The influence of pallets on the behaviour and design of steel drive-in storage racks - Part II Design

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1 University of Wollongong Researh Online Faulty of Engineering and Information Sienes - Papers: Part A Faulty of Engineering and Information Sienes 2013 The influene of pallets on the behaviour and design of steel drive-in storage raks - Part II Design B P. Gilbert Griffith University, b.gilbert@griffith.edu.au L H. Teh University of Wollongong, lteh@uow.edu.au R X. Badet Griffith University K J. R Rasmussen The University of Sydney, k.rasmussen@usyd.edu.au Publiation Details Gilbert, B. P., Teh, L. H., Badet, R. X. & Rasmussen, K. J. R. (2013). The influene of pallets on the behaviour and design of steel drivein storage raks - Part II Design. Researh and Appliations in Strutural Engineering, Mehanis and Computation - Proeedings of the 5th International Conferene on Strutural Engineering, Mehanis and Computation, SEMC 2013 (pp ). CRC Press. Researh Online is the open aess institutional repository for the University of Wollongong. For further information ontat the UOW Library: researh-pubs@uow.edu.au

2 The influene of pallets on the behaviour and design of steel drive-in storage raks - Part II Design Abstrat This paper analyses the influene of the horizontal restraints provided by pallets on the ultimate apaity of drive-in raks. The paper is based on the assumption that one an aurately determine the oeffiient of frition between the rail beams and the pallets or an design a devie that restrains the pallets from sliding on the rail beams. Thirty-six drive-in raks representing the global sale of an Australian manufaturer over three years are analysed for all possible loading senarios. For the sake of omputational effiieny, the simple 2D model introdued in the ompanion paper is used for the study. The load ase(s) governing the strutural design is(are) also larified and the frition oeffiient or strength of a restraining devie required to prevent the pallets from sliding is determined. Keywords behaviour, design, steel, drive, pallets, storage, influene, raks, part, ii Disiplines Engineering Siene and Tehnology Studies Publiation Details Gilbert, B. P., Teh, L. H., Badet, R. X. & Rasmussen, K. J. R. (2013). The influene of pallets on the behaviour and design of steel drive-in storage raks - Part II Design. Researh and Appliations in Strutural Engineering, Mehanis and Computation - Proeedings of the 5th International Conferene on Strutural Engineering, Mehanis and Computation, SEMC 2013 (pp ). CRC Press. This onferene paper is available at Researh Online:

3 The influene of pallets on the behaviour and design of steel drive-in storage raks Part II Design B.P. Gilbert Griffith Shool of Engineering, Griffith University, Australia L.H. Teh Shool of Civil, Mining and Environmental Engineering, University of Wollongong, Australia R.X. Badet Griffith Shool of Engineering, Griffith University, Australia K.J.R. Rasmussen Shool of Civil Engineering, The University of Sydney, Australia ABSTRACT: This paper analyses the influene of the horizontal restraints provided by pallets on the ultimate apaity of drive-in raks. The paper is based on the assumption that one an aurately determine the oeffiient of frition between the rail beams and the pallets or an design a devie that restrains the pallets from sliding on the rail beams. Thirty-six drive-in raks representing the global sale of an Australian manufaturer over three years are analysed for all possible loading senarios. For the sake of omputational effiieny, the simple 2D model introdued in the ompanion paper is used for the study. The load ase(s) governing the strutural design is(are) also larified and the frition oeffiient or strength of a restraining devie required to prevent the pallets from sliding is determined. 1 INTRODUCTION This paper analyses the influene of the horizontal restraints provided by pallets on the ultimate apaity of drive-in raks. As introdued in the ompanion paper (Gilbert et al., 2013a), by ating as horizontal braes between adjaent uprights, pallets signifiantly influene the strutural behaviour of drive-in raks and must be onsidered in order to aurately apture the 3D behaviour of this type of struture. However, due to the unertainty onerning the frition between the pallet bases and the rail beams, drive-in raks are urrently designed without onsidering this braing effets. If a devie an prevent the pallets from sliding on the rail beams or if the oeffiient of frition between the pallet bases and the rail beams an be reliably determined, the horizontal braing effet provided by the pallets ould be fully exploited in the design. The urrent paper analyses the influene of the horizontal braing effet of pallets on the design of steel drive-in raks in the down-aisle diretion only. As mentioned in the ompanion paper (Gilbert et al., 2013a), due to the upright frames, pallets are not believed to influene the