Finite element analysis of alternative load paths in a platform-framed CLT building

Cross-laminated timber (CLT) is used in increasing proportions for the bearing structures of multi-storey buildings. CLT is composed of cross-wise laminae of parallel timber boards and is used for wall and floor panels (Brandner, 2013). Currently, the tallest timber buildings (both 18 storeys) are Mjøstårnet in Brumunddal, Norway (Abrahamsen, 2017) and Brock Commons Tallwood House in Vancouver, Canada (Fast et al., 2017), and both use CLT panels as floors. Pure CLT buildings can either be balloon-framed, with continuous walls, or platform-framed, where the floors of each storey are supported on top of the walls of the storey below, which results in across-the-grain compression in the floors and thus limits the achievable building height (Gagnon and Pirvu, 2011). The nine-storey Stadthaus in London, UK, is an example of a platform-framed CLT building (Wells, 2011).

In a multi-storey building with high occupancy, disproportionate collapse resulting from an unforeseeable event such as an accident or act of terrorism needs to be avoided as the consequences would be severe (BSI, 2006). The total probability of a disproportionate collapse, $P(C)$⁠, is usually expressed by (Ellingwood and Dusenberry, 2005)

where $P(E)$ is the probability of an unforeseen event, $P(D|E)$ is the probability of initial damage given the unforeseen event and $P(C|D)$ is the probability of disproportionate collapse given the initial damage. These terms are respectively referred to as exposure, vulnerability and robustness (Starossek and Haberland, 2010), each posing a line of defence (Ellingwood et al., 2007), of which mostly vulnerability and robustness can be affected by engineering choices (Starossek and Haberland, 2010).

Compared with concrete and steel buildings, a lack of guidance has been identified concerning the design for the structural robustness of multi-storey CLT buildings (Huber et al., 2019). Robustness requires the availability of alternative load paths (ALPs) that are to be activated when a part of the vertical bearing structure has been removed (Ellingwood et al., 2007). Examples of ALPs include catenary action in beams, membrane action in floors and deep beam action of wall sections above removed walls (Huber et al., 2019). The ability for load transfer under large deformations in the connections is essential for an ALP to function as intended (Byfield et al., 2014).

An ALP analysis yields the response of a structure to an assumed component loss (Ellingwood et al., 2007) and assesses how the ALPs develop; this is usually achieved by finite element analysis (FEA) to account for non-linearities and dynamic effects (Izzuddin et al., 2008). Using FEA, Mpidi Bita et al. (2018) conducted an ALP analysis of a 12-storey platform-framed CLT building by dynamic removal of the middle support wall of a double-span floor at the ground storey. They found that the ALPs required larger capacities than those supplied by commonly used fasteners. Mpidi Bita and Tannert (2019a) conducted an ALP analysis using FEA of a nine-storey glue laminated (glulam) timber column-framed building with CLT floors by removing various columns. They found that the structure could engage in a hanging action of the floors from the remaining columns, in catenary action of the floor panels and in a horizontal tie action of the damaged bay from the remaining building core. Mpidi Bita and Tannert (2019b) presented an analytical linear elastic procedure for designing ALPs in platform-framed CLT buildings, assuming that catenary action of the floor panels, cantilever action in a damaged corner bay and deep beam action in an internal bay would develop after removal of a wall.

In the studies reported in the literature so far, ALPs have been investigated on a global building level where components and their interactions have been simplified and the mechanical behaviour of multiple fasteners in a connection has been condensed to a single point. However, a recent study by Huber et al. (2018) showed that modelling single fasteners between CLT components may reveal progressive rupture in a zipper-like fashion under non-uniform loading after wall removal. Furthermore, the ALPs in platform-framed CLT buildings, which – for the sake of sound insulation – consist of separated bays with single-span floors have so far not been investigated. It is assumed that, after a removal in these buildings, the compressed floor panels between the walls could result in friction and local timber crushing, governing the ALP development with varying extents at different storeys. A detailed understanding of the mechanisms governing the development of ALPs at the component level is required in order to correctly assess the behaviour of the entire building at a global level after a wall removal. The goal of this work was to address the following research questions, considering the removal of a single wall panel at the ground storey of a single-span, platform-framed CLT bay.

• What ALPs may develop on single storeys?

• How do the building components and connections contribute to the development of ALPs on single storeys?

