Enhancing High-Bay Warehouse Sustainability: High-Strength and Low-Carbon Steel for Weight, Cost, and CO₂ Optimization

Abstract

Online shopping has experienced rapid growth in recent years, driven by evolving consumer habits and the impact of the COVID-19 pandemic. With increasing demand for quick and efficient product delivery, retailers are turning to advanced storage solutions to support logistics and distribution. High Bay Warehouses (HBW) have emerged as a key solution, offering high-density vertical storage to maximize space utilization. This study focuses on optimizing HBW structures through the use of high-strength steels, particularly HyPer^® Steel grades. By replacing conventional steels such as S350GD with higher-strength alternatives, this study demonstrates the potential to reduce the overall structural weight, lower carbon emissions, and improve cost efficiency, while maintaining equivalent structural performance. The research explores how the conjunction of material optimization and the use of low-carbon steel (XCarb^®) can contribute to more sustainable and efficient storage solutions for the growing demands of modern logistics.

1. Introduction

In recent years, online shopping has seen remarkable growth, driven largely by behavioral shifts toward e-commerce platforms, changes influenced both by consumer habits formed during the COVID-19 pandemic and broader transformations in purchasing behavior [1].

Today, virtually anything can be purchased online, from traditional items such as clothing and books to more complex and less conventional goods like perishables, furniture, home appliances, and beyond. This expansion in product variety has been driven by the digital transformation of retail and the growing trust consumers place in e-commerce platforms. Moreover, the immediacy of online shopping is increasingly matched by consumer expectations for fast and often same-day delivery, which has become a key differentiator among retailers [2]. These evolving behaviors have profoundly impacted supply chain strategies, leading to a rapid expansion of automated and high-capacity storage facilities such as High Bay Warehouses (HBWs). HBWs offer the vertical storage efficiency and automation potential required to support fast-moving, high-volume order fulfillment operations [3,4]. In particular, the rise of omnichannel retailing and just-in-time logistics has made proximity, responsiveness, and storage density crucial factors in warehouse design [5]. As such, HBWs represent a strategic infrastructure solution in response to the new demands of online consumers who prioritize speed, variety, and availability. These facilities offer high-density vertical storage to maximize space within limited footprints. HBWs are lightweight structures primarily composed of cold-formed steel (CFS) elements such as uprights, bracings, and pallet beams. Stored goods are generally placed on pallets resting on horizontal beams, which are attached to frames consisting of columns and bracing. The links between the various elements use fasteners or bolted joints. The configuration of each HBW can be customized to meet the specific needs of each customer: storage systems may be configured in single, double or multi-depth layout [6].

Cold-rolled steel is widely used in HBWs due to its favorable strength-to-weight ratio, manufacturability, and recyclability, making it a suitable material for lightweight, prefabricated storage systems [7,8]. Recent developments in high-strength steels (HSS) further enable the optimization of these structures by reducing material thickness while maintaining comparable structural performance, which results in reduced weight, cost, and environmental impact [9,10]. In the context of increasing focus on sustainability, the steel industry is adopting low-carbon production routes and long-lasting coatings, which help reduce the embodied carbon and improve durability [11,12]. The integration of advanced high-strength materials (i.e., HyPer^® HSS grades), combined with optimized design practices and durable coating materials, which ensure longer durability, can significantly improve both the structural and environmental performance of HBWs.

1.1. Sustainability of Steel and Construction Products

Climate change is widely recognized as a critical environmental challenge, with extensive scientific evidence identifying human activities, such as unsustainable consumption patterns and resource exploitation, as the primary drivers of global warming. This growing awareness has led to increased demand for environmentally responsible products and practices, particularly in sectors with high energy consumption and emissions, such as transportation and construction.

In response, regulatory frameworks and market mechanisms have evolved to promote sustainability. One example is the revision of the Construction Products Regulation (CPR) initiated in April 2022 [13], which aims to enhance resource efficiency and circularity by introducing new requirements in the Declaration of Performance (DoP) and implementing Digital Product Passports (DPPs). These measures support the integration of environmental considerations into product design and specification.

Environmental Product Declarations (EPDs) have become essential tools for assessing and communicating the environmental performance of construction materials. Based on standardized Life Cycle Assessment (LCA) methodologies, EPDs provide transparent, third-party verified data across the product’s life cycle, enabling informed decision-making in sustainable design.

Steel remains a key material in the construction industry due to its favorable mechanical properties, including high strength, durability, and ductility, combined with its capacity to be infinitely recyclable without significant loss of performance. Its alignment with circular economy principles, supported by established recycling infrastructure, reinforces its role in sustainable building practices. To further reduce its environmental footprint, the steel industry is advancing low-emission production technologies and developing high-strength steel grades that enable material efficiency without compromising structural performance [14,15,16,17]. These innovations, reflecting the steel industry’s growing commitment to achieving carbon neutrality by 2050, contribute to reduced embodied carbon and improved durability, supporting the transition toward more sustainable construction systems. In this context, this study examines the potential of XCarb^®, a low-carbon steel, as a sustainable alternative to conventional steel, and assesses its implications for HBW sustainability.

