Flexural behaviour of steel storage rack beam-to-upright bolted connections

Thin-Walled Structures 124 (2018) 202–217

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Full length article

Flexural behaviour of steel storage rack beam-to-upright bolted connections a,c

Liusi Dai , Xianzhong Zhao a b c

a,b,⁎

, Kim J.R. Rasmussen

T

c

Department of Structural Engineering, Tongji University, Shanghai 200092, China State Key Laboratory of Disaster Reduction in Civil Engineering, Shanghai 200092, China School of Civil Engineering, The University of Sydney, Sydney, NSW 2006, Australia

A R T I C L E I N F O

A B S T R A C T

Keywords: Steel storage pallet racks Beam-to-upright bolted connections Experimental investigation Moment-rotation curves Component method

Steel storage pallet racks are usually unbraced in the down-aisle direction in order to make palletised goods always accessible. The down-aisle stability of unbraced rack structures mainly depends on the performance of beam-to-upright connections and column bases. Beam-to-upright boltless connections are commonly employed for their convenience in assembly and adjustment. Since storage racks are being designed to considerable heights for the purpose of improving warehouse efficiency, steel storage rack beam-to-upright bolted connections are gradually being introduced to improve the structural stability. The paper presents an experimental investigation into the flexural behaviour of beam-to-upright bolted connections of steel storage pallet racks. A total of twentyone specimens were tested under monotonic loading in a single cantilever test setup, including three different size pallet beams, three different upright thicknesses, and beam-end-connectors with two or three tabs. This study examines deformation patterns and failure modes of the connections, their rotational stiffness, moment resistance and corresponding connection rotations. The results show that steel storage rack beam-to-upright bolted connections, classified as “semi-rigid” and “partial-strength” connections, generally experience ductile failure modes. The effects of critical geometric parameters, i.e. upright thickness, beam height and the number of tabs, on the flexural behaviour of bolted connections are also investigated. In addition, comparisons of performance and failure modes between bolted and boltless connections are made. Moreover, in order to promote the design by advanced analysis of rack structures, a preliminary theoretical model based on the Component Method is proposed to predict the initial rotational stiffness of beam-to-upright bolted connections in steel storage pallet racks. A good agreement is obtained between the initial rotational stiffness derived from the theoretical model and the experimental tests.

1. Introduction One of the significant applications of cold-formed steel is storage racks [1], which are widely used in fields such as warehouses and other short and long term storage facilities. In practical use, a variety of rack structures are available which can be distinguished based on the structural scheme and the picking modalities, such as selective pallet racks, drive-in/drive-through racks and cantilever racks [2]. This study focuses on the behaviour of steel storage selective pallet racks, and their typical configuration is illustrated in Fig. 1. The main structural frame of storage pallet racks is composed of cold-formed thin-walled steel members, such as uprights, pallet beams and bracings. Pallet beams are welded to beam-end-connectors, and upright members have arrays of holes along the length, which allow pallet beams to be connected at variable heights and brace members to be bolted to form upright frames (see Fig. 1). The lateral loads in the cross-aisle direction are resisted by the upright frames, which consist of two uprights and diagonal bracings ⁎

(see Fig. 1). In the down-aisle direction, bracings are rarely installed in order to make palletised goods always accessible, and thus the downaisle stability of steel storage pallet racks largely depends on the performance of beam-to-upright connections and column bases [3–6]. Boltless beam-to-upright connections are commonly used in steel storage racks for their convenience in assembly and adjustment, and they are categorised on the basis of the connector features by Markazi et al. [7] as Class A-Tongue and slot design, Class B-Blanking design, Class C-Stud-incorporated design and Class D-Dual integrated tab design. The complex constructional details make numerical analysis too complicated to be adopted in the design of beam-to-upright connections associated with storage racks. Therefore, experimental test methods are provided to evaluate the stiffness and strength of beam-to-upright connections in the main international design codes for steel storage racks, such as Australian Standard AS 4048 [8], the Rack Manufacturers Institute (RMI) specification [9] and European Standard EN 15512 [10]. Two alternative test setups, i.e. cantilever tests and portal tests,

Corresponding author at: Department of Structural Engineering, Tongji University, Shanghai 200092, China E-mail address: [email protected] (X. Zhao).

https://doi.org/10.1016/j.tws.2017.12.010 Received 16 August 2017; Received in revised form 14 November 2017; Accepted 5 December 2017 0263-8231/ © 2017 Published by Elsevier Ltd.

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Fig. 1. Configuration of steel storage selective pallet racks.

pallet racks in order to improve the connection properties. Compared with traditional boltless connections (Fig. 2(a)), in bolted beam-to-upright connections (Fig. 2(b)), a single bolt is installed to replace the locking pin, the purpose of which is to resist accidental uplift loads. Extensive studies [12,21–24] have been reported to evaluate the behaviour of bolted connections between cold-formed steel members, and design formulae have been proposed for use in codes [25–27]. Limited research has been conducted on bolted connections used in cold-formed steel storage racks. Gilbert and Rasmussen [12] performed portal tests to investigate the behaviour of bolted connections in drive-in and drive-through storage racks, and pointed out that compared with tab connectors bolted connections are feasible and economical with a higher moment resistance and stiffness. Yin et al. [24] carried out experimental tests on speed lock connections with bolts to examine the monotonic and cyclic connection behaviour. This study focuses on comparisons between five types of beam-to-upright speedlock connections to determine the effects of additional bolts and welds on the behaviour of the connections. However, due to the increasing use of bolted connections in pallet racks, further studies are required to evaluate the flexural behaviour of bolted connections in storage pallet racks. In addition, detailed comparisons between boltless and bolted connections are required to determine the improvement of connection behaviour in terms of stiffness, strength and ductility achieved by adding a bolt. Moreover, current design of beam-to-upright connections in steel storage racks largely relies on experimental tests, which are expensive and time-consuming. As an alternative method, finite element analyses have been applied for evaluating the behaviour of beamto-upright connections, but currently high accuracy numerical analysis requires great computational efforts mainly due to the complex nature of beam-to-upright connections in steel storage racks [28,29]. Therefore, considering the limitations of the finite element method, a theoretical model based on the Component Method has been proposed to

