On the seismic design and behavior of Automated Rack Supported Warehouses

Automated Rack Supported Warehouses, consisting of huge steel buildings offering optimized storage solutions, have been facing a huge diffusion in the last decade, mainly due to the necessity of having bigger and more efficient places to stock and handle goods through automated systems. However, there is not a specific regulatory framework for them, and they are currently being designed to adopt the approach used for traditional steel racks. Even if traditional steel racks and ARSWs have several common aspects, there are relevant differences that do not allow to adopt the same design approach, especially for seismic actions. To highlight the factors and parameters currently influencing the seismic design and the behavior of these constructions, and the consequent need for a different design approach, the present paper presents a critical analysis of the seismic design approach currently adopted by technicians and designers. Then, a set of 5 structures designed by 5 of the major European companies specialized in this field is used to perform both the critical analysis of the different design approaches adopted and the assessment of the seismic performance. The seismic assessment results highlight the typical criticalities and the necessity of a novel proper design approach.

1 3 multi-depth, based on the global and functional organization and the number of continuative available spots for each load level (Fig. 1a). For all the structural types it's possible to individuate a Cross-Aisle (CA) and Down-Aisle (DA) directions; the former is perpendicular to the aisles and is in-plane with the upright trusses constituting the racks, and the latter is parallel to the aisles and in-plane with pallet beams (Fig. 2).
ARSWs constitute the direct upgrade of traditional pallet racks. In such construction works, racks have the double function of stoking goods and providing stability, resistance, and rigidity against the various actions applied to the warehouse. Although this upgrade of structural function makes ARSWs' racks a primary structural system and can strongly modify the loads applied, ARSWs racks acquired most of the traditional ones' structural features to follow the fast-evolving market request, but they were not supported by a specific regulatory framework. The confusion between these two systems and the adoption of the same guidelines defined for traditional steel racks to design ARSWs ('BS EN 16,681:2016   choices and technical solutions that the last seismic events proved to be not always adequate (Haque and Alam 2015). In this regard, Caprili et al. (2018) tried to apply the Eurocode standards for steel structures to design a seismic-resistant dissipative double-depth warehouse. One of the most relevant results is the hard applicability of capacity design rules, e.g. the maximum variability of the over-strength factor. Given the short inter-storey height of these structures if compared to buildings (in general, from 1 to 1.5-1.8 m vs. 3 m), it was not possible to fulfil this design request neither varying steel grade nor section geometrical properties.
ARSWs are characterized, on one hand, by peculiar structural configurations that strongly influence the global behaviour and, on the other hand, by unique non-standard and ad-hoc made structural components and connections. Following this observation, the numerous pieces of research carried out on steel racks, being them traditional or innovative as ARSWs', can be divided between those dealing with the analysis of the global behavior and those with the single elements and connections (as uprights, diagonal-to-upright connections, pallet beam-to-upright connections and upright base connections).
In the last decades, the global structural behaviour of traditional racks along both CA and DA directions has been investigated focusing especially on seismic response. In this framework, Baldassino et al (1999;2000) analysed, tested and carried out a numerical study on the response of pallet racks commonly used in Europe. Within SEISRACKS and SEISRACKS2 research projects (European Commission. Directorate-General for Research 2009; Castiglioni et al. 2014;Kanyilmaz et al. 2016a, b;Kanyilmaz et al. 2016a, b), experimental tests were carried out in both CA and DA direction, performing quasi-static monotonic, pseudo-dynamic and dynamic tests, aiming at pointing out the failure modes and defining q-factors to be used in seismic design. Degee et al (2011) conducted a parametric study comparing the various methods commonly used in practice for analysing the seismic structural behaviour of racks (i.e. modal response spectrum analysis and lateral force method analysis) as well as the different ways to account for geometrical nonlinear effects in these conventional methods of analysis in case of structures designed for low ductility. In the more recent literature, Tsarpalis et al (2021) investigated the influence of the pallets and their sliding in the seismic assessment of racking structures. Tsarpalis et al (2021;2022) show first a simplified modelling method for the assessment of the seismic performance of ARSWs and then the main relevant characteristics of steel racking systems for seismic vulnerability analysis. Kondratenko et al (2021) evaluate the structural performance of ARSW multi-depth structures under low-to-moderate seismic actions. The final aim of this paper is shared with the present research, but here the study is applied to a different structural type (double-dept warehouses) meaning a different distribution of internal actions under horizontal loads. Besides, a high seismic action is adopted as an input for the design. The works above mentioned are among the very few contributions to the structural analysis of steel racks implemented in ARSWs.
Many recent studies are focused on the behaviour of components, as the ones of Becque e Rasmussen (2009a, b), Schafer (2000), Gilbert et al (2012), Kanyilmaz et al (2016a, b), stressing the high influence of their peculiarities on the global behaviour. As an instance, the typical uprights adopted in racks are usually realized with thin-walled sections and are often characterized by an open mono-symmetric and lipped cross-section, with continuous perforation along their height. These characteristics make the behaviour of this element different not only from hot-rolled sections but also from common structural cold-formed profiles used in light-weight constructions, especially in compression and bending (Kesti and Davies 1999;Godley and Beale 2008;Smith and Moen 2014;Dinis et al. 2014;Liu et al. 2021). Despite plenty of studies have been conducted, it seems that the awareness 1 3 of changing structural function is missing. This aspect inevitably changes the structural design and opens to different construction and engineering issues, as highlighted by Haque and Alam (2015), hence the necessity of analyzing and developing design rules dedicated to ARSWs specifically. The lack of dedicated design strategies is especially felt in seismic applications and highlighted by damages and collapses of such structures after seismic events (Morita and Takayama 2017;Affolter et al. 2009), or the occurrence of other kinds of critical situations-as pallets falling from their spots-which may get as relevant as structural damage, causing interruption of the activities of the warehouse, hence economic losses to the owner. In this regard, recent studies have investigated the use of seismic isolation on ARSWs structures (Kilar et al. 2011(Kilar et al. , 2013Pollino et al. 2014;Takeuchi et al. 2016), which may limit the seismic acceleration transmitted to the structure and also interstorey deformation (preventing pallets overturning), whit the cons of: (i) high costs for installation of the isolation system; (ii) the necessity of installing a full rigid diaphragm; and (iii) problems related to the tensile forces that may occur at base connections. The (i) is a relevant point concerning the desirability of the solution from a market perspective, which can be in some ways compensated with a careful design of the structure, reducing the amount of steel needed as much as possible. This is by no means trivial, considering the additional need to control the deformability relating to the automatic handling of goods. The (ii) is necessary to avoid different deformations among the upright trusses and is not feasible for all the ARSWs structural types: for the single or double depths, or in general for those solutions where aisles for stacker cranes divide the lines of upright trusses, full rigid diaphragm cannot be installed since they would cross the aisles and make impossible for stacker cranes to go along the aisles. Regarding the (iii), tensile forces at the base cannot be covered by all the devices on the market (Simoncelli et al. 2020), unless specific measures are adopted (Roussis 2009).
Although all these studies surely aim at providing solutions for ARSWs to be safe in seismic conditions, the focus is not on the structure, and to properly develop a design method for seismic-resistant ARSWs, it is necessary first to fully comprehend the structural behaviour resulting from current design. To this end, the present research mainly aims at providing an insight into the current technical regulations, design strategies and technical solutions adopted by the major designing and producing companies as well as the seismic performance of nowadays ARSWs. To this end, the technical regulations and guidelines adopted in the current practice are first critically analysed and described, highlighting the inconsistencies mainly deriving from the use of the regulations originally developed for traditional racks. Then, the effects of adopting these regulations and guidelines in the practical design of ARSWs are highlighted by comparing the design solutions of the same structure carried out by five big European racks designing and producing companies. Finally, the seismic performance of these structures is assessed through numerical simulations, pointing out the main parameters that influence the structural behaviour, as well as the main structural criticalities, suggesting then the necessity of a befitting design approach for ARSWs.