1.2. Optimised and Sustainable HBW

All the commitments to reach sustainability targets are reshaping market expectations, especially in sectors with high environmental impact like construction and logistics. As part of this shift, sustainability is becoming a central design driver for new infrastructures, including High-Bay Warehouses. HBWs, due to their scale and material intensity, must increasingly align with circular economy principles and demonstrate reduced carbon footprints through tools like Environmental Product Declarations (EPDs). In this context, steel, a key material in HBW structures, emerges as a strategic enabler of sustainable design, thanks to its strength, recyclability, and evolving low-carbon production methods.

This study focuses on designing and optimizing a typical HBW structure initially designed with conventional S350GD+ZM steel and evaluates an alternative solution using new high-strength steel S550GD HyPer^®+ZM. The structure considered in this work is 35 m high, 86.2 m in the down-aisle direction, and 36.7 m in the cross-aisle direction. The study primarily outlines the reference case, loading assumptions, structural modeling, and performance evaluations under Ultimate and Serviceability Limit States (ULS and SLS). It then assesses the weight and cost savings from the optimized high-strength steel designs, compared to the baseline model (designed with traditional steel S350GD+ZM). In addition, a sustainability assessment is conducted to highlight how material optimization combined with low-carbon steel production can enhance the environmental efficiency of HBWs. Results indicate that the use of HSS can achieve up to approximately 15% weight savings and approximately 13% cost reduction. Furthermore, by reducing material quantities and using lower-emission steel, an additional reduction in CO₂-equivalent emissions is realized [11,12].

2. Standards and Materials

2.1. Reference Case Study

A market analysis was conducted to collect the main features of more than 60 warehouses in use across Europe and the United States. The aim of this analysis was to determine the reference geometry of the warehouse to be studied, in order to make the case study representative of the market. The reference structure is made up of the following elements and is presented in Figure 1 and Figure 2.

• Storage configuration: double-deep racking system
• Vertical capacity: 14 storage levels
• Longitudinal layout: 32 bays along the aisle direction
• Total pallet capacity: 17,920 units
• Overall dimensions: 35 m (height) × 86.2 m (length) × 36.7 m (depth)
• Base material specification: S350GD+ZM in accordance with EN 10346 [18]

Pallets are housed within storage bays, the configuration of which, single, double, or multi-depth, is determined by the number of pallet positions along the bay depth. A bay is structurally defined by horizontal load-bearing members (upper and lower pallet beams) and vertical framing elements (uprights) on either side. In the configuration analyzed, the warehouse utilized a double-deep racking system, accommodating two pallet positions along the transverse axis of the beam, as depicted in Figure 2. The pallet beams employed cold-formed C-section profiles. When automated storage and retrieval (S/R) systems are implemented, the racking structure must comply with the operational specifications of the S/R equipment. This primarily involves satisfying deflection criteria under the Serviceability Limit State (SLS) to maintain alignment tolerances and ensure reliable machine operation.

Upright frames, made up of vertical columns and diagonal braces, support the horizontal pallet beams. These beams are attached to the uprights using either bolted connections or hooked joints. Hooked connections are preferable when the bay height is expected to be adjusted throughout the structure’s lifetime, whereas bolted connections are more suitable for systems with fixed bay heights. In this study, bolted connections were adopted between the beams and the uprights. For the bracings, cold-formed C-section profiles were used, while a typical open-section profile was selected for the uprights. Although the same section geometry was applied to all columns in the warehouse, the thickness varied along the column height. Columns positioned closer to the ground were assigned greater thickness to accommodate the higher loads they must support, whereas those near the roof were thinner due to lower loading demands. In the cross-aisle direction, adjacent upright frames were connected using HEA profiles to ensure global structural continuity and stability.

To improve structural stiffness and control deformations caused by lateral forces such as wind, vertical bracing systems were implemented along the longitudinal axis. These structural elements were integrated into the current warehouse design. As the study assumes a clad-rack warehouse configuration, the structural racking system also serves as the building’s primary framework. In this configuration, the racking system supports external cladding and roofing panels, and the steel structure must be designed to withstand environmental actions such as wind and snow loads, in accordance with the Eurocode provisions.

