**1. Introduction**

In recent years, there has been a significant increase in consumption, which has led to an increase of producing the storage racking systems. The products are often stored in pallet raking systems in super-markets or in warehouses of products or raw materials within factories.

Pallet racking systems are self-supporting structures that need to support considerable vertical weights. They are generally made of two main types of components: frames and beams. The frames are made of thin-walled upright profiles that have perforations in their length through which the joints with the beams are usually realized by using metallic connectors with tabs [1,2]. Such connectors are welded to both ends of the beams. Horizontal and diagonal braces welded between the uprights ensure the stability of the frame in a cross-aisle direction. The beams provide the stability in down-aisle direction and the stiffness of the connections is an important characteristic of the storage racking systems from this point of view.

Besides metallic connectors with tabs, there are other types of connections used in constructions, which include metallic connectors with screws or bolts [3], wood-steel-wood connections whose external parts are made of wood and the internal part is made of steel [4], and connectors with tabs

combined with additionally fixing using bolts [5,6]. The last type of connections are commonly known as speed lock connections [7].

In a simple way, the connections used between beams and uprights are either hinged (pin-connected) or rigid connections. In practice, for almost all connections, even for those considered as rigid connections, there may be certain rotations that influence the internal forces, especially the bending moments. Not all the connections that are considered as being rigid connections are completely rigid in reality. On the other hand, the connections considered as being hinged are not perfectly hinged because, in practice, frictions can take place and the friction influences the rotation of the connection. Therefore, estimating the sti ffness of the connections becomes a necessity, especially for the connections used for the storage racking structures.

Following the emergence of EN 1993-1-3, Eurocode 3 [8], a classification of the connections used between beams and uprights was made, based on their corresponding sti ffness. The connections that are investigated within this research fall into the category of those considered as being semi-rigid connections. The sti ffness of such connections is experimentally determined, according to the EN 15512 standard [9]. It is essential to understand that is crucial to determine the rotational sti ffness of the connections and the capable bending moment because, otherwise, the racking storage systems do not work safety.

The literature is devoid of publications on the behavior in bending tests, of the beam-to-upright connections used in storage racking systems, and results related to the e ffect of the geometry of di fferent components (beam, upright profile, and beam-end connector) on the connection sti ffness and capable moment. Some recent studies [2,10] on the beam-to-upright connections reported the e ffects of both depth of the beam and type of the tab connection on the connection sti ffness and on the failure modes of the connections with tabs in bending tests. It was shown that the common failure modes are tearing of the uprights near the slots for tabs and cracking of the tabs of the connectors [2]. No remarks were made about the failure modes of the beams in bending tests of the beam-to-upright connections. These papers did not make a comparison of the failure modes depending on the number of the tabs for each type of the connector involved. The authors showed the e ffects of the cross section shapes of the upright profiles on the connections' sti ffness.

From a theoretical point-of-view, some researchers proposed in recent published works [11–13] the mechanical model, which includes five basic deformable components (tab in bending, wall of the upright profile in bearing and bending, tab connector in bending and shear) of the beam-to-upright connections in order to predict the initial rotational sti ffness of the connections.

Regarding the beams used for storage racking systems, because these are cold-formed steel structural elements with thin-walls, distortional buckling failures may occur in bending and the e ffects of the shearing force must be accurately evaluated in bending, especially in case of the thin-walled elements having opened a cross section [14,15]. An interesting study [16] presents the results concerning the elastic shear buckling loads and ultimate strength by using numerical simulations of the stresses and strains in case of the finite element models of cold-formed steel channels with slotted webs subjected to shear.