• How is the entire bay affected after the removal?

To approach answers to these questions, FEA using the commercial software Abaqus (DS, 2014) was used, accounting for non-linearities – that is, fastener failure, frictional contact, compressive crushing, tensile failure and large displacements.

The conducted analysis was based on an existing eight-storey platform-framed CLT building in Sweden, made of separated bays with single-span floors and balconies (see Figure 1(a)). The storey height is 3 m. For the worst case scenario, a corner bay was investigated, with simplifications for the sake of modelling (see Figure 1): (a) any openings in the panels were ignored; (b) each storey was assumed to be similar; (c) the shape of the floor plan of the bay was made more quadratic to obtain a generic setup and to capture a recommended wall removal length of approximately twice the storey height (Huber et al., 2019); (d) the surrounding structure was coupled by linear springs at four locations on each storey. The surrounding spring stiffness was set to 7·4 kN/mm, which was estimated by loading the remaining structure sideways in a separate finite element (FE) model and measuring the reactions. All panels were five-ply CLT made of C24 graded timber with lap-joints between the floor panels (see Figure 2). The removal of a wall panel supporting all three floor panels at the bottom storey was studied.

Four connections exist in the structure (see Figure 3) – floor-to-floor (F2F) connections in the lap-joints, floor-to-wall (F2W) connections between the floor panels and their supporting walls, wall-to-wall (W2W) connections in the corners and angle bracket connections between the floor panels and the walls of the next storey. Between the floors and the edges of the wall panels of the next storey, a 25 mm thick rubber sound insulation exists; this was ignored in all but the simplified dynamic model (see Section 2.4). In the connections, self-tapping screws (ETA-12/0063 (Eota, 2012); ETA-12/0373 (Eota, 2017)) and angle brackets of type TTF200 (ETA-12/0496 (Eota, 2014)) are installed (see Table 1). The angle brackets are 3 mm thick and fixed with 30 ring-shanked anchor nails (see Table 1) on each flange.

The component method was used to model the connections, which has previously been successfully applied to model steel and concrete connections after removal of an element (Stoddart et al., 2014; Stylianidis and Nethercot, 2015) and to evaluate timber connections under seismic loads (Fragiacomo et al., 2011; Rinaldin et al., 2013). The active parts of connections were substituted by their respective force–deformation behaviour to save computational cost while keeping the model sufficiently realistic. In the models, the screws and brackets were replaced by ‘finite connector elements’ to account for non-uniform loading and progressive rupture. Henceforth, the finite connector elements are referred to as ‘connector elements’, while the screws and angle brackets as referred to as ‘fasteners’.

The Abaqus connector element in three-dimensional (3D) space (Conn3D2) is a two-node 1D element that defines a constitutive behaviour between the degrees of freedom (DoF) of its nodes (node a and node b) (DS, 2014). Attached to each node, the element contains a coordinate system (directions $x1$⁠, $x2$ and $x3$⁠) to follow their motions. The nodes were coupled to a cloud of mesh nodes on the respective surfaces in connection. All relative motions between the nodes were measured as seen from the coordinate system of node a. The constitutive mechanical behaviour of the element was based on the relative changes in translation (⁠$δxi$⁠) and rotation (⁠$δϕi$⁠), which obey Equations 2 and 3 for an arbitrary motion of node b from position b′ to b, considering large deformations.

Here, $xi,b$ and $xi,b′$ denote the coordinates of b and b′ respectively in system a, and $ϕi,b$ and $ϕi,b′$ denote the components of the rotation vector (⁠$ϕ$⁠), which positions the coordinate axes at b and b′ relative to the axes at a (DS, 2014).

The constitutive behaviour was specified for each DoF. Figure 4 shows the generic force–displacement behaviour used in this study, equivalently applied for moments, along DoF $i$⁠. The elastic stiffness was $Ki$⁠, optionally followed by a plastic yield point at ${xi,y,Fi,y}$ and a subsequent hardening up to a plastic plateau at ${xi,plat,Fi,max}$⁠, ultimately followed by the motion-based damage initiation point at ${xi,d,Fi,max}$⁠. After damage initiation, the force responses along all DoFs were degraded exponentially until total failure (rupture) at $xi,r$⁠. The failure motion (i.e. $xi,r−xi,d$⁠) was set to approximately $xi,d/10$ to avoid abrupt stiffness changes that could jeopardise convergence.