Analysis of current regulations and standards for the seismic design
In current applications, the lack of specific regulations for the design of ARSW is covered by adopting the design strategies that are defined for traditional racks, often without proper theoretical and experimental evidence. EN 15,512 (2020) andEN 16,681 (2016) are the 1 3 most used references respectively for the static and the seismic design. These documents are dedicated to traditional steel pallet racks but, as stated by both, they can also be taken as guidelines for the design of clad rack buildings when requirements are not covered in Eurocodes ( §1). They take into account several aspects typical of racks and ARSWs that can be individuated in: (i) the contribution to the global damping due to the possible sliding of the pallets; (ii) the automated handling of goods and or the nature of their contents, which can strongly influence the seismic mass in the CA and DA directions; iii) the influence of the shear deformability of the upright frames, that can sensibly increase the fundamental period of vibration; iv) the design rules associated to behaviour factors.
The indications for the seismic design of racks included in EN 16,681 (2016) that consider these aspects can be in deep contrast with the design principles included in Eurocodes and strongly influence both the seismic demand and the design approach for the ARWs. The following paragraphs analyse in detail these aspects.

Design parameters for seismic analysis: importance factor and definition of the design response spectrum
As provided by prEN 16,618 (2015), the seismic design of racks can be performed using the modal response spectrum analysis and adopting a design spectrum S d,mod based on Eurocodes and equal to: where S d (T) is the design spectrum as defined in Eurocodes for the associated important factor, considering a viscous damping factor ξ equal to 3%, and K D is a factor that takes into consideration the participation of the pallets in the dissipation of the seismic energy and possible consecutive effects, when friction is overcome. In particular, K D takes into consideration the fact that most of the seismic mass, represented by the stored goods, is not necessarily rigidly connected to the rack, therefore goods-structure friction limits the inertial forces transmitted and, when it is overcome, unit loads participate to seismic energy dissipation. Following the provision of prEN 16,618 (2015), K D can be calculated as: where P E,prod and P E are respectively the weight of the stored goods and the total weight of the structure (dead, permanent and goods weight), whereas E D1 and E D3 are the modification factors that consider the effects of not-fixed pallets in the dynamic behaviour of racks, which can be included in the definition of the seismic demand. E D1 takes into account the effects of the sliding of the unit loads on supports when the inertial forces exceed the resistance provided by the friction (when pallets are fixed to the beams is equal to 1.0). E D3 is introduced to consider the phenomena typical of the dynamic behaviour racks under seismic action and that are not directly included in the formulation of the spectrum. E D3 is introduced to consider the phenomena typical of the dynamic behaviour racks under seismic action and that are not directly included in the formulation of the spectrum. Indeed, as resulting from shaking table tests executed in Seisracks (Proença et al. 2009), loaded racks are characterized by a damping higher than 10%, which is higher than the 3% one assumed for unloaded racks and considered in the definition of the design response spectrum Sd(T). This effect is indirectly accounted by the E D3 coefficient, which is equal to 0.8 and corresponds to a damping between 10 and 11%, which is considered a reliable value ( §6.3 (1) Seisracks II final report (Castiglioni et al. 2014)). The P E,prod over P E ratio can be very close to 1 since the weight of the structure and the permanent loads are a very low percentage of the total weight of the fully loaded rack. Indeed, when P E,prod is greater than or equal to 90% of P E , K D can be assumed equal to E D1 ⋅ E D3 .