Another critical issue of the metallic storage structures is related to the fire design methodologies so that all thin-walled structural elements to keep the load-bearing capacity as long as possible in the event of the accidental fire. In practice, in order to improve the load-bearing capacity in fire conditions, there are some types of passive or active protection systems [17]. Passive protection systems generally refer to special materials, manufacturing, or surface coating technologies in order to delay the spread of fire [4]. However, in the case of storage systems for supermarkets or warehouses, it usually uses active fire protection systems, which include automatic fire detection and extinguishing equipment (for example, a network of water pipes that are equipped with discharge nozzles called sprinklers) [17]. Regarding the cold-formed steel beams with opened and closed cross sections, a unique fire design methodology validated by experimental tests, was developed in Reference [18]. Experimental and numerical results concerning the mechanical behavior of the cold-formed steel columns subjected in fire conditions are presented in Reference [19]. Regarding the connections, there are numerical models used to predict the load-bearing capacity of the connections with and without passive protection. This is similar to the numerical model for wood-steel-wood connections [4].

Since the main target of the researchers from the industry of the storage racking systems is to increase the rotational sti ffness of the beam-to-upright connections, some innovative beam-end connectors with tabs having one additional bolt fixed in the side part of the upright [1] or two additional bolts fixed in the front part of the upright [3,6] were proposed and investigated in monotonic and cyclic bending tests. However, it is known that the increase of the rotational sti ffness of the beam-to-upright connections leads to the rise of the bending moment at the beam ends when the beams are mechanically loaded in storage systems. It follows that the beam-to-uprights connections should be evaluated by taking into account the ratio between the capable bending moment and the real value of the bending moment. Moreover, the external force is a distributed force applied on the length of the beam in a real case of loading while the force is applied to the free end of the beam in the bending tests used in research on beam-to-upright connections, according to EN 15512 [9] and MH16.1 [20].

In this context, in the present research, the sti ffness and capable moment is experimentally determined in bending tests carried-out on 18 di fferent groups of beam-connector-upright assemblies prepared by combining three types of beams (di fferent sizes of the box cross section), three kinds of uprights profiles (with di fferent thickness of the section wall), and two types of connectors (four-tab connector and five-tab connector). This work is a part of the report research on the mechanical behavior of the thin-walled metal parts used in the racking storage systems subjected to bending and buckling [21].

The main purpose of this research to analyze the e ffects of the connector type with tabs and the e ffects of the dimensions of the assembled elements (beams and uprights) used in the racking storage systems on both the rotational sti ffness and the capable bending moment at failure of that connection in order to predict the safety coe fficients of the beam-to-upright connections. For this purpose, the following objectives are established: (i) testing of di fferent groups of assemblies between the beams and the uprights by using two types of connectors (with four or five tabs), (ii) comparison of the sti ffness of the connections in function of the type of the connector, (iii) analysis of the e ffects of the wall thickness of the upright profile and of the size of a beam cross section on the rotational sti ffness and on the capable moment at failure for all beam-to-upright connections involved, (iv) comparison of estimated safety coe fficients for all beam-to-upright connections tested in order to predict the best type of connection for each group containing beams of the same size for the case of the beam loaded by the distributed weight of the pallets, (v) comparison of the estimated maximum deflections for beams with the same type of semi-rigid connections at both ends by taking into account the sti ffness experimentally obtained.

The authors also aim to use the results obtained experimentally by focusing on the sti ffness of the connections in order to compare the maximum deflections of the beams having such semi-rigid connectors at both ends with the maximum deflections computed for the beams pin-connected or with rigid connectors at both ends. Bending moments developed at the midpoint of the beam and at the ends of the beam are also evaluated for di fferent boundary conditions.

### **2. Materials and Methods**

### *2.1. Beam-to-Upright Connections Tested*

The main structural elements of such a semi-rigid joint used for the pallet racking structures are shown in Figure 1.

The upright (Figure 1c,d) is a cold-formed omega-profile made of a thin steel sheet (Figure 2). The upright profile has perforations along its length that facilitate the connection with the beam end connectors welded at the beam end. The main dimensions of the cross sections of the uprights involved in this research are shown in Table 1.