2.2. Design Standards

The primary guidelines followed in the HBW design were derived from Eurocodes and regulations associated with storage structures, as outlined below [19,20]:

• EN 1993-1-1: Eurocode 3: Design of steel structures—Part 1–1: General rules and rules for building [21]
• EN 1993-1-3: Eurocode 1: Action on structures—Part 1–3: General action—Snow loads [22]
• EN 1991-1-4: Eurocode 1: Action on structures—Part 1–4: General actions: wind loads [23]
• EN 1993-1-5: Eurocode 3: Design of steel structures—Part 1–5: Plated structural elements [24]
• EN 1993-1-12: Eurocode 3: Eurocode 3. Design of steel structures—Additional rules for the extension of EN 1993 up to steel grades S 700 [25]
• prEN 15512:2018—Steel static storage systems—Adjustable pallet racking systems—Principles for structural design [26]
• FEM 9.831: 1995—Calculation principles of storage and retrieval machines [27]

The structural design and analysis of the warehouse were conducted in accordance with the provisions of the Eurocodes, which served as the primary regulatory framework. These standards guided the definition of load cases, the verification of the resistance of steel members and connections, and the assessment of both ultimate and serviceability limit states. Global structural analyses were performed using SAP2000 and SCIA (release 20.2.0) software, while detailed checks of cross-sections and connections were executed in compliance with Eurocode specifications. Additionally, the design of the racking system incorporated the [26] as a complementary reference. This standard provided essential guidance for evaluating steel profiles, conducting experimental validation, and verifying material performance criteria.

2.3. High-Strength Steel for Cold Forming

This study examines a range of high-strength galvanized steel grades from the Hyper Steel family developed by ArcelorMittal. These materials conform to EN 15512, meeting requirements for parameters such as the yield-to-tensile strength ratio (fy/fu) and minimum ductility. The baseline configuration utilizes the conventional S350GD+ZM grade, while higher-strength alternative S550GD HyPer^®+ZM is evaluated during the optimization phase. All selected grades are manufactured in accordance with EN 10346 and exhibit enhanced mechanical properties suitable for structural applications. They also comply with the ductility and performance criteria specified in [21,22,25], as well as the warehousing-specific standard [26].

In addition to their high strength-to-weight ratio, these steels offer a favorable combination of strength and ductility, along with controlled tensile strength levels that facilitate manufacturing processes such as punching and piercing. Their excellent formability makes them particularly well-suited for cold roll-forming, the primary production method for structural components in high-bay warehouse systems.

Table 1. ArcelorMittal’s HyPer offer: Mechanical Properties [28].

Constrauction Grades—Mechanical Properties in Rolling Direction
Grade	Norm	YS (MPa)	TS (MPa)	A80% mini	TS/YS
S350GD	EN 10346	>350	>420	>16	-
S390GD	EN 10346	>390	>460	>16	-
S420GD	EN 10346	>420	>480	>15	-
S420GD-HyPer®	EN 10346	>420	480–620	>15	>1.1
S450GD	EN 10346	>450	>510	>14	-
S450GD-HyPer®	ArcelorMittal	>450	510–650	>15	>1.1
S550GD	EN 10346	>550	>560	-	-
S550GD-HyPer®	ArcelorMittal	>550	600–760	>13	>1.05
S650GD-HyPer®	ArcelorMittal	>650	700–860	>8	>1.05
S700GD-HyPer®	ArcelorMittal	>700	750–910	>8	>1.05

summarizes the key mechanical properties of the steel grades considered.

3. Design and Optimization

Warehouse layout design is generally derived from a detailed analysis of client-specific requirements, operational workflows, and site-specific constraints. In the context of this study, the warehouse configuration was established based on market research intended to identify a representative structural typology aligned with prevailing industry practices and trends. The initial layout, employing the standard S350GD steel grade, was chosen based on the findings of the previously described market analysis. The structural design of the reference case was carried out through analytical checks and finite element modeling using SCIA Engineer software, ensuring compliance with the relevant Eurocodes and warehouse-specific standards. Once the reference configuration was fully validated, a material optimization phase was undertaken. This phase involved replacing conventional steel with high-strength steel grade, specifically S550GD HyPer^®+ZM, alongside a targeted reduction in cross-sectional thickness. The verification of this optimized configuration followed the same analytical methodology applied to the reference case.

To obtain more accurate input parameters, particularly regarding mechanical properties and connection stiffness, an experimental testing campaign was conducted for the S550GD HyPer^®+ZM configuration, in accordance with the recommendations of EN 15512. The results from this campaign were integrated into the structural analysis, replacing theoretical assumptions in a second design iteration applied across all steel grades from S350GD+ZM to S550GD HyPer^®+ZM. Moreover, the test data were used to validate and calibrate the finite element (FE) models. These validated models were not only employed to evaluate the performance of components that were not directly tested but also served as a basis for further design optimization.

3.1. Structural Design of the Reference Solution (S350GD)

A representative central segment of the High-Bay Warehouse (HBW) was modeled using SCIA Engineer to evaluate the global structural response of the system. The finite element model comprised eleven storage aisles and ten bays, with structural members represented using beam elements. Although the vertical bracing towers positioned along the longitudinal (aisle) direction were not explicitly included in the model, equivalent boundary conditions were applied to simulate their stabilizing effects on the overall structure.

