The Link Frame Model (LFM), a tool for the seismic analysis of timber frame buildings considering system effects

The Link Frame Model (LFM), a tool for the seismic analysis of timber frame buildings considering system effects | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article The Link Frame Model (LFM), a tool for the seismic analysis of timber frame buildings considering system effects Nicol López, Sebastián Berwart, Pablo Guindos This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4643226/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 04 Feb, 2025 Read the published version in European Journal of Wood and Wood Products → Version 1 posted 11 You are reading this latest preprint version Abstract This article proposes a model that makes possible the seismic analysis of timber frame multistory buildings in general-purpose software. The model is entitled Link Frame Model (LFM) and shows the following advantages in comparison to previous models: (1) it can model shearwalls only with frame elements and links with errors close to 0% with respect to analytical code models such as e.g. the Special Design Provisions for Wind and Seismic (SDPWS); (2) it can be used for both equivalent lateral force procedures and modal spectral analysis and gravitational calculations; (3) the computation of the natural period shows deviations close to 0% in comparison with eigenvalues and eigenvectors; (4) it can be implemented in general purpose structural analysis software such as e.g. ETABS or SAP2000; and (5) building system effects, i.e. interaction of shearwalls with other assemblies, can optionally be captured if assigning the proper diaphragm out-of-plane flexural stiffness. Given the great impact of this last aspect in practical design, and the lack of its research, this paper does not only present the model and validation itself, but also analyzes the consequences of considering system effects in a representative case study building. The analysis demonstrates that the average shearwall tension (uplift) of regular buildings can decrease by 80% if considering system effects, which could make timber buildings much more cost competitive in seismic countries. timber building multistory building modelling simulation structural analysis seismic analysis system effect Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 Figure 11 Figure 12 Figure 13 Figure 14 1. Introduction The lateral systems based on wood shearwalls have in general demonstrated good seismic performance, as reported in post-earthquake damage reports (Osteraas et al., 2000 ) and in iconic shake table tests (Ceccotti et al., 2013 ; Pei et al., 2010 ; Quizanga et al., 2024 ). This, along with the inherent sustainability and lightness of the material, has triggered an increasing interest on using wood in seismic-prone countries such as Chile, New Zealand, Japan, Canada, Italy, and the USA, among others. Nowadays, given the current context of urban population concentration (Mishra et al., 2022 ), there is an increasing interest in using timber for medium and tall buildings. However, the design of medium rise and tall timber buildings in seismic areas presents several challenges, one of great importance relates to the difficulty of setting up a reliable calculation model. In this context, various modeling design, and construction guidelines have been developed, such us (Chen et al., 2022 ) and (Karacabeyli & Lum, 2022 ), with the aim of establishing concepts, parameters, and requirements for a tall timber building. Light wood frame construction system is dominant for single and multi-family low-rise housing. This system consists of lumber framing and wood-based sheating connected to each other with metal fasteners. These buildings have typically been designed using manual calculations or spreadsheets. The increasing interest in taller buildings entails more complex modelling techniques (Chen et al., 2022 ). The difficulty arises because the analytical procedures prescribed in standards are based on very simplistic assumptions (American Wood Council, 2020 ; Canadian Standard Association CSA O86-14, 2014 ; European Standard, 2004 ), which are difficult to model. For instance, three assumptions that pose modelling challenges are: (a) shearwalls in standards are idealized as cantilever beams; (b) overturning is not restricted and can accumulate between floors and (c) axial load does not significantly contribute to deformation. While these assumptions have eased the hand calculations of low-rise buildings, they may greatly overestimate deformations of medium and tall buildings, and eventually turning unconservative by underestimating equivalent lateral stiffness and thus lateral design forces. The timber construction codes, under the aforementioned assumptions, present the calculation of individual walls and do not consider system effects. There is evidence showing that the three-dimensional interaction of lateral assemblies with each other has significant impact in practice; a review of the state of the art is provided in the following section. In reality, shearwalls not work individually and interact with transverse shearwalls, diaphragms, and axial loads such that additional stiffening and restraining of uplift is evidenced. Since most models cannot capture and elucidate such effects, it endures the difficulty of critically assess the drawbacks of current codes for the lateral design of timber buildings. Another challenge is that general purpose software commonly does not include specific modelling tools for timber, and timber assemblies are physically complicated since they are composed of many components joined together (framings, nails, sheathing, anchors, etc.). This difficulty further hampers the establishment of standardized modelling procedures for seismic calculation of timber buildings. Thus, there is a need of consistency on how to model a wood building in a way that accurately represents the code analytical methods, it can be built-in general-purpose software, and it is sufficiently simplified for practical use. In this context, the objective of this research is proposing a simplified model of timber frame buildings applicable in general-purpose software, that encompasses seismic code requirements, and allows for considering system effects if desired. The article is organized by first reviewing previous models and system effects in timber buildings, then proposing and validating a modelling approach termed as Link Frame Model (LFM), both at shearwall and entire building levels, and finally exploring the consequences of considering system effects in a representative case study building. 2. Code standards and state of the art of timber buildings lateral calculation General overview of standards The Special Design Provisions for Wind and Seismic standard (American Wood Council, 2020 ) is based on controlling the lateral deflection of an individual wall, given by the bending of the edge studs, shear of the sheathing and nailing pattern, and overturning due to anchorage. This expression in SI units is presented in Eq. 1, where L and H are the length and height of the wall, E and Aext are the modulus of elasticity and area of the edge studs, \({G}_{a}\) is the apparent shear stiffness, \({\varDelta }_{anchorage}\) is the uplift of the anchorage, and v is the shear per unit length. The 2008 version splits the shear component into the sheathing stiffness and nail deformation. \(\delta ={\left(\frac{2\bullet v\bullet {H}^{3}}{3\bullet E{\bullet A}_{ext}\bullet L} \right)}_{Flexure}+{\left(\frac{v\bullet H}{{G}_{a}}\right)}_{Shear}+{\left(\frac{H\bullet {\varDelta }_{achorage}}{L}\right)}_{Overturning}\) Eq. (1) The Canadian Standards Association O86 standard (Canadian Standard Association CSA O86-14, 2014 ) calculates lateral deflection based on the same components as the 2008 SDPWS. This expression is presented in Eq. 2, where \({B}_{v}\) corresponds to the sheathing stiffness and \({e}_{n}\) is the nail deformation. Hence, lateral deflection according to the US and Canadian standards represents the same concept. \(\delta ={\left(\frac{2\bullet v\bullet {H}^{3}}{3\bullet E{\bullet A}_{ext}\bullet L} \right)}_{Flexure}+{\left(\frac{v\bullet {H}_{s}}{{B}_{v}}\right)}_{Shear, sheathing}+{\left(\text{0,0025}{H}_{s}{e}_{n}\right)}_{Shear,nails}+{ \left(\frac{H\bullet {\varDelta }_{anchorage}}{L}\right)}_{Overturning}\) Eq. (2) Eurocode 8 (European Standard, 2004 ) analytically determines the capacity of a shearwall based on its geometry and connectors and does not present an equation for lateral deflection. In the upcoming version (Boggian et al., 2020 ), there will be a proposal that includes the contribution of six terms: deformation due to nail slip, deformation of the studs, rotation due to anchor elongation, translation due to horizontal base displacement, deformation due to perpendicular sole plate compression, and deformation due to shear in the sheathing panel. The chilean standard of timber design NCh 1198 (Instituto Nacional de Normalización, 2014 ), in its current form does not even include any methodology for shearwall calculations. However, the future version will likely include a methodology similar to that proposed in the USA. The Chilean standard of general seismic design provisions NCh 433 (Instituto Nacional de Normalización, 2009 ) sets a response modification factor R = 5.5 for timber buildings and a maximum inter-story drift of 2‰ regardless of the building construction material. This code delineates two seismic design methodologies, static and modal spectral analyses, with their application depending on the number of floors and building characteristics. In the case study building, a static analysis will be conducted. Cumulative overturing Bagheri and Doudak ( 2021 ) investigated the behavior of multi-story light-frame walls, including the effect of out-of-plane diaphragm stiffness. Considering cumulative effects and without out-of-plane diaphragm stiffness, the estimated deflection closely approximated that observed in the experimental study. It was concluded that the accumulated bending is insignificant, unlike the accumulated overturning. Rossi (2016) conducted a seismic analysis of wood platform-frame buildings and assessed the lateral deflection of a multi-story wall. The wall model consisted of three linear elastic springs in series: an anchorage system, shear connectors, and sheathing with a nailing pattern. It was concluded that overturning is relevant for multi-story walls and depends on the active or inactive state of the anchors due to vertical loading. In Canadian Standard Association CSA O86-14 ( 2014 ) an expression is provided for the deflection of a multi-story wall, considering the cumulative effects of bending and overturning. The deflection due to accumulated overturning at level i is shown in Eq. 3, where \({a}_{j}\) represents the angle of deformation of the story j and \({\left({d}_{a}\right)}_{j}\) represents the total vertical elongation of the anchor system to the wall on the j floor. $${\varDelta }_{a,i}^{storey}={H}_{i}\left(\sum _{j=1}^{i}{a}_{j}\right)={H}_{i}\bullet {a}_{i}+{H}_{i}\left(\sum _{j=1}^{i-1}{a}_{j}\right){a}_{j}=\frac{{\left({d}_{a}\right)}_{j} }{L} \text{E}\text{q}. \left(3\right)$$ System effects While the cumulative effects of overturning are significant from the theoretical standpoint, only individual walls rotate freely, and it is expected that they would experience larger displacements than in a wall system like those of real buildings. In buildings, the interaction between the diaphragm and walls hinders overturning, an aspect not addressed in regulations. Valdivieso (2024) investigated the effects of transverse shear walls, out-of-plane bending stiffness of diaphragms, and axial loading on the lateral response of light frame shear walls. Through experimental tests, it was observed that the stiffness and strength of the shear walls increased when considering these aspects. Dolan (1989) studied perpendicular walls to enhance design without anchorages. Experimentally, it was demonstrated that transverse wall segments reduce uplift and enhance capacity and ductility compared to unrestricted walls. In the NEESWood Project, seismic tests on a 6-story timber structure showed one side of the building being in tension and the other in compression (Pei et al., 2010 ). This effect was attributed to the edge conditions of perpendicular walls acting as a restraint against overturning. Ruggeri (2023) modeled the interaction between perpendicular CLT walls. It was concluded that the increase in lateral capacity depends on the position and connection of the transverse wall. The effect is more pronounced in the tension zone than the central zone and does not contribute to the compression zone. Foliente (2000) conducted full-scale tests on a one-story house to study how the diaphragm and transverse walls affect load distribution. Shared loading was observed in the system attributed to the transverse walls. Additionally, it was concluded that the stiffness of individual walls is underestimated by up to 80%. Hopkins (2014) evaluated shear walls with perpendicular walls. The stiffness, strength, and capacity increased compared to individual walls, with a significant influence from the connection. Bagheri and Doudak ( 2021 ) investigated how out-of-plane diaphragm stiffness influences shear walls. When the diaphragm was flexible, walls rotated freely, and cumulative effects occurred. In contrast, these effects were absent with out-of-plane stiffness, reducing deflection by an average of 80%. Even conservative estimates of stiffness led to a significant reduction in deflection. Girhammar y Källsner (2006) studied the behavior and capacity of partially anchored shear walls considering three-dimensional behavior. Through theoretical and experimental analysis, it was demonstrated that properly connected transverse walls act as anchors. Kochkin y McKee (2001) numerically and experimentally studied the lateral response of shear walls with and without anchors, along with corner walls. The transverse walls generated a confinement effect, increasing capacity and reducing wall ductility, altering the failure mode. In summary, there is substantial evidence of the relevance of three-dimensional effects in force distribution, deformations, and overturning. Nevertheless, current recommendations focus on subsystem behavior and overlook system-level effects. Axial loading effects Regarding axial load, international standards often do not explicitly detail whether it should be considered in lateral deflection calculation. When they do, they establish a safety factor to not account for its entirety. Rossi (2016) indicated that overturning, among other factors, depends on the active or inactive state of the anchor, which in turn relies on the relationship between tension and axial load at the anchor. Orellana (2021) tested shear walls subjected to axial load and moment for lateral behavior. An increase in stiffness, strength, and energy dissipation was observed, which could be attributed to a change in wall kinematics due to a reduced contribution of overturning in deformation. Simplified models proposed by researchers Cárcamo ( 2017 ) presented a model of platform frame walls using equivalent area elements (shells) within a finite element program. The equivalent modulus of elasticity and shear were calculated based on an equivalence between the platform frame wall and a homogeneous isotropic wall. The results showed that the model's accuracy depends on mesh sensitivity: lateral displacement is better represented with a finer mesh, while axial displacement is optimal without mesh divisions. The model did not account for vertical uplift due to anchorage and was not explored for multi-story walls being directly implemented in a building. González ( 2019 ) proposed a method that involves applying modification factors to the rigidities acting in the wall plane. The coefficients were derived by equating the stiffness from (American Wood Council, 2020 ) with the stiffness of a cantilever wall. A correction factor was also proposed based on the average error between theoretical and model stiffness. The model was sensitive to meshing and did not consider cumulative effects. Vogrinec (2016) proposed a model consisting of a simple braced frame with a fictitious diagonal. The diagonal section was determined from the shear and bending stiffness of a cantilever beam, the stiffness due to perpendicular bottom plate compression, and the stiffness of the anchorage. The model did not address loading in the opposite direction, was not validated for walls taller than one story, and did not accommodate vertical displacement. Chen (2014) presents a model composed of three boundary-framing members, one diagonal hysteretic spring, and two vertical translational spring. The model allows for lateral and rotational deformation, and was developed in ABAQUS, software that is not commonly used in practice. Furthermore, since there is only one diagonal, it supports lateral loading in one direction. Moroder (2015) studied the role of the floor diaphragm in lateral resistance and proposed a strut-and-tie model. The method involved assigning equivalent stiffness and area to elements, where the diagonal depends on the sheathing and connector properties, and the frame properties depend on the framing. The model approximates the stresses, forces, and deformations and applies to various geometries. Detailed models proposed by researchers Estrella (2020) modeled the nonlinear behavior of walls under large displacement demands in M-CASHEW and conducted 12 full-scale tests. The model represented studs using frame elements, OSB using shell elements, and connectors using link elements. Nails were modeled as nonlinear hysteretic springs. While the model provided information about the response of each element, it required a significant computational cost. Estrella (2020) also proposed a simplified model for