**Figure 1.** Main elements of the connections tested: (**<sup>a</sup>**,**b**) upright-connector-beam assembly, (**<sup>c</sup>**,**d**) upright, (**<sup>e</sup>**,**f**) beam with welded beam end connector.

**Figure 2.** Cross section of the upright profile (dimensions D, W, b, t are given in Table 1).

**Table 1.** Dimensions of the cross sections of the uprights.


\* Dimensions of the uprights are shown in Figure 2.

Beams having a box cross section (Figure 1e,f) are manufactured by using two C-profiles assembled together in a rectangular shape (Figure 3). The connectors are welded at both ends of the beam and those connectors are used to hook the beam by perforations of the upright. The main dimensions of the cross sections of the beams involved in this study are shown in Table 2.

In Table 4, all upright-connector-beam assemblies tested in bending are shown in this research in order to determine the sti ffness of those connections. The corresponding identification codes are also shown in Table 4. The main components of each assembly are: upright, beam, and beam and connector. Three types of upright profiles were used, which have the same geometry of the cross-section (Figure 2) but have di fferent thicknesses of the profile wall (Table 1). Three types of box beams (Figure 3) are used whose dimensions are given in Table 2. For each type of upright used in an assembly, two types of connectors were considered, which include a four-tab connector and a five-tab connector. Lastly, six di fferent types of upright-connector-beam assemblies were tested for each beam type (Table 4). Multiple individual tests were performed for each type of assembly (last column of Table 4). Lastly, 101 individual tests were carried out.

**Figure 3.** Shape and dimensions of the cross-sections of the beams (dimensions H, W, t are given in Table 2).


\* Dimensions of the uprights are shown in Figure 3.

In Table 3, the overall dimensions (Figure 4) are shown as well as the designation codes corresponding to both types of beam end connectors used in this research.

**Table 3.** Dimensions of the beam end connectors.


\* Dimensions of the beam end connectors are shown in Figure 4.

**Figure 4.** Shape and dimensions of the beam end connectors involved in the research (dimensions H, W, D are given in Table 3).


**Table 4.** Upright-connector-beam assemblies tested.

### *2.2. Work Methods*

### 2.2.1. Tensile Tests

The component parts (upright, beam, and beam end connector) are made of steel. Tensile tests were carried out for the tensile specimens cut from each component part of the assemblies involved in order to experimentally obtain the following characteristics of the materials: yield stress, ultimate stress, and elongation until maximum force. The material properties are used in data processing obtained in bending tests of the connections in accordance with EN 15512 standard [9].

Tensile specimens were cut from each component part (upright, beam end connector, and beam), as shown in Figure 5.

**Figure 5.** Locations from where we have cut the samples to make tensile tests: (**a**) from upright, (**b**) from beam, and (**c**) from beam end connector.

Universal testing machine INSTRON 3369 (INSTRON, Norwood, MA, USA) with digital controls and a maximum force of 50 kN was used in tensile tests. The tensile testing machine pulls the sample clamped at both ends and records the tensile force related to the elongation of the tensile specimen until it ruptures. By using the force-elongation curve, the stress-strain curve is obtained and we ge<sup>t</sup> the yield stress and ultimate stress. In tensile tests, the strain rate was equal to 0.00025 per second until the strain ε = 0.003 and then the strain rate equaled 0.0067 per second until to failure in accordance with the standard EN ISO 6892 [22].

### 2.2.2. Bending Test of the Connections

Tests have been carried out according to the standard EN 15512 [9]. The scheme of loading used in the bending test of the connection and the photo of the experimental setup are shown in Figure 6.

