Engineering; 2016. [36] Rinaldin G, Fragiacomo M. Non-linear simulation of shaking-table tests on 3-and 7storey X-Lam timber buildings. Eng Struct 2016;113:133–48. [37] OpenSees. Open System for Earthquake Engineering Simulation, an object-oriented

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