behaviour of the raks in the ross-aisle diretion. It should also be noted that the frition between pallet bases and the rail beams would prevent the pallets from dropping through on aount of the upright bowing deformations. As suh, the servieability hek against upright bowing deformations is not onsidered in this paper. Thirty six drive-in raks representing the global sale of an Australian manufaturer over three years are then analysed using the improved 2D single model introdued in the ompanion paper (Gilbert et al., 2013a) under all possible loading senarios, alternately onsidering and ignoring the pallet braing restraints. This paper evaluates the influene of pallet braing restraints on the ultimate apaity of steel drive-in raks in the down-aisle diretion, larifies the loading senario(s) governing the design and determines the frition oeffiient or the strength of a restraining devie required to prevent the pallets from sliding. 2 PARAMETRIC STUDIES Thirty-six rak onfigurations, representing the global sale of an Australian manufaturer over three years and designed using industry pratie (Demati, 2006), are analysed using the improved single upright models introdued in the ompanion paper (Gilbert et al., 2013a). The raks are onsidered to be 4 pallets deep, with rail beams equally spaed apart along the rak height. The uprights are referred to as SD for standard uprights and RF for rear flanged uprights, their widths range from 70 mm to 150 mm and their thiknesses from 1.2 mm to 2.4 mm. Table 1 summarises the rak onfigurations inluding the rak height, design pallet load, number of stories and upright type. More details an be found in (Gilbert, 2010, Gilbert et al., 2013b).

4 Rak n o Height (mm) Table 1: Rak onfigurations Nb stories Design pallet load (kg) Type Upright Width (mm) thk. (mm) SD SD RF RF SD SD RF RF RF SD RF RF RF RF SD RF SD SD RF RF RF RF RF SD RF RF RF SD SD RF SD RF SD RF RF RF Speifially, three different single upright models are onsidered and their member ation-to-apaity ratios are used as a measure to quantify the influene of the pallet restraints on the design of drive-in raks: Model A onsiders the pallet braing restraints and represents the Bay loading senario A. The model is desribed in the ompanion paper (Gilbert et al., 2013a) in its Setion and illustrated in its Figure 6. Model B onsiders the pallet braing restraints and represents the Bay loading senario B. The model is desribed in the ompanion paper (Gilbert et al., 2013a) in Setion and illustrated in its Figure 7. Model C is based on the urrent industry pratie of negleting the pallet braing restraints. The model is similar to Model A at the exeption of Step 4 in Setion of the ompanion paper (Gilbert et al., 2013a). 2.1 Design parameters Base plate to floor onnetion stiffness Base plates are generally bolted to the floor, and the strength and initial rotational stiffness of the base plate to floor onnetion depend on the axial load in the upright (Godley et al., 1998). Numerial investigations on the non-linear behaviour of a typial storage rak base plate assembly (Gilbert and Rasmussen, 2011) showed that (i) the onnetion strength is proportional to the upright width, (ii) in the presene of axial load in the upright, the initial rotational stiffness of the base plate to floor onnetion is proportional to the ube of the upright width and (iii) when no axial load is applied to the upright, the initial rotational stiffness is independent of the upright width. The rules desribed above, ombined with the test results in (Gilbert and Rasmussen, 2011) and applied to a 125 mm wide base plate assembly, are used in the following setions to determine the initial stiffness and strength of base plate to floor onnetions as funtions of base plate widths. Detailed momentrotation urves used in the present work are given in Gilbert et al. (2013b) Out-of-plumb The main international raking speifiations (AS 4084, 2012, EN 15512, 2009, RMI, 2008) onsider the initial looseness in the member onnetions as well as the initial out-of-plumb as frame imperfetions, whih are generally aounted for in the design by means of horizontal fores F out-of-plumb applied at eah rail beam elevation as, F out of plumb = αw (1) where α is the out-of-plumb angle and W is the vertial load applied to the upright by the pallets at the rail beam elevation. The out-of-plumb angle α is typially a funtion of the number of interonneted bays and the looseness in the portal beam to upright onnetions. A out-of-plumb angle of rad (about 1/250) is used in the present work. See Gilbert et al. (2013b) for more details Other parameters Other design parameters used in the present work, whih orrespond to some drive-in rak onfigurations urrently ommerialised in Australia, are given in Gilbert et al. (2013b). The height of the rak H, the number of pallet levels N s and the ross-setional area of the upright A u depend on the studied rak harateristis and are given in Table 1 and Gilbert et al. (2013b).