are included in AS 4048 [8] and RMI specifications [9], while only the cantilever test method is included in EN 15512 [10]. Note that in cantilever tests, the full-range moment-rotation behaviour of beam-toupright connections can be obtained including the initial rotational stiffness and strength. However, a monotonic cantilever test applies to one direction, upward or downward, each of which has different moment-rotation response. When a rack buckles by sway, the relative rotations between the pallet beam and the upright are in opposite directions at the two ends. Also, the moment-shear ratio is different from the actual frame. These difficulties can be overcome by performing a portal test which determines an average connection stiffness for the correct moment-shear ratio, as required [11,12]. However, portal tests are laborious to set up and difficult to conduct to full collapse. Consequently, usually only the initial stiffness is obtained from a portal test, whereas a cantilever test is used when the full-range moment-rotation response is required, as in this paper. Over recent decades, substantial investigations have been conducted to evaluate the behaviour of boltless beam-to-upright connections in terms of stiffness, strength and cyclic behaviour [7,13–17]. As highlighted in [16], boltless connections generally experience brittletype failure modes relating to the fracture of tabs and/or upright walls, and a sudden decrease is observed in the moment capacity of a connection after the peak load. When the down-aisle stability of an unbraced pallet rack is mainly provided by the beam-to-upright connections and column bases, the sudden loss in the strength of beam-toupright connections may give rise to the collapse of the overall structure, especially when the rack is subjected to accidental dynamic loads, such as sudden impacts and seismic loads [18–20]. Moreover, in order to improve the efficiency of warehouses, storage racks are designed to considerable heights, which makes the improvement of the structural stability especially important. Under these circumstances, beam-to-upright bolted connections are gradually being applied in steel storage

203

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Fig. 2. (a) Boltless connections “1.8C5-B120-4T”; (b) Bolted connections “1.8C2-B120-3TB”; (c) Regular perforations in upright webs and the corresponding beam-end-connectors.

one specimens were tested under monotonic loading in a single cantilever test setup, considering three different size pallet beams, three upright thicknesses, and beam-end-connectors with two or three tabs. The experimentally obtained deformation patterns and failure modes, rotational stiffness, moment resistance and ductility are presented and discussed. On the basis of the test results, the effects of critical geometric parameters, i.e. beam height, upright thickness and the number of tabs, on the flexural behaviour of bolted connections are also investigated. Moreover, comparisons of the performance and failure modes between bolted and boltless connections are highlighted. Based on the Component Method, a theoretical model is proposed to predict the initial rotational stiffness of beam-to-upright bolted connections in cold-formed steel storage racks.

evaluate the initial rotational stiffness of boltless connections [30]. This work encourages further investigation to promote the use of theoretical models to predict the flexural behaviour of bolted connections in steel storage racks. Note that to date the theoretical model has been established to determine the initial rotational stiffness of the connections. This is because the stiffness is mostly used in the design and linear analysis of rack structures, reflecting the flexibility of the connection. Moreover, the initial rotational stiffness is also one of the most important parameters required to evaluate the full-range moment-rotation behaviour of the connection. This paper presents an experimental investigation into the flexural behaviour of bolted connections in steel storage pallet racks. A total of twenty204

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Table 1 Specimen details. Specimen label

Upright Type

Upright Thickness (mm)

Beam Type

Beam-end-connector type

Number of specimens

Variation

2.3C2-B105-3TB 2.3C2-B120-3TB 2.3C2-B145-3TB 1.8C2-B120-3TB 2.8C2-B120-3TB 2.3C2-B120-2TB 2.3C2-B120-3TB-NB

C2 C2 C2 C2 C2 C2 C2

2.3 2.3 2.3 1.8 2.8 2.3 2.3

B105 B120 B145 B120 B120 B120 B120

3TB 3TB 3TB 3TB 3TB 2TB 3TB-NB

3 3 3 3 3 3 3

Beam height

2. Experimental program

Upright thickness Tab number With and without a bolt

loading point and the face of the upright was 400 mm. Note that in order to ensure the applied load remained vertical during the test, the actuator was connected to a sliding device at one end and to a hinge connection at the other end (see Fig. 4). As a result of this arrangement, the actuator was not always perpendicular to the beam in the loading process, which induced an axial force in the beam. However, the axial force was comparatively small due to the limited rotation of the beam. Therefore, in the present tests and in bending tests on beam-to-upright connections in general, the effect of the axial component of the applied load on the test results is ignored [8–10]. Moreover, the out-of-plane displacement at the end of the beam was restrained by the lateral bracing. The specimen was tested at a slow loading rate of 0.5 mm/min at the beginning, which was increased to 1–2 mm/min after the peak load. The test was executed incrementally until the load decreased to 50% of the peak load or when the specimen was not suitable for further loading due to large deformations. The arrangement of ten Linear Variable Differential Transducers (LVDTs) is presented in Fig. 5(a). LVDTs 1–4 are mounted at the beam end to measure the in-plane horizontal displacements of the top and the bottom flanges of the beam, and the corresponding in-plane displacements of the upright are measured via LVDTs 5–6. LVDTs 7 and 8 are located along the beam to capture the vertical displacement of the beam, and LVDTs 9 and 10 are employed to monitor the in-plane horizontal and vertical displacements of the actuator, respectively. As shown schematically in Fig. 5(b), sixteen strain gauges S1-S16, mounted on the flanges of the beam at distances of 10 mm, 60 mm, 110 mm and 160 mm away from the beam-end-connector, were used to evaluate the moment applied to the beam at the initial stage of loading.