When replacing a self-tapping screw, the screw axis was aligned with $x3$ of node a, and only translational DoFs were used. For the lateral stiffness (along $x1$ and $x2$⁠), $Klat$ was used from Equation 4 (taken from BS EN 1995-1-1:2004 (BSI, 2004)). For the axial stiffness, $Kax$ from Equation 5 (taken from ETA-12/0063 (Eota, 2012) and ETA-12/0373 (Eota, 2017)) was used.

Here, $ρm$ is the mean timber density (in kg/m³), $d$ is the nominal screw diameter in mm, $l$ is the penetration length of the screw thread in mm and K is in N/mm.

For axial screw loading, brittle behaviour was assumed (i.e. no plastic branch in Figure 4). For the W2W and F2F screws, thread extraction governed the axial strength, and $Fax,max$ (in N) was calculated using Equation 6 from Uibel and Blaß (2014). For the F2W screws, head pull-through governed the strength, and $Fax,max$ was calculated using Equation 7 from ETA-12/0373 (Eota, 2017).

In these equations, $ρk$ is the characteristic density (in kg/m³), $α$ the angle between the screw axis and the fibres (in degrees) and $fhead,k$ is the characteristic pull-through parameter of the screw head (in N/mm²) at the reference timber density $ρa$ (in kg/m³), $fhead,k$ and $ρa$ given in ETA-12/0373 (Eota, 2017).

For lateral screw loading, ideal plasticity was assumed (i.e. no hardening branch in Figure 4). The yield point (⁠$Flat,y$⁠) was calculated using Equation 8, after evaluating all six Johansen failure modes (⁠$FR,a$ to $FR,f$⁠, in N) from BS EN 1995-1-1:2004 (BSI, 2004). The Johansen modes are functions of the characteristic embedment strength of the timber (⁠$fh,k$⁠, in N/mm²), which was calculated according to Equation 9 from Blaß et al. (2006), the thickness of the connected components, the screw diameter and the characteristic screw yield moment (taken from ETA-12/0063 (Eota, 2012) and ETA-12/0373 (Eota, 2017)). Three of the failure modes additionally depend on $Fax,max$ due to the roping effect (BSI, 2004).

No interaction was modelled between the DoF in the elastic branches. However, for the yield point in the screws, a coupled criterion according to Equation 10 was assumed to ensure an equal yield point in the plane perpendicular to $x3$ (i.e. a cylindrical yield surface), which follows the reasoning in BS EN 1995-1-1:2004 (BSI, 2004) for mixed load states of fasteners. Similarly, the damage initiation point was coupled between all DoFs according to Equation 11 (i.e. an ellipsoid damage surface).

where the common value $x1,d=x2,d=20mm$ was set and $x3,d=Fax,max/Kax$⁠.

The bracket was first studied in a separate FEA with a 2D shell model of the bracket steel, connector elements for the nails and 3D solids to represent the wooden contact areas of the flanges (see Figure 5). For the nails, the trilinear force–displacement behaviour given by Izzi et al. (2018) was used, who experimentally validated their modelling approach of the same bracket. The force–deformation behaviour of the bracket was recorded while moving the lower contact area in shear (⁠$x1$ in Figure 5), uplift (⁠$x2$ and $x3$⁠) and hinging rotation (⁠$ϕ1$⁠), one at a time. The model accounted for plasticity, friction, contact and large deformations. The results were then used as input values for the connector elements substituting the brackets.

Since a 3D analysis of the entire bay at the desired level of detail was deemed to be too computationally expensive, the analysis was subdivided into three representative compartment models (see Figure 6) – one for the bottom storey, one for the top storey and one for the storeys in between. Each compartment included the walls of the respective storey and the floor panels supported by them. The surroundings were replaced by suitable boundary conditions and simplifications (as described in Section 2.3). The modelling of all compartments was similar; as an example, Figure 7 shows the upper quarter of the bottom compartment model. Each floor panel was modelled by an outer ‘cage’, finely meshed with quadratic brick elements (C3D20R), which was tied to an inner ‘core’, coarsely meshed with continuum shell elements (SC8R). In thickness, the cages contained two elements per CLT ply to increase the stress resolution with regard to compressive crushing, while the cores contained a single element that accounted for all CLT plies by a composite layup, enforcing shear flexible (Mindlin–Reissner) plate theory (DS, 2014). The walls below were modelled in a similar way to the cores and the walls of the next storey were simplified by L-shaped rigid surfaces since the vertical deflection of these walls was estimated to be small compared with that of the floor panels. The L-shape provided both a horizontal contact surface for the vertical loads and a vertical surface that the connector elements substituting the brackets could be coupled to. The surrounding structure beyond the bay was modelled as rigid in the background around the compartment. The connector elements were inserted at the fastener locations between the connected parts and at the locations of the stiffness between the surrounding structure and the bay (see Figure 7(b)).