practical implementation of nonlinear time history modeling. By calibrating a one-degree-of-freedom nonlinear spring with experimental data in MSTEW, it was determined that such a spring could adequately capture the nonlinear behavior of the wall. The model allowed predicting the cyclic response of walls with the same properties and different lengths. Malesza ( 2017 ) introduced a wall model using shell elements, which condensed at the edges to represent panel-structure connectors. Modelling parameters were obtained from experimental tests. This approach allowed for solving specific problems within a building, but a comprehensive analysis with this level of detail is computationally challenging. Follesa ( 2018 ) estimated the behavior factor of the CLT-light frame hybrid system, which accounted for the nonlinear response of the structure according to European Standard ( 2004 ). The linear elastic model consisted of shell elements with axial, shear, and equivalent flexural stiffness and link elements representing shear connectors. Anchors were not explicitly modeled. Based on the linear model, a nonlinear model was developed in the Drain-3DX software, which included rigid articulated frame elements, nonlinear diagonal links representing nails, nonlinear tension and compression links to simulate anchors, and horizontal links to represent shear connectors. Dinehart ( 2000 ) developed a discrete 3-degree-of-freedom model. Linear viscoelastic elements with experimental properties represented panel-stud connections. It was assumed that the frame studs were rigid, and there was no consideration of panel-to-panel or panel-slab connections. The frame was embedded in the foundations, preventing uplift. The model accurately predicted the hysteretic behavior of the wall for low to moderate displacements. The linear model captured effective stiffness and energy dissipation for large displacements but did not predict hysteresis. Conclusion of the state of the art Although specialized software tools for modelling wood are available in the market, such as S-timber, Timbertech, RFEM, and Sapwood, among others, their usage is not common in many engineering offices. The most widely used software tools are ETABS or SAP2000, among others, which do not typically include timber modelling tools. Therefore, spreading timber calculation models requires the creation of specific modelling procedures. While there is a large amount of research that has focused on seismic modelling of timber buildings, with varying degrees of simplification, most models encounter difficulties in representing the system effects, which are significant according to empirical evidence of several authors. Moreover, detailed models entail a high computational cost due to their nonlinearity and quantity of structural components that comprise timber shear walls. International standards and design documents often provide manual calculation guidelines for individual wall elements, but their inherent assumptions can highly impact the results in mid- and high-rise structures. Therefore, a model that reflects the behavior of light-frame walls based on current standards, can consider system effects if desired, and is simplified for practical use in generalist software is needed. 3. Description of the proposed model The Link-Frame-Model (LFM) is a macro model which represents a light frame shear wall. LFM is composed of two horizontal frame elements (top and bottom plate), two vertical link elements (anchorage), and two diagonal link elements (studs, sheathing, and nailing pattern). LFM is suitable for modeling shear walls for static and modal analysis. Figure 1 depicts a wall modeled with LFM, with dimensions L (wall length), H (wall height), and L' (distance between anchors), and angle α between H and L’. The wall is modeled with a length L', corresponding to the lever arm that resists the overturning moment. The self-weight of the wall is applied as a uniformly distributed load on the top frame. The stiffnesses of the elements are determined based on the indications from American Wood Council ( 2020 ). However, if the designer wishes to add other sources of stiffness, depending on their nature, they are added in the vertical or diagonal links. The frame elements are axially and flexurally rigid, and to achieve this condition, a value of around 10^6 kN/mm is suggested for the corresponding modification factors. The aim of this is to ensure that the flexibility of these elements does not contribute to the deformation of the wall, as indicated in Eq. 1. The link elements are of the multilinear elastic type, which means that are loaded and unloaded following the same curve (without hysteresis) and therefore do not dissipate energy. Vertical links in tension represent the stiffness of the anchorage, and in compression are infinitely rigid, for which a stiffness of around 10^6 kN/mm is suggested. If the designer wishes to consider other sources of stiffness such as axial compression of the studs and perpendicular compression of the bottom plate, the value of 10^6 should be replaced by the corresponding stiffness. The diagonal links represents the bending and shear component of Eq. 1. Since the earthquake can act in both directions, the model must include two diagonals. To avoid duplicating the stiffness of the wall and considering force equilibrium, the diagonals should only work in compression. The stiffness in horizontal compression determined must be converted to diagonal stiffness using \({\text{cos}}^{2}\left(\alpha \right)\) . Therefore, in tension diagonal links are very flexible, for which a value of around 10^-6 kN/mm is suggested. In any case, the designer could modify the behavior in tension and compression of the links based on considering other sources of flexibility. For a modal analysis, it should be noted that considers effective stiffness. To avoid duplication of stiffness due to the two diagonals, the effective stiffness of these elements is half of their compression stiffness. Regarding the vertical links, it is common and often conservative to impose an inactive anchorage condition through a high effective stiffness, meaning that the shear walls are assumed to have no flexibility in overturning. However, according to the designer’s criteria, the anchorage could have certain flexibility, for example, to evaluate its effect considering longer periods depending on the region of the spectrum where the structure is located. Generally, the inactive condition tends to yield conservative results in static analysis compared to an excessively flexible period estimation. The tension force in the anchorages is directly obtained from the axial tension stress of the vertical link. The unit shear of the wall is determined as the axial stress of the diagonal link multiplied by \({cos}\left(\alpha \right)\) divided by the real length of the wall. The compression of the wall is given by the sum of the axial compression stress of the vertical links and the respective vertical contribution in the diagonal links. 4. Model validation and analysis In this section, the behavior of a 4-story individual wall is analyzed. The period, displacements, and stresses obtained using different methods are compared. Subsequently, conclusions are drawn concerning the LFM implemented in ETABS compared to current design codes. Also, the LFM was validated by comparing the periods of a 6-story light-frame experimental building known as Torre Peñuelas (Alarcón et al., 2022 ). 4.1. Validation and analysis at the multistory individual shear wall level Case study description The single multi-story shear wall is labeled as F.1, which was studied in Montaño et al. ( 2021 ). It has a height per floor of 2.47 m and distance between anchors of 4.39 m. More details of its configuration are presented in Table A.1 and A.2 in annex. The wall was analyzed in the plane under a lateral load, which involves restraining degrees of freedom out-of-plane to avoid instability in the model. Table 1 displays the flexural, shear, and overturning stiffness according to the SDPWS standard and the properties from the Cárcamo ( 2017 ) and Vogrinec (2016) models. Figure 2 illustrates wall F.1 modeled with LFM in ETABS with the stiffness of diagonal and vertical link. Table 1 A.1. Design details of wall F.1. N° Floor Quantity of OSB boards OSB board thickness [mm] Nail type Perimeter nailing pattern [mm] N° Bottom plate 4 1 9,5 8d 150 4 3 1 9,5 8d 100 4 2 1 9,5 8d 50 4 1 2 9,5 8d 50 4 Period results The fundamental period was calculated using two methodologies to enhance the comparison with LFM: (1) equation proposed by Nassani ( 2014 ) and (2) eigenvalues and eigenvectors. Table 2 displays the obtained periods, and it was observed that LFM showed a 7% difference compared to the Nassani equation and a 0% difference relative to the analytical calculation using eigenvalues and eigenvectors. Therefore, a proper implementation of the model for predicting the period was achieved. Table 2 A.2. Bending and anchoring design of wall F.1. N° Floor Structural grade radiata pine Square b [mm] x h [mm] Shearwall studs Hold-down anchorage model N° Border frame stud Distributed frame stud type Spacing frame stud [mm] 4 MGP10 35x90 6 Simple 600 HD5B 3 MGP10 35x90 6 Simple 400 HD5B 2 MGP10 35x138 6 Simple 600 HD7B 1 MGP10 35x138 6 Simple 400 HD9B Drift results Figure 3 displays the drift of wall F.1 according to various methodologies: Cárcamo Model, Vogrinec Model, LFM, SDPWS code, and CSA O86 code with accumulated effects. Compared to the SDPWS, LFM shows higher displacements due to accumulated overturning. The drift of LFM is like that of the CSA O86 code with accumulated effects. The Cárcamo and Vogrinec models differ from the SDPWS and CSA O86 codes, even on the first floor. These models face limitations in capturing the accumulated rotation, as presented in previous studies (Bagheri and Doudak, 2021 ; Rossi et al., 2016 ). Table A.3 in annex displays the resulting lateral displacements of wall F.1 according to LFM and the SDPWS code including accumulated overturning, with a difference of about 0%. LFM is the model that best aligns with current codes and research, as it accurately represents the flexure, shear, and accumulated overturning of a multi-story individual wall. Tension and shear results Tables 3 and 4 compare the tension and shear analytical of wall F.1 with LFM, Cárcamo model, and Vogrinec model. The analytical tension corresponds to the following expression: \({T}_{i}=\frac{{F}_{i}\bullet \text{H}}{{L}^{{\prime }}}\) , and the unit shear is \(v=\frac{{F}_{i}}{L}\) . It was observed that in tension, LFM coincides with the analytical calculation with a difference of 0%, the Cárcamo model with an average difference of 33%, and the Vogrinec model with an average difference of 62%. Concerning the shear stress, in all models, it is equal to the analytical value. Table 3 − 1. Wall F.1 Properties according to SDPWS, Cárcamo and Vogrinec methodologies. N° Floor SDPWS Cárcamo Vogrinec Flexural Stiffness Shear Stiffness Overturning Stiffness SDPWS Stiffness Section Modulus Elasticity Modulus of Shear Diagonal Section [kN/mm] [kN/mm] [kN/mm] [kN/mm] [mm2] [N/mm2] [N/mm] [mm2] 4 422,95 5,72 8,08 3,32 471630 1269,79 21,19 3830 3 422,95 8,41 16,71 5,52 471630 1537,11 35,41 5597 2 648,52 15,13 23,77 9,12 699150 1313,41 39,7 10041 1 648,52 30,26 28,30 14,30 744180 1493,71 58,99 19635 Table 4 − 2. Periods of Wall F.1 according to different approaches Method Fundamental period (s) Difference [%] LFM 0,097 - Nassani equation 0,090 -7% Eigenvalues and eigenvectors 0,097 0% Conclusions at the isolated multistory shearwall level The period, drift and stresses were analyzed at the wall level comparing different methodologies. Regarding the fundamental period, a 0% difference was obtained from the method of eigenvalues and eigenvectors. The tensile and shear stresses of the model exhibit a 0% difference compared to the analytical calculation. LFM allows capturing the cumulative overturning, which is significant at the individual wall level, according to previous researchs (Bagheri and Doudak, 2021 ; Canadian Standard Association CSA O86-14, 2014 ; Rossi et al., 2016 ). LFM represents Eq. 4, corresponding to the lateral deflection at the individual multi-story wall level according to the SDPWS including cumulative overturning. The first term corresponds to the bending of the edge studs, the second term refers to the shear of the sheathing and nail pattern, and the third term corresponds to the cumulative overturning due to the anchorage considering the lift concerning its position. \(\delta ={\left(\frac{2\bullet v\bullet {H}^{3}}{3\bullet E{\bullet A}_{ext}\bullet L} \right)}_{flexure}+{\left(\frac{v\bullet H}{{G}_{a}}\right)}_{shear}+{\left({H}_{i}\left(\sum _{j=1}^{i}\frac{{\left({d}_{a}\right)}_{j} }{L{\prime }}\right)\right)}_{overturning}\) Eq. (4) The other simplified models exhibit displacements and stresses different from theoretical values in walls with more than one story, suggesting that these differences may propagate to the building level. Based on the above results, LFM correctly represents a multi-story individual light-frame wall concerning current codes and studies. 4.2. Validation and analysis at the entire building level In Alarcón et al., ( 2022 ), the structural configuration of the tower called Torre Peñuelas and the seismic instrumentation system implemented to measure various properties, including dynamic characteristics through ambient vibration testing, are thoroughly described. The periods were measured under ambient vibrations, which vary between cold and warm days. The average values were Tx = 0.35s and Ty = 0.32s, which do not account for the anchors’ flexibility due to their inactive state at ambient vibrations. The Torre Peñuelas was modeled using LFM in SAP2000, as presented in Fig. 4 . The periods obtained through LFM were almost the same Tx = 0.33s and Ty = 0.32s, with a difference of 6% and 2%, respectively. Additionally, both the model showed a significant similarity in the modal shapes. In particular, the assumption of anchor inactivity was confirmed by the modal shapes, represented by the vertical links' effective stiffness. Therefore, the implementation of LFM was proofed accurate also at the building level. 4.3. In-depth case study building analysis considering system effects Case study description Once validated at the building level, the performance of the LFM was in-depth analyzed and compared with traditional modelling methods, with emphasis in its capability for considering system effects. To conduct that analysis a 4-story residential building that represents an average Chilean archetype of timber buildings was considered in order to analyze the consequences with a standard architecture. The full characteristics of the building are detailed in Montaño et al. ( 2021 ), where the analysis considered the SDPWS methodology and the equivalent stiffness method for distributing lateral forces. The objective of this section is to compare the LFM model with the traditional method develop in Montaño et al. ( 2021 ). Figure 5 displays the structural walls in the global directions. The total height of the building is 10.72 m above ground level, with a height per floor of 2.47 m. The residential building is located in seismic zone 2 of Chile, with soil type C according to the NCh433 standard (Instituto Nacional de Normalización, 2009 ), which also represents an average seismic load of the country. The static analysis method from NCh 433 standard (Instituto Nacional de Normalización, 2009 ) was applied for the seismic analysis. The lateral forces per floor are 50 kN, 60 kN, 77 kN, and 168 kN. Modelling considerations The slab was modelled based on the Veliz methodology (Véliz et al., 2024 ). The model almost concentrates the rigidity of the connections and the cutting of the panels in an equivalent diagonal, which are modelled as link to avoid their gravitational contribution. The elements supporting gravitational load are modelled as frame elements and it was assumed a diaphragm semi-rigid. A summary of the elements of the model is schematized in Fig. 6 . The shearwalls were decoupled (there was not set any lineal stiffness among walls in T, L, C or cross wall clusters) and they connected to the diaphragm by only the top and bottom beams. The wall supports were simply supported with restrictions on out-of-plane rotation. Because the traditional by hand calculation methodology does not allow for a three-dimensional analysis, an analysis was performed in the XZ and YZ planes to compare both methodologies. Figure 7 shows the implementation of the LFM for the building in ETABS. All elements were defined without self-weight and were applied as an external load. The self-weight of the walls varied between 0.80–1.43 kN/m, and the floor self-weight was 1.75 kN/m 2 . A 2 kN/m 2 live load was also applied to the diaphragm. The building was studied using a nonlinear static analysis. This study evaluated the behavior under lateral loads without considering gravitational load to directly compare it with the traditional method. However, the LFM can consider gravitational loads by simply including it as an initial condition in the seismic load case. This way, gravity-induced forces and P-Δ effects could be captured. This analysis works well for medium-rise buildings with a regular configuration. In cases where this analysis is not appropriate, it could be an effective design tool to investigate aspects of the model and nonlinear response when applying dynamic analysis (Deierlein et al., 2010 ). Period results The building was analyzed using the traditional manual methodology, i.e. considering individual shear walls, and the LFM implemented in ETABS, which captures 3D system effects. In both cases, the period was calculated without considering the flexibility of the anchors. The periods from LFM were analyzed by plane to compare it with the traditional methodology and the