Design parameters for seismic analysis: definition of the participant mass
The seismic participant mass takes into consideration the quasi-permanent value of the permanent loads, W E,G , and the variable loads, W E,Q , together with the design seismic weight of the goods, W E,UL , and itis expressed by: W E,UL is strongly influenced by the characteristics of the pallets and stored goods. It can be determined as follows: where R F is the rack filling grade reduction factor, that is related to the occupancy of the stored goods in the rack that can be assumed during the seismic event: it is assumed 1.0 in the CA direction, where it is more probable to have frames fully loaded, and values between 1.0 and 0.8 in the DA direction, considering the lower probability of full load conditions. E D2 represents the effects of the interaction between goods and racking structure which affect the seismic response in terms of participating mass and modification of the period of vibration: if the stored goods are compact, constrained or liquid, this factor is equal to 1.0, while, in the opposite condition, meaning that the content is loose and unconstrained, E D2 is equal to 0.7. Finally, Q P,rated is the specified value of the weight of unit loads, and this is given by the owner of the warehouse, based on the foreseen goods flows.

Other relevant parameters: shear flexibility of upright frames along CA direction
The typical connection between uprights and diagonals along CA direction is realized by directly connecting the diagonal to the column through a bolt. This solution implies a reduction of the stiffness of the structure along the CA direction and affects the dynamic response of the system. Given the many parameters that influence the value of the lateral stiffness of these structures (e.g. the eccentricity of connection with respect to the centreline of the upright, the looseness and the deformability of connection), it's not easy to analytically determine it. Different codes for steel racks (RMI (1997), FEM (2000)) provide Timoshenko's formula to evaluate the stiffness of built-up columns, which some studies highlighted to be not appropriate for racks, causing a relevant over-estimation of the stiffness of these systems (Sajja et al. 2008;Gilbert et al. 2012;Talebian et al. 2019). The use of this formula could assure a higher safety for the design in terms of resistance, but lateral deformations could be under-estimated, and deformability limits may not be respected, affecting the serviceability states-overturning of pallets (Pollino et al., 2014) and occurrence of early plastic deformations of some elements-and the global stability of the structure. Within EN 15,512 (2020), the use of Timoshenko's formula is suggested to be replaced by the execution of experimental tests on the upright truss. The procedure for these tests is given by this standard. (3)

Possible approaches for dissipative design and behaviour factors
Besides elastic design, earthquake-resistant racks can be designed also adopting dissipative approaches ( § 8.1 EN 16,681 (2016)). Low dissipative and dissipative structural behaviour concepts can be assumed: in the former, the effects of seismic action are calculated through elastic global analysis without considering non-linear material behaviour, while, in the latter, plastic deformations are expected in particular elements of the structure (the dissipative ones), and their capacity in dissipation is considered in the design phase through the behaviour factor q. If adopting the low dissipative concept, a q-factor up to 2 can be used, while in the other case major than 2. It is useful to remember that this definition of "low dissipative" and "dissipative" is in contrast to the definition of Eurocode 8 (2019), where behaviour factors up to 1.5 are associated with low dissipative structures.

Structural types, behaviour factors and design rules
In general, it is allowed to use moment resisting frames and braced frames to design low dissipative racks (1.5 ≤ q ≤ 2). The former is mostly used for DA direction. Referring to the CA one, the upright trusses that constitute steel racks are designed to resist both vertical and horizontal actions, and many layouts for diagonals are allowed: the X-one with tension-only diagonals (Fig. 3a); the K, D, Z bracings (Fig. 3b); the X bracings without horizontal members, in which the resistance to horizontal actions is provided also by diagonals in compression (Fig. 3c). If adopting the tension-only X bracings, a behaviour factor of 2 is suggested, and no capacity design rules are mandatory to be applied in the design of the components (neither in the dissipative elements, nor in their connections, nor the other non-dissipative components), and this is in deep contrast with Eurocode 8 prescriptions (2019). If adopting one among K, D and Z configurations, a behaviour factor equal to 1.5 is suggested, and no capacity design rules are mandatory to be applied in the design of the components, with only a few exceptions (e.g. amplify the design effect due to seismic action by 1.5 for selected components). In any case, no safety factors shall be adopted for the design of the other non-dissipative elements and their connections. The K and Z structural types are designed in the elastic field, and if buckling is prevented, they may be also in line with Eurocode 8 design prescriptions for such systems (2019). On the contrary, the D one can be associated with a system with K bracings (as defined by Eurocodes, Fig. 3d), which is not allowed by Eurocodes (2019) to be adopted for seismic-resistant structures ( §11.4.1). Finally, dealing with the X bracings without horizontal members, the EN 16,681 (2016) provides using a behaviour factor of 1.5 with no adoption of capacity design, with the only exception of diagonal elements to be designed by amplifying the design seismic force by 1.5 if their buckling mode in axial compression is local. Anyway, this structural type can be associated with the K bracings one as defined by Eurocodes (Fig. 3d), which is not allowed to be adopted according to them, as previously highlighted.

Influence on the final seismic design approach
The possibility of adopting a different-from-Eurocodes design approach can lead to an evident reduction of the seismic demand for ARSWs, which is in most parts not very well justified and demonstrated. Depending on the combinations of design hypotheses, and therefore of the key design parameters previously introduced, different reductions of the spectral accelerations can be obtained, whose value varies from case to case. However, to give an idea of the order of magnitude of the reduction that it is possible to achieve, it is assumed a reference configuration as a starting point to assess the maximum reduction of the seismic action. The reference configuration is characterized by: • A design life of 50 years and an importance factor of 0.8. • A European high seismic zone with a Peak Ground Acceleration (PGA) equal to 0.30 g for a return period equal to 475 years. • A period of 2.10 s associated with the CA frame, and of 1.50 for the DA.
Starting from this reference configuration, Table 1 gives the design hypotheses (DH) that induce the most sensitive reduction for the seismic action in terms of base shear for both the CA and DA directions (DH "Reduction"). Figure 4 shows the variation in terms of spectral acceleration. The reduction of stiffness along CA direction is not included in this comparison, since it depends on many parameters (profiles and connections geometric characteristics) and cannot be standardized but supported by experimental evidence.
The maximum reduction of the base shear associated with the seismic action is quite sizeable, up to 54% for CA direction and to 69% for DA. Even if these values are obtained for a specific configuration, they give the idea of the influence of these parameters on the seismic design of the ARSWs. It is worth highlighting that the choice of different parameters in the range used for the above example does not lead to different relevant design constraints.
The real issue is that the possibility of using most of these parameters is experimentally and scientifically justified for traditional racks, but not for ARSWs. Furthermore, a deep inconsistency among Eurocodes and EN 16,681 (2015) (when EN 16,681 are used to design ARSWs) is in the possibility of using a behavior factor up to 2 without adopting properly capacity design rules. This comparison points out the confusion created by the absence of a specific standard, which may result in an unsafe design.