In accordance with Figure 6 and EN 15512 [9], a short upright cut between two sets of perforations was connected to a very stiff testing frame in two points apart at the distance g = 470 mm from each other. A short beam with a length of 650 mm is connected to the upright region by means of the connector. Sideways movement and twisting of the beam were prevented. The beam is able to move freely in the vertical direction of the load by guiding the free end vertically because a steel plate welded at the free end of the beam is sliding between the bearings. The vertical force was applied at distance b = 400 mm from the face of the upright region by using the force transducer of type S-E-G Instruments (S-E-G Instruments AB, Bromma, Sweden) whose accuracy is 0.001 kN and maximum force is 12.5 kN.

Rotation angle θ of the beam end at the connection with the upright was measured by using the displacement transducers whose rods are in permanent contact with the plate fixed to the beam close to the connector so that the distance is equal to 50 mm (Figure 6a). The displacement transducers of type WA-100 (manufactured by HBM–Hottinger Baldwin Messtechnik Gmbh, Darmstadt, Germany) may record displacements with a size less than 100 mm having the accuracy of 0.001 mm.

**Figure 6.** Bending test of the connection according to EN 15512 [9]: (**a**) scheme of the test stand and(**b**) photo of the experimental setup.

The force transducer and both displacement transducers are connected to the QuantumX MX840 Universal Measuring Amplifier (manufactured by Hottinger HBM, Darmstadt, Germany) that transmits the data to Easy Catman software (version 3.1, Hottinger Baldwin Messtechnick Gmbh, Darmstadt, Germany) on the computer. The data acquisition device QuantumX MX840 (Hottinger Baldwin Messtechnick Gmbh, Darmstadt, Germany) works at a frequency of 19.2 kHz.

In the beginning of the bending test, an initial force of approximately 10% of the maximum failure load is applied and, then, the vertical force is increased gradually until failure occurs. Tests were repeated identically for all the upright-connector-beam assemblies involved in this study (Table 4). A minimum of five tests were made for each kind of upright-connector-beam assembly shown in Table 4. In this way, the scattering rate of the results is also analyzed.

The value of the external force F acquired by the force transducer is used to compute the bending moment M by using Equation (1).

$$\mathbf{M} = \mathbf{F}\mathbf{b},\tag{1}$$

in which b is the dimension shown in Figure 6a.

The deflections D1 and D2 acquired by the displacement transducers (Figure 6a) are used to compute the rotation angle θ of the beam end at the connection by using Equation (2).

$$\Theta = (\mathbf{D}\_2 - \mathbf{D}\_1) / \text{h} \tag{2}$$

in which h is the distance between the rods of the displacement transducers (Figure 6a). In Equation (2), the deflection D1 has a positive value while the deflection D2 is a negative value. The rotation angle θ of the beam end computed with Equation (2) is expressed in radians.

The failure mode of the component parts (beam end connector, upright) was also noted in the testing report in the case of each bending test carried out.

The bending moment M and rotation angle θ experimentally obtained were corrected in accordance with the standard EN 15512 [9]. Therefore, the correction procedure is described below.

The corrections are required because there are variations of the yield stress of the material corresponding to each component part (upright, beam, connector) and variations of the thickness corresponding to those components. As a result, the correction factor Cm was computed by using Equation (3) and Cm must be less than or equal to 1, according to EN 15512 [9].

$$\mathbf{C}\_{\mathbf{m}} = \left[ \left( \frac{\mathbf{f}\_{\mathbf{y}}}{\mathbf{f}\_{\mathbf{t}}} \right)^{\alpha} \frac{\mathbf{t}}{\mathbf{t}\_{\mathbf{t}}} \right]\_{\max} \text{ and } \mathbf{C}\_{\mathbf{m}} \le 1,\tag{3}$$

where ft is the yield stress obtained by testing the tensile specimens, fy is the nominal yield stress and the values are given in standard EN 10346 [23], tt is the measured thickness for the tensile specimen, t is the design thickness, α = 0 when fy ≥ ft, and α = 1 when fy < ft.