The structural model was subjected to dead loads, pallet loads, wind and snow actions, along with a global sway imperfection of 1/200 to account for geometric imperfections. A total of five load combinations were evaluated to verify Ultimate Limit State (ULS) compliance in accordance with [26]; all the combinations are given in

Table 2. Summary of the load combinations and coefficients. Where A: full loading on pallet. B: alternate patterns on pallet loads.

Combination ID	Actions (Load Type|Safety Factor)
SLU01-NL	DEAD LOAD|1.30 PALLET-A|1.40 IMPERFECTION-A|1.40
SLU02-NL	DEAD LOAD|1.30; PALLET-B|1.40; IMPERFECTION-B|1.40
SLU03-NL	DEAD LOAD|1.30; PALLET|1.26; WIND|1.35; SNOW|1.35; IMPERFECTION|1.26
SLU04-NL	DEAD LOAD|1.30 PALLET-B|1.26 WIND|1.35 SNOW|1.35 IMPERFECTION-B|1.26
SLU05-NL	DEAD LOAD|1.30 WIND|1.50

. Additionally, two serviceability load combinations were analyzed to assess deflection limits based on [27], both for the overall structural response under environmental loading and for pallet beam performance under working loads. Static nonlinear analyses incorporating second-order (P-Δ) effects were conducted to capture the global stability behavior of the warehouse system. The load-bearing capacity of structural components, including uprights, bracing, and beams, was verified through analytical calculations in accordance with Eurocode standards and EN 15512.

The initial reference design, made with S350GD+ZM steel, was developed through analytical calculations and finite element modeling using SCIA Engineer, as illustrated in Figure 3. Key structural components along with their respective dimensions are detailed. As previously noted, each component was assigned a uniform cross-sectional profile; however, variations in thickness were implemented to meet performance requirements and optimize the overall system. The total mass of the modeled reference HBW was approximately 315 tons, corresponding to a unit weight of 408 kg/m².

Detailed specifications for all designed components in the reference configuration are provided in

Table 3. Summary of elements used in the reference configuration with S350GD+ZM steel.

S350GD+ZM
Element	Section#Thickness [mm]	From [m]	To [m]	Weight [kg/m]
UPRIGHTS—SIDE	C140 × 140 × 30#6.0	0.000	11,710	27.11
	C140 × 140 × 30#4.0	11,710	23,710	18.16
	C140 × 140 × 30#3.0	23,710	35,000	13.65
UPRIGHTS—CENTRAL	C140 × 140 × 30#4.0	0.000	6300	18.16
	C140 × 140 × 30#3.0	6300	13,500	13.65
	C140 × 140 × 30#2.5	13,500	35,000	11.39
BRACINGS—SIDE	C80 × 80 × 15#2.0			4.03
	C80 × 50 × 15#1.5			2.32
BRACINGS—CENTRAL	C80 × 50 × 15#1.5			2.32
	C80 × 50 × 15#1.5			2.32
PALLET BEAMS	C120 × 60 × 25#2.0			4.29
BACKS	Section HEA140			24.65
ROOF BEAM	Section HEA200			42.23

.

3.2. Optimization with the Use of HSS

The objective of the project was to optimize the High-Bay Warehouse (HBW) structural elements through the use of high-strength steels (HSS). This material optimization is particularly advantageous when the governing design criterion is related to ultimate limit state (ULS) resistance, as opposed to serviceability limit state (SLS) deflection requirements, where HSS offers limited immediate benefits. A detailed structural behavior analysis of the primary warehouse components was conducted to identify critical failure modes and dominant design parameters, thereby highlighting areas where HSS implementation could effectively enhance optimization. The upright elements are primarily subjected to axial compression and bending forces. Thin-walled cold-formed sections under such loading conditions are highly susceptible to buckling phenomena, which may occur in local, distortional, or global modes depending on the member length and slenderness ratio. Key parameters influencing the load-bearing capacity of these components include the effective cross-sectional area and the structural slenderness. The use of high-strength steel (HSS) offers potential for optimizing these profiles by maintaining the original geometry while reducing the wall thickness, provided that equivalent mechanical performance, particularly in terms of resistance criteria, is preserved. The bracing elements, which are connected to the uprights via bolted joints, primarily experience axial forces in both compression and tension. Particular attention must be given to the risk of buckling, as for the verification of the uprights. Observations highlighted in the case of the uprights can be transferred to the bracings, where the use of high-strength steel (HSS) proves beneficial for structural optimization. Assuming a low seismic hazard zone, the design of the horizontal beams considered only the vertical loads applied by the pallets. These beam elements are predominantly subjected to bending, with the effective section modulus being the critical design parameter. In this context, reducing the thickness and employing HSS alone does not yield significant optimization benefits for the beams. Consequently, the optimization strategy, based on thickness reduction and the use of HSS, was applied exclusively to the uprights and bracings. For the pallet beams, achieving meaningful optimization would require a redesign of the cross-sectional geometry. To enhance the performance of the uprights, minor adjustments were made to the cross-sectional geometry to preserve equivalent structural characteristics and to reduce the likelihood of local buckling, which could be intensified by the reduction in wall thickness. In the optimized configurations, transverse reinforcements were incorporated along the lateral faces of the profiles, as depicted in Figure 4. All other geometric parameters were retained, with the exception of the wall thickness, which was the primary variable in the optimization process alongside the implementation of high-strength steel (HSS). For the bracing components, the optimization strategy was limited to a reduction in the wall thickness of the C-shaped profiles, without further geometric modifications.