Table 1
Possible combinations of key design parameters and resulting acceleration and base shear for the defined elastic response spectrum ΔM = variation of participant Mass; ΔT = variation of period; ΔS d = variation of design seismic acceleration; q = behavior factor; kd = seismic acceleration modification factor (*) Calculated for each direction with respect to the respective reference design hypothesis

Current design approach
To understand to which extent the design choices influence the final design, a common design problem was proposed to 5 of the biggest European companies specialized in designing and manufacturing steel racks and ARSWs and the resulting solutions were compared in terms of both structural choices and seismic performance. It should be pointed out that the study is focused on the seismic design approach and that it is assumed that the wind action does not influence the overall design. This latter assumption can result realistic only in high seismicity zones characterized by low-medium wind but, in any case, it has been done to obtain more clear results not influenced by both wind-earthquake actions. The design had the following common input design parameters: (i) Structural typology. The assigned structural typology is a double-depth warehouse (Fig. 1a). (ii) Input geometry parameters, see Table 2  The seismic design is carried out for a European high seismic zone with a Peak Ground Acceleration (PGA) equal to 0.30 g for a return period equal to 475 years. Figure 6 represents the horizontal acceleration elastic response spectrum assumed, the two corresponding design response spectra corresponding to behaviour factors equal to 1.5 and 2. The importance class I is assumed, with a design life equal to 50 years, according to EN 16681 (2016).   Load combinations and related factors have also been fixed for static and seismic design, as well as material factors to calculate design capacity forces, and defined in agreement with Eurocodes. Regarding the design in seismic conditions, the combination of vertical loads to be used for the definition of seismic mass has been defined as in §2.3, where the RF is taken equal to 1.0 and 0.8 respectively for CA and DA direction. The Ψ 2 factor is equal to 0.8 (it replaces the E D2 parameter). Besides the fixed design inputs, several parameters have been set free to be chosen by the designers to highlight the current trends: (i) Structural types and corresponding behaviour factors. (ii) Components characteristics, such as cross-section shapes, steel grade and connection typologies. (iii) The number of pallets per beam pair (2 or 3).
Finite Element Modelling (FEM) is adopted to perform modal response spectrum analyses of the structures. Considering that double-depth ARSWs are slender structures, the applicability of this analysis has been evaluated by the designers by calculating the interstorey drift sensitivity coefficient θ or equivalently the buckling load multiplier (in line with EN16681 (2016), §7.3, where an alternative formulation for the θ factor is provided, where it is proportional to the latter). It has been checked that the obtained values of θ are in the range that allows the correct use of this type of analysis ( §7.4.2.2 for structures designed in the low-dissipative concept, EN16681 (2016)). In the most cases, the θ factor resulted minor than 0.1, meaning that the second order effects are negligible. Only in a few cases, θ factor resulted between 0.1 and 0.2. In those cases, modal response spectrum analysis has been still adopted with the amplification of seismic action by the factor 1/ (1 − θ). The Case Studies (CS), from 1 to 5, are described in the following paragraphs. The main characteristics of the structural elements and the design assumptions are given respectively in Tables 3 and 4. Due to the sensitivity of some information, only the general characteristics of the structural elements are provided. From Table 4 it can be noticed that shear deformability has not been considered by all the designers. As discussed in §2, this parameter can be properly defined only with experimental tests on the upright truss. When not applied in the design, it means that the tests were not available. Considering the purposes of the study and that this parameter plays on the safe side for resistance demand, this is not considered a relevant lack in this phase of the research.

Case Study 1
The structure is composed of 46 CA frames, among which the standard and non-standard ones can be individuated. The latter are those in correspondence with bracing towers, which are the horizontal forces resisting system for DA direction and are characterized by different uprights in steel quality and sections (Fig. 7b). Structural optimization is made along the height of the structure (lower, upper part, Fig. 7a). The upright trusses are organized in the K layout (tension-compression diagonals and horizontal elements), and the adjacent ones are connected through hinged elements called "spacers" in jargon. Along DA direction, each frame is constituted by uprights, pallet beams and bracing towers. The X-shaped tension-only horizontal forces resisting systems (bracing towers) are placed at the beginning and middle length of the frame (Fig. 7b).

Case Study 2
The structure is composed of 50 CA frames, among which the standard and non-standard ones can be individuated. Structural optimization is made along the height of the structure (lower, upper part, Fig. 8a). Each frame is composed of 8 upright trusses, whose diagonals are arranged in a D layout (tension-compression diagonals, no horizontal beams), and are not reciprocally connected. Along DA direction, each frame is constituted by uprights, pallet beams and 4 bracing towers (Fig. 8b). Table 3 gathers the cross-sections and the relevant characteristics of the main structural elements and their connections. Table 4 gathers the definition of the free design parameters for CS2.

Case Study 3
The structure is made of a total of 33 CA frames, with 4 bracing towers along DA direction (Fig. 9). There are 8 uprights trusses in the CA frames, whose diagonals are organized in a V layout (tension-compression diagonals, Fig. 9a). Along DA direction, bracing towers constitute the horizontal resisting system, where diagonals are arranged in the X layout (tension-only, Fig. 9b). The bracing towers are placed in an eccentric position with  Fig. 9 CS3 a structural elements belonging to CA frames and b layout and organization along DA direction respect to uprights (Fig. 9a). The connection between the bracing towers and the respective trusses is assured at each load level by both horizontal bracing system and transversal beams. Structural optimization is made along the height of the structure (lower, medium, and upper part, Fig. 9a). Along DA direction, the CA upright trusses are connected through the pallet beams. All the uprights' base connections are fixed to the concrete slab with threaded bars.