method of eigenvalues and eigenvectors. Table 5 shows the periods where a difference of 14% and 15% was observed compared to the Nassani equation (Nassani, 2014 ) for the X-axis and Y-axis periods, and differences of 1% and 1% compared to eigenvalues and eigenvectors. Table 5 A.3. Displacement of wall F.1 Story LFM displacement [mm] Analytical displacement [mm] 4 26,24 26,23 3 16,88 16,88 2 8,95 8,95 1 3,23 3,23 Drift results Figure 8 depicts the building drift according to LFM and analytical SDPWS method with and without accumulated overturning for X-axis and Y-axis. LFM provides significantly lower drifts compared to the analytical method of the SDPWS code with accumulated overturning. This illustrates that the diaphragm and transverse walls prevents the walls from freely rotating. This implies that if the displacement is analytically verified, including cumulative effects (gray line in Fig. 8 ), the stiffness requirements are higher for the same base shear, resulting in increased building cost. Neglecting the out-of-plane diaphragm stiffness and considering cumulative effects leads to larger displacements, overestimation of the period, and potential underestimation of the building's base shear. Table A.4 in annex shows the percentage differences of drift for Sx and Sy between the traditional methodology and LFM. By considering system effects, it is expected that the drift decreases compared to by-hand calculation, where an analysis at the level of individual walls is considered. Shear results Figure 9 shows the X-axis wall shear of floor 1 according to LFM and the traditional methodology. They exhibit a similar distribution but with ratio of LFM shear to traditional shear ranging from 0.71 to 1.90 in the X-axis and from 0.55 to 1.67 in the Y-axis. The sum of the total shear per floor remained the same in both methodologies, but the distribution is different. In those walls with greater stress, there would be a redesign with minimal adjustments such as the nailing pattern. The shear distribution in both methodologies is proportional to the stiffness of the wall. It is interesting to note that the four walls along axis 4 have the same geometry, but different shear distribution in the LFM method and the same distribution in the traditional method. To study this phenomenon, the boundary conditions of axis 4 were analyzed, mainly focusing on the floor diaphragm framing, as shown in Fig. 10 . The shear wall 4.1 was the least rigid because in the tension zone it only had transverse edge beams and none along the axis. However, the wall 4.2 turns out to be the most rigid due to the coupling beam between 4.1 and 4.2 and the transverse edge beams along axis E in the tension zone. Between wall 4.3 and 4.4, the former is stiffer due to the inter-floor beams along axis H and I in the tension zone, unlike wall 4.4, which only has a coupling beam along axis L . Lastly, wall 4.2 is stiffer than wall 4.3 because of the length of the inter-floor beam that connects the walls along axis 4. All this illustrates how important the effect of out of plane diaphragm stiffness turns out to be for determining the stiffness of shearwalls. Tension results Figure 11 presents the X-axis load tension on floor 1 for the X-axis and Y-axis walls. The tensile stress in the X-axis walls, according to the LFM, varies between 11 kN and 29 kN, averaging 40% of the tension compared to traditional method. The LFM generates tensions in the Y-axis walls, which is not covered by the traditional method, and show a general area of both tension and compression with axial forces between − 5 kN and 13 kN. This provides a visualization of the magnitude of tensile stress in transverse walls and corresponding reduction in stress along the axis of analysis. Table 6 shows the average X-axis tension per floor of LFM and traditional methodology. It is observed that there is a difference ranging from 63–76% between the two methodologies. Table 6 − 3. Tension [kN] of Wall F.1 according to LFM, Cárcamo model and Vogrinec model. Story Analytical LFM Difference [%] Cárcamo Model Difference [%] Vogrinec Model Difference [%] 4 5,87 5,86 0% 3,15 -46% 0 -100% 3 14,27 14,27 0% 9,58 -33% 5,43 -62% 2 24,65 24,65 0% 17,25 -30% 13,22 -46% 1 36,66 36,66 0% 28,39 -23% 22,83 -38% This important difference is primarily justified by the coupling effects of the diaphragm and perpendicular walls that arise in the three-dimensional model. These system effects are not evident in the traditional methodology, as the analysis is performed for individual walls without considering boundary conditions. This effect has been studied by various authors, concluding that the transverse walls generate an anchor effect, and the diaphragm couples and restrains the wall overturning, which can be accounted for by the LFM. Discussion of system effects As presented previously, building behavior is influenced by system effects, specifically by out-of-plane stiffness of the diaphragm and the transverse walls. The out-of-plane state of the flexible and rigid diaphragms was further studied, along with the effect of the flexibility of the transverse wall anchors. Figure 12 shows the drift from seismic case under different out-of-plane diaphragm stiffness conditions: real, flexible and rigid, which depend on the stiffness of gravitational beam. The model with the real stiffness of the slab exhibits an intermediate behavior between the rigid and flexible models, however it is clearly much closer to the rigid assumption. The flexible slab results turn very similar to the by-hand results considering accumulated overturning, which is logical since the flexibility of the beams allows the wall to be free to overturn. This supports the hypothesis from Bagheri and Doudak ( 2021 ) that assuming infinite stiffness out-of-plane seems to be the most reasonable simplification, but with non-conservative results. Figure 13 shows the X-axis seismic tension on the first floor for walls for X-axis and Y-axis direction. It was observed that the out-of-plane stiffness of the diaphragm stiffens the walls against overturning, as the tensions are significantly reduced in LFM with real (bars in blue) and rigid (bars in green) model of slab. Transverse wall anchors, in Y-axis, experience tension when the diaphragm has a specific stiffness, as the tendency to overturn lifts the surrounding walls due to geometric compatibility. To estimate the influence of the transverse walls, the anchors of these walls were set very flexible to 0.001 kN/m . The X-axis seismic analysis revealed that the anchors along the Y-axis did not experience tension, while those along the X-axis increased their demand by an average of 56%. This highlights the anchorage effect of the transverse walls. Concerning shear forces, the distribution changed slightly while the average was maintained. Table 7 displays the average forces per floor. Table 7 − 4. Shear [kN/m] of Wall F.1 according to LFM, Cárcamo model and Vogrinec model. Story Analytical LFM Difference [%] Cárcamo Model Difference [%] Vogrinec Model Difference [%] 4 2,2 2,2 0% 2,2 0% 2,2 0% 3 3,15 3,15 0% 3,15 0% 3,15 0% 2 3,89 3,89 0% 3,89 0% 3,89 0% 1 4,51 4,5 0% 4,5 0% 4,5 0% Table 8 − 5. Building periods [s] Method Tx [s] Difference [%] Ty [s] Difference [%] LFM 0,309 - 0,298 - Nassani equation 0,272 -14% 0,260 -15% Eigenvalues and Eigenvectors 0,290 1% 0,281 1% Table 9 A.4. Comparison of drift Sx and Sy of the traditional method and the LFM. Story Drift Sx Drift Sy Traditional method LFM Difference [%] Traditional method LFM Difference [%] 1 0,00153 0,0009 -43% 0,00134 0,0006 -59% 2 0,00153 0,0011 -30% 0,00134 0,0009 -32% 3 0,00136 0,0011 -17% 0,00134 0,0012 -10% 4 0,00162 0,0018 10% 0,00124 0,0013 5% Table 10 − 6. Average tension [kN] per floor in X-axis Story LFM Traditional methodology Difference [%] 4 2.78 7.70 -64% 3 4.74 19.35 -76% 2 9.21 34.07 -73% 1 18.58 49.59 -63% Table 11 − 7. Effect of transverse anchors on tensile shear stiffness. Story Average Tension [kN] Average Shear [kN] LFM with transverse anchoring LFM without transverse anchoring Difference [%] LFM with transverse anchoring LFM without transverse anchoring Difference [%] 4 2.78 4.64 67% 7.62 7.62 0% 3 4.74 8.29 75% 11.47 11.47 0% 2 9.21 13.74 49% 13.85 13.85 0% 1 18.58 24.43 31% 16.15 16.15 0% 5. Practical consequences and advantages Practical consequences of system effects in the structural design The previous building was redesigned considering the stresses obtained using the LFM with system effects implemented in ETABS. Anchorages have the potential to strongly influence the design as tend to be the costliest elements within a timber building in seismic areas. And it was observed that the design was governed by stiffness rather than strength. Based on this, the structure was first stiffened in terms of shear by modifying the number of sheathing panels and nailing patterns and then overturning. Figure 14 compares the hold-downs design from traditional method and the redesign considering model tension. Regarding design stiffness, in the X-axis there was an average reduction of 25%, and in the Y-axis there was an average reduction of 53%. The design of the anchorages was governed by drift rather than strength. This illustrates that in general the system effects can yield to an increase of need in shearing stiffening, which typically it is not expensive, and a significant decrease of anchoring needs, which typically is very expensive. Since the floor beams are the elements that couple the walls. it is essential to verify the bending and shear design of these elements due to seismic loads, and not only for gravitational loads as in traditional method. Moment and shear demand greater than those designed using traditional method were obtained from the model, so a redesign of these elements is necessary. Advantages The LFM macro model accurately represents the analytical equations for the lateral deflection of light frame shear walls, as proposed by standards such as SDPWS and CSA O86-14. The model has several comparative advantages over previously developed models: (i) has the versatility to include other sources of stiffness/flexibility in a simple manner, according to the criteria designer; for example, considering shear connectors in the diagonal links, and/or considering the compression of the end studs, perpendicular compression of the bottom plate, contribution of the concrete cone in the base anchors, among others, in the vertical links; (ii) is capable of representing the accumulated overturning both at the wall and building level, an aspect that not all previous models consider; (iii) has the versatility to consider or not the system effects (out-of-plane stiffness of the diaphragm and transverse walls), which have significant implications in design, as demonstrated above; (iv) is applicable in any finite element software, as it uses link and frame elements; (v) allows for nonlinear static elastic and modal analysis, with low computational cost and analysis time compared to nonlinear models; (vi) allows reproducing the inelastic behavior of the walls, both at the level of anchors and by shear, through the constitutive lines of the real envelope of an experimental test. 6. Conclusion Despite various methodologies have been proposed for the seismic modelling of timber buildings, none of them demonstrated a combination of: (i) high accuracy in capturing the prescriptions of codes such as the SDPWS or CSA, (ii) the simplicity and versatility to be used in general purpose software to conduct both equivalent lateral load and modal analyses, and (iii) the possibility of considering system effects if desired. This research proposed a macro model entitled Link Frame Model (LFM) consisting of modelling shearwalls as top and bottom rigid beams, two diagonals modelling shear stiffness and two vertical springs modelling anchoring. The results indicate that the model produces virtually the same results of analytical by-hand code calculations, with errors close to 0%, and can be implemented in general purpose software such as e.g. ETABS or SAP2000. This was not only verified at the multistory shearwall level, but also at entire building level, by using the experimental results of a 6-story experimental building monitoring. Apart from proposing this new macro model of shear wall, the LFM model has also been used to analyze system effects, because there is plenty of evidence in previous research that proofs the inaccuracy of individual and free shearwall rotation premise of codes. This analysis considering system effects has been possible by simply modelling the actual flexural out-of-plane stiffness of the diaphragms above shearwalls via explicit modelling of the flexural stiffness of each beam of floors. An average multistory building representing a national Chilean archetype, subjected to an average seismic load, was considered to conduct an in-depth analysis of a representative standard case study. The results show that, even when shearwalls are not connected among each other, the diaphragms couple them. Actually, the hypothesis of rigid diaphragm turns to be much closer to the actual stiffness than a flexible diaphragm. This strongly influences the building lateral behavior and has great practical consequences. In general, uplift anchorages work not only due to in-plane shearwall loads, but also due to out-of-plane shearwall loads. Furthermore, anchorages are strongly overdesigned (an average 70% tension reduction was found), even without considering axial loads, and, in contrast, shears of shearwalls and diaphragm beams can be underdesigned. Still, the results indicate that costs of this type of buildings may be significantly more competitive considering the actual system effects, because anchorages tend to be the most expensive component. By artificially setting close to null the flexural stiffness of diaphragms, the LFM releases virtually the same results of analytical methods with cumulative overturning, which in turns demonstrates the versatility of the LFM to be used both when considering or neglecting system effects. Given the evidence demonstrated by previous research of system effects, the overall tendency to construct tall buildings with timber, and the capability of models as the LFM here proposed in capturing the 3D behavior of buildings, it is suggested that future code revisions allow estimators to consider system effects in design for these types of buildings. This will not only yield to designs that match much better with actual shears and tensions, but also avoid unconservative designs. Note that the traditional individual and free-rotating shearwall hypothesis of traditional methods may yield to exaggerated lateral flexibility, which in turn tend to cause underestimation of equivalent lateral loads. Declarations The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgements The authors acknowledge the support of Matías Alarcón for the modelling of the Peñuelas Tower and the financial support of Centro Nacional de Excelencia para la Industria de la Madera (CENAMAD ANID BASAL FB210015) of the Pontificia Universidad Católica de Chile. The authors also acknowledge the financial support of University of A Coruña for letting us publishing this article in Open Access. References Alarcón, M., Hernández, F., & Guindos, P. (2022). Structural health monitoring of South-America’s first 6-story experimental light-frame timber-building by using a low-cost Raspberryshake seismic instrumetation. Engineering Structures , 275 . American Wood Council. (2020). Special Design Provisions for Wind and Seismic . www.awc.org. Bagheri, M. M., & Doudak, G. (2021). 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Cite Share Download PDF Status: Published Journal Publication published 04 Feb, 2025 Read the published version in European Journal of Wood and Wood Products → Version 1 posted Editorial decision: Revision requested 19 Dec, 2024 Reviews received at journal 13 Dec, 2024 Reviewers agreed at journal 22 Nov, 2024 Reviewers agreed at journal 11 Aug, 2024 Reviews received at journal 08 Jul, 2024 Reviewers agreed at journal 08 Jul, 2024 Reviewers agreed at journal 04 Jul, 2024 Reviewers invited by journal 04 Jul, 2024 Editor assigned by journal 03 Jul, 2024 Submission checks completed at journal 27 Jun, 2024 First submitted to journal 26 Jun, 2024 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-4643226","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":326850133,"identity":"1e1e51cd-9eca-4f7f-a1b9-a1029133e1c1","order_by":0,"name":"Nicol López","email":"","orcid":"","institution":"Centro Nacional de Excelencia para la Industria de la Madera (CENAMAD), Pontificia Universidad Católica de Chile","correspondingAuthor":false,"prefix":"","firstName":"Nicol","middleName":"","lastName":"López","suffix":""},{"id":326850134,"identity":"9e7aa600-a142-460e-a4b3-45009dcb8393","order_by":1,"name":"Sebastián Berwart","email":"","orcid":"","institution":"Centro Nacional de Excelencia para la Industria de la Madera (CENAMAD), Pontificia Universidad Católica de Chile","correspondingAuthor":false,"prefix":"","firstName":"Sebastián","middleName":"","lastName":"Berwart","suffix":""},{"id":326850135,"identity":"ad8bccc3-4a48-483c-91de-3b00382e1b4b","order_by":2,"name":"Pablo Guindos","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA5ElEQVRIiWNgGAWjYFACHsYDIIqNgcGAgaGCgbGBCC0MSFrOkKKFAaSFsY0ILebsZw8c+MBQm9gn3bzx4c95h2X7G5gPf8CnxbInL+HgDIbjiW0yx4qNebcdNp5xgC1NAp8WgwM5Bod5GI4ltknkmEkzbjucuIGBxwyvwwzOv0Fokfw5B6SF/zNehxncANtSA9YiwdsAtoUBr8MsZ7wD+sXggHGbRFqxMc+xdOMZh9nM8Gox5889+OBDRZ3s/BnJGx/+qLGW7W9vfozfYRDyMJIQMz71cC0MdQSUjYJRMApGwYgGAP8gTeVFbvFKAAAAAElFTkSuQmCC","orcid":"","institution":"University of A Coruña","correspondingAuthor":true,"prefix":"","firstName":"Pablo","middleName":"","lastName":"Guindos","suffix":""}],"badges":[],"createdAt":"2024-06-26 13:58:01","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-4643226/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4643226/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s00107-025-02201-7","type":"published","date":"2025-02-04T15:57:42+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":60709833,"identity":"02c654ee-534b-45af-be96-230502a9a121","added_by":"auto","created_at":"2024-07-19 19:58:08","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":51080,"visible":true,"origin":"","legend":"\u003cp\u003eShearwall modeled with LFM.