Material data for timber grade C24 based on characteristic strengths were used for all components according to Table 2, with Poisson's ratios set to zero. An orthotropic linear elastic material model was applied for all the flexible components. For the floor cages, additionally an ideal-plastic material model was used to account for compressive timber crushing, which was based on a Tsai–Wu yield surface (Tsai and Wu, 1971) by implementing an Abaqus subroutine presented by Ekevad (2006). The uniaxial yield points were set to the strength values in Table 2. Furthermore, brittle failure in only tension and shear was tracked in the subroutine by applying a maximum stress criterion according to

where $σt$ and $τ$ are the tensile and shear stresses, respectively and subscripts 0 and 90 denote the angle to the fibre direction and LS and RS denote longitudinal and rolling shear, respectively. Between all the components, normal contact was modelled with a ‘hard’ pressure–overclosure law, where arbitrarily large contact stresses could occur to prohibit penetration (DS, 2014), and tangential friction was modelled with an isotropic coefficient of 0·3.

To elicit the ALPs, a pushdown analysis was conducted, during which the section above the removed wall was pushed down quasi-statically until ultimate failure occurred and the respective force–displacement response (i.e. the pushdown curve) was recorded (Izzuddin et al., 2008; Khandelwal and El-Tawil, 2011). Separate analyses were conducted on the three compartment models (see Figure 6), with the assumption that the behaviour of the entire bay could be described by combining the behaviour of the single compartments in a later step. In the bottom compartment, the removed wall was not modelled and a gap existed instead. Each compartment model thus contained at least three walls, henceforth called ‘stationary walls’, in vertical alignment with the remaining walls on the bottom storey. The middle and top compartments additionally contained a wall that was assumed to move downwards, above the gap. The stationary walls of each compartment model were rigidly fixed at their bottom as a first approximation of their rather stiff connection by angle brackets to the floor below, which was not modelled. The bottom movement of the stationary walls was considered less significant for the analyses because most movement was expected in the floor panels. The moving walls were unrestrained by external boundary conditions. In the bottom and middle compartments, the pushdown was performed by moving down the rigid L-surface above the gap in a deformation-controlled manner; for the top compartment, the bottom of the moving wall was pulled down instead.

Before the pushdown was started, vertical loads $w~j$ were applied as pressures on the rigid L-surfaces for the bottom and middle compartment and on a corresponding surface on the outer edges of the roof panels for the top compartment. For simplification, no floor and snow loads were applied; instead, their contribution was accounted for in $w~j$⁠. For storey j, $w~j$ was calculated according to Equation 13, which corresponds to the accidental load combination required for ALP analyses in BS EN 1990:2002 (BSI, 2002).

In Equation 13, $Gj$ and $Qj$ are, respectively, the total dead and live loads (in N) of storey $j$⁠, $S$ is the total snow load (in N) and $A$ is the total horizontal cross-sectional surface of four wall panels (in m²). It was assumed that the four walls of a compartment carried the loads equally before the removal. For the middle compartment, the loads of the storey directly above the removed wall (⁠$j=2$⁠) were used. Large deformations were accounted for and a quasi-static implicit dynamic calculation regime using the backward Euler integrator was applied to increase convergence (DS, 2014).

Lacking experimental data, a manual criterion was introduced (see Figure 8) to evaluate whether brittle shear failure would occur in the floor panels above the support; only the strongest plies regarding transverse shear were considered (i.e. ply 2 and ply 4), which were loaded in longitudinal shear. The elements marked as failed by the maximum stress criterion in the finely meshed cages were projected onto a cross-section above the support walls. The criterion was met when, in the projection, the cross-section of one ply was entirely marked as failed. Thereafter, any load transfer by way of the cross-section of the floor panels was considered to be inhibited in the models. The assumption behind the criterion was that a crack could propagate along the ply if, in the projection, the entire ply was marked as failed.