The bolted connection considered in the present study is a tabconnected beam-to-upright connection with a bolt. Fig. 2 illustrates the typical configurations of bolted and boltless connections associated with steel storage pallet racks. As shown in the figure, compared with boltless connections, the typologies of uprights and end connectors in bolted connections are altered to accommodate the installation of a bolt. The specimens and test arrangements were designed in accordance with EN15512 [10] and are similar to the monotonic tests on boltless connections by Zhao et al. [16], in order to ensure the reliability and comparability of the test results. 2.1. Specimen details A total of twenty-one individual specimens were designed, categorised into seven groups of three nominally identical specimens each, as listed in Table 1. The specimens were mainly composed of an upright of 760 mm in length, a beam of 800 mm in length and a corresponding beam-end-connector (see Fig. 3(a)). Note that the beam is fillet welded to the end connector all around using gas metal arc welding (GMAW). Figs. 2 and 3 illustrate the geometric details of the test specimens, including the nominal dimensions of uprights, pallet beams and beamend-connectors. The upright, C2-100 × 90, was selected with varied thicknesses, and beams with nominal heights of 105 mm, 120 mm and 145 mm were considered. The nominal major axis second moments of area of the beams are listed as follows: 0.74 × 106 mm4 for beam B105, 0.97 × 106 mm4 for beam B120 and 1.65 × 106 mm4 for beam B145. Two types of corresponding beam-end-connectors were designed with varied tab numbers, and an M10 bolt was applied in each bolted connection. The specimens were labelled to specify the connection details. For example, ‘2.3C2-B105-3TB’ indicates a bolted connection with an upright of C2 type, an upright thickness of 2.3 mm, a beam height of 105 mm and a beam-end-connector of three tabs. No bolt was installed in the connection type “2.3C2-B120-3TB-NB” in order to evaluate the contribution of an additional bolt to the overall behaviour of the connection (see Table 1). The material properties of uprights, beams and beam-end-connectors were determined from a series of coupon tests according to GB/T228-2002 [31]. Table 2 lists the average 0.2% proof stresses and the average ultimate tensile strengths derived from three coupon samples for each structural element. It is worth mentioning that concerning the commercial confidentiality some dimensions of the complex cross-sections are not provided in the paper.

3. Tests results and analysis 3.1. General The moment-rotation responses of the tested bolted connections are presented in this section. According to the cantilever test arrangement, as has been explained in Section 2, the connection rotation, ϕ , is determined using the following equation.

ϕ = ϕb − ϕc

(1)

where ϕb and ϕc are the rotations of the beam axis and the upright axis respectively. The rotation of beam axis ϕb can be calculated by Eq. (2) or Eq. (3), and the rotation of column axis ϕc can be calculated by Eq. (4).

2.2. Test setup and instrumentation In order to investigate the full-range behaviour of bolted connections, the cantilever test method described in EN15512 [10] was adopted. As shown schematically in Fig. 4, the test setup mainly consisted of a self-balanced reaction frame, a 20 kN electric actuator, a sliding device for vertical loading, and a lateral bracing. The upright was bolted to the reaction frame to create a fixed boundary condition, and a quasi-static load was applied to the top of the beam by the actuator using displacement control. The initial distance between the

ϕb = 1/2 × [(D1 − D3)/ h13 + (D2 − D 4)/ h24]

(2)

ϕb = (D7 − D8)/ h 78

(3)

ϕc = (D5 − D6)/ h56

(4)

where Di (i = 1~10 ) are the displacements recorded by LVDTs 1–10, and hij is the distance between LVDT-i and LVDT-j. Due to the minor influence of beam flexural deformations on the connection rotation [5], the values of ϕb derived from Eqs. (2) and (3) were close at the beginning of the test. It should be mentioned that four steel rods were welded to the webs of the beam near the end (highlighted in Fig. 5) in 205

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Fig. 3. Geometric details of specimens (dimensions in mm).

order to attach LVDTs 1–4. In the case of tests on bolted connections, as the load increased, the beam buckled locally at the compression region in some tests, which lead to the tilting of the rods. After that, the

readings of LVDTs 1–4 could not properly predict the connection rotation ϕb , and Eq. (3) was thus adopted for the calculation of ϕb . The connection moment, M , was calculated by multiplying the beam tip 206

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obtained from comparison type specimens without bolts are presented in Fig. 9. It should be noticed that the results of three nominally identical tests for each connection type, denoted as H1, H2 and H3, are given in Figs. 7 and 8. Generally, similar behaviour was observed in these nominally identical tests. The Class A specimens, composed of type “2.3C2-B105-3TB”, “2.3C2-B120-3TB” and “2.8C2-B120-3TB” specimens, demonstrated similar deformation patterns and failure modes, as illustrated in Fig. 7. In particular, an idealised characteristic moment-rotation curve is depicted in Fig. 7(d). It can be observed from the tests that at the beginning of loading, the connections deformed elastically, and no significant looseness was observed due to the installation of the bolt. With the load increased to point A1 in Fig. 7, the connections started to behave nonlinearly with the stiffness decreasing progressively. Herein, as shown in Fig. 7(e) Point A1, the top tab in contact with the upright wall gradually distorted, while the lower part of end-connector started to be in contact with the upright flange. Failure was initiated by local buckling of the beam end in the compression region near the upright (Point A2 in Fig. 7). Subsequently, due to the load redistribution in the connection region, the load bearing capacity of the specimen was not significantly decreased until the beam end cracked at the upper welding area between the beam and the end-connector (Point A3 in Fig. 7). Meanwhile, cracks also developed at the top tab. With further increase in rotation, these cracks developed rapidly, as did the local buckling deformations of the beam end (Point A4 in Fig. 7), leading to a continuous decrease in the applied load. The failure mode of these specimens is termed as “Failure mode I – Tab crack + Beam end failure”. The Class B specimens, consisting of type “2.3C2-B145-3TB”, “1.8C2-B120-3TB” and “2.3C2-B120-2TB” specimens, were characterised by the same idealised moment-rotation curve, which can be divided into three phases: linear elastic, nonlinear inelastic and plastic, as shown in Fig. 8(d). It is important to note that a significant fluctuation in load was observed in the plastic phase of the tests. The initial development of the moment-rotation curves was identical to that of the

Table 2 Material properties. Structural elements

Upright

Beam Beam-end-connectors

1.8C2 2.3C2 2.8C2 B105/B120/B145 2TB/3TB

Yield strength

Ultimate strength

f y (N / mm2)

fu (N / mm2)

288 366 340 323 230

355 448 418 445 320

load by the actual loading arm. Since LVDT 9 records the horizontal movement of the actuator, the actual loading arm was defined as the initial distance between the loading point and the face of the upright (d = 400 mm ), plus half the width of the upright and the reading of LVDT 9. Fig. 6 shows load-strain curves of a typical connection type “2.3C2B120-3TB”. It can be seen from the figure that due to the eccentricity of the connector (see Fig. 5(b)), the readings of strain gauges marked as even numbers were numerically larger than those marked as odd numbers. In addition, the measured strains near the beam end, viz. S6, S8, S10 and S12, exceeded the yield strain of the beam, which means that the bolted connections might fail at the beam end during the tests. The detailed explanations of moment-rotation performances and failure mechanism of all tested connections are presented in the following section. 3.2. Moment-rotation response and failure modes The specimens were categorised into two classes: Class A and Class B according to the ductility observed in the experimental moment-rotation responses. Figs. 7 and 8 illustrate the moment-rotation curves of these two classes of specimens, along with the associated key deformation stages during the loading process. The experimental results

Fig. 4. Test setup.