The same structural verifications conducted for the reference configuration using S350GD+ZM steel were also applied to the optimized designs: (a) global assessment of the structure behavior with SCIA version 22.1 Engineer Software; (b) analytical checks of elements sections and connections according to EN15512 and Eurocodes. The outcomes of the optimization process, derived from analytical calculations and numerical modeling using SCIA Engineer software, are presented in

Table 4. Overview of the components for the reference case in S550GD HyPer^®+ZM.

S550GD HyPer®+ZM
Element	Section#Thickness [mm]	From [m]	To [m]	Weight [kg/m]
UPRIGHTS—SIDE	C140 × 140 × 30#3.8	0	6300	17.26
	C140 × 140 × 30#3.5	6300	15,900	15.91
	C140 × 140 × 30#3.0	15,900	25,500	13.65
	C140 × 140 × 30#2.5	25,500	35,000	11.39
UPRIGHTS—CENTRAL	C140 × 140 × 30#3.0	0000	6300	13.65
	C140 × 140 × 30#2.5	6300	35,000	11.39
BRACINGS—SIDE	C80 × 80 × 15#2.0	0	7,500	4.03
	C80 × 50 × 15#2.0	7500	35,000	4.03
	C80 × 50 × 15#0.8			1.31
BRACINGS—CENTRAL	C80 × 50 × 15#1.2	0	5,100	2.32
	C80 × 50 × 15#1.0	5,100	12,300	2.32
	C80 × 50 × 15#0.8	12,300	35,000
	C80 × 50 × 15#0.8
PALLET BEAMS	C120 × 60 × 25#2.0			4.29
BACKS	Section HEA140 *			24.65
ROOF BEAM	Section HEA200 *			42.23

* Hot-rolled steel beam.

.

Table 3 details the optimized components using S550GD HyPer^®+ZM steel. For comparison, the reference configuration employing S350GD+ZM is summarized in Table 1. The total mass of the optimized high-bay warehouse (HBW) structure was approximately 270 metric tons, corresponding to a surface weight of 350 kg/m². This optimization resulted in a total weight reduction of approximately 14%.

3.3. Experimental Testing for Optimized Case (S550GD HyPer^®+ZM)

The experimental trials were conducted in accordance with the specifications outlined in EN 15512. Tests were selected to characterize the mechanical behavior of the uprights and bracings, the two primary components subject to optimization in this study. For each test type, a minimum of three repetitions were performed to ensure the repeatability and reliability of the results. All tests were carried out in collaboration with the University of Pisa, utilizing their structural engineering laboratories in Italy. A series of compression tests were designed to investigate various failure mechanisms affecting the uprights and upright-bracing sub-assemblies. The first test involved a stub column with a height of 420 mm, aimed at evaluating the impact of local buckling on the compressive capacity of the upright profile. Although this test is typically used to assess the influence of perforations, in this case, perforations were present only at specific locations necessary for connecting the bracings and pallet beams. Instrumentation for each test included load cells, strain gauges, and displacement transducers, allowing for detailed data collection used to calibrate finite element (FE) models. The second compression test used a longer column (1200 mm) to investigate distortional buckling behavior. The third test involved full upright frames, assembled from two uprights and bracings, to evaluate their compressive strength. Three different frame heights (L1 = 2610 mm, L2 = 3810 mm, and L3 = 5010 mm) were tested to capture varying buckling modes.

In addition to these compression and bending tests, a shear stiffness test was conducted on a full-scale upright frame with a height of 4.5 m, as illustrated in Figure 5. This test was designed to evaluate the transverse shear stiffness of the frame and to quantify any looseness in the connections between the uprights and bracings under lateral displacement. The setup consisted of applying a horizontal load at the top of the frame while fixing the base, simulating the boundary conditions typically encountered in actual warehouse installations. The horizontal displacement was imposed incrementally using a hydraulic actuator, and the corresponding lateral force was recorded using a load cell. Linear variable differential transformers (LVDTs) were placed at key points along the frame to capture lateral deformations, while strain gauges were installed on both the uprights and bracings to monitor the distribution of internal stresses. The measured response allowed for the determination of the frame’s effective shear stiffness and the identification of any non-linear behavior due to connection flexibility or joint slip.