The pushdown curves (P_j) elicited during the ALP analysis were subsequently used to substitute the force–displacement behaviour of the respective storeys in a simplified dynamic model of the entire bay (see Figure 9). Those parts of the storeys that were assumed to be moving were condensed to point masses (⁠$Mj$⁠), which were interlinked by an inter-compartment stiffness (⁠$KIC$⁠), and those parts that were assumed to remain stationary were substituted by a fixed background point at each storey. $KIC$ was calculated by assuming a parallel action of the stiffness of the angle brackets and the sound insulation along the wall edges. Each point mass was coupled to its background point by a connector element that substituted the elastic, plastic and damage behaviour of the pushdown curve (i.e. the aggregated behaviour of the ALPs) of the respective storey.

The reassembled dynamic model is shown in Figure 10; the system could only move vertically (along $x$⁠) subjected to gravitational acceleration g, the time-dependent force $R0(t)$ substituted the wall to be removed and the equivalent shares of the live load (⁠$qj$⁠) and the snow load (⁠$s$⁠) were applied as point loads. It was assumed that only the moving walls and a quarter of the floor weight would contribute to the moving masses, which resulted in $Mj=0⋅25Gj/g$⁠, and, correspondingly, $qj=0⋅5Qj/4$ and $s=0⋅2S/4$⁠. $R0(t)$ kept the system in static equilibrium at $t=0$ and was subsequently reduced to zero along a sigmoid curve over the removal time. Following a recommendation of the US Department of Defense (US DoD, 2016), the removal time was set to slightly less than one tenth of the period of the first vertical eigenmode of the compartment models. The eigenmodes were evaluated by modal analyses in the FE software and the shortest period among the compartments was used. The forces directed to ground at the respective background points, $Rj(t)$⁠, were recorded. An implicit dynamic calculation regime using the Hilber–Hughes–Taylor integrator with the default transient fidelity settings (DS, 2014) was applied to capture the transient response.

The input values for the connector elements of all the fasteners are shown in Table 3. For translational movement of the bracket, the stiffness values in Table 3 were based on the simulations; however, the yield and ultimate strength values (66·5 kN in shear and 50 kN in uplift) were approximations to the results reported by Izzi et al. (2018). All rotational results were based on the simulations. The bracket behaved differently in opening and closing rotations (see Figure 11) mainly because, during closing, the flanges were fully supported by the contacting surfaces whereas, during opening, the flanges were only supported by the nails. Nevertheless, in the connector elements, the hardening behaviour was simplified by averaged values to facilitate implementation.

Four different ALPs were identified in the compartment models. Figure 12 shows a schematic illustration of the ALPs in each compartment model.

• ALP I – a shearing action in the outer floor panels, transferring loads from the pushing wall from above to the supporting stationary walls below. This ALP was limited by transversal shear failure in the floor panels due to the load concentrations beneath the pushing wall.

• ALP II – an arching action of the moving wall, transferring loads to the stationary walls by way of the W2W connectors. This ALP was limited by the capacity of the W2W connectors.

• ALP III – a mechanism resembling catenary action between the floor panels, transferring loads by way of various connectors and friction horizontally. This ALP was predominantly sustained by the tensile capacity of the F2F joints.

• ALP IV – a hanging action from the roof panels, transferring loads by way of the W2F screws to the roof. This ALP was limited by the rip-out capacity of the W2F screws.

ALP II could not occur in the bottom compartment because it lacked a moving wall and, naturally, ALP IV could only occur in the top compartment. The contributions of different components to the ALPs in the compartments were estimated from measurements in the FE models at the maximum load state for each ALP (a summary is provided in Table 4). For all the compartments, ALP III provoked non-uniform loading of the F2F screws along the lap-joints, with the screws closest to the moving wall taking the highest loads and the screws furthest away being barely loaded. However, loading of the F2F screws never exceeded 50% of their capacity.