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Fig. 5. Schematic arrangement of LVDTs and strain gauges.

significant drops in the moment capacity of these connections. The failure mode, termed as “Failure mode IV – Tab crack”, is highlighted in Fig. 8(e). It is apparent that the initial performance of these two groups of specimens are similar (see Figs. 7 and 8). Also, bolt failure was not observed in any of the tests. The failure modes of the connections can be summarised as follows: (BE) Beam end failure, (T) Tab crack, (C) Tearing and/or buckling of the upright, and combinations of the abovementioned failure modes (T+BE, T+C). It can be derived that the relative strengths of the three component parts in a typical connection, namely the beam end, the end-connector and the upright, determine the failure mode of the connection. The experimental tests on boltless connections of rack structures [16] show that the relative thickness of the upright and end-connector determines whether the connection fails by ‘tab crack’ or ‘tearing of upright wall’. This rule can also be applied to the bolted connections. For example, if the connection had a thinner upright wall (1.8C2), (C) Tearing of the upright wall mostly happened rather than (T) tab crack. Otherwise, (T) tab crack occurred during the loading process. However, (T) tab crack was usually not the dominating failure mode in bolted connections, since both tabs and bolts contributed to resist the applied moment. In summary, the parameters

Class A specimens, i.e. the connection behaved elastically until nonlinear deformations occurred in the elements of connections, especially the distortion of tabs (Point B1/C1/D1 in Fig. 8). The failure mechanisms of these specimens were varied. For specimen type “2.3C2-B1453TB”, the failure initiated as a crack of the top tab formed (Point B2 in Fig. 8(a)), whereas local buckling of the beam end was not observed, since the beam flange force was reduced with the increased beam height. Finally, the top tab crack propagated to tear out, and the upright buckled locally because of the strong contact action between the beam bottom flange and the upright (Point B3 in Fig. 8(a)). This failure mode was termed as “Failure mode II- Tab crack + Upright buckling”. Note that specimen type “1.8C2-B120-3TB” has a thinner upright wall which is weaker than that of the connection tab. Thus this connection failed by tearing of the upright wall around the top tab, and by local buckling of the upright wall around the bottom tab (Point C2 in Fig. 8(b)). Moreover, the moment-rotation curve fluctuated due to the progressive buckling of the upright wall in contact with the bottom tab (Point C3 in Fig. 8(b)). This failure mode was defined as “Failure mode III – Tearing and local buckling of upright wall”. One other failure mode was observed in the tests on specimen type “2.3C2-B120-2TB”. As shown in Fig. 8(c), the continuous development of cracks in tabs caused two 208

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Fig. 6. Load-strain curves of a typical connection type “2.3C2-B120-3TB”.

3.3. Stiffness and strength of the connections

influencing the failure mode of the bolted connection are the ratio of the upright thickness to the thickness of the beam end connector, along with the comparative strengths of the upright and beam end. It is worth noting that the strength of the beam end is determined by the moment capacity of the beam, as well as the capacity of the weld between the beam and the end connector. The failure modes of each test specimen are given in Table 3. As mentioned, additional tests were carried out on boltless specimens type “2.3C2-B120-3TB-NB” comprised of the same upright, beamend-connector and beam as specimens type “2.3C2-B120-3TB”, in order to perform a direct comparison between bolted and boltless connections. Fig. 9 shows the experimental moment-rotation curves of specimens type “2.3C2-B120-3TB-NB”, and includes the following significant observation points: (E1) distortion of tabs, (E2) top tab crack, (E3) middle tab crack and (E4) load termination. It can be deduced from Fig. 9(a) that the connection behaviour was significantly improved in terms of stiffness, strength and ductility by the inclusion of a bolt. As seen from Fig. 9, the boltless connections failed abruptly after the formation of a crack in the top tab, whereas for the bolted specimens, after the crack formed in the top tab the moment resistance could be maintained by the bolt in shear and by the upright in compression (see Fig. 7).

The behavioural parameters, including the initial rotational stiffness (ke ), equivalent stiffness according to European Standard EN 15512 (kEN ), moment capacity (Mc ) and corresponding rotation (θm ), as obtained from the moment-rotation curves, are summarised in Table 3. The initial stiffness, ke , was determined as the tangent slope of the initial loading branch. The stiffness, kEN , was obtained as the secant slope of a line through the origin which isolates equal areas between the line and the experimental curve. The moment capacity, Mc , was the maximum recorded moment during the tests. Due to random variables in the fabrication and assembly of the test specimens, a slight deviation is observed in the results of three nominally identical tests. Therefore, their average values are used to represent the connection properties, as listed in Table 3. It can be seen clearly from Table 3 that the specimens type “2.3C2B120-2TB” have the lowest stiffness and moment capacity. The particular configuration has only two tabs and the bolt is located near the neutral axis of the beam section. Seeing the relatively poor performance, this connection type is not recommended for joining pallet beams to uprights. For the other tested connections with bolts, the initial stiffness values range from 80.5 kN m/rad to 130.5 kN m/rad, while the values of moment capacity vary from 3.37 kN m to 4.97 kN m. It is obvious that the initial stiffness values are greater than 209

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Fig. 7. Experimental moment-rotation responses for specimens – Class A (“2.3C2-B105-3TB”, “2.3C2-B120-3TB” and “2.8C2-B120-3TB”).

the stiffness values obtained according to EN15512 [10]. Generally, the secant stiffness kEN is employed in the linear analysis model for rack structural design, but the tangent stiffness ke is a key parameter for

determining the full-range moment-rotation behaviour of a connection. Therefore, a theoretical model, based on the Component Method, has been developed for evaluating the initial stiffness of bolted rack 210

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Fig. 8. Experimental moment-rotation responses for specimens – Class B (“2.3C2B145-3TB”, “1.8C2-B120-3TB” and “2.3C2B120-2TB”).

connections, as described in Section 4. The elastic first-yield moment resistance of the beams, Mbe , are listed as follows: 3.70 kN m for beam B105, 4.35 kN m for beam B120 and 6.02 kN m for beam B145,

obtained as the product of the nominal elastic section modulus and the nominal yield stress. It can be derived from Table 3 that the moment capacities of the connections, Mc , are less than those of the beams. 211

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Fig. 9. Experimental moment-rotation responses for the specimens “2.3C2-B120-3TB-NB”.