\u003c/p\u003e","description":"","filename":"Fig1.png","url":"https://assets-eu.researchsquare.com/files/rs-4643226/v1/8b02e19bd78aa0d50be70e5c.png"},{"id":60710501,"identity":"aac230dd-c191-4a78-bcb6-9c0881984955","added_by":"auto","created_at":"2024-07-19 20:06:08","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":127229,"visible":true,"origin":"","legend":"\u003cp\u003eLFM of wall F.1\u003c/p\u003e","description":"","filename":"Fig2.png","url":"https://assets-eu.researchsquare.com/files/rs-4643226/v1/a6f7d6d41114f4d9c85c3a85.png"},{"id":60709840,"identity":"7d61b2dd-3190-433d-b47b-08b95b206579","added_by":"auto","created_at":"2024-07-19 19:58:08","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":339857,"visible":true,"origin":"","legend":"\u003cp\u003eDrift of Wall F.1 according to different methodologies\u003c/p\u003e","description":"","filename":"Fig3.png","url":"https://assets-eu.researchsquare.com/files/rs-4643226/v1/f8b5f2809f721cf1122b2b1b.png"},{"id":60709839,"identity":"57e84ba9-f1cb-4a06-816f-b4b352ac422d","added_by":"auto","created_at":"2024-07-19 19:58:08","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":917554,"visible":true,"origin":"","legend":"\u003cp\u003eThe experimental building Torre Peñuelas and its LFM model implemented in SAP2000\u003c/p\u003e","description":"","filename":"Fig4.png","url":"https://assets-eu.researchsquare.com/files/rs-4643226/v1/8d60f987f4857c0d014414a3.png"},{"id":60709837,"identity":"92c60fd9-efb9-4ee0-a8aa-8f79d6876dae","added_by":"auto","created_at":"2024-07-19 19:58:08","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":101696,"visible":true,"origin":"","legend":"\u003cp\u003eBuilding floor plan with shearwalls in each direction, Montaño et al. (2021)\u003c/p\u003e","description":"","filename":"Fig5.png","url":"https://assets-eu.researchsquare.com/files/rs-4643226/v1/f1cf0929ad87d8a3792e1de6.png"},{"id":60709836,"identity":"73718326-22a2-40e1-91d5-01d6cbdb8e90","added_by":"auto","created_at":"2024-07-19 19:58:08","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":585200,"visible":true,"origin":"","legend":"\u003cp\u003eScheme of the slab model, Véliz et al. (2024)\u003c/p\u003e","description":"","filename":"Fig6.png","url":"https://assets-eu.researchsquare.com/files/rs-4643226/v1/7e41bb721e4971ccadfeb832.png"},{"id":60709841,"identity":"ee2384ff-aecb-4855-9c44-8cf014d4eb70","added_by":"auto","created_at":"2024-07-19 19:58:08","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":697602,"visible":true,"origin":"","legend":"\u003cp\u003eETABS implementation of the LFM for the case study building calculated in Montaño et al. (2021)\u003c/p\u003e","description":"","filename":"Fig7.png","url":"https://assets-eu.researchsquare.com/files/rs-4643226/v1/aaa4c89134563c49cbd299d7.png"},{"id":60709834,"identity":"8097eee3-7a92-4498-95a6-54c15545d4c6","added_by":"auto","created_at":"2024-07-19 19:58:08","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":214533,"visible":true,"origin":"","legend":"\u003cp\u003eBuilding drift according to different methodologies: (left) drift Sx, (right) drift Sy.\u003c/p\u003e","description":"","filename":"8.png","url":"https://assets-eu.researchsquare.com/files/rs-4643226/v1/7ca95f763cfad6438765c825.png"},{"id":60709846,"identity":"a72c50aa-df5e-44f7-a3c0-7dfce8d18b9d","added_by":"auto","created_at":"2024-07-19 19:58:09","extension":"png","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":223035,"visible":true,"origin":"","legend":"\u003cp\u003eWall shear distribution in the X-axis of floor 1\u003c/p\u003e","description":"","filename":"Fig9.png","url":"https://assets-eu.researchsquare.com/files/rs-4643226/v1/b1f1ae5e46b2ac895cfca1a1.png"},{"id":60709843,"identity":"de3d94e7-0ef6-4c57-b49e-e4bfd416d8d1","added_by":"auto","created_at":"2024-07-19 19:58:09","extension":"png","order_by":10,"title":"Figure 10","display":"","copyAsset":false,"role":"figure","size":178060,"visible":true,"origin":"","legend":"\u003cp\u003eFloor Diaphragm Framing\u003c/p\u003e","description":"","filename":"Fig10.png","url":"https://assets-eu.researchsquare.com/files/rs-4643226/v1/6ce2aa924142e38deb5e6ce1.png"},{"id":60709842,"identity":"588d0499-0b5f-48e6-975e-4b357900fd44","added_by":"auto","created_at":"2024-07-19 19:58:08","extension":"png","order_by":11,"title":"Figure 11","display":"","copyAsset":false,"role":"figure","size":333131,"visible":true,"origin":"","legend":"\u003cp\u003eTension due seism in X at floor 1: (left) X-axis walls, (right) Y-axis walls.\u003c/p\u003e","description":"","filename":"11.png","url":"https://assets-eu.researchsquare.com/files/rs-4643226/v1/c156265043d2df33738bea13.png"},{"id":60709838,"identity":"d2556dca-47f5-483a-bf32-45ee25d74442","added_by":"auto","created_at":"2024-07-19 19:58:08","extension":"png","order_by":12,"title":"Figure 12","display":"","copyAsset":false,"role":"figure","size":467486,"visible":true,"origin":"","legend":"\u003cp\u003eDrift with out-of-plane stiffness variant: (left) X-axis, (right) Y-axis\u003c/p\u003e","description":"","filename":"12.png","url":"https://assets-eu.researchsquare.com/files/rs-4643226/v1/0910dd9c5cbaf5449e60eb32.png"},{"id":60709845,"identity":"b5b2c3a7-aa24-40df-9a97-e6b7edb072e3","added_by":"auto","created_at":"2024-07-19 19:58:09","extension":"png","order_by":13,"title":"Figure 13","display":"","copyAsset":false,"role":"figure","size":686852,"visible":true,"origin":"","legend":"\u003cp\u003eTension in shearwalls at 1st floor: (above) X-axis walls; (below) Y-axis walls.\u003c/p\u003e","description":"","filename":"13.png","url":"https://assets-eu.researchsquare.com/files/rs-4643226/v1/f5407b93e314ef76ea2382a5.png"},{"id":60709844,"identity":"1aac24fb-cc1e-4eff-9092-316d9ada1357","added_by":"auto","created_at":"2024-07-19 19:58:09","extension":"png","order_by":14,"title":"Figure 14","display":"","copyAsset":false,"role":"figure","size":251633,"visible":true,"origin":"","legend":"\u003cp\u003eComparison of hold-downs according to the design from traditional method and the redesign: (left) X-axis, (right) Y-axis.\u003c/p\u003e","description":"","filename":"14.png","url":"https://assets-eu.researchsquare.com/files/rs-4643226/v1/a45f18298b2184bff86181e8.png"},{"id":75930450,"identity":"1b3e65aa-0281-489f-9806-ed7aa01efca7","added_by":"auto","created_at":"2025-02-10 16:11:55","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":7149377,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4643226/v1/0c64c209-9bef-4ab9-85b5-5ad739add2c1.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"The Link Frame Model (LFM), a tool for the seismic analysis of timber frame buildings considering system effects","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eThe lateral systems based on wood shearwalls have in general demonstrated good seismic performance, as reported in post-earthquake damage reports (Osteraas et al., \u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e2000\u003c/span\u003e) and in iconic shake table tests (Ceccotti et al., \u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e2013\u003c/span\u003e; Pei et al., \u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e2010\u003c/span\u003e; Quizanga et al., \u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e2024\u003c/span\u003e). This, along with the inherent sustainability and lightness of the material, has triggered an increasing interest on using wood in seismic-prone countries such as Chile, New Zealand, Japan, Canada, Italy, and the USA, among others. Nowadays, given the current context of urban population concentration (Mishra et al., \u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e2022\u003c/span\u003e), there is an increasing interest in using timber for medium and tall buildings. However, the design of medium rise and tall timber buildings in seismic areas presents several challenges, one of great importance relates to the difficulty of setting up a reliable calculation model. In this context, various modeling design, and construction guidelines have been developed, such us (Chen et al., \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e2022\u003c/span\u003e) and (Karacabeyli \u0026amp; Lum, \u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e2022\u003c/span\u003e), with the aim of establishing concepts, parameters, and requirements for a tall timber building.\u003c/p\u003e \u003cp\u003eLight wood frame construction system is dominant for single and multi-family low-rise housing. This system consists of lumber framing and wood-based sheating connected to each other with metal fasteners. These buildings have typically been designed using manual calculations or spreadsheets. The increasing interest in taller buildings entails more complex modelling techniques (Chen et al., \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e2022\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eThe difficulty arises because the analytical procedures prescribed in standards are based on very simplistic assumptions (American Wood Council, \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2020\u003c/span\u003e; Canadian Standard Association CSA O86-14, \u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e2014\u003c/span\u003e; European Standard, \u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e2004\u003c/span\u003e), which are difficult to model. For instance, three assumptions that pose modelling challenges are: (a) shearwalls in standards are idealized as cantilever beams; (b) overturning is not restricted and can accumulate between floors and (c) axial load does not significantly contribute to deformation. While these assumptions have eased the hand calculations of low-rise buildings, they may greatly overestimate deformations of medium and tall buildings, and eventually turning unconservative by underestimating equivalent lateral stiffness and thus lateral design forces.\u003c/p\u003e \u003cp\u003eThe timber construction codes, under the aforementioned assumptions, present the calculation of individual walls and do not consider system effects. There is evidence showing that the three-dimensional interaction of lateral assemblies with each other has significant impact in practice; a review of the state of the art is provided in the following section. In reality, shearwalls not work individually and interact with transverse shearwalls, diaphragms, and axial loads such that additional stiffening and restraining of uplift is evidenced. Since most models cannot capture and elucidate such effects, it endures the difficulty of critically assess the drawbacks of current codes for the lateral design of timber buildings.\u003c/p\u003e \u003cp\u003eAnother challenge is that general purpose software commonly does not include specific modelling tools for timber, and timber assemblies are physically complicated since they are composed of many components joined together (framings, nails, sheathing, anchors, etc.). This difficulty further hampers the establishment of standardized modelling procedures for seismic calculation of timber buildings. Thus, there is a need of consistency on how to model a wood building in a way that accurately represents the code analytical methods, it can be built-in general-purpose software, and it is sufficiently simplified for practical use.\u003c/p\u003e \u003cp\u003eIn this context, the objective of this research is proposing a simplified model of timber frame buildings applicable in general-purpose software, that encompasses seismic code requirements, and allows for considering system effects if desired. The article is organized by first reviewing previous models and system effects in timber buildings, then proposing and validating a modelling approach termed as Link Frame Model (LFM), both at shearwall and entire building levels, and finally exploring the consequences of considering system effects in a representative case study building.\u003c/p\u003e"},{"header":"2. Code standards and state of the art of timber buildings lateral calculation","content":"\u003cp\u003e \u003cem\u003eGeneral overview of standards\u003c/em\u003e \u003c/p\u003e \u003cp\u003eThe Special Design Provisions for Wind and Seismic standard (American Wood Council, \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2020\u003c/span\u003e) is based on controlling the lateral deflection of an individual wall, given by the bending of the edge studs, shear of the sheathing and nailing pattern, and overturning due to anchorage. This expression in SI units is presented in Eq.\u0026nbsp;1, where \u003cem\u003eL\u003c/em\u003e and \u003cem\u003eH\u003c/em\u003e are the length and height of the wall, \u003cem\u003eE\u003c/em\u003e and \u003cem\u003eAext\u003c/em\u003e are the modulus of elasticity and area of the edge studs, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({G}_{a}\\)\u003c/span\u003e\u003c/span\u003e is the apparent shear stiffness, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\varDelta }_{anchorage}\\)\u003c/span\u003e\u003c/span\u003e is the uplift of the anchorage, and v is the shear per unit length. The 2008 version splits the shear component into the sheathing stiffness and nail deformation.\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\(\\delta ={\\left(\\frac{2\\bullet v\\bullet {H}^{3}}{3\\bullet E{\\bullet A}_{ext}\\bullet L} \\right)}_{Flexure}+{\\left(\\frac{v\\bullet H}{{G}_{a}}\\right)}_{Shear}+{\\left(\\frac{H\\bullet {\\varDelta }_{achorage}}{L}\\right)}_{Overturning}\\)\u003c/span\u003e \u003c/span\u003e Eq.\u0026nbsp;(1)\u003c/p\u003e \u003cp\u003eThe Canadian Standards Association O86 standard (Canadian Standard Association CSA O86-14, \u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e2014\u003c/span\u003e) calculates lateral deflection based on the same components as the 2008 SDPWS. This expression is presented in Eq.\u0026nbsp;2, where \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({B}_{v}\\)\u003c/span\u003e\u003c/span\u003e corresponds to the sheathing stiffness and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({e}_{n}\\)\u003c/span\u003e\u003c/span\u003e is the nail deformation. Hence, lateral deflection according to the US and Canadian standards represents the same concept.\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\(\\delta ={\\left(\\frac{2\\bullet v\\bullet {H}^{3}}{3\\bullet E{\\bullet A}_{ext}\\bullet L} \\right)}_{Flexure}+{\\left(\\frac{v\\bullet {H}_{s}}{{B}_{v}}\\right)}_{Shear, sheathing}+{\\left(\\text{0,0025}{H}_{s}{e}_{n}\\right)}_{Shear,nails}+{ \\left(\\frac{H\\bullet {\\varDelta }_{anchorage}}{L}\\right)}_{Overturning}\\)\u003c/span\u003e \u003c/span\u003e Eq.\u0026nbsp;(2)\u003c/p\u003e \u003cp\u003eEurocode 8 (European Standard, \u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e2004\u003c/span\u003e) analytically determines the capacity of a shearwall based on its geometry and connectors and does not present an equation for lateral deflection. In the upcoming version (Boggian et al., \u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e2020\u003c/span\u003e), there will be a proposal that includes the contribution of six terms: deformation due to nail slip, deformation of the studs, rotation due to anchor elongation, translation due to horizontal base displacement, deformation due to perpendicular sole plate compression, and deformation due to shear in the sheathing panel.\u003c/p\u003e \u003cp\u003eThe chilean standard of timber design NCh 1198 (Instituto Nacional de Normalizaci\u0026oacute;n, \u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e2014\u003c/span\u003e), in its current form does not even include any methodology for shearwall calculations. However, the future version will likely include a methodology similar to that proposed in the USA. The Chilean standard of general seismic design provisions NCh 433 (Instituto Nacional de Normalizaci\u0026oacute;n, \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e2009\u003c/span\u003e) sets a response modification factor R\u0026thinsp;=\u0026thinsp;5.5 for timber buildings and a maximum inter-story drift of 2\u0026permil; regardless of the building construction material. This code delineates two seismic design methodologies, static and modal spectral analyses, with their application depending on the number of floors and building characteristics. In the case study building, a static analysis will be conducted.\u003c/p\u003e \u003cp\u003e \u003cem\u003eCumulative overturing\u003c/em\u003e \u003c/p\u003e \u003cp\u003eBagheri and Doudak (\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e2021\u003c/span\u003e) investigated the behavior of multi-story light-frame walls, including the effect of out-of-plane diaphragm stiffness. Considering cumulative effects and without out-of-plane diaphragm stiffness, the estimated deflection closely approximated that observed in the experimental study. It was concluded that the accumulated bending is insignificant, unlike the accumulated overturning. Rossi (2016) conducted a seismic analysis of wood platform-frame buildings and assessed the lateral deflection of a multi-story wall. The wall model consisted of three linear elastic springs in series: an anchorage system, shear connectors, and sheathing with a nailing pattern. It was concluded that overturning is relevant for multi-story walls and depends on the active or inactive state of the anchors due to vertical loading. In Canadian Standard Association CSA O86-14 (\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e2014\u003c/span\u003e) an expression is provided for the deflection of a multi-story wall, considering the cumulative effects of bending and overturning. The deflection due to accumulated overturning at level \u003cem\u003ei\u003c/em\u003e is shown in Eq.