To make the correction for a moment-rotation curve (M–θ), some steps should be covered in accordance with the EN 15512 standard [9]. First, for each bending test of a connection, the moment-rotation curve (M–θ) is plotted and the slope of the curve K0 is measured at the origin. Then, the elastic rotation M/K0 is subtracted from the measured rotation θ to obtain the plastic rotation θp by using Equation (4), according to EN 15512 [9].

$$
\Theta\_{\mathbf{p}} = \Theta - \mathbf{M}/\mathsf{K}\_0. \tag{4}
$$

The corrected moment Mn is computed by using Equation (5).

$$\mathbf{M}\_{\rm n} = \mathbf{M} \cdot \mathbf{C},\tag{5}$$

where C is another correction factor related to Cm whose value is computed by using Equation (6) and must be less than or equal to 1, according to EN 15512 [9].

$$\mathbf{C} = 0.15 + \mathbf{C\_m} \le 1.\tag{6}$$

The corrected value of the elastic rotation θe is computed by using Equation (7).

$$\boldsymbol{\Theta}\_{\text{e}} = \mathbf{M}\_{\text{n}} / \mathbf{K}\_{0} \tag{7}$$

and the corrected rotation angle θn is computed by using Equation (8), according to EN 15512 [9].

$$
\boldsymbol{\Theta}\_{\rm \rm \rm \rm \/P} = \boldsymbol{\Theta}\_{\rm \rm P} + \boldsymbol{\Theta}\_{\rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \$$

The adjusted moment-rotation curve (Mn–θn) is plotted and its initial slope K0 is the same for the initial moment-rotation curve (M–θ).

The failure moment Mni is considered to be the maximum corrected moment from the adjusted moment-rotation curve (Mn–θn) shown in Figure 7, which is plotted for each upright-connector-beam assembly. The subscript i of the failure moment Mni represents the number of the test with i = 1,n, where n is the number of tests corresponding to each upright-connector-beam assembly. The moment Mm is the mean value of failure moments Mni and it is computed with Equation (9), according to EN 15512 [9].

$$\mathbf{M}\_{\rm m} = \frac{1}{\mathbf{n}} \sum\_{i=1}^{n} \mathbf{M}\_{\rm ri}. \tag{9}$$

**Figure 7.** Computing of the rotational stiffness kni, according to EN15512 [9].

The standard deviation of the adjusted test results denoted with s is computed with Equation (10), according to EN 15512 [9].

$$\mathbf{s} = \sqrt{\frac{1}{\mathbf{n} - 1} \sum\_{i=1}^{n} \left( \mathbf{M}\_{\text{ni}} - \mathbf{M}\_{\text{m}} \right)^{2}}.\tag{10}$$

For each upright and connector assembly, the characteristic failure moment Mk is the characteristic failure moment computed by Equation (11), according to EN 15512 [9].

$$\mathbf{M}\_{\mathbf{k}} = \mathbf{M}\_{\mathbf{m}} - \mathbf{s} \mathbf{K}\_{\mathbf{s}}.\tag{11}$$

where Ks is the coefficient based on a 95% fractile at a confidence level of 75% in accordance with EN 15512 [9].

The design moment for the connection is denoted by MRd and is given by Equation (12) [9].

$$\mathbf{M}\_{\rm Rd} = \eta \frac{\mathbf{M}\_{\rm k}}{\gamma\_{\rm M}} \,\tag{12}$$

where γM is a partial safety factor for the connection and γM = 1.1, according to EN 15512 [9]. η is the variable moment reduction factor selected by the designer so that η ≤ 1.

The rotational stiffness kni (i = 1,n) of the connection is obtained as the slope of a line through the origin, which isolates equal areas (A1 and A2 in Figure 7) located between that line and the experimental curve below the design moment MRd. The rotational stiffness kni is computed for each test using Equation (13), according to EN 15512 [9].

$$\mathbf{k}\_{\rm nl} = \frac{1.15 \mathbf{M}\_{\rm Rd}}{\Theta\_{\rm ki}},$$

where θki (i = 1,n) is the rotation corresponding to the design moment MRd on the adjusted moment-rotation curve (Mn–θn) shown in Figure 7.