The corresponding pushdown curves for the various compartment models are shown in Figure 13. The bottom and middle compartments both exhibited a non-linear hardening response up to approximately 7 mm of pushdown displacement, which was primarily a result of compressive timber crushing as a result of ALP I. At larger displacements, the shear failure criterion was met and the loads along ALP I and ALP III dropped to zero. In the middle compartment, only ALP II could subsequently transfer loads until itself was ultimately exhausted at 20 mm of displacement (i.e. when the W2W screws failed). The top compartment exhibited a linear response up to approximately 1·5 mm of displacement, which was predominantly carried by ALP II (here in the flipped direction; see Figure 12(a)). At larger displacements, the rotation of the floor panels led to non-uniform loading of the W2F screws, resulting in a zipper-like progressive rip-out of all the W2F screws, which was completed at approximately 9 mm displacement (see the magnified inset in Figure 13). Subsequently, only ALP II transferred the loads, until ultimate failure occurred.

A cut through the load situation at the load concentration above the gap, beneath the pushing L-surface, can be seen in Figure 14. The top layer of the floor cage crushed locally (i.e. deformed plastically) in the region of edge contact with the pushing L-surface above and to the stationary wall below. The crushing remained local because the stresses could distribute in the deeper layers of the cross-section. As the pushdown movement of the L-surface proceeded, it provoked a rotation of the floor panel and subsequently an outwards movement of the supporting wall, resulting in a reaction force of the spring towards the surrounding structure, normal and frictional reactions in the walls, reactions in the fasteners and friction between the L-surface and the floor panel. Spring, friction and normal forces contributed the most, and the fasteners contributed only negligibly to the force balance at the shown location.

The removal time was 0·0078 s and K_IC = 320 kN/mm. The reactions $Rj$ at the fixed background points for each storey are shown in Figure 15(a); the system started to oscillate without collapse after approximately 15 ms, with the loads being higher at the lower storeys. As no damping was applied, the oscillations continued indefinitely, including resonance effects among the storeys and load reversals. However, since a fully undampened system is unrealistic, only the values close to the initial peak reactions should be interpreted. Figure 15(b) shows $Rj$ for $10KIC$ rather than $KIC$ (Figure 15(a)). In this case, more load-sharing among storeys occurred compared with the original case because the dead time between the peak reactions was reduced. The first peak reaction was lower for storeys one to five, and higher for the remaining storeys. Figure 15(c) shows $Rj$ for $KIC/20$ rather than $KIC$⁠. This extreme case resulted in such a long dead time between the peak reactions that the ALPs exhausted sequentially from the bottom storey to the top; in other words, progressive collapse occurred. Values between $KIC$ and $KIC/20$ did not result in a bay collapse.

Separate ALP analyses were conducted for three representative storeys in the studied bay by means of quasi-static pushdown analyses that accounted for single fasteners, friction, timber crushing, brittle failure and geometric non-linearities. The force–displacement behaviours elicited under the ALP analyses were then inserted in a simplified dynamic model to evaluate the transient response of the entire bay.

ALP I led to a concentration of transverse shear loads above the removed wall and the corresponding strength of the floor panels limited the ultimate load along this ALP. However, the true capacity of this ALP remains uncertain because an unvalidated – yet in the authors’ opinion conservative – failure criterion was used. Nevertheless, the load concentration is regarded as disadvantageous as it could provoke a brittle shear failure depending on the load redistribution capability inside the CLT. The vertical alignment of the wall joints provoked this load concentration and it seems that it could be mitigated by avoiding the repetitive pattern of isolated bays and instead shifting the wall panels horizontally at various storeys – for example, like bricks in a masonry wall. ALP II limited the arching action of the moving walls due to yielding of the W2W screws; the arching could be exploited to a greater extent by using stiffer and stronger W2W fasteners (e.g. angle brackets). ALP III provided support for ALP I and ALP IV: a failure would let the floor panels rotate and sag downwards. ALP IV was impaired by progressive rip-out of the W2F screws due to the rotation of the roof panels. Stiffening of the roof (e.g. by an additional beam) in combination with stronger fasteners may exploit this ALP to a greater extent (compare with the improved roof design proposed by Mpidi Bita and Tannert (2019a)).