Case Study 4
The structure is made of a total of 33 CA frames, that are connected along DA direction through the pallet beams. Each CA frame is composed of eight upright trusses, where diagonals are organized in a D layout (tension-compression diagonals, Fig. 10a). The adjacent upright trusses are connected through fixed spacers. Structural optimization is made along the height of the structure (lower, medium and upper part, Fig. 10a). Along DA direction,  Fig. 10 CS4 a structural elements belonging to CA frames and b layout and organization along DA direction the rectangular-sectioned cold-formed bracings are diffused all along the length of the structure and are arranged in the X-shaped tension-only layout (Fig. 10b). The horizontal forces resisting systems are placed in an eccentric position with respect to the upright trusses (Fig. 10a).

Case Study 5
The structure is made of 33 CA frames which are mutually connected through the pallet beams. Each CA frame has 8 upright trusses, where diagonals are organized in a D layout (tension-compression diagonals, Fig. 11a Fig. 11 gives a representation of a representative module). Within each bracing tower, diagonals are arranged in the X layout (tension-only diagonals). The horizontal resisting systems are placed in an eccentric position with respect to the upright shelves (Fig. 11a).

Comparison among the design solutions
The analysis of the configurations, the structural choices, and the design strategies adopted for the 5 case studies highlights that there are some common paths and distinguishing features that identify the current seismic design approach for double-depth ARSWs.
From the global point of view, different configurations can be identified along CA and DA directions: the CA frames are constituted by repeated modular upright trusses, whose diagonals are arranged in different layouts (K, V, D schemes), corresponding to different structural behavior. These configurations allow the trusses to resist both to vertical and horizontal loads. As highlighted in §2.6, the K layout can also be assumed according to Eurocodes for seismic-resistant structures, if the building is designed in the elastic field, or with low dissipation concept (q-factor up to 1.5). On the other hand, the use of the D layout -which is comparable to the K layout as defined by Eurocode 8 (2019) (Fig. 3d)-is not allowed, due to the bad demand on columns when one of the two diagonals buckles. The V layout can be adopted according to Eurocodes with the use of hierarchy rules if q-factors major than 1.5 are used. On the other hand, EN 16,681 (2016) allows to not adopt hierarchy rules for q-factors up to two. This is indeed in deep contrast with Eurocodes.
The consecutive adjacent upright trusses may be reciprocally connected through transversal elements (spacers) that can be hinged or fixed to the uprights (in case of using more rigid connection, the adjacent trusses are coupled, significantly affecting the stiffness of the structure along CA direction, as well as the distribution of forces in the uprights in case of horizontal forces acting). Looking at Table 60, the use of hinged and flexible spacers (CS1, T main_CA = 2.61) implies similar effects of not adopting them (CS2, main period T main_CA is 2.70) in terms of stiffness and load distributions (especially on uprights) along CA direction. In the same way, the use of fixed and more rigid spacers (CS4 and CS5) makes the structures more rigid (the main periods are respectively 0.96 and 1.10).
The CA frames are repeated and connected by the pallet beams along DA direction. The DA horizontal forces resisting systems can be diffused along the length of the structure (CS4, Fig. 10b) or located in strategic positions (in this case called "bracing towers", CS1- Fig. 7b, CS2-Fig. 8b, CS3-Fig. 9b, and CS5-Fig. 11b), and the only structural scheme adopted for them within the analyzed case studies is the X one (tension-only diagonals). The bracing system can be aligned with the upright trusses (CS1- Fig. 7a, and CS2- Fig. 8a) or placed in an eccentric position (CS3- Fig. 9a, CS4, Fig. 10a, and CS5- Fig. 11a). In this second configuration, the connection of the bracing system to the respective shelves is made through rigid transversal elements, that are usually placed in correspondence with load levels and connect all the uprights of the trusses. This kind of solution implies, for the external shelves, an eccentricity of the center of mass with respect to the center of stiffness, and so, there may be not negligible rotational modes in addition to the translational ones that can influence the response of the structure to horizontal forces along DA direction. The horizontal bracing system is placed in line with the load levels, directly connected to pallet beams or uprights. Being necessary to leave the aisles free, no global rigid plane can be found in these structures: each group of upright trusses which are separated by the aisles can be considered almost independent from the other ones. The only connection that involves all the upright trusses is the one at the top of the structure (constituted of the roof truss), that in any case is very far from the base of the uprights.
From the local point of view, the solutions proposed by the 5 different companies share similar choices in terms of main profiles cross-sections and type of connections (Table 3). All the uprights are characterized by a lipped U cross-section and are perforated along their length (only one CS out of the 5 considered has uprights with holes only where needed, in correspondence with connections with diagonals and pallet beams). The lipped U section, which is opened in the inner side, allows faster and easy connection of diagonals, which are directly bolted to the uprights in correspondence with the lips without using additional sheets (Fig. 12). The diagonals used for the CA frames are characterized by C, U or rectangular sections. Besides, uprights are often locally reinforced at the bottom, where forces are higher, through an additional profile that is welded or bolted to the original column. This solution allows to limit the number of different cross-sections for uprights, without introducing discontinuities but providing higher resistance where needed.
According to the analyzed case studies, the main path that guides all the structural choices is structural optimization, which aims to balance the structural needs with: limiting the costs connected to the necessary amount of steel and the additional processes at workshops (i.e. welds or additional sheets for connections are very limited); limiting the number of different cross-sections needed for the same element (i.e. diagonals, uprights, pallet beams), which implies an easier and cost-effective production and a less probability of mistakes during the construction phases that may occur due to the very low involved thicknesses. Indeed, the cross-section is always kept the same for each type of element, and thicknesses change a maximum of three times along the height of the structure. Structural optimization is performed by the designers by adopting a trial-and-error procedure, driven by the experience of the designers themselves and considering the necessity of simplifying the assembly procedures that need the less variations of elements/profiles. In the research field, studies are investigating alternative automatic procedures for the structural pre-design of racks (Bové et al. 2020), which may be adopted for a faster and effective design of the elements, limiting the iterations to the final configuration. These procedures could be also extended for being applied to ARSWs given the repetitiveness of the primary structures.