The experimental results served a dual purpose: they were used to refine global structural models developed in SCIA Engineer software, and to calibrate FE models more accurately. In particular, the experimentally determined shear stiffness was integrated into SCIA calculations through a modified area reduction factor, improving the representation of the bracing-to-upright connection in the global model. These experimental insights significantly improved the reliability of the numerical simulations and supported the development of optimized designs using high-strength steel grades. Furthermore, the test results serve as a benchmark for future design guidelines and numerical validation procedures in the context of clad-rack and high-bay warehouse structures.

3.4. Numerical Correlation and Post-Processing

Numerical models were developed for each of the five test configurations with multiple objectives. First, they were designed to replicate the experimental setups, enabling direct comparison and correlation with the corresponding test results. Second, the models were employed to investigate the behavior of components not physically tested, for example, to evaluate the performance of the same upright profile with increased wall thickness. Finally, the numerical simulations facilitated detailed post-processing and analysis of the structural response. Numerical modelling was performed with Abaqus software. Each numerical model used shell elements, with mesh dimensions determined through a mesh convergence study to achieve an optimal balance between computational efficiency and result accuracy. To take into account the specific experimental setup, two types of analyses were performed. The first was a linear buckling analysis to identify the component’s eigenmodes. This was followed by a nonlinear static analysis, in which the most critical eigenmodes identified in the previous step were introduced as initial geometric imperfections (see Figure 6).

The eigenmode that most accurately represented the experimentally observed deformation pattern was selected as the initial geometric imperfection in the static analysis. Corresponding eigenvalues were calibrated based on experimental measurements. Depending on the type of analysis, either linear elastic or elasto-plastic material models were employed. In cases where elements underwent plastic deformation, the elasto-plastic model was preferred to better capture the material behavior. Material properties were characterized through tensile testing in accordance with ISO 6892-1 [29]. Boundary conditions were refined to more closely replicate the experimental setup, for instance, by incorporating spring elements to simulate the flexibility of the connections. For each test configuration, numerical results were validated against experimental data, including deformed shapes, force–displacement responses, peak load capacities, and other measurements obtained from instrumentation such as strain gauges, displacement transducers, and load cells. An illustrative comparison is provided in Figure 7.

Once all numerical models were calibrated, post-processing based on numerical and experimental results was carried out. Data were post-processed according to EN15512 recommendations to consider the actual thickness of components and yield strength, when specified in the test description.

In the compression tests performed on the stub column and upright specimens, the maximum load values obtained experimentally were used to evaluate the effective cross-sectional area, accounting for reductions due to local and distortional buckling, respectively. In both cases, the effective area was determined to be 1022 mm². For the upright frame subjected to axial compression, the primary outcome was the determination of the reduction factor χ, which is used to evaluate buckling resistance in accordance with Eurocode provisions. The buckling reduction factor ($\chi$), according EN 1993-1-1:2005 section 6.3.1, represents the loss of compression load-bearing capacity of a structural member due to its buckling vulnerability.

$$N_{b,Rd}={\displaystyle \frac{{\chi N}_{Rk}}{{\gamma }_{M1}}}$$

(1)

In Equation (1), $N_{b,Rd}$is the design buckling resistance in compression. $\chi$ is the buckling reduction factor, given in Equation (2), and determined as a function of two factors: the relative slenderness λ of the compression member, for the relevant buckling mode; and $\mathsf{\Phi }$, which is calculated in Equation (3). $N_{Rk}$ is the characteristic value of the resistance to compression. It links idealized material resistance and the actual resistance that accounts for geometric imperfections, residual stresses, and member slenderness.

$$\chi ={\displaystyle \frac{1}{\Phi +\sqrt{{\Phi }^2-{\lambda }^2}}}$$

(2)

$$\mathsf{\Phi }=0.5\left[1+\alpha \left(\lambda -0.2\right)+{\lambda }^2\right]$$

(3)

where

• λ is the relative slenderness from the relevant buckling curve
• α is the imperfection factor

Physically, the buckling reduction factor symbolizes that the stability of a compression member diminishes as its slenderness increases. A value of 0.695 was obtained. The effective section modulus was calculated from the bending test on the upright, with no reduction observed in the cross-sectional capacity.