The dynamic analysis showed that collapse is unlikely in the studied bay with the assumed value for the inter-storey stiffness $KIC$⁠. Load-sharing among the storeys increased for a high value of $KIC$ but decreased for a low value, enabling progressive collapse. $KIC$ was estimated by hand calculation and this remains to be investigated more thoroughly; nevertheless, to pose a serious threat, at least a twenty-fold reduction in $KIC$would be required. The omission of damping in the dynamic model may be unrealistic, but this approximation seemed sufficient to study the first peak reactions at each storey and, furthermore, the results can be regarded as more conservative because damping would lower the peaks. An estimation of damping and further variations of the variables may be necessary to improve the dynamic model.

Experimental investigations are necessary for validation of the model and the details of this study are contingent to the specific case building. Nevertheless, the mechanisms governing ALPs in a single-span platform-framed CLT building were studied in general, contributing to the sparse knowledge in this field and providing valuable information for structural engineers to design safer platform-framed CLT buildings. CLT buildings may offer a sustainable choice when facing the challenges of climate change regarding the housing demands of the future.

For the studied model of the bay, it was found that

• ALP I was a transverse shear action in the floor panels, ultimately limited by shear failure in the CLT

• ALP II supported an arching (deep beam) action of the walls, limited by the lateral capacity of the W2W fasteners

• ALP III supported a catenary action in the floor panels, predominantly governed by the capacity of the F2F fasteners

• ALP IV supported a hanging action from the roof, limited by the axial capacity of the W2F fasteners

• the bay could sustain a dynamic single wall removal on the bottom storey without collapsing.

However, as already noted, experimental validations are required in the future, specifically for the failure mode under the shear concentration of ALP I.

The authors thank the Vinnova BioInnovation project for funding of this work.

$A$

total horizontal cross sectional surface of four wall panels (m²)

$C$

disproportionate collapse

$D$

local damage

$d$

nominal screw diameter (mm)

$E$

unexpected event

$Fax,max$

axial screw strength (N)

$Fi$

force along the ith degree of freedom (DoF) (kN)

$Flat,y$

yield point of lateral screw loading (N)

$Fmax$

maximum or ultimate force (kN)

$FR,a$ to $FR,f$

Johansen yield strengths (N)

$Fy$

yield force (kN)

$fc,k$

characteristic compressive strength (MPa)

$fh,k$

characteristic embedment strength (N/mm²)

$fhead,k$

characteristic pull-through parameter of screw head (N/mm²)

$ft,k$

characteristic tensile strength (MPa)

$fv,k$

characteristic shear strength

$G$

elastic shear modulus (MPa)

$Gj$

total dead load of storey j (N)

g

gravitational acceleration (kg/(ms²))

$Kax$

axial stiffness

$Ki$

elastic stiffness along DoF $i$ (kN/mm)

$KIC$

inter-compartment stiffness (kN/mm)

$Klat$

lateral stiffness

$l$

penetration length of thread (mm)

$Mj$

equivalent moving mass of storey j (kg)

$Mmax$

maximum or ultimate moment (Nm)

$My$

yield moment (Nm)

$P(X)$

probability of event $X$

$P(X|Y)$

probability of $X$⁠, given $Y$

$Pj(δ)$

pushdown curve of storey j (kN)

$Qj$

total live load of storey j (N)

$qj$

equivalent moving live load of storey j (N)

$R0(t)$

force replacing the removed wall (N)

$Rj(t)$

reaction at background point of storey j (N)

$S$

total snow load (N)

$s$

equivalent moving snow load (N)

$t$

time (s)

$w~j$

vertical pressure in walls (MPa)

$xd$

displacement at damage initiation (mm)

$xi$

relative translation in DoF $i$ (mm)

$xplat$

displacement at start of plastic plateau (mm)

$xr$

ultimate displacement at rupture (mm)

$xy$

displacement at yield point (mm)

$α$

angle between screw axis and fibres (degrees)

$δ$

pushdown displacement (mm)

$ρa$

reference timber density (kg/m³)

$ρk$

characteristic timber density (kg/m³)

$ρm$

mean timber density (kg/m³)

$σt,0$

tensile stresses along fibres (MPa)

$σt,90$

tensile stresses perpendicular to fibres (MPa)

$τLS$

longitudinal shear stresses (MPa)

$τRS$

rolling shear stresses (MPa)

$ϕ$

positioning rotation vector (degrees)

$ϕd$

rotation at damage initiation (degrees)

$ϕi$

relative rotation around DoF $i$ (degrees)