5 2.2 Upright load ases Aording to the draft FEM speifiation for the design of drive-in raks (FEM , 2010), the load ase involving the loading senario depited in Figure 5 in the ompanion paper (Gilbert et al., 2013a) and a fully loaded upright are usually suffiient to onsider the pattern load effets for the Ultimate Limit State (ULS) design in the down-aisle diretion. However, it is urrently unlear if a different load ase may govern the design. Moreover, in light of the horizontal braing effet offered by the pallets, the load ase involving the loading senario depited in in Figure 5 in the ompanion paper (Gilbert et al., 2013a) and a fully loaded upright may not always be suffiient for the ULS design of the upright. Consequently, every possible load ase is investigated in the present work for the 36 drive-in raks given in Table 1. Seond-order geometri analyses are arried out using the general purpose FE software Strand7 (2010). The number of load ases analysed per rak is a funtion of the number rail beams and is equal to 4 Ns, where N s is the number of rail beam elevations. 2.3 Ultimate apaity For eah of the three rak models and eah upright load ase, the Australasian old-formed steel strutures standard AS/NZS 4600 (2005) is used to alulate the member ation-to-apaity ratios of the ritial upright. When seond order-geometri analyses are used, members subjeted to ombined axial ompression and bending must satisfy the ULS design hek in Eq. (2), N φ N x M + φ M b bx y M + φ M b by 1 (2) where N is the design axial ompression load, and M x and M y are the design bending moments about the x- (ross-aisle) and y- (down-aisle) axes, respetively, N is the nominal axial ompression member apaity, M bx and M by are the nominal member bending moment apaities about the x- and y- axes, respetively, φ and φ b are redution apaity fators for members in ompression and bending, taken as 0.85 and 0.90, respetively. As the present work is onerned with the design of drive-in raks in the down-aisle diretion, the bending moment about the down-aisle axis is onsidered negligible and for the 2D single upright model, Eq. (2) beomes, N φ N x M + φ M b bx 1 (3) A load fator of 1.4 is used for the pallets to determine the design loads N and bending moments M x. The self-weight of the rak is ignored. The Diret Strength Method (Shafer, 2006) in Setion 7 of the AS/NZS 4600 (2005) is used in the present work to alulate the nominal apaities N and M bx of the upright. Speifially, the axial apaity in ompression N is defined as the lesser of the axial global, loal and distortional nominal apaities N e, N l and N d, respetively, as, ( N, N N ) N = min, (4) e l d and the nominal bending moment apaity M bx about the x-axis of bending is defined as the lesser of the global, loal and distortional nominal moment apaities M bxe, M bxl, M bxd, respetively, as, bx ( M, M M ) M = min, (5) bxe bxl bxl Speifially, the global nominal apaity M bxe is a funtion of the bending moment distribution in the upright through the elasti bukling moment M o, M = C A r f f (6) o b u ol oy oz where C b is a oeffiient depending on moment distribution in the unbraed segment of the upright, A u is the gross ross-setional area, r ol is the polar radius of gyration about the shear entre and f oy and f oz are the elasti bukling stresses for flexural bukling about the y-axes (perpendiular to the symmetry axis) and torsional bukling, respetively. Detailled rules to determine N e, N l, N d, M bxe, M bxl, M bxd are given in AS/NZS 4600 (2005) Effetive bukling lengths The Australian Standard AS 4084 (2012) reommends effetive lengths l ey and l ez for bukling about the y- (down-aisle) and z- (torsional) axes equal to h and 0.7 times h, respetively, where h represents the upright frame braing pith, as shown in Figure 1. These values are adopted in the present work. Figure 1: Frame braing pith h, unbraed segment For eah member of the simple upright model, the effetive length l ex for bukling about the x-axis (in

6 the down-aisle plane) is alulated as (Teh and Gilbert, 2013), l π EI x ex = (7) Nrb where I x is the seond moment of area about the x axis, and N rb is the elasti bukling load of the upright determined from a rational frame bukling analysis (Teh and Gilbert, 2013). bending moment of the upright under the ritial load ase. Figure 3 shows the bending moment distribution in the upright for Models A and C, and the oeffiient C b in Eq. (6), under the ritial load ase of Rak 25. It an be seen that ignoring the pallet restraints leads to a design bending moment that is 12% less than when onsidering same, but with similar C b oeffiient. 