In the shear stiffness tests performed on the upright frame, no corrections were applied to the experimental data, in accordance with the procedures outlined in EN 15512. From these tests, both the initial stiffness, associated with the inherent looseness of the upright frame, and the transverse shear stiffness were derived from the initial and secondary slopes of the force–displacement curves. The looseness effect can be represented either as an initial geometric imperfection (e.g., out-of-plumb condition) or by introducing a spring element to simulate joint flexibility. This spring-based approach can also be applied to model transverse shear stiffness. Alternatively, a reduction factor for the effective bracing area may be used. In this study, the latter approach was adopted. A transverse stiffness value of 4.3 kN/mm was obtained, and a corresponding reduction factor of 0.102 was determined through localized finite element modeling.

The area reduction factors in the SCIA models were applied through a two-step calibration based on experimental and numerical results. In the first step, the measured shear stiffness of upright frames and the observed connection looseness were used to quantify the actual flexibility of the bracing-to-upright connections under lateral loads. In the second step, these observations were incorporated into the SCIA models by adjusting the effective cross-sectional area of the bracings. The resulting reduction factor of 0.102 reflects the flexibility and local deformation of the connections, ensuring that the SLS and ULS checks accurately represent the behavior observed in the experiments.

Regarding generalization to other structural typologies, the method is transferable provided that relevant experimental data are available for calibration.

3.5. Update of Reference and Optimized Global Models

The global structural models, made using SCIA Engineer software, were updated with the parameters derived from the post-processing of both experimental and numerical analyses. These refinements necessitated a redesign of the structure for both the baseline configuration using S350GD+ZM steel and the optimized configuration employing S550GD HyPer^®+ZM. The introduction of a reduction factor for the effective bracing area led to non-compliance with serviceability limit state (SLS) criteria related to horizontal deflections under wind loading in both configurations. To restore compliance, the bracing thicknesses were incrementally increased until the SLS requirements were satisfied. Subsequently, ultimate limit state (ULS) verifications were performed to complete the structural assessment. Following these updates, the total structural mass of the revised reference design was approximately 376 metric tons, corresponding to a surface weight of 488 kg/m². For the optimized configuration, the total mass was reduced to approximately 339 metric tons, corresponding to 440 kg/m². The revised geometrical layout and distribution of structural elements along the cross-aisle direction are illustrated in Figure 8 for the reference case and in Figure 9 for the optimized configuration.

The distribution of mass savings across individual components and the total structure is presented in

Table 5. Contribution to weight reduction of final optimization in S550GD HyPer^®+ZM.

	S350GD+ZM	S550GD Hyper®+ZM	Contribution to Weight Reduction [%S350GD+ZM]
Element	Weight [kg]	Weight [kg]	[%]
Uprights	221,128	186,257	62.0%
Bracings	65,748	44,360	38.0%
Pallet Beams	50,452	50,452	0.0%
Backs	22,016	22,016	0.0%
Roof Beams	16,571	16,571	0.0%
Total [kg]	375,915	319,656	100.0%
Overall mass reduction from S350GD to S550GD:			15%

, which provides a comprehensive overview of the effectiveness of the optimization strategy.

The majority of the mass savings, approximately 62%, originated from the optimization of the upright elements. This significant contribution is attributed to the combined effect of thickness reduction and geometric enhancement. In contrast, the optimization potential for the bracing members was constrained. The application of an area reduction factor, derived from shear stiffness testing of the upright frame, led to non-compliance with serviceability limit state (SLS) requirements. As a result, the bracing thickness had to be increased in both the reference and optimized configurations to meet deflection criteria, thereby limiting the extent of achievable weight reduction in these components.

An overall mass reduction of approximately 15% was achieved through the transition from S350GD+ZM to S550GD HyPer^®+ZM steel in the optimization of the bracing and upright components. For the bracing members, the optimization strategy involved solely a reduction in wall thickness. In contrast, the uprights underwent both a thickness reduction and a geometric refinement, which included the integration of lateral stiffeners to preserve comparable structural performance and mechanical characteristics.

In parallel with structural optimization, a cost analysis was performed to assess the economic viability of the proposed design changes. This evaluation focused exclusively on the cost of the base material, under the assumption that the manufacturing processes for both configurations are equivalent and therefore do not contribute to cost differentiation. Based on material pricing data from November 2023, the optimized design yielded a cost saving of approximately 13%.

4. Improving Sustainability of HBW with Low Carbon Steel

Climate change is widely recognized as the most critical environmental challenge of our era, with scientific consensus attributing its acceleration primarily to human activities, including unsustainable consumption patterns and resource exploitation. HBWs, due to their scale and material intensity, must increasingly align with circular economy principles and demonstrate reduced carbon footprints through tools like Environmental Product Declarations (EPDs). An EPD is a standardized document that provides verified, transparent data regarding the environmental impacts associated with a product throughout its life cycle. These declarations are grounded in Life Cycle Assessment (LCA) methodologies and adhere to the principles outlined in ISO 14025 [30]. EPDs are commonly utilized in the construction industry to support sustainable decision-making. Within the European context, the framework for construction-related EPDs is defined by EN 15804 [31], issued by the European Committee for Standardization, which establishes the core rules for product category declarations in the building sector. In this context, steel, a key material in HBW structures, emerges as a strategic enabler of sustainable design, thanks to its strength, recyclability, and evolving low-carbon production methods.