Upright
For all the designers, as suggested and prescribed by EN15512 (2020), some of the key design parameters are defined with the support of experimental activity (e.g. shear flexibility, effective properties of uprights under compression load). In such peculiar structures, experimental tests seem relevant for the proper characterization and assessment of local and global structural behavior. The design parameters to be freely adopted by the designers are all gathered Table 4, and the effects of the resulting design strategies on the determination of the design base shear are highlighted in Table 5. The considerations previously made in Sect. 2.7 can be here reintroduced considering the influence of the parameters in the definition of the design response spectrum, in the definition of the participant mass, and in the possible reduction of the lateral stiffness of the frames along CA direction. Concerning the analysis made in Sect. 2.7: -The reduction of lateral stiffness is also taken into consideration, only when considered by the designer. -The definition of the participating mass and its reduction due to the use of Ψ2 and RF factors reduces the total seismic base shear but also increases the design seismic acceleration. For sake of simplicity, the consequences of the definition of participating mass are not considered in the calculation of the total seismic base shear reduction.
The reduction of lateral stiffness does not play on the safe side for the design in terms of resistance-at the Ultimate Limit State (ULS)-since it allows the use of smaller and less thick elements. This aspect should be balanced with the increase of the deformations under horizontal actions (as wind), to check static Serviceability Limit State (SLS).
Looking at the total seismic base shear reduction within Table 5, it can be noticed that, in some cases, quite high reductions are reached (up to 60%), and could get even higher due to the reduction of the participant mass. It should be assessed if the use of these parameters, which is justified for traditional racks, is also admissible for ARSWs' racks, or if this could lead to an unsafe and not conservative design. Table 5 Influence of the design assumptions in the reduction of the seismic design base shear (q = behaviour factor; kd = seismic acceleration modification factor; Ψ2 = combination factor; RF = rack filling grade reduction factor)

Seismic assessment of double-depth ARSWs and critical analysis of the seismic design
The analysis of only the design seismic demand is surely not sufficient to understand the effects of the design choices on the overall seismic behavior of the ARSWs and on their safety levels. The design seismic demand shall be necessarily analyzed together with the resultant seismic performance and their coherence thoughtfully checked. For this purpose, the seismic assessment of the case studies is made through FEM numerical simulations and the evaluation of the safety level at Life Safety Limit State (LSLS) by executing safety checks of the main components (elements and connections). The final aim is to point out the criticalities and the structural behavior resulting from the adopted design strategies. All the input data are the same adopted by the designers. Firstly, for each structure, modal analysis is performed to point out the main modes and the corresponding natural frequencies. Then, Non-Linear Time History Analyses (NLTHA) are carried out using a set of 15 natural accelerograms as seismic input.
Even if 3 out of 5 designers assumed a dissipative behavior (q = 2), no real capacity design is adopted for the dimensioning of the structural elements ( §0). Therefore, limited values of global ductility are expected from the structural analysis of these structures. For this reason, and to understand the eventual benefits deriving from the local strengthening of the first elements to fail, the non-linear time history analyses are performed considering only the geometrical non-linearities. Then, the weaker parts of the structure and the chain of failure mechanisms are individuated by putting in order (from the highest to the lowest) the demand-capacity ratios obtained from the execution of the safety checks of elements and connections. These re-arranged demand-capacity ratios represent the so-called "hierarchy of criticalities". This hierarchy is representative of the order of the most critical elements until a mechanism with relevant ductility is highlighted, after that the model adopted is no longer able to represent the effective behavior of the structure.

Modal analysis
Modal analysis is performed for a full characterization of the dynamic behavior of the case study, to understand if the structures are represented coherently to the designers', and to catch possible ways to simplify the numerical model, for the further analysis step. To this ends, 3D representative portions for both CA and DA directions are extracted. Material is linear elastic, the elements are modelled as mono-dimensional, and participant mass is lumped and placed at each load level and modelled as suggested for rack structures within Annex C of EN16681 (2016). Being such slender structures, to account for possible second order effects, at first a non-linear analysis with P-Delta effects included and gravity load acting is performed to update the stiffness matrix; then, modal analysis is run from this updated condition. Table 6 gathers the relevant eigenmodes of all the CSs. No relevant variability of periods can be found among the main modes of DA direction, especially referring to the case studies with bracing towers along DA direction. On the contrary, a wider range of values is detected for the CA modes, depending on the presence of and type of connection between adjacent upright trusses, as highlighted in §0. CS1 and CS2 are characterized by the highest periods: in the former, the adjacent upright trusses are connected by hinged and very flexible elements and in the latter, there is no connection at all. In all the other case studies, the adjacent upright trusses are connected by rigid transversal beams at each load level, which also allow the connection of the trusses to the corresponding bracing tower. These rigid elements couple the trusses, making the structure more rigid.