However, for connections experiencing beam end failure (BE), the ratios of Mc / Mbe are close to unity (see Table 4). According to Eurocode 3 [27], a connection can be classified based on the values of initial rotational stiffness and strength in bending. The classification by stiffness is determined via the comparison between kea and the ratio of EIb/ Lb , where E , Ib and Lb represent the elastic modulus, moment of inertia and span of the connected beam respectively. If kea is

larger than 25EIb/ Lb , the connection is defined as rigid, and it is nominally pinned if kea is lower than 0.5EIb/ Lb . A connection not satisfying the requirements for a rigid or a pinned connection is classified as semirigid. Moreover, the ratio of Mca/ Mb, pl determines the connection classification by strength, in which Mca refers to the moment capacity of the connection, and Mb, pl corresponds to the plastic moment resistance of the beam. The connection is full-strength, if the ratio is greater than 1.0, 212

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Table 3 Summary of test results. Specimen ID

2.3C2-B105-3TB

2.3C2-B120-3TB

2.3C2-B145-3TB

1.8C2-B120-3TB

2.8C2-B120-3TB

2.3C2-B120-2TB

2.3C2-B1203TB-NB

Test number

H1 H2 H3 H1 H2 H3 H1 H2 H3 H1 H2 H3 H1 H2 H3 H1 H2 H3 H1 H2 H3

Initial stiffness

Average Initial stiffness

Stiffness per EN15512

Average of kEN

Moment capacity

ke kN m/rad

k ea kN m/rad

kEN kN m/rad

kENa kN m/rad

Mc kN m

89.2 73.5 78.8 99.4 100.9 87.0 129.7 121.2 140.6 94.2 96.7 100.2 91.4 98.1 115.4 37.8 37.4 37.8 95.4 95.5 86.3

80.5

75.4 67.6 66.4 86.4 89.0 80.2 118.8 110.6 121.2 80.0 83.1 84.8 82.1 83.3 92.4 35.1 36.5 37.9 83.3 67.9 68.6

69.8

3.62 3.61 3.51 3.99 3.98 4.02 4.84 5.08 4.98 3.33 3.36 3.43 4.4 4.13 3.98 2.11 1.77 1.95 2.95 2.81 2.58

95.8

130.5

97.0

101.6

37.7

92.4

85.2

116.9

82.6

85.9

36.5

73.3

Average moment capacity Mca kN m 3.58

4.00

4.97

3.37

4.17

1.94

2.78

Rotation at Mc

Average of θm

θm rad

θma rad

0.079 0.089 0.092 0.077 0.086 0.099 0.055 0.108 0.086 0.072 0.077 0.077 0.095 0.085 0.089 0.083 0.068 0.064 0.048 0.044 0.046

0.087

0.088

0.083

0.075

0.090

0.072

0.046

Failure modes

T+BE T+BE T+BE T+BE T+BE T+BE T+C T+C T+C C C C T+BE T+BE T+BE T T T T T T

Table 4 Stiffness and strength. Specimen ID

2.3C2-B105-3TB 2.3C2-B120-3TB 2.3C2-B145-3TB 1.8C2-B120-3TB 2.8C2-B120-3TB 2.3C2-B120-2TB 2.3C2-B120-3TB-NB

Stiffness Average initial stiffness k ea

Classification

kN m/rad

k ea/(EIb/ Lb) -

80.5 95.8 130.5 97.0 101.6 37.7 92.4

1.42 1.29 1.04 1.30 1.37 0.51 1.24

Semi-rigid Semi-rigid Semi-rigid Semi-rigid Semi-rigid Semi-rigid Semi-rigid

Strength Average moment capacity Mca

Mca/ Mbe

Mca/ Mb, pl

kN m

-

-

3.58 4.00 4.97 3.37 4.17 1.94 2.78

0.97 0.92 0.83 0.77 0.96 0.45 0.64

0.78 0.79 0.65 0.67 0.82 0.38 0.55

Classification

Partial-strength Partial-strength Partial-strength Partial-strength Partial-strength Partial-strength Partial-strength

the connections was considerably increased by 19% and was associated with a transition from upright buckling to beam end failure. As the thickness was further increased to 2.8 mm, only a slight growth in strength was observed. Furthermore, the connections stiffness is seen not to be sensitive to upright thickness.

and it is nominally pinned if the ratio is less than 0.25. If the ratio of Mca/ Mb, pl falls between the two boundaries, the connection is defined as partial-strength. The ratios of kea/(EIb/ Lb) and Mca/ Mb, pl are shown in Table 4, and according to the abovementioned classifications, all test specimens are classified as “semi-rigid” and “partial-strength” connections. Therefore, a semi-rigid joint model should be adopted for the analysis of unbraced pallet racks with bolted connections. The influences of different geometric parameters on the connection properties, i.e. rotational stiffness and moment capacity, are described in the next section.

3.4.2. Effect of beam height It can be seen clearly from Tables 3 and 4 that the beam height has a significant influence on the flexural behaviour of bolted connections. Comparing the specimens with the same type of upright “2.3C2” and beam-end-connector “3TB”, the stiffness and moment capacity of the connections are found to increase monotonically with the beam height increasing from 105 mm through 120 mm to 145 mm.