\u0026nbsp;3, where \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({a}_{j}\\)\u003c/span\u003e\u003c/span\u003e represents the angle of deformation of the story j and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\left({d}_{a}\\right)}_{j}\\)\u003c/span\u003e\u003c/span\u003e represents the total vertical elongation of the anchor system to the wall on the j floor.\u003cdiv id=\"Equa\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equa\" name=\"EquationSource\"\u003e\n$${\\varDelta }_{a,i}^{storey}={H}_{i}\\left(\\sum _{j=1}^{i}{a}_{j}\\right)={H}_{i}\\bullet {a}_{i}+{H}_{i}\\left(\\sum _{j=1}^{i-1}{a}_{j}\\right){a}_{j}=\\frac{{\\left({d}_{a}\\right)}_{j} }{L} \\text{E}\\text{q}. \\left(3\\right)$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003e \u003cem\u003eSystem effects\u003c/em\u003e \u003c/p\u003e \u003cp\u003eWhile the cumulative effects of overturning are significant from the theoretical standpoint, only individual walls rotate freely, and it is expected that they would experience larger displacements than in a wall system like those of real buildings. In buildings, the interaction between the diaphragm and walls hinders overturning, an aspect not addressed in regulations. Valdivieso (2024) investigated the effects of transverse shear walls, out-of-plane bending stiffness of diaphragms, and axial loading on the lateral response of light frame shear walls. Through experimental tests, it was observed that the stiffness and strength of the shear walls increased when considering these aspects. Dolan (1989) studied perpendicular walls to enhance design without anchorages. Experimentally, it was demonstrated that transverse wall segments reduce uplift and enhance capacity and ductility compared to unrestricted walls. In the NEESWood Project, seismic tests on a 6-story timber structure showed one side of the building being in tension and the other in compression (Pei et al., \u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e2010\u003c/span\u003e). This effect was attributed to the edge conditions of perpendicular walls acting as a restraint against overturning. Ruggeri (2023) modeled the interaction between perpendicular CLT walls. It was concluded that the increase in lateral capacity depends on the position and connection of the transverse wall. The effect is more pronounced in the tension zone than the central zone and does not contribute to the compression zone. Foliente (2000) conducted full-scale tests on a one-story house to study how the diaphragm and transverse walls affect load distribution. Shared loading was observed in the system attributed to the transverse walls. Additionally, it was concluded that the stiffness of individual walls is underestimated by up to 80%. Hopkins (2014) evaluated shear walls with perpendicular walls. The stiffness, strength, and capacity increased compared to individual walls, with a significant influence from the connection. Bagheri and Doudak (\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e2021\u003c/span\u003e) investigated how out-of-plane diaphragm stiffness influences shear walls. When the diaphragm was flexible, walls rotated freely, and cumulative effects occurred. In contrast, these effects were absent with out-of-plane stiffness, reducing deflection by an average of 80%. Even conservative estimates of stiffness led to a significant reduction in deflection. Girhammar y K\u0026auml;llsner (2006) studied the behavior and capacity of partially anchored shear walls considering three-dimensional behavior. Through theoretical and experimental analysis, it was demonstrated that properly connected transverse walls act as anchors. Kochkin y McKee (2001) numerically and experimentally studied the lateral response of shear walls with and without anchors, along with corner walls. The transverse walls generated a confinement effect, increasing capacity and reducing wall ductility, altering the failure mode. In summary, there is substantial evidence of the relevance of three-dimensional effects in force distribution, deformations, and overturning. Nevertheless, current recommendations focus on subsystem behavior and overlook system-level effects.\u003c/p\u003e \u003cp\u003e \u003cem\u003eAxial loading effects\u003c/em\u003e \u003c/p\u003e \u003cp\u003eRegarding axial load, international standards often do not explicitly detail whether it should be considered in lateral deflection calculation. When they do, they establish a safety factor to not account for its entirety. Rossi (2016) indicated that overturning, among other factors, depends on the active or inactive state of the anchor, which in turn relies on the relationship between tension and axial load at the anchor. Orellana (2021) tested shear walls subjected to axial load and moment for lateral behavior. An increase in stiffness, strength, and energy dissipation was observed, which could be attributed to a change in wall kinematics due to a reduced contribution of overturning in deformation.\u003c/p\u003e \u003cp\u003e \u003cem\u003eSimplified models proposed by researchers\u003c/em\u003e \u003c/p\u003e \u003cp\u003eC\u0026aacute;rcamo (\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e2017\u003c/span\u003e) presented a model of platform frame walls using equivalent area elements (shells) within a finite element program. The equivalent modulus of elasticity and shear were calculated based on an equivalence between the platform frame wall and a homogeneous isotropic wall. The results showed that the model's accuracy depends on mesh sensitivity: lateral displacement is better represented with a finer mesh, while axial displacement is optimal without mesh divisions. The model did not account for vertical uplift due to anchorage and was not explored for multi-story walls being directly implemented in a building. Gonz\u0026aacute;lez (\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e2019\u003c/span\u003e) proposed a method that involves applying modification factors to the rigidities acting in the wall plane. The coefficients were derived by equating the stiffness from (American Wood Council, \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2020\u003c/span\u003e) with the stiffness of a cantilever wall. A correction factor was also proposed based on the average error between theoretical and model stiffness. The model was sensitive to meshing and did not consider cumulative effects. Vogrinec (2016) proposed a model consisting of a simple braced frame with a fictitious diagonal. The diagonal section was determined from the shear and bending stiffness of a cantilever beam, the stiffness due to perpendicular bottom plate compression, and the stiffness of the anchorage. The model did not address loading in the opposite direction, was not validated for walls taller than one story, and did not accommodate vertical displacement. Chen (2014) presents a model composed of three boundary-framing members, one diagonal hysteretic spring, and two vertical translational spring. The model allows for lateral and rotational deformation, and was developed in ABAQUS, software that is not commonly used in practice. Furthermore, since there is only one diagonal, it supports lateral loading in one direction. Moroder (2015) studied the role of the floor diaphragm in lateral resistance and proposed a strut-and-tie model. The method involved assigning equivalent stiffness and area to elements, where the diagonal depends on the sheathing and connector properties, and the frame properties depend on the framing. The model approximates the stresses, forces, and deformations and applies to various geometries.\u003c/p\u003e \u003cp\u003e \u003cem\u003eDetailed models proposed by researchers\u003c/em\u003e \u003c/p\u003e \u003cp\u003eEstrella (2020) modeled the nonlinear behavior of walls under large displacement demands in M-CASHEW and conducted 12 full-scale tests. The model represented studs using frame elements, OSB using shell elements, and connectors using link elements. Nails were modeled as nonlinear hysteretic springs. While the model provided information about the response of each element, it required a significant computational cost. Estrella (2020) also proposed a simplified model for practical implementation of nonlinear time history modeling. By calibrating a one-degree-of-freedom nonlinear spring with experimental data in MSTEW, it was determined that such a spring could adequately capture the nonlinear behavior of the wall. The model allowed predicting the cyclic response of walls with the same properties and different lengths. Malesza (\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e2017\u003c/span\u003e) introduced a wall model using shell elements, which condensed at the edges to represent panel-structure connectors. Modelling parameters were obtained from experimental tests. This approach allowed for solving specific problems within a building, but a comprehensive analysis with this level of detail is computationally challenging. Follesa (\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e2018\u003c/span\u003e) estimated the behavior factor of the CLT-light frame hybrid system, which accounted for the nonlinear response of the structure according to European Standard (\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e2004\u003c/span\u003e). The linear elastic model consisted of shell elements with axial, shear, and equivalent flexural stiffness and link elements representing shear connectors. Anchors were not explicitly modeled. Based on the linear model, a nonlinear model was developed in the Drain-3DX software, which included rigid articulated frame elements, nonlinear diagonal links representing nails, nonlinear tension and compression links to simulate anchors, and horizontal links to represent shear connectors. Dinehart (\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e2000\u003c/span\u003e) developed a discrete 3-degree-of-freedom model. Linear viscoelastic elements with experimental properties represented panel-stud connections. It was assumed that the frame studs were rigid, and there was no consideration of panel-to-panel or panel-slab connections. The frame was embedded in the foundations, preventing uplift. The model accurately predicted the hysteretic behavior of the wall for low to moderate displacements. The linear model captured effective stiffness and energy dissipation for large displacements but did not predict hysteresis.\u003c/p\u003e \u003cp\u003e \u003cem\u003eConclusion of the state of the art\u003c/em\u003e \u003c/p\u003e \u003cp\u003eAlthough specialized software tools for modelling wood are available in the market, such as S-timber, Timbertech, RFEM, and Sapwood, among others, their usage is not common in many engineering offices. The most widely used software tools are ETABS or SAP2000, among others, which do not typically include timber modelling tools. Therefore, spreading timber calculation models requires the creation of specific modelling procedures.\u003c/p\u003e \u003cp\u003eWhile there is a large amount of research that has focused on seismic modelling of timber buildings, with varying degrees of simplification, most models encounter difficulties in representing the system effects, which are significant according to empirical evidence of several authors. Moreover, detailed models entail a high computational cost due to their nonlinearity and quantity of structural components that comprise timber shear walls. International standards and design documents often provide manual calculation guidelines for individual wall elements, but their inherent assumptions can highly impact the results in mid- and high-rise structures. Therefore, a model that reflects the behavior of light-frame walls based on current standards, can consider system effects if desired, and is simplified for practical use in generalist software is needed.\u003c/p\u003e"},{"header":"3. Description of the proposed model","content":"\u003cp\u003eThe Link-Frame-Model (LFM) is a macro model which represents a light frame shear wall. LFM is composed of two horizontal frame elements (top and bottom plate), two vertical link elements (anchorage), and two diagonal link elements (studs, sheathing, and nailing pattern). LFM is suitable for modeling shear walls for static and modal analysis. Figure\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e depicts a wall modeled with LFM, with dimensions L (wall length), H (wall height), and L' (distance between anchors), and angle α between H and L\u0026rsquo;. The wall is modeled with a length L', corresponding to the lever arm that resists the overturning moment. The self-weight of the wall is applied as a uniformly distributed load on the top frame. The stiffnesses of the elements are determined based on the indications from American Wood Council (\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2020\u003c/span\u003e). However, if the designer wishes to add other sources of stiffness, depending on their nature, they are added in the vertical or diagonal links.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe frame elements are axially and flexurally rigid, and to achieve this condition, a value of around 10^6 kN/mm is suggested for the corresponding modification factors. The aim of this is to ensure that the flexibility of these elements does not contribute to the deformation of the wall, as indicated in Eq.\u0026nbsp;1. The link elements are of the multilinear elastic type, which means that are loaded and unloaded following the same curve (without hysteresis) and therefore do not dissipate energy. Vertical links in tension represent the stiffness of the anchorage, and in compression are infinitely rigid, for which a stiffness of around 10^6 kN/mm is suggested. If the designer wishes to consider other sources of stiffness such as axial compression of the studs and perpendicular compression of the bottom plate, the value of 10^6 should be replaced by the corresponding stiffness. The diagonal links represents the bending and shear component of Eq.\u0026nbsp;1. Since the earthquake can act in both directions, the model must include two diagonals. To avoid duplicating the stiffness of the wall and considering force equilibrium, the diagonals should only work in compression. The stiffness in horizontal compression determined must be converted to diagonal stiffness using \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\text{cos}}^{2}\\left(\\alpha \\right)\\)\u003c/span\u003e\u003c/span\u003e. Therefore, in tension diagonal links are very flexible, for which a value of around 10^-6 kN/mm is suggested. In any case, the designer could modify the behavior in tension and compression of the links based on considering other sources of flexibility.\u003c/p\u003e \u003cp\u003eFor a modal analysis, it should be noted that considers effective stiffness. To avoid duplication of stiffness due to the two diagonals, the effective stiffness of these elements is half of their compression stiffness. Regarding the vertical links, it is common and often conservative to impose an inactive anchorage condition through a high effective stiffness, meaning that the shear walls are assumed to have no flexibility in overturning. However, according to the designer\u0026rsquo;s criteria, the anchorage could have certain flexibility, for example, to evaluate its effect considering longer periods depending on the region of the spectrum where the structure is located. Generally, the inactive condition tends to yield conservative results in static analysis compared to an excessively flexible period estimation.\u003c/p\u003e \u003cp\u003eThe tension force in the anchorages is directly obtained from the axial tension stress of the vertical link. The unit shear of the wall is determined as the axial stress of the diagonal link multiplied by \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({cos}\\left(\\alpha \\right)\\)\u003c/span\u003e\u003c/span\u003e divided by the real length of the wall. The compression of the wall is given by the sum of the axial compression stress of the vertical links and the respective vertical contribution in the diagonal links.\u003c/p\u003e"},{"header":"4. Model validation and analysis","content":"\u003cp\u003eIn this section, the behavior of a 4-story individual wall is analyzed. The period, displacements, and stresses obtained using different methods are compared. Subsequently, conclusions are drawn concerning the LFM implemented in ETABS compared to current design codes. Also, the LFM was validated by comparing the periods of a 6-story light-frame experimental building known as Torre Pe\u0026ntilde;uelas (Alarc\u0026oacute;n et al., \u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e2022\u003c/span\u003e).\u003c/p\u003e \u003cdiv id=\"Sec5\" class=\"Section2\"\u003e \u003ch2\u003e4.1. Validation and analysis at the multistory individual shear wall level\u003c/h2\u003e \u003cp\u003e \u003cem\u003eCase study description\u003c/em\u003e \u003c/p\u003e \u003cp\u003eThe single multi-story shear wall is labeled as F.1, which was studied in Monta\u0026ntilde;o et al. (\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). It has a height per floor of 2.47 m and distance between anchors of 4.39 m. More details of its configuration are presented in Table A.1 and A.2 in annex. The wall was analyzed in the plane under a lateral load, which involves restraining degrees of freedom out-of-plane to avoid instability in the model. Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e displays the flexural, shear, and overturning stiffness according to the SDPWS standard and the properties from the C\u0026aacute;rcamo (\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e2017\u003c/span\u003e) and Vogrinec (2016) models. Figure\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e illustrates wall F.1 modeled with LFM in ETABS with the stiffness of diagonal and vertical link.