Non-linear time history analyses
NLTHAs are carried out using a set of 15 natural accelerograms as seismic input, which is selected from the NGA-West2 database (Bozorgnia et al. 2014) that matches the target conditional spectra (Baker 2011;Lin et al. 2013a; b) at a 2475 years return period, or equivalently an exceedance probability of 2% in 50 years, and that has been extended to a wider range of probabilities of exceedance (Kohrangi M., Tsarpalis D.,Vamvatsikos D. Deliverable D.4.2. From Steelwar Research Project). For this study, the set corresponding to an exceedance probability of 10% is adopted (Fig. 13).
All the numerical models are developed in OpenSEES (Mazzoni 2017). From the modal analyses performed and the dynamic behavior detected, separate 2D finite models are adopted for the two directions for the case studies in which the behavior of the CA direction can be assumed as independent from the one in the DA direction. Where this hypothesis is considered not realistic, 3D models of the structures are assumed. In all the models, material is linear elastic and the elements are modelled as 3D beam elements based on Euler-Bernoulli formulation (beam column element, (Mazzoni 2017)). Cross sections and geometrical characteristics of the elements are defined accordingly to the designers' choices (Table 3). Specifically referring to uprights, to consider the presence of continuous perforation and so to obtain the actual stiffness of the structure, the indications within Annex G of EN15512 (2020) are adopted, which consists into an equivalent thickness of the element based on the layout, geometry and distribution of the perforation itself. Zero length elements (Mazzoni 2017) are adopted to adequately model elements' connections, which are characterized within Table 3. All the connections are hinged, with the only exception of upright base connections and pallet beam-to-upright connections, that are modelled as semi-rigid elastic connections, whose elastic stiffness is defined according to derivations from designers' experimental tests on these components.
Since no real capacity design has been adopted in the design phase, limited values of global ductility are expected from the structural analysis of these structures. Considering this, and to understand the eventual benefits deriving from the local strengthening of the first components that fail, the non-linear time history analyses are performed considering only the geometrical non-linearities. Indeed, P-Delta effects are included to take into account possible second order effects. Brittle failures are detected and checked in the postprocess by executing the safety checks.
The effects of eccentricities of diagonal-to-upright connections are neglected since they respect the limits expressed within §9.1.2.4 of EN15512 (2020). Warping, torsional, and distortional effects typical of upright elements are all considered in the post-process when determining the effective properties to check the element for combined axial compression and bending ( §). Concerning warping effects, the post-process activities handle how they affect the resistance of upright elements. In general, the adoption of an advanced finite element solver that considers these effects directly in the analysis may have surely given a more appropriate characterization of uprights ) and of the structure in terms of displacements. The effective properties of uprights are provided by the designers who performed specific experimental tests of the components (distortional and compression tests, §A.2.1, A.2.2 from EN15512 (2020)).

3
The participant mass is defined accordingly to the hypotheses of the case studies' designers (Table 4) and modelled in accordance with the strategies suggested within Annex C of EN16681 (2016).

Vulnerability assessment and hierarchy of criticalities
The vulnerability assessment is carried out through the execution of the safety checks of the main components according to Eurocode 3 (in particular, prEN 1993-1-1:2019, prEN 1993-1-3:2019and prEN 1993-1-8:2019 and EOTA documents for base connections when post-installed anchors are used (EOTA TR45 (2013) and EOTA TR49 (2016)). EN15512 (2020) are also adopted to define specific properties or coefficients contained in Eurocodes formulas and there indicated specifically for rack components. The post-process of the huge quantity of data from the analyses and the associated safety checks are handled through a tailored-developed MATLAB® code ('MATLAB® Version (R2019b). Natick, Massachusetts: The MathWorks Inc.').
The D/C ratios are re-organized from the highest to the lowest and gathered in consecutive steps of which a graphical representation is given in the hierarchy of criticalities. The most representative steps of the hierarchies are shown, for each direction, in Figs. 14 and 15. In these representations, two steps are gathered: the criticalities belonging to first one, which is characterized by the highest D/Cs, are represented in red, while those of the

Fig. 13
Selected records corresponding to a probability of exceedance of 10% in 50 years, and corresponding scale factors second one (lower D/Cs) are in yellow. The range of D/Cs for each step is defined by the ratio among the highest D/C detected and lower/upper bound ones represented in the step: for example, if the highest D/C is 1.50, and the first step gathers the mechanisms from 1.50 to 1.30 while the second one from 1.30 to 0.80, the range of the first step is 1.00-0.87, and the range for the second step is 0.87-0.53. To give the major homogeneity to the results, the first step gathers the criticalities in the first 10% of the variation of the D/Cs for the CA direction, and in the first 25% for the DA direction. A quite similar behavior among all the case studies can be individuated for CA direction. The highest D/Cs ratios are detected at the base of the structure, where high forces are acting. From the bottom, the criticalities spread through the height of the structure. A major diffusion is allowed when different thicknesses along the height of the structure are used for diagonal or upright elements. In all the case studies, the components that are characterized by the highest D/C ratios -belonging to the first represented step-are diagonal connections and uprights base connections: the leading mechanism for diagonal connections is bearing (mainly due to the very low thickness of these elements), while the leading one for base connections is failure due to tensile (concrete-cone mechanism) and shear force on anchors. Failure of base connections is detected in all the case studies where postinstalled anchors are used, while threaded bars allow better performance (see CS3, where this last solution is adopted, Fig. 14c).
As regards diagonal elements, it can be noticed that the ultimate resistance of the element (both in tension and in compression) is always higher than the resistance of the connection (at least 40% higher). This is the consequence of not applying hierarchy design rules for behaviour factors up to 2, in agreement with EN 16,681 (2016). The only request is to avoid a brittle failure of connection by having the shear resistance of bolts at least 1.20 times the bearing resistance. This design strategy implies that, although a brittle failure of connection is prevented, no over-resistance is provided to connection with respect to the diagonal element. In any case, for the adopted profiles, which are characterized by a low thickness, it is very hard for the bearing resistance of the connection to be higher than the tensile resistance of the element. Looking at the formula for the bearing resistance («prEN 1993-1-3: 2019 Eurocode 3-Design of steel structures-Part 1-3: General rules-Supplementary rules for cold-formed members and sheeting»), it depends on the ultimate strength of the steel, on the thickness of the profile and the number and position of the holes. Increasing one or both the steel grade and the thickness leads to the increase of both the bearing resistance and the resistance of the element, keeping the ratio between the resistances associated with the two mechanisms unchanged. On the other hand, using more bolts would allow the increase of the bearing resistance only. Anyway, this option is not easily applicable to ARSWs' market, where a one-bolt connection is preferred, since it makes the system more flexible and its geometry more adaptable. Indeed, the assembly is faster and easier, the production of the diagonal profiles is more standardized, as well as the production of uprights that would need a different pattern of the holes in correspondence of connections.
The next criticality that occurs is buckling failure of uprights for combined axial compression and bending at the bottom of the structure or where the uprights reinforcement stops.
Along DA direction, the highest D/C ratios are concentrated in the bottom part of the bracing systems and, particularly, in the central bracing tower for which the participant mass is higher (CS3 Fig. 15c, CS4 Fig. 15d and CS5 Fig. 15e). The first components involved are diagonal to upright connections and upright base connections. For the former, the leading mechanism is mainly the bearing of diagonal, or the plate connecting the diagonal to the upright. For the latter, the leading failure is due to the failure of the anchors under tensile (concrete-cone mechanism) and shear forces. The next criticality occurs in the uprights belonging to the bracing towers, due to axial compression. All the other elements of the structure not belonging to the bracing systems are characterized by lower D/C ratios: when the DA bracing system is aligned with the upright trusses (CS1 Fig. 15a and  CS2 Fig. 15b), the elements that are involved after the bracing towers are pallet beams, that work in compression to transfer the forces among the bracing towers. On the contrary, in case of eccentric bracing system (CS3 Fig. 15c, CS4 Fig. 15d and CS5 Fig. 15e), the elements that are involved after the bracing systems are the uprights that are closer and directly connected to the bracing system itself, and failure is due to axial compression and bending.