The design rotational stiffness km is computed by Equation (14) [9].

$$\mathbf{k}\_{\rm m} = \frac{1}{\mathbf{n}} \sum\_{i=1}^{n} \mathbf{k}\_{\rm ni}. \tag{14}$$

#### 2.2.3. Theoretical Aspects Regarding the Effects of the Stiffness of Connection on Deflections

In strength calculus of the beams of the racking storage systems, the beam is considered to be subjected to uniformly distributed force q given by the specific weight of the goods on the pallets stored on the shelf. It is considered that the modulus of rigidity EI in bending is considered to be constant along the axis of the beam with the length L. By considering the traditional methods to analyze the beams in a racking storage system for which the connections between beam and upright are considered as pin-connections (hinged), the rotation θ is equal to qL<sup>3</sup>/24EI at the beam end at that connection while the bending moment Mb developed at the pin-connection is equal to zero. In case the end connections considered as rigid-like is the fixed support, the rotation θ is equal to zero at that connection while the bending moment Mb is equal toqL<sup>2</sup>/12EI.

On the other hand, for the semi-rigid connections between the beam and upright region, the values of the rotation angle θ and of the bending moment Mb are between the values corresponding to the pin-connection and fixed support. Depending on the rigidity of the connection, in Figure 8, a classification of the connections is presented, according to EN 1993-1-3, Eurocode 3 [8].

**Figure 8.** Classes of the beam-end-connections related to the rigidity, according to EN 1993-1-3 [8].

For the beam connected with the uprights of the storage system, by using semi-rigid connections whose rigidity km was experimentally determined, the bending moment Mend developed at the ends of the beam subjected to the uniformly distributed force q, is computed by using Equation (15).

$$\mathbf{M}\_{\text{end}} = \frac{\mathbf{q}\mathbf{L}^3}{24\text{EI}\left(\frac{1}{\mathbf{k}\_\text{m}} + \frac{\mathbf{L}}{2\text{EI}}\right)}.\tag{15}$$

The bending moment Mmid developed at the middle cross section of the beam is computed using Equation (16).

$$\mathbf{M}\_{\rm mid} = \frac{\mathbf{q}\mathbf{L}^2}{8} - \mathbf{M}\_{\rm end}.\tag{16}$$

In order to analyze the capacity of the semi-rigid connections of the beam, it is computed by the safety coefficient c of the connection as the ratio between the design moment MRd computed by using Equation (12), based on experimental results, and the bending moment Mend developed at the end of the beam with semi-rigid connections at both ends and loaded with the uniformly distributed force q. The safety coefficient c of the connection is computed by Equation (17).

$$\mathbf{c} = \frac{\mathbf{M}\_{\text{Rd}}}{\mathbf{M}\_{\text{end}}}.\tag{17}$$

The value of the maximum deflection vmax having two semi-rigid connections at both ends, whose rigidity km was experimentally determined, is computed by using Equation (18).

$$\mathbf{v}\_{\text{max}} = \frac{\mathbf{q}\mathbf{L}^4 (10\mathbf{E}\mathbf{I} + \mathbf{L}\mathbf{k}\_{\text{m}})}{384\mathbf{E}\mathbf{I} (2\mathbf{E}\mathbf{I} + \mathbf{L}\mathbf{k}\_{\text{m}})}.\tag{18}$$

Practically, customizing Equation (18) for the case of the beam pin-connected (hinged) at both ends for which the rigidity of the connection km is equal to zero, leads to the maximum deflection vmax equal with5qL<sup>4</sup>/ 384EI. On the other hand, customizing Equation (18) for the case of the beam fixed at both ends (embedded ends) for which the rigidity of the connection km tends to infinity, leads to the maximum deflection vmax equal toqL<sup>4</sup>/ 384EI.