3.4. Effects of different parameters on the connection behaviour This section presents the effects of different parameters, i.e. upright thickness, beam height and the number of tabs, on the behaviour of the connections in terms of the stiffness and strength. It should be noted that the reported effects of the identified parameters pertain to the particular joint geometrics studied and may not be generally applicable to bolted beam-to-upright connections in steel storage racks.

3.4.3. Effect of the number of tabs The number of tabs on the beam-end-connector significantly influences the behaviour of bolted connections. Compared with specimen type “2.3C2-B120-2TB” (2 tabs), the average stiffness and moment capacity of specimen type “2.3C2-B120-3TB” (3 tabs) were significantly increased by 154% and 106% respectively, as illustrated in Tables 3 and 4.

3.4.1. Effect of upright thickness The influence of the upright thickness on the flexural behaviour of the bolted connections can be examined from the comparisons between specimen types “1.8C2-B120-3TB”, “2.3C2-B120-3TB” and “2.8C2B120-3TB”. As shown in Tables 3 and 4, with the upright thickness increasing from 1.8mm to 2.3 mm, the average moment resistance of

4. Comparisons between boltless and bolted connections The direct comparison between bolted and boltless connections has been presented in Section 3 based on the test results of specimen types 213

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“2.3C2-B120-3TB” and “2.3C2-B120-3TB-NB” in terms of deformation patterns and failure modes, stiffness and strength. It is highlighted that with an additional bolt, the moment capacity of a connection is dramatically increased by 43.9% and it is associated with a transition from brittle to ductile type of failure, whereas the increase in connection stiffness is insignificant, as illustrated in Figs. 7–9 and Table 3. Two major changes have been made in order to install an additional bolt in the beam-to-upright connection. Firstly, the spacing and shapes of upright perforations are altered. As shown in Fig. 2(c), the hole spacing of uprights changes from 50 mm to 75 mm in order to accommodate the bolt hole between the two tab holes. Secondly, the corresponding beam-end-connector is modified to match the upright. Therefore, for the same height of the beam end connector (200 mm), the boltless connection has four tab rows, while the bolted connection has three tab rows plus one bolt row (see Fig. 2). As a result, in order to further evaluate the efficiency of bolted connections, a comparison is made between bolted and boltless connections featuring the same types of uprights and beams connected by beam-end-connectors with the same height, namely specimen types “1.8C2-B120-3TB” and “1.8C5-B120-4T” (see Fig. 2). It is worth noting that slight differences in the configurations of web holes exist in uprights C2 and C5 (see Fig. 2(c)), but the influence thereof on the connection behaviour is sufficiently small to be neglected. As highlighted in Fig. 2, the boltless connection type “1.8C5-B120-4T” has four tab rows, and the lower tabs are bent to be compatible with the upright perforations under positive (downward) loads. Whereas the bolted connection type “1.8C2-B120-3TB” has three tab rows plus one bolt row, and the lower tab is in poor contact with the upright hole under positive loads due to the lack of compatible design in tab directions. It should be noted that similar poor contact between tabs and upright perforations commonly exists in beam-to-upright tab connections in steel storage racks. This may be mainly due to the variations in the detailed configurations of the connections, e.g. the directions of tabs (see Fig. 2). Fig. 10 shows the moment-rotation curves of these two groups of connections, where the results of connections type “1.8C5-B120-4T” are obtained from the experiments described in the companion paper [16]. The initial rotational stiffness, ke , the equivalent stiffness, kEN , and the moment capacity, Mc , of the connections are also provided in the figure. It can be seen clearly that compared with the boltless connections (“1.8C5-B120-4T”), a ductile behaviour is demonstrated in the bolted connections (“1.8C2-B120-3TB”), and the moment resistance is greatly improved. Conversely, due to the decreased number of tab rows and poor contact between tabs and upright perforations, the stiffness of the bolted connection is significantly reduced, which may cause a dramatic decrease in the lateral stiffness of unbraced storage racks. In addition, large deformations are also observed during the tests in the connection

components, such as the upright and the beam, which makes the replacement of structural components more difficult (see Fig. 7). Also, higher costs are usually incurred in the fabrication and assembly of bolted connections. In summary, the connection strength and ductility are greatly improved by adding a bolt to the connector, while the stiffness of the connection is not effectively improved. It is worth noting that the seismic behaviour of an overall rack structure is inevitably improved due to the better ductility of the joints, but this improvement cannot be evaluated through linear dynamic analyses, such as Modal Response Spectrum Analysis (MRSA). This is because in linear vibration analyses only stiffness is employed to define the connection property, whereas the ductility of joints is not. However, in the case of rack structures subjected to high seismic loads, nonlinear dynamic analysis is commonly performed considering the full-range moment-rotation behaviour of the connections, and thus the improvement of the structural seismic behaviour caused by the increase in connections ductility is accounted for. Hence, in the design of steel storage rack beam-to-upright connections, many factors should be evaluated with respect to structural properties, cost-effectiveness, as well as efforts required for installation and replacement. 5. Theoretical model for predicting the rotational stiffness of bolted connections According to the test observations and analysis in Section 3, a theoretical model is developed to predict the initial rotational stiffness of beam-to-upright bolted connections in steel storage pallet racks. The model is established based on a set of realistic assumptions, taking advantage of the Eurocode 3 framework for determining the theoretical load-displacement behaviour of basic components [27], as well as the theoretical model of boltless connections presented in the companion paper [30]. The identification, evaluation and assembly of basic deformable components contributing to the initial rotational stiffness of bolted rack connections are summarised in this section. To validate the proposed model, the initial stiffness obtained from the mechanical model is subsequently compared with those obtained from the experimental data presented in Section 3. The basic assumptions made for the mechanical model are listed as follows: – The beam end connector is assumed not to be in contact with the upright flange initially, whereas tabs and bolts are considered to be in contact with the upright wall at the early stage of loading. – “Tab in bending” is an important component contributing to the connection rotation. However, the component behaviours of tabs located above and below the rotation centre are not identical due to their different contact areas, as shown in Fig. 11(a). – With the installation of a bolt in the connection, the bearing deformation of plates in contact with the bolt is taken into account. – The shear deformation of the bolt is too small to be considered in the model for predicting the initial stiffness of connections, as is the tensile deformation of the weld between the beam and the end connector. – The deformations, caused by beam flange and web in compression, beam web in tension and upright web in compression, are not significant, and thus can be neglected. – Except for plates in bending, bolted connections have similar deformable components as boltless connections, and thus the same equations can be used in evaluating the behaviour of these components. Based on the assumptions listed above, seven elementary deformable components, contributing to the initial stiffness of steel storage rack bolted connections, are schematically illustrated in Fig. 11(a), viz. tab in bending (tb), upright wall in bearing (cwc), upright wall in

Fig. 10. Comparison of moment-rotation curves between specimens “1.8C2-B120-3TB” and “1.8C5-B120-4T”.