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eA.1. Design details of wall F.1.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"6\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eN\u0026deg; Floor\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eQuantity of OSB boards\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eOSB board thickness [mm]\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eNail type\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003ePerimeter nailing pattern [mm]\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eN\u0026deg; Bottom plate\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e9,5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e8d\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e150\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e4\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e9,5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e8d\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e100\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e4\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e9,5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e8d\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e50\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e4\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e9,5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e8d\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e50\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e4\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003cem\u003ePeriod results\u003c/em\u003e \u003c/p\u003e \u003cp\u003eThe fundamental period was calculated using two methodologies to enhance the comparison with LFM: (1) equation proposed by Nassani (\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e2014\u003c/span\u003e) and (2) eigenvalues and eigenvectors. Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e displays the obtained periods, and it was observed that LFM showed a 7% difference compared to the Nassani equation and a 0% difference relative to the analytical calculation using eigenvalues and eigenvectors. Therefore, a proper implementation of the model for predicting the period was achieved.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eA.2. Bending and anchoring design of wall F.1.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"7\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eN\u0026deg; Floor\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eStructural grade radiata pine\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eSquare b [mm] x h [mm]\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"3\" nameend=\"c6\" namest=\"c4\"\u003e \u003cp\u003eShearwall studs\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eHold-down anchorage model\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eN\u0026deg; Border frame stud\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eDistributed frame stud type\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eSpacing frame stud [mm]\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eMGP10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e35x90\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eSimple\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e600\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eHD5B\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eMGP10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e35x90\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eSimple\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e400\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eHD5B\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eMGP10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e35x138\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eSimple\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e600\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eHD7B\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eMGP10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e35x138\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eSimple\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e400\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eHD9B\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003cem\u003eDrift results\u003c/em\u003e \u003c/p\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e displays the drift of wall F.1 according to various methodologies: C\u0026aacute;rcamo Model, Vogrinec Model, LFM, SDPWS code, and CSA O86 code with accumulated effects. Compared to the SDPWS, LFM shows higher displacements due to accumulated overturning. The drift of LFM is like that of the CSA O86 code with accumulated effects. The C\u0026aacute;rcamo and Vogrinec models differ from the SDPWS and CSA O86 codes, even on the first floor. These models face limitations in capturing the accumulated rotation, as presented in previous studies (Bagheri and Doudak, \u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e2021\u003c/span\u003e; Rossi et al., \u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e2016\u003c/span\u003e). Table A.3 in annex displays the resulting lateral displacements of wall F.1 according to LFM and the SDPWS code including accumulated overturning, with a difference of about 0%. LFM is the model that best aligns with current codes and research, as it accurately represents the flexure, shear, and accumulated overturning of a multi-story individual wall.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003cem\u003eTension and shear results\u003c/em\u003e \u003c/p\u003e \u003cp\u003eTables\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e and \u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e compare the tension and shear analytical of wall F.1 with LFM, C\u0026aacute;rcamo model, and Vogrinec model. The analytical tension corresponds to the following expression: \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({T}_{i}=\\frac{{F}_{i}\\bullet \\text{H}}{{L}^{{\\prime }}}\\)\u003c/span\u003e\u003c/span\u003e, and the unit shear is \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(v=\\frac{{F}_{i}}{L}\\)\u003c/span\u003e\u003c/span\u003e. It was observed that in tension, LFM coincides with the analytical calculation with a difference of 0%, the C\u0026aacute;rcamo model with an average difference of 33%, and the Vogrinec model with an average difference of 62%. Concerning the shear stress, in all models, it is equal to the analytical value.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab3\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003e\u0026thinsp;\u0026minus;\u0026thinsp;1. Wall F.1 Properties according to SDPWS, C\u0026aacute;rcamo and Vogrinec methodologies.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"9\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c9\" colnum=\"9\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\" morerows=\"2\" rowspan=\"3\"\u003e \u003cp\u003eN\u0026deg; Floor\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"4\" nameend=\"c5\" namest=\"c2\"\u003e \u003cp\u003eSDPWS\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"3\" nameend=\"c8\" namest=\"c6\"\u003e \u003cp\u003eC\u0026aacute;rcamo\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c9\"\u003e \u003cp\u003eVogrinec\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eFlexural Stiffness\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eShear Stiffness\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eOverturning Stiffness\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eSDPWS Stiffness\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eSection\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003eModulus Elasticity\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c8\"\u003e \u003cp\u003eModulus of Shear\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c9\"\u003e \u003cp\u003eDiagonal Section\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003e[kN/mm]\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003e[kN/mm]\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003e[kN/mm]\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003e[kN/mm]\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003e[mm2]\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003e[N/mm2]\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c8\"\u003e \u003cp\u003e[N/mm]\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c9\"\u003e \u003cp\u003e[mm2]\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e422,95\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e5,72\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e8,08\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e3,32\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e471630\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e1269,79\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e21,19\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e3830\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e422,95\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e8,41\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e16,71\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e5,52\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e471630\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e1537,11\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e35,41\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e5597\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e648,52\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e15,13\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e23,77\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e9,12\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e699150\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e1313,41\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e39,7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e10041\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e648,52\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e30,26\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e28,30\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e14,30\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e744180\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e1493,71\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e58,99\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e19635\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab4\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 4\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003e\u0026thinsp;\u0026minus;\u0026thinsp;2. Periods of Wall F.1 according to different approaches\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"3\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMethod\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eFundamental period (s)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eDifference [%]\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLFM\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0,097\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eNassani equation\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0,090\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-7%\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eEigenvalues and eigenvectors\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0,097\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0%\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003cem\u003eConclusions at the isolated multistory shearwall level\u003c/em\u003e \u003c/p\u003e \u003cp\u003eThe period, drift and stresses were analyzed at the wall level comparing different methodologies. Regarding the fundamental period, a 0% difference was obtained from the method of eigenvalues and eigenvectors. The tensile and shear stresses of the model exhibit a 0% difference compared to the analytical calculation. LFM allows capturing the cumulative overturning, which is significant at the individual wall level, according to previous researchs (Bagheri and Doudak, \u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e2021\u003c/span\u003e; Canadian Standard Association CSA O86-14, \u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e2014\u003c/span\u003e; Rossi et al., \u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e2016\u003c/span\u003e). LFM represents Eq.\u0026nbsp;4, corresponding to the lateral deflection at the individual multi-story wall level according to the SDPWS including cumulative overturning. The first term corresponds to the bending of the edge studs, the second term refers to the shear of the sheathing and nail pattern, and the third term corresponds to the cumulative overturning due to the anchorage considering the lift concerning its position.\u003cdiv class=\"BlockQuote\"\u003e\u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\(\\delta ={\\left(\\frac{2\\bullet v\\bullet {H}^{3}}{3\\bullet E{\\bullet A}_{ext}\\bullet L} \\right)}_{flexure}+{\\left(\\frac{v\\bullet H}{{G}_{a}}\\right)}_{shear}+{\\left({H}_{i}\\left(\\sum _{j=1}^{i}\\frac{{\\left({d}_{a}\\right)}_{j} }{L{\\prime }}\\right)\\right)}_{overturning}\\)\u003c/span\u003e \u003c/span\u003e Eq.\u0026nbsp;(4)\u003c/p\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eThe other simplified models exhibit displacements and stresses different from theoretical values in walls with more than one story, suggesting that these differences may propagate to the building level. Based on the above results, LFM correctly represents a multi-story individual light-frame wall concerning current codes and studies.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec6\" class=\"Section2\"\u003e \u003ch2\u003e4.2. Validation and analysis at the entire building level\u003c/h2\u003e \u003cp\u003eIn Alarc\u0026oacute;n et al., (\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e2022\u003c/span\u003e), the structural configuration of the tower called Torre Pe\u0026ntilde;uelas and the seismic instrumentation system implemented to measure various properties, including dynamic characteristics through ambient vibration testing, are thoroughly described. The periods were measured under ambient vibrations, which vary between cold and warm days. The average values were Tx\u0026thinsp;=\u0026thinsp;0.35s and Ty\u0026thinsp;=\u0026thinsp;0.32s, which do not account for the anchors\u0026rsquo; flexibility due to their inactive state at ambient vibrations. The Torre Pe\u0026ntilde;uelas was modeled using LFM in SAP2000, as presented in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e. The periods obtained through LFM were almost the same Tx\u0026thinsp;=\u0026thinsp;0.33s and Ty\u0026thinsp;=\u0026thinsp;0.32s, with a difference of 6% and 2%, respectively. Additionally, both the model showed a significant similarity in the modal shapes. In particular, the assumption of anchor inactivity was confirmed by the modal shapes, represented by the vertical links' effective stiffness. Therefore, the implementation of LFM was proofed accurate also at the building level.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec7\" class=\"Section2\"\u003e \u003ch2\u003e4.3. In-depth case study building analysis considering system effects\u003c/h2\u003e \u003cp\u003e \u003cem\u003eCase study description\u003c/em\u003e \u003c/p\u003e \u003cp\u003eOnce validated at the building level, the performance of the LFM was in-depth analyzed and compared with traditional modelling methods, with emphasis in its capability for considering system effects. To conduct that analysis a 4-story residential building that represents an average Chilean archetype of timber buildings was considered in order to analyze the consequences with a standard architecture. The full characteristics of the building are detailed in Monta\u0026ntilde;o et al. (\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e2021\u003c/span\u003e), where the analysis considered the SDPWS methodology and the equivalent stiffness method for distributing lateral forces. The objective of this section is to compare the LFM model with the traditional method develop in Monta\u0026ntilde;o et al. (\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e2021\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e displays the structural walls in the global directions. The total height of the building is 10.72 m above ground level, with a height per floor of 2.47 m. The residential building is located in seismic zone 2 of Chile, with soil type C according to the NCh433 standard (Instituto Nacional de Normalizaci\u0026oacute;n, \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e2009\u003c/span\u003e), which also represents an average seismic load of the country. The static analysis method from NCh 433 standard (Instituto Nacional de Normalizaci\u0026oacute;n, \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e2009\u003c/span\u003e) was applied for the seismic analysis. The lateral forces per floor are 50 kN, 60 kN, 77 kN, and 168 kN.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003cem\u003eModelling considerations\u003c/em\u003e \u003c/p\u003e \u003cp\u003eThe slab was modelled based on the Veliz methodology (V\u0026eacute;liz et al., \u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e2024\u003c/span\u003e). The model almost concentrates the rigidity of the connections and the cutting of the panels in an equivalent diagonal, which are modelled as link to avoid their gravitational contribution. The elements supporting gravitational load are modelled as frame elements and it was assumed a diaphragm semi-rigid. A summary of the elements of the model is schematized in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e. The shearwalls were decoupled (there was not set any lineal stiffness among walls in T, L, C or cross wall clusters) and they connected to the diaphragm by only the top and bottom beams. The wall supports were simply supported with restrictions on out-of-plane rotation. Because the traditional by hand calculation methodology does not allow for a three-dimensional analysis, an analysis was performed in the XZ and YZ planes to compare both methodologies. Figure\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e shows the implementation of the LFM for the building in ETABS. All elements were defined without self-weight and were applied as an external load. The self-weight of the walls varied between 0.80\u0026ndash;1.43 kN/m, and the floor self-weight was 1.75 kN/m\u003csup\u003e2\u003c/sup\u003e. A 2 kN/m\u003csup\u003e2\u003c/sup\u003e live load was also applied to the diaphragm. The building was studied using a nonlinear static analysis.