3 RESULTS 3.1 Effets of pallet restraint In this study, two values for the frame braing pith h, being 1,500 mm and 2,000 mm, are onsidered Frame braing pith h = 1,500 mm Figure 2 plots the ratios of the maximum member ation-to-apaity ratio of Model C (urrent industry pratie) to that of Model A, and to that of Model B, for the 36 raks given in Table 1 having a frame braing pith h of 1500 mm. Detailed results an be found in Gilbert et al. (2013b). A ratio greater than 1.0 in Figure 2 indiates that the urrent industry pratie results in uneonomial designs. (a) (b) Figure 3: Bending moment distribution for the ritial load ase for rak 25 for (a) Model A and (b) Model C Table 2 summarises the average maximum member ation-to-apaity ratios given in Figure 2. Figure 2: Influene of the horizontal pallet restraint on the ation-to-apaity ratio for h = 1,500 mm Figure 2 shows that for 12 raks out of 36, inorporating the horizontal restraining effet provided by the pallets would provide more eonomial designs than the urrent industry pratie, with a derease in the member ation-to-apaity ratio of up to 6% (Rak 1). On average for the 12 raks, the derease is 2%. For the remaining 24 raks, ignoring the pallet restraints would lead to less onservative designs, with a inrease in the member ation-to-apaity ratio of up to 7% (Rak 30). On average for the 24 raks, ignoring the pallet restraints inreases the design apaity by 3%. This ounterintuitive result is mainly due to the effet of the pallet restraints on the design Table 2: Ratio of the maximum member ation-to-apaity ratios of Model C(urrent industry pratie) to the Models A and B Model C (urrent pratie) / Model A Model C (urrent pratie) / Model B h (mm) Average Average CoV ratio ratio CoV 1,500 mm ,000 mm Frame braing pith h = 2,000 mm Figure 4 plots the ratios of the maximum member ation-to-apaity ratio of Model C (urrent industry pratie) to that of Model A, and to that of Model B, for the 36 raks given in Table 1 having a frame braing pith h of 2000 mm. Detailed results an be found in Gilbert et al. (2013b). Similar onlusions to those in Setion an be drawn. Results show that for 11 raks out of 36,

7 onsidering the horizontal restraining effet provided by the pallets would provide more eonomial designs than the urrent industry pratie, with a derease in the member ation-to- apaity ratio of up to 5% (Rak 1) and an average derease of 2%. For the remaining 25 raks, ignoring the pallet restraints would lead to less onservative designs, with a maximum inrease in the member ation-to-apaity ratio of 5% (Rak 25) and an average inrease of 3%. Table 2 summarises the average maximum member ation-to-apaity ratios given in Figure 4. (a) (b) () (d) Figure 5: Speifi load ases governing the design Figure 4: Influene of the horizontal pallet restraint on the ation-to-apaity ratio for h = 2,000 mm Critial load ases When the pallet restraints are onsidered in the analysis (Models A and B), the load ase involving the loading senario shown in Figure 5 in the ompanion paper (Gilbert et al., 2013a), whih orresponds to a fully loaded rak exept for one ompartment at the first rail beam elevation, is found to govern the design in general. However, for the 4-storey drive-in raks number 26 and 30, the load ase shown in Figure 5 (a) is found to provide an ation-to-apaity ratio up to 13% higher than the load ase involving the loading senario shown in Figure 5 in the ompanion paper (Gilbert et al., 2013a). Despite a lower axial load inurred in the ritial upright, the loading senario indues a bukling length l ex about twie that for the loading senario shown in Figure 13, and therefore leads to a redued axial apaity. When the pallet restraints are ignored in the analysis, the load ase involving the loading senario shown in Figure 5 in the ompanion paper (Gilbert et al., 2013a) is also found to generally govern the design. However, the load ases shown in Figure 5 (b) for the 4-storey drive-in rak number 4, Figure 5 () for the 5-storey rak number 21 and Figure 5 (d) for the 6-storey drive-in raks number 21, 22 and 36 govern the design with an ation-to-apaity ratio 2%, 3% and 4.5% higher that the loading senario shown in Figure 5 in the ompanion paper (Gilbert et al., 2013a), respetively. In view of the above results, for ULS design ignoring pallet braing effets, limiting the analysis to the load ase involving the loading senario shown in Figure 5 in the ompanion paper (Gilbert et al., 2013a) and a fully loaded rak, would only indue a limited error in the ation-to-apaity ratio and may be onsidered to be suffiient for onsidering the pattern load effets. 