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Fig. 11. Mechanical model for bolted connections.

and ht (see Table 5, “Tab in bending”), are determined by the assumed degree of connectivity between the tabs and the perforations under pull and push actions, respectively. If tabs are under pull action, the value of the contact length, hc , is taken as 17 mm, being the nominal length of the tab end. As has been explained above, the tabs of the bolted connections are in poor contact with upright perforations when they are under push action. Since nominally identical tabs and upright perforations are employed in all tested connections, the lengths, ht , are only measured in typical connections and the average value being equal to 4 mm is used in the model. Note that since the theoretical model is proposed to predict the initial rotational stiffness of the connections, it provides satisfactory accuracy to adopt the values of ht measured at the initial stage of loading. Based on the proposed mechanical model shown in Fig. 11(b) and formulations for evaluating the equivalent extensional stiffness of basic

bending (cwb), beam-end-connector in bending and shear (bcb), upright web in shear (cws) and plates in bearing (b-bcb, b-cwc). Fig. 11(b) shows the proposed mechanical model, in which each component is characterised by an extensional linear-elastic equivalent spring. As to the component properties, the calculation methods, used for predicting the extensional stiffness corresponding to the components of a boltless connection, have been provided in the companion paper [30]. Table 5 summarises the equations for calculating the stiffness of the key components presented in Fig. 11(a). Regarding bolted connections, components such as plates in bearing (b-bcb, b-cwc), can also be taken into account, and their stiffness are defined in Table 5 in accordance with the approach proposed in Eurocode 3 [27]. It is important to note that the tabs located below the rotation centre are in poor contact with the upright perforations during the loading process (see Fig. 11(a)). Therefore, the contact lengths between tabs and upright perforations, hc 215

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Table 5 Equations for stiffness of key deformable components [27,30].

components listed in Table 5, the initial stiffness of steel storage rack beam-to-upright bolted connections, k 0 , can be obtained according to the procedures shown in Fig. 11(c). Table 6 presents a comparison between the theoretical rotational stiffness (k 0 ) and the experimental initial stiffness (ke ) of the tested specimens, as described in Section 3. The ratios of k 0/ ke are highlighted in the table. It can be observed that the average value of k 0/ ke is close to 1.0, and the standard deviation of the ratio is equal to 0.15, which indicates that the proposed theoretical model provides a satisfactory prediction of the initial stiffness of steel storage rack beam-to-upright bolted connections. However, it is worth noting that a lower stiffness is estimated for the two-tab connection, which may be due to a possible increase of the contact length between the tabs located below the rotation centre and the upright perforations,

Table 6 Comparison of initial rotation stiffness between predicted values and experimental results. Specimen ID

k 0 (kN . m /rad)

k e (kN . m /rad)

k 0/ kE

2.3C2-B105-3TB 2.3C2-B120-3TB 2.3C2-B145-3TB 1.8C2-B120-3TB 2.8C2-B120-3TB 2.3C2-B120-2TB Average Standard Deviation

95.7 97.2 138.7 93.0 100.1 27.6

80.5 95.8 130.5 97.0 101.6 37.7

1.19 1.01 1.06 0.96 0.99 0.73 0.99 0.15

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Acknowledgements

ht , as illustrated in Table 5, compared to the length used in the model. Herein the theoretical model based on the Component Method is developed to predict the initial rotational stiffness of the connections. Some of the assumptions listed above apply to the initial stage of loading and may not be applicable to models for determining the fullrange moment-rotation behaviour of the connections. For example, the deformable components that develop as a result of contact between beam end connector and the side plate of the upright, including upright web in compression and upright flange in bending and shear, may significantly contribute to the nonlinear deformations of the connection, and are considered in ongoing studies to determine the full-range moment-rotation behaviour of beam-to-upright rack connections.