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThis study evaluated the behavior under lateral loads without considering gravitational load to directly compare it with the traditional method. However, the LFM can consider gravitational loads by simply including it as an initial condition in the seismic load case. This way, gravity-induced forces and P-Δ effects could be captured. This analysis works well for medium-rise buildings with a regular configuration. In cases where this analysis is not appropriate, it could be an effective design tool to investigate aspects of the model and nonlinear response when applying dynamic analysis (Deierlein et al., \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e2010\u003c/span\u003e).\u003c/p\u003e \u003cp\u003e \u003cem\u003ePeriod results\u003c/em\u003e \u003c/p\u003e \u003cp\u003eThe building was analyzed using the traditional manual methodology, i.e. considering individual shear walls, and the LFM implemented in ETABS, which captures 3D system effects. In both cases, the period was calculated without considering the flexibility of the anchors. The periods from LFM were analyzed by plane to compare it with the traditional methodology and the method of eigenvalues and eigenvectors. Table\u0026nbsp;\u003cspan refid=\"Tab5\" class=\"InternalRef\"\u003e5\u003c/span\u003e shows the periods where a difference of 14% and 15% was observed compared to the Nassani equation (Nassani, \u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e2014\u003c/span\u003e) for the X-axis and Y-axis periods, and differences of 1% and 1% compared to eigenvalues and eigenvectors.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab5\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 5\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eA.3. Displacement of wall F.1\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"3\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eStory\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eLFM displacement [mm]\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eAnalytical displacement [mm]\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e26,24\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e26,23\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e16,88\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e16,88\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e8,95\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e8,95\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e3,23\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e3,23\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003cem\u003eDrift results\u003c/em\u003e \u003c/p\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003e depicts the building drift according to LFM and analytical SDPWS method with and without accumulated overturning for X-axis and Y-axis. LFM provides significantly lower drifts compared to the analytical method of the SDPWS code with accumulated overturning. This illustrates that the diaphragm and transverse walls prevents the walls from freely rotating. This implies that if the displacement is analytically verified, including cumulative effects (gray line in Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003e), the stiffness requirements are higher for the same base shear, resulting in increased building cost. Neglecting the out-of-plane diaphragm stiffness and considering cumulative effects leads to larger displacements, overestimation of the period, and potential underestimation of the building's base shear. Table A.4 in annex shows the percentage differences of drift for Sx and Sy between the traditional methodology and LFM. By considering system effects, it is expected that the drift decreases compared to by-hand calculation, where an analysis at the level of individual walls is considered.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003cem\u003eShear results\u003c/em\u003e \u003c/p\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e9\u003c/span\u003e shows the X-axis wall shear of floor 1 according to LFM and the traditional methodology. They exhibit a similar distribution but with ratio of LFM shear to traditional shear ranging from 0.71 to 1.90 in the X-axis and from 0.55 to 1.67 in the Y-axis. The sum of the total shear per floor remained the same in both methodologies, but the distribution is different. In those walls with greater stress, there would be a redesign with minimal adjustments such as the nailing pattern.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe shear distribution in both methodologies is proportional to the stiffness of the wall. It is interesting to note that the four walls along axis 4 have the same geometry, but different shear distribution in the LFM method and the same distribution in the traditional method. To study this phenomenon, the boundary conditions of axis 4 were analyzed, mainly focusing on the floor diaphragm framing, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig10\" class=\"InternalRef\"\u003e10\u003c/span\u003e. The shear wall 4.1 was the least rigid because in the tension zone it only had transverse edge beams and none along the axis. However, the wall 4.2 turns out to be the most rigid due to the coupling beam between 4.1 and 4.2 and the transverse edge beams along axis \u003cem\u003eE\u003c/em\u003e in the tension zone. Between wall 4.3 and 4.4, the former is stiffer due to the inter-floor beams along axis \u003cem\u003eH\u003c/em\u003e and \u003cem\u003eI\u003c/em\u003e in the tension zone, unlike wall 4.4, which only has a coupling beam along axis \u003cem\u003eL\u003c/em\u003e. Lastly, wall 4.2 is stiffer than wall 4.3 because of the length of the inter-floor beam that connects the walls along axis 4. All this illustrates how important the effect of out of plane diaphragm stiffness turns out to be for determining the stiffness of shearwalls.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003cem\u003eTension results\u003c/em\u003e \u003c/p\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig11\" class=\"InternalRef\"\u003e11\u003c/span\u003e presents the X-axis load tension on floor 1 for the X-axis and Y-axis walls. The tensile stress in the X-axis walls, according to the LFM, varies between 11 kN and 29 kN, averaging 40% of the tension compared to traditional method. The LFM generates tensions in the Y-axis walls, which is not covered by the traditional method, and show a general area of both tension and compression with axial forces between \u0026minus;\u0026thinsp;5 kN and 13 kN. This provides a visualization of the magnitude of tensile stress in transverse walls and corresponding reduction in stress along the axis of analysis. Table\u0026nbsp;\u003cspan refid=\"Tab6\" class=\"InternalRef\"\u003e6\u003c/span\u003e shows the average X-axis tension per floor of LFM and traditional methodology. It is observed that there is a difference ranging from 63\u0026ndash;76% between the two methodologies.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab6\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 6\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003e\u0026thinsp;\u0026minus;\u0026thinsp;3. Tension [kN] of Wall F.1 according to LFM, C\u0026aacute;rcamo model and Vogrinec model.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"8\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eStory\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eAnalytical\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eLFM\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eDifference [%]\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eC\u0026aacute;rcamo Model\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eDifference [%]\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003eVogrinec Model\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c8\"\u003e \u003cp\u003eDifference [%]\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e5,87\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e5,86\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e3,15\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-46%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e-100%\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e14,27\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e14,27\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e9,58\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-33%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e5,43\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e-62%\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e24,65\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e24,65\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e17,25\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-30%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e13,22\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e-46%\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e36,66\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e36,66\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e28,39\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-23%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e22,83\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e-38%\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eThis important difference is primarily justified by the coupling effects of the diaphragm and perpendicular walls that arise in the three-dimensional model. These system effects are not evident in the traditional methodology, as the analysis is performed for individual walls without considering boundary conditions. This effect has been studied by various authors, concluding that the transverse walls generate an anchor effect, and the diaphragm couples and restrains the wall overturning, which can be accounted for by the LFM.\u003c/p\u003e \u003cp\u003e \u003cem\u003eDiscussion of system effects\u003c/em\u003e \u003c/p\u003e \u003cp\u003eAs presented previously, building behavior is influenced by system effects, specifically by out-of-plane stiffness of the diaphragm and the transverse walls. The out-of-plane state of the flexible and rigid diaphragms was further studied, along with the effect of the flexibility of the transverse wall anchors. Figure\u0026nbsp;\u003cspan refid=\"Fig12\" class=\"InternalRef\"\u003e12\u003c/span\u003e shows the drift from seismic case under different out-of-plane diaphragm stiffness conditions: real, flexible and rigid, which depend on the stiffness of gravitational beam. The model with the real stiffness of the slab exhibits an intermediate behavior between the rigid and flexible models, however it is clearly much closer to the rigid assumption. The flexible slab results turn very similar to the by-hand results considering accumulated overturning, which is logical since the flexibility of the beams allows the wall to be free to overturn. This supports the hypothesis from Bagheri and Doudak (\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e2021\u003c/span\u003e) that assuming infinite stiffness out-of-plane seems to be the most reasonable simplification, but with non-conservative results.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig13\" class=\"InternalRef\"\u003e13\u003c/span\u003e shows the X-axis seismic tension on the first floor for walls for X-axis and Y-axis direction. It was observed that the out-of-plane stiffness of the diaphragm stiffens the walls against overturning, as the tensions are significantly reduced in LFM with real (bars in blue) and rigid (bars in green) model of slab. Transverse wall anchors, in Y-axis, experience tension when the diaphragm has a specific stiffness, as the tendency to overturn lifts the surrounding walls due to geometric compatibility.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eTo estimate the influence of the transverse walls, the anchors of these walls were set very flexible to \u003cem\u003e0.001 kN/m\u003c/em\u003e. The X-axis seismic analysis revealed that the anchors along the Y-axis did not experience tension, while those along the X-axis increased their demand by an average of 56%. This highlights the anchorage effect of the transverse walls. Concerning shear forces, the distribution changed slightly while the average was maintained. Table\u0026nbsp;\u003cspan refid=\"Tab7\" class=\"InternalRef\"\u003e7\u003c/span\u003e displays the average forces per floor.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab7\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 7\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003e\u0026thinsp;\u0026minus;\u0026thinsp;4. Shear [kN/m] of Wall F.1 according to LFM, C\u0026aacute;rcamo model and Vogrinec model.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"8\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eStory\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eAnalytical\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eLFM\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eDifference [%]\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eC\u0026aacute;rcamo Model\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eDifference [%]\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003eVogrinec Model\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c8\"\u003e \u003cp\u003eDifference [%]\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e2,2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e2,2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e2,2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e2,2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0%\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e3,15\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e3,15\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e3,15\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e3,15\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0%\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e3,89\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e3,89\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e3,89\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e3,89\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0%\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e4,51\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e4,5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e4,5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e4,5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0%\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab8\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 8\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003e\u0026thinsp;\u0026minus;\u0026thinsp;5. Building periods [s]\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"5\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMethod\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eTx [s]\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eDifference [%]\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eTy [s]\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eDifference [%]\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLFM\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0,309\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0,298\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eNassani equation\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0,272\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-14%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0,260\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-15%\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eEigenvalues and Eigenvectors\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0,290\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0,281\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1%\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab9\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 9\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eA.4. Comparison of drift Sx and Sy of the traditional method and the LFM.