3.2 Frition oeffiient analysis The minimum frition oeffiient µ needed to prevent the pallets from sliding on the rail beams is investigated herein for Model A. The frition fores S f developed between the pallets and the rail beams are extrated from the horizontal reations at eah loaded rail beam elevation of the single upright model. The frition oeffiient µ is then alulated as, S f µ = (8) W where W is the axial load applied by the pallets to the upright at the rail beam elevation. Figure 6 shows the minimum frition oeffiient needed to prevent sliding of the pallets found for all loading ases and for the 36 drive-in raks in Table 1. All values in Figure 6 are less than the design stati frition oeffiient of reommended by Hua and Rasmussen (2010) (see ompanion paper), indiating that, under normal operating onditions, sliding is unlikely to our between the pallets and the rail beams, and that pallet braing restraints ould be onsidered in the design of drive-in raks. Moreover, the minimum frition oeffiient µ is dependent on the number of stories (or rail beam elevations), as seen in Figure 6. The more the stories, the more likely the pallets are to slide. Results show that, for a given number of stories, the minimum oeffiient of

8 frition required to avoid sliding of the pallets dereases somewhat linearly with the height of the rak. Figure 6: Minimum frition oeffiient µ needed to prevent pallets from sliding 4 CONCLUSIONS This paper analyses the influene of horizontal braing restraints provided by the pallets on the design of steel drive-in raks. Using the improved single upright model presented in the ompanion paper, analyses were run for 36 drive-in rak onfigurations. All possible loading ases were analysed. Results showed that ignoring the pallet braing effets in design, as in the urrent industry pratie, usually leads to a less onservative design with an ation-toapaity ratio for the ritial upright being redued in the order of 4%. The load ase involving a fully loaded rak exept for one ompartment at the first rail beam elevation was found to govern the Ultimate Limit State design of most raks. However, loading senarios induing the maximum bending moments were also found to govern the design of some drive-in raks having 4 to 6 storeys, with ation-to-apaity ratios up to 5% greater than the previous load ase when pallets are ignored. Results show that under normal operating onditions, the frition oeffiient between the pallets and the rail beams is suffiient to prevent sliding of the pallets, and therefore pallets ould be onsidered in the design of drive-in raks. EN Steel stati storage systems - Adjustable pallet raking systems - Priniples for strutural design. European Committee for Standardization (CEN), Brussels, Belgium. FEM Version Draft - The Design of 'Drive-in' and 'Drive-through' pallet raking. Federation Europeenne de la Manutention, Brussels, Belgium. GILBERT, B. P The behaviour of steel drive-in raks under stati and forklift truk impat fores. PhD PhD, Shool of Civil Engineering, The University of Sydney. GILBERT, B. P. & RASMUSSEN, K. J. R Determination of the base plate stiffness and strength of steel storage raks. Journal of Construtional Steel Researh, 67, GILBERT, B. P., TEH, L. H., BADET, R. X. & RASMUSSEN, K. J. R. The influene of pallets on the behaviour and design of drive-in steel storage raks Part I Behaviour. Fifth International Conferene on Strutural Engineering, Mehanis and Computation, 2013a Cape Town, South Afria. GILBERT, B. P., TEH, L. H., BADET, R. X. & RASMUSSEN, K. J. R. 2013b. Determination of the influene of the pallets on the design of drive-in steel storage raks. Researh Report CIEM/2013/R04. Centre for Infrastruture Engineering and Management, Griffith University, Australia. GODLEY, M. H. R., BEALE, R. G. & FENG, X. Rotational stiffness of semi-rigid baseplates. In: Yu, W.W. & Laboule, R.A., eds. 14th International Speialty Conferene on Cold- Formed Steel Strutures, Otober, St Louis, Missouri, U.S.A., HUA, V. & RASMUSSEN, K. J. R Stati frition oeffiient between pallets and beam rails and pallet shear stiffness tests. Researh Report 914. Shool of Civil Engineering, The University of Sydney, Australia. RMI Speifiation for the design, testing and utilization of industrial steel storage raks. Rak Manufaturers Institute, Charlotte, U.S.A. SCHAFER, B. W. Designing old-formed steel using the diret strength method. In: Laboule, R.A. & Yu, W.W., eds. 18th International Speialty Conferene on Cold-Formed Steel Strutures Otober 2006 Orlando, Florida STRAND Using Strand7 - User manual - Release 2.4.4, Sydney, Australia, G+D Computing Pty Ltd. TEH, L. H. & GILBERT, B. P Seond-order elasti analysis based design of drive-in raks. ASCE Journal of Strutural Engineering (in preparation). REFERENCES AS Steel storage raking. Standards Australia, Sydney, Australia. AS/NZS Cold-formed steel strutures. Standards Australia, Sydney, Australia. DEMATIC RAD - User manual, Sydney, Australia, Demati, Pty. Ltd.