The test specimens for the experiments were kindly provided by WAP Shanghai Ltd. The first author expresses her thanks for the scholarships offered by the China Scholarship Council and the Centre for Advanced Structural Engineering at the University of Sydney. References [1] G.J. Hancock, Cold-formed steel structures, J. Constr. Steel Res. 59 (4) (2003) 473–487. [2] T. Pekoz, G. Winter, Cold-formed steel rack structures, in: Proceedings of the Second Specialty Conference on Cold-Formed Steel Structures, 1973. [3] F.S. Cardoso, K.J.R. Rasmussen, Finite element (FE) modelling of storage rack frames, J. Constr. Steel Res. 126 (2016) 1–14. [4] N. Baldassino, C. Bernuzzi, Analysis and behaviour of steel storage pallet racks, Thin-Walled Struct. 37 (4) (2000) 277–304. [5] M. Abdel-Jaber, R.G. Beale, M.H.R. Godley, A theoretical and experimental investigation of pallet rack structures under sway, J. Constr. Steel Res. 62 (1) (2006) 68–80. [6] C. Bernuzzi, M. Simoncelli, An advanced design procedure for the safe use of steel storage pallet racks in seismic zones, Thin-Walled Struct. 109 (2016) 73–87. [7] F.D. Markazi, R.G. Beale, M.H.R. Godley, Experimental analysis of semi-rigid boltless connectors, Thin-Walled Struct. 28 (1) (1997) 57–87. [8] AS/NZS 4084. Steel storage racking, Standards Australia/Standards New Zealand, Sydney, Australia, 2012. [9] RMI. Specification for the design, testing and utilization of industrial steel storage racks, ANSI MH16.1-2012, Rack Manufacturers Institute, Technical report. [10] EN 15512. Steel static storage systems, European Technical Committee CEN/TC 344, European Specifications, 2009. [11] E. Harris, Sway Behaviour of High Rise Steel Storage Racks (Ph.D. Thesis), University of Sydney, 2006. [12] B.P. Gilbert, K.J.R. Rasmussen, Bolted moment connections in drive-in and drivethrough steel storage racks, J. Constr. Steel Res. 66 (6) (2010) 755–766. [13] C. Bernuzzi, C.A. Castiglioni, Experimental analysis on the cyclic behaviour of beam-to-column joints in steel storage pallet racks, Thin-Walled Struct. 39 (10) (2001) 841–859. [14] C. Aguirre, Seismic behavior of rack structures, J. Constr. Steel Res. 61 (5) (2005) 607–624. [15] P. Prabha, V. Marimuthu, M. Saravanan, S.A. Jayachandran, Evaluation of connection flexibility in cold formed steel racks, J. Constr. Steel Res. 66 (7) (2010) 863–872. [16] X. Zhao, T. Wang, Y. Chen, K.S. Sivakumaran, Flexural behavior of steel storage rack beam-to-upright connections, J. Constr. Steel Res. 99 (2014) 161–175. [17] S.N.R. Shah, N.H.R. Sulong, R. Khan, M.Z. Jumaat, M. Shariati, Behaviour of Industrial Steel Rack Connections, Mech. Syst. Signal Process. 70–71 (2016) 725–740. [18] A.L.Y. Ng, R.G. Beale, M.H.R. Godley, Methods of restraining progressive collapse in rack structures, Eng. Struct. 31 (7) (2009) 1460–1468. [19] C.K. Chen, Seismic Study on Industrial Steel Storage Racks, National Science Foundation, URS/John A. Blume and Associate Engineers, 1980. [20] C.A. Castiglioni, N. Panzeri, J.C. Brescianini, P. Carydis, Shaking table tests on steel pallet racks, in: Proceedings of the Conference on Behaviour of Steel Structures in Seismic Areas-stessa, Naples, Italy, 2003, pp. 775–781. [21] J.B.P. Lim, D.A. Nethercot, Ultimate strength of bolted moment-connections between cold-formed steel members, Thin-Walled Struct. 41 (11) (2003) 1019–1039. [22] J.B.P. Lim, D.A. Nethercot, Stiffness prediction for bolted moment-connections between cold-formed steel members, J. Constr. Steel Res. 60 (1) (2004) 85–107. [23] K.F. Chung, K.H. Ip, Finite element investigation on the structural behaviour of cold-formed steel bolted connections, Eng. Struct. 23 (9) (2001) 1115–1125. [24] L. Yin, G. Tang, M. Zhang, et al., Monotonic and cyclic response of speed-lock connections with bolts in storage racks, Eng. Struct. 116 (2016) 40–55. [25] Cold-formed Steel Structure code AS/NZ 4600. Sydney: Standards Australia/ Standards New Zealand, 2005. [26] North American Specification for the Design of Cold-formed Steel Structural Members, AISI S100-12. Washington D.C., American Iron and Steel Institute, 2012. [27] EN 1993-1-8:2005, Eurocode 3: Design of Steel Structures—Part 1–8: Design of Joints. Brussels, Belgium: European Committee for Standardization, 2005. [28] F.D. Markazi, R.G. Beale, M.H.R. Godley, Numerical modelling of semi-rigid boltless connector, Comput. Struct. 79 (26–28) (2001) 2391–2402. [29] K.M. Bajoria, R.S. Talikoti, Determination of flexibility of beam-to-column connectors used in thin walled cold-formed steel pallet racking systems, Thin-Walled Struct. 44 (3) (2006) 372–380. [30] X. Zhao, L. Dai, T. Wang, et al., A theoretical model for the rotational stiffness of storage rack beam-to-upright connections, J. Constr. Steel Res. 133 (2017) 269–281. [31] Metallic Materials Tensile Test Procedure at Ambient Temperature, GB/T228-2002. Beijing, Ministry of Construction of China, 2002.

6. Conclusions This paper presents an experimental investigation into the behaviour of bolted connections in steel storage pallet racks. A total of twenty-one individual tests were conducted under monotonic loads in a single cantilever test setup. The deformation patterns and failure modes, rotational stiffness and moment capacity of all tested specimens are presented and discussed, as are the effects of critical geometric parameters on the connection behaviour. Comparisons of the performance and failure modes between bolted and boltless connections are also provided in the paper. Based on the test results and analysis thereof, the following conclusions can be drawn: (1) Typical failure modes for steel storage rack beam-to-upright bolted connections are: (BE) Beam end failure, (T) Tab crack, (C) Tearing and/or buckling of the upright, and combinations of abovementioned failure modes (T+BE, T+C). Two main factors determine the failure mode of the connection, viz. the ratio of upright thickness to the thickness of beam-end-connector, and the relative strengths of the beam end section and the upright. Ductile momentrotation behaviour was observed in all bolted connections, especially the connections experiencing beam end failure which exhibited superior post-peak behaviour compared with other failure modes. (2) The main geometric parameters influencing the stiffness and strength of bolted connections are the upright thickness, beam height and the number of tabs, of which the number of tabs is the most influential parameter. However, two-tab bolted connections are not recommended for use in pallet racking due to their low stiffness and strength. (3) Compared with boltless connections, more commonly used in pallet racks, the strength and ductility of bolted connections are greatly improved and it is associated with a transition from brittle to ductile type of failure. However, in many cases, a dramatic reduction of the stiffness is observed compared with boltless connections. (4) In practical use, several factors should be evaluated in choosing the optimal connection type, such as structural performance, cost-effectiveness, and efforts required for installation and replacement. Based on the available experimental results, bolted connections have more ductile moment-rotation behaviour, and they are thus more appropriate to use in high-rise racking systems located in seismic areas. Further investigations are ongoing into the hysteretic behaviour of steel storage rack beam-to-upright bolted connection. (5) In order to promote the design of rack structures by advanced analysis, a preliminary theoretical model based on the Component Method is proposed to predict the initial rotational stiffness of beam-to-upright bolted connections used in steel storage pallet racks. Further studies are in progress to extend the theoretical model to determine the full-range moment-rotation behaviour of the connections, including stiffness, strength and ductility.

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