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"7\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eStory\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"3\" nameend=\"c4\" namest=\"c2\"\u003e \u003cp\u003eDrift Sx\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"3\" nameend=\"c7\" namest=\"c5\"\u003e \u003cp\u003eDrift Sy\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eTraditional method\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eLFM\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eDifference [%]\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eTraditional method\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eLFM\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003eDifference [%]\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0,00153\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0,0009\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-43%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0,00134\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0,0006\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e-59%\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0,00153\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0,0011\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-30%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0,00134\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0,0009\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e-32%\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0,00136\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0,0011\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-17%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0,00134\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0,0012\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e-10%\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0,00162\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0,0018\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e10%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0,00124\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0,0013\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e5%\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab10\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 10\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003e\u0026thinsp;\u0026minus;\u0026thinsp;6. Average tension [kN] per floor in X-axis\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"4\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eStory\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eLFM\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eTraditional methodology\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eDifference [%]\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e2.78\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e7.70\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-64%\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e4.74\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e19.35\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-76%\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e9.21\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e34.07\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-73%\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e18.58\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e49.59\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-63%\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab11\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 11\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003e\u0026thinsp;\u0026minus;\u0026thinsp;7. Effect of transverse anchors on tensile shear stiffness.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"7\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eStory\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"3\" nameend=\"c4\" namest=\"c2\"\u003e \u003cp\u003eAverage Tension [kN]\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"3\" nameend=\"c7\" namest=\"c5\"\u003e \u003cp\u003eAverage Shear [kN]\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eLFM with transverse anchoring\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eLFM without transverse anchoring\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eDifference [%]\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eLFM with transverse anchoring\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eLFM without transverse anchoring\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003eDifference [%]\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e2.78\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e4.64\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e67%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e7.62\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e7.62\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0%\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e4.74\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e8.29\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e75%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e11.47\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e11.47\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0%\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e9.21\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e13.74\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e49%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e13.85\u003c/p\u003e \u003c/td\u003e \u003ctd 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\u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e"},{"header":"5. Practical consequences and advantages","content":"\u003cp\u003e \u003cem\u003ePractical consequences of system effects in the structural design\u003c/em\u003e \u003c/p\u003e \u003cp\u003eThe previous building was redesigned considering the stresses obtained using the LFM with system effects implemented in ETABS. Anchorages have the potential to strongly influence the design as tend to be the costliest elements within a timber building in seismic areas. And it was observed that the design was governed by stiffness rather than strength. Based on this, the structure was first stiffened in terms of shear by modifying the number of sheathing panels and nailing patterns and then overturning.\u003c/p\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig14\" class=\"InternalRef\"\u003e14\u003c/span\u003e compares the hold-downs design from traditional method and the redesign considering model tension. Regarding design stiffness, in the X-axis there was an average reduction of 25%, and in the Y-axis there was an average reduction of 53%. The design of the anchorages was governed by drift rather than strength. This illustrates that in general the system effects can yield to an increase of need in shearing stiffening, which typically it is not expensive, and a significant decrease of anchoring needs, which typically is very expensive.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eSince the floor beams are the elements that couple the walls. it is essential to verify the bending and shear design of these elements due to seismic loads, and not only for gravitational loads as in traditional method. Moment and shear demand greater than those designed using traditional method were obtained from the model, so a redesign of these elements is necessary.\u003c/p\u003e \u003cp\u003e \u003cem\u003eAdvantages\u003c/em\u003e \u003c/p\u003e \u003cp\u003eThe LFM macro model accurately represents the analytical equations for the lateral deflection of light frame shear walls, as proposed by standards such as SDPWS and CSA O86-14. The model has several comparative advantages over previously developed models: (i) has the versatility to include other sources of stiffness/flexibility in a simple manner, according to the criteria designer; for example, considering shear connectors in the diagonal links, and/or considering the compression of the end studs, perpendicular compression of the bottom plate, contribution of the concrete cone in the base anchors, among others, in the vertical links; (ii) is capable of representing the accumulated overturning both at the wall and building level, an aspect that not all previous models consider; (iii) has the versatility to consider or not the system effects (out-of-plane stiffness of the diaphragm and transverse walls), which have significant implications in design, as demonstrated above; (iv) is applicable in any finite element software, as it uses link and frame elements; (v) allows for nonlinear static elastic and modal analysis, with low computational cost and analysis time compared to nonlinear models; (vi) allows reproducing the inelastic behavior of the walls, both at the level of anchors and by shear, through the constitutive lines of the real envelope of an experimental test.\u003c/p\u003e"},{"header":"6. Conclusion","content":"\u003cp\u003eDespite various methodologies have been proposed for the seismic modelling of timber buildings, none of them demonstrated a combination of: (i) high accuracy in capturing the prescriptions of codes such as the SDPWS or CSA, (ii) the simplicity and versatility to be used in general purpose software to conduct both equivalent lateral load and modal analyses, and (iii) the possibility of considering system effects if desired. This research proposed a macro model entitled Link Frame Model (LFM) consisting of modelling shearwalls as top and bottom rigid beams, two diagonals modelling shear stiffness and two vertical springs modelling anchoring. The results indicate that the model produces virtually the same results of analytical by-hand code calculations, with errors close to 0%, and can be implemented in general purpose software such as e.g. ETABS or SAP2000. This was not only verified at the multistory shearwall level, but also at entire building level, by using the experimental results of a 6-story experimental building monitoring.\u003c/p\u003e \u003cp\u003eApart from proposing this new macro model of shear wall, the LFM model has also been used to analyze system effects, because there is plenty of evidence in previous research that proofs the inaccuracy of individual and free shearwall rotation premise of codes. This analysis considering system effects has been possible by simply modelling the actual flexural out-of-plane stiffness of the diaphragms above shearwalls via explicit modelling of the flexural stiffness of each beam of floors. An average multistory building representing a national Chilean archetype, subjected to an average seismic load, was considered to conduct an in-depth analysis of a representative standard case study. The results show that, even when shearwalls are not connected among each other, the diaphragms couple them. Actually, the hypothesis of rigid diaphragm turns to be much closer to the actual stiffness than a flexible diaphragm. This strongly influences the building lateral behavior and has great practical consequences. In general, uplift anchorages work not only due to in-plane shearwall loads, but also due to out-of-plane shearwall loads. Furthermore, anchorages are strongly overdesigned (an average 70% tension reduction was found), even without considering axial loads, and, in contrast, shears of shearwalls and diaphragm beams can be underdesigned. Still, the results indicate that costs of this type of buildings may be significantly more competitive considering the actual system effects, because anchorages tend to be the most expensive component. By artificially setting close to null the flexural stiffness of diaphragms, the LFM releases virtually the same results of analytical methods with cumulative overturning, which in turns demonstrates the versatility of the LFM to be used both when considering or neglecting system effects.\u003c/p\u003e \u003cp\u003eGiven the evidence demonstrated by previous research of system effects, the overall tendency to construct tall buildings with timber, and the capability of models as the LFM here proposed in capturing the 3D behavior of buildings, it is suggested that future code revisions allow estimators to consider system effects in design for these types of buildings. This will not only yield to designs that match much better with actual shears and tensions, but also avoid unconservative designs. Note that the traditional individual and free-rotating shearwall hypothesis of traditional methods may yield to exaggerated lateral flexibility, which in turn tend to cause underestimation of equivalent lateral loads.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003eThe authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAcknowledgements\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors acknowledge the support of Mat\u0026iacute;as Alarc\u0026oacute;n for the modelling of the Pe\u0026ntilde;uelas Tower and the financial support of Centro Nacional de Excelencia para la Industria de la Madera (CENAMAD ANID BASAL FB210015) of the Pontificia Universidad Cat\u0026oacute;lica de Chile. The authors also acknowledge the financial support of University of A Coru\u0026ntilde;a for letting us publishing this article in Open Access.\u003c/p\u003e\n\u003cp\u003e\u0026nbsp;\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eAlarc\u0026oacute;n, M., Hern\u0026aacute;ndez, F., \u0026amp; Guindos, P. (2022). Structural health monitoring of South-America\u0026rsquo;s first 6-story experimental light-frame timber-building by using a low-cost Raspberryshake seismic instrumetation. \u003cem\u003eEngineering Structures\u003c/em\u003e, \u003cem\u003e275\u003c/em\u003e.\u003c/li\u003e\n\u003cli\u003eAmerican Wood Council. (2020). \u003cem\u003eSpecial Design Provisions for Wind and Seismic\u003c/em\u003e. www.awc.org.\u003c/li\u003e\n\u003cli\u003eBagheri, M. M., \u0026amp; Doudak, G. (2021). 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Structural performance of strong timber diaphragms: High-capacity light-timber frames and cross-laminated timber. \u003cem\u003eStructures\u003c/em\u003e, \u003cem\u003e63\u003c/em\u003e. https://doi.org/10.1016/j.istruc.2024.106335\u003c/li\u003e\n\u003cli\u003eVogrinec, K., Premrov, M., \u0026amp; Kozem \u0026Scaron;ilih, E. (2016). Simplified modelling of timber-framed walls under lateral loads. \u003cem\u003eEngineering Structures\u003c/em\u003e, \u003cem\u003e111\u003c/em\u003e, 275\u0026ndash;284. https://doi.org/10.1016/j.engstruct.2015.12.029\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"european-journal-of-wood-and-wood-products","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"harw","sideBox":"Learn more about [European Journal of Wood and Wood Products](http://link.springer.com/journal/107)","snPcode":"107","submissionUrl":"https://submission.nature.com/new-submission/107/3","title":"European Journal of Wood and Wood Products","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"timber building, multistory building, modelling, simulation, structural analysis, seismic analysis, system effect","lastPublishedDoi":"10.21203/rs.3.rs-4643226/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4643226/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThis article proposes a model that makes possible the seismic analysis of timber frame multistory buildings in general-purpose software. The model is entitled Link Frame Model (LFM) and shows the following advantages in comparison to previous models: (1) it can model shearwalls only with frame elements and links with errors close to 0% with respect to analytical code models such as e.g. the Special Design Provisions for Wind and Seismic (SDPWS); (2) it can be used for both equivalent lateral force procedures and modal spectral analysis and gravitational calculations; (3) the computation of the natural period shows deviations close to 0% in comparison with eigenvalues and eigenvectors; (4) it can be implemented in general purpose structural analysis software such as e.g. ETABS or SAP2000; and (5) building system effects, i.e. interaction of shearwalls with other assemblies, can optionally be captured if assigning the proper diaphragm out-of-plane flexural stiffness. Given the great impact of this last aspect in practical design, and the lack of its research, this paper does not only present the model and validation itself, but also analyzes the consequences of considering system effects in a representative case study building. The analysis demonstrates that the average shearwall tension (uplift) of regular buildings can decrease by 80% if considering system effects, which could make timber buildings much more cost competitive in seismic countries.\u003c/p\u003e","manuscriptTitle":"The Link Frame Model (LFM), a tool for the seismic analysis of timber frame buildings considering system effects","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-07-19 19:58:02","doi":"10.21203/rs.3.rs-4643226/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2024-12-19T09:13:53+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2024-12-13T22:37:25+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"167585133992490440135987056320234584464","date":"2024-11-22T14:11:39+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"135909606642176325042632752632502887255","date":"2024-08-11T04:57:04+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2024-07-08T07:13:34+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"170943284709561969680870586266403291173","date":"2024-07-08T06:51:25+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"170161159865447050209294710496211845764","date":"2024-07-04T12:56:20+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2024-07-04T10:44:36+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2024-07-03T09:32:30+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2024-06-27T12:04:02+00:00","index":"","fulltext":""},{"type":"submitted","content":"European Journal of Wood and Wood Products","date":"2024-06-26T13:56:37+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"european-journal-of-wood-and-wood-products","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"harw","sideBox":"Learn more about [European Journal of Wood and Wood Products](http://link.springer.com/journal/107)","snPcode":"107","submissionUrl":"https://submission.nature.com/new-submission/107/3","title":"European Journal of Wood and Wood Products","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"2a17bda1-3a11-4027-bf50-8dea458d305b","owner":[],"postedDate":"July 19th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[],"tags":[],"updatedAt":"2025-02-10T16:02:58+00:00","versionOfRecord":{"articleIdentity":"rs-4643226","link":"https://doi.org/10.1007/s00107-025-02201-7","journal":{"identity":"european-journal-of-wood-and-wood-products","isVorOnly":false,"title":"European Journal of Wood and Wood Products"},"publishedOn":"2025-02-04 15:57:42","publishedOnDateReadable":"February 4th, 2025"},"versionCreatedAt":"2024-07-19 19:58:02","video":"","vorDoi":"10.1007/s00107-025-02201-7","vorDoiUrl":"https://doi.org/10.1007/s00107-025-02201-7","workflowStages":[]},"version":"v1","identity":"rs-4643226","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-4643226","identity":"rs-4643226","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}