Conclusions
This paper critically analyses the current structural choices, solutions and resulting performance of Automated Rack Supported Warehouses. These buildings are largely used all over the world as automated and advanced storage systems for palletized goods and are currently designed by adopting approaches and regulations not specifically developed for them, causing confusion in application, possible not-safe design and, in some cases, poor performance, especially for seismic applications.
The study is focused on analyzing the design methods and the structural response in seismic conditions; hence 5 double-depth case studies are designed by 5 European manufacturer companies that nowadays design and produce ARSWs. Being these structures high, slender, and deformable, horizontal loads -wind and seismic action-surely drive their design, together with the high vertical ones acting (the pallet load). Anyway, considering the aims of the study and for the sake of obtaining clearer results, the seismic input is selected to match the intensity of a medium-high European seismic zone, and wind load is neglected, assuming the low probability of the simultaneity of the two actions.
The key design parameters have been demonstrated of having a relevant impact on the definition of the design response spectrum and the modal parameters of the structure (natural frequencies), and consequently on the value of the seismic design force. As highlighted in Table 1, the adoption of different values of these parameters and their combinations can bring relevant differences in the definition of the design seismic base shear, with a maximum reduction of 54% for CA direction and 69% for DA with respect to the elastic design value. Even if this evaluation is made for a specific configuration, it gives the idea of the influence of these parameters on the seismic design of the ARSWs. It should be also highlighted that the choice of one value for a parameter with respect to another one is not associated with different design constraints. Besides, the use of most of these parameters is widely scientifically justified for traditional racks, but it is not for ARSWs, so it's not clear if they lead to an unsafe and not conservative design.
From the analysis of the configurations and the structural choices made by 5 European manufacturer companies, it seems that the main path that guides all these structural choices is structural optimization, which aims to balance the structural needs with limiting the costs connected to the necessary amount of steel and the additional processes at workshops (i.e. welds or additional sheets for connections are very limited), and, for the same element (i.e. diagonals, uprights, pallet beams), limiting the number of different cross-sections needed. In any case, the structural solutions can be deeply different from each other.
Dealing with the structural performance and vulnerability assessment along the CA direction a similar behavior can be individuated among all the case studies in terms of hierarchy of criticalities, and the components that are characterized by the highest D/C ratios are diagonal connections (due to bearing) and uprights base connections (with postinstalled anchors, due to tensile and shear force). Along DA direction, the same criticalities can be found: the highest D/C ratios are concentrated in the bracing systems, starting from the bottom, and firstly involving diagonal to upright connections, where the leading failure is bearing, and upright base connections, especially when post-installed anchors are used, due to tensile and shear force. The failure of connections is the most critical in both directions. This is one of the possible consequences of not applying any hierarchy rule in the design of the structure, although a behavior factor major than 1.5 has been used. If plastic ovalization of diagonal-to-upright connection occurs first, these connections would become loose without the possibility of dissipating energy anymore and with an asymmetric behavior (due to the different distance of the hole from the free edges in tension and compression). Indeed, this could be accepted only if limited dissipative capacity is expected, and preventing any other brittle mechanism in diagonal-to-upright connection and all the other components from failing. On the other hand, if crisis of an upright base connection is the first to happen, this could trigger a series of chain collapses, leading to the collapse of the whole structure.
These outcomes highlight that the current design approach could be applied only if the structure is designed to remain in the elastic field, but also in this case, the use of the key design parameters for the definition of the response spectrum should be justified. On the other hand, if the structure is designed to be dissipative using EN 16,681 (2016) design rules for low dissipative concept racks does not allow the occurrence of any ductile mechanism to prevent the early trigger of brittle mechanisms. Although the latter is typically experienced in thin-walled structures, this behaviour does not match the expected-even low-dissipative behavior. Therefore, to obtain dissipative structures, these failures prevented by developing a proper design approach for these structures, that should foresee the use of capacity design to drive the chain of failure in the proper direction and control the global collapse mechanism. Besides, lateral deformation limits of the structure connected to serviceability limit states have not been treated in this study. Indeed, the adopted technical regulations for the design (EN16681 (2016)) do not provide any indication about this for racks. This aspect should be properly analyzed and considered from the perspective of defining a new dedicated design method for warehouses.
Funding This study is executed in the framework of STEELWAR research project that has received funding from the Research Fund for Coal and Steel under Grant agreement No 754102, which is gratefully acknowledged. Besides, the authors are grateful for the efforts and for the detailed work made by the two anonymous Reviewers that helped in significantly improving the quality of the paper.