Global Warming Potential Comparison of Refence Design and Optimized Design by HSS

This publication provides an understanding of the Global Warming Potential associated with HBW structure and compares different production routes of the steel elements considered in the design. For evaluating the environmental impacts associated with steel production in the HBW design, the EPD values provided for standard and XCarb^® recycled and renewably produced Hot Dip Galvanised steel coils with Magnelis^®, based on a functional unit of 1 ton (t) of steel, were used. The environmental data are structured according to the modular life cycle framework defined in EN 15804, considering:

• Modules A1–A3, which represent the product stage, covering raw material extraction (A1), transportation to the manufacturing site (A2), and the manufacturing process itself (A3).
• Module C, which addresses the end-of-life stage, including deconstruction, waste processing, and final disposal.
• Module D, which accounts for potential environmental benefits beyond the system boundary, such as material recovery, reuse, or recycling that may offset future impacts.

These values are reported in the following

Table 6. Extract from EPD for standard (a) and recycled and renewably produced Hot Dip Galvanised steel coils with Magnelis^® coating (b).

(a) Mandatory impact category indicators according to EN 15804+A2:2019 [31]
Results per 1 metric ton of hot dip galvanised steel coils with Magnelis® coating
Indicator	Unit	A1–A3	C1	C2	C3	C4	D
GWP-fossil	kg CO2 eq.	2.51 × 103	4.16 × 101	2.60 × 101	1.34 × 100	2.96 × 10−1	−1.54 × 103
(b) Mandatory impact category indicators according to EN 15804+A2:2019
Results per 1 metric ton of XCarb® recycled and renewably produced hot dip galvanised steel coils with Magnelis® coating
Indicator	Unit	A1–A3	C1	C2	C3	C4	D
GWP-fossil	kg CO2 eq.	8.98 × 102	4.16 × 101	2.60 × 101	1.34 × 100	2.96 × 10−1	−1.39 × 103

for the GWP-fossil category as the designated indicator for quantifying environmental impact [32,33].

Taking into account the results of the design optimization by using HSS summarized in Table 4, an optimization of the CO₂ emission of the structure has also been performed. Figure 10 shows the GWP results focusing on the influence of the different materials sources, at life cycle stage A1–A3, using traditional steel vs. a low-carbon alternative. Although the A1–A3 life cycle modules (covering raw material extraction, transport, and manufacturing) do not account for the full life cycle of a structural product, they typically represent the most carbon-intensive stages. In fact, these upstream processes can be responsible for approximately 50–60% of the total greenhouse gas emissions over the product’s entire life span. In this study, two steel types were assessed: conventional Blast Furnace steel with environmental data retrieved from the EPD and presented in Table 6a, and a low-carbon alternative XCarb^® (Table 6b), manufactured primarily from scrap and powered by renewable electricity. The latter aims to significantly reduce embodied carbon during the production phase, aligning with decarbonization strategies in structural engineering.

Overall, the HBW system with the S550GD HyPer^®+ZM performs better in terms of CO₂eq per tons. When compared to the reference case solution made of S350GD +ZM, the HBW with S550GD HyPer^® +ZM reduces the GWP emissions by up to 15% in the case of standard route steel production and up to about 70% when recycled and renewably produced XCarb^® steel coils are used.

5. Conclusions

Employing high-strength steel grades presents a promising approach for enhancing the structural efficiency of high-bay warehouse systems. Such materials contribute to reductions in both structural mass and associated CO₂ emissions, alongside potential cost benefits. This investigation primarily addressed the optimization of uprights and bracing members, with a focus on decreasing material thickness. Additional gains could be realized by modifying the geometric configurations of these components or by extending the optimization strategy to other structural elements not covered in this work, such as pallet beams and beam-end connectors. It should also be emphasized that the advantages of high-strength steels are more pronounced when structural performance is governed by ultimate limit state (ULS) requirements rather than serviceability limit state (SLS) criteria. In deformation-driven designs, effective use of high-strength materials may demand consistent geometric adaptations to fully exploit their potential. The Global Warming Potential (GWP) is assessed for both standard and recycled, renewably produced hot-dip galvanized steel coils. The results indicate that HBWs made with HSS S550GD HyPer^®+ZM exhibit a lower GWP compared to the reference solution, which uses a lower-strength steel grade. An even greater reduction in GWP is achieved by combining high-strength steel (HSS), which allows for optimized and reduced material use, with ArcelorMittal’s XCarb^®steel, produced using high recycled steel content and renewable energy.