r901

School of Civil Engineering Sydney NSW 2006 AUSTRALIA http://www.civil.usyd.edu.au/ Centre for Advanced Structural Engineering

Finite Element modelling of steel drive-in rack structures Research Report No R901 Benoit P. Gilbert, MScEng Kim J.R. Rasmussen, MScEng, PhD October 2009 ISSN 1833-2781

School of Civil Engineering Centre for Advanced Structural Engineering

http://www.civil.usyd.edu.au/

Finite Element modelling of steel drive-in rack structures

Research Report No R901

Benoit P. Gilbert, MScEng Kim J.R. Rasmussen, MScEng, PhD

October 2009

Abstract: Steel storage racks, principally made from cold-formed steel profiles, are freestanding structures and designed to carrying heavy loads. Yet the amount of material used in their fabrication is minimised in structural design and racking companies often rely on 3-Dimensional second-order Finite Element Analysis to design storage racks as economically as possible. The FEA often includes non-linear material and/or connection stiffness. As storage racks are complex and slender structures, whose behaviour is influenced by the base plate to floor connection and by the pallet beam to upright connection (Baldassino and Bernuzzi (2000)), building accurate FE models is challenging. This report presents a Finite Element model of an unloaded and loaded drive-in rack structure. Contrary to the main type of racking system, referred to as “selective rack”, where racks are one pallet deep and separated by aisles allowing each pallet to be always accessible, “drive-in” racks are typically 3 to 7 pallets deep and store pallets one after the other, with no space between them, on the “first-in last-out” principle. By optimising floor allocation, drive-in racks are often an attractive alternative to selective racks. The reported FE model is built using the commercial software Abaqus (2005) and numerical results are found to accurately reproduce experimental static test results performed on a full-scale drive-in rack (Gilbert and Rasmussen (2009b)). The FE model is used to study the influence of the uplift of base plates on the global behaviour of the rack. Results show that the uplift of the base plate may significantly influence the overall displacement of the rack, and needs to be considered in design. Finally, the influence of pallets on the bending moment distribution in the uprights is analysed and reported herein. Keywords: Steel storage racks, drive-in racks, FE modelling, base plate uplift.

Finite Element modelling of steel drive-in rack structures October 2009

School of Civil Engineering Research Report No R901

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Copyright Notice School of Civil Engineering, Research Report R901 Finite Element modelling of steel drive-in rack structures © 2009 Benoit P. Gilbert and Kim J.R. Rasmussen Email: [email protected] [email protected] ISSN 1833-2781 This publication may be redistributed freely in its entirety and in its original form without the consent of the copyright owner. Use of material contained in this publication in any other published works must be appropriately referenced, and, if necessary, permission sought from the author. Published by: School of Civil Engineering The University of Sydney Sydney NSW 2006 AUSTRALIA October 2009 This report and other Research Reports published by the School of Civil Engineering are available on the Internet: http://www.civil.usyd.edu.au



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1 INTRODUCTION ................................................................................................................................................. 5

2 FULL-SCALE TESTS PERFORMED ON A DRIVE-IN RACK STRUCTURE......................................... 6 2.1 GENERAL ......................................................................................................................................................... 6 2.2 NON DESTRUCTIVE STATIC TESTS.................................................................................................................... 7 2.3 TRANSDUCER LOCATIONS ............................................................................................................................... 9

3 FINITE ELEMENT MODEL............................................................................................................................ 10 3.1 GENERAL ....................................................................................................................................................... 10 3.2 CONSTRAINTS BETWEEN MEMBERS............................................................................................................... 11

3.2.1 Connection between uprights and bracing members of the upright frames ........................................... 12 3.2.2 Connection between uprights and portal beams ..................................................................................... 13 3.2.3 Connection between uprights and rail beams ......................................................................................... 14 3.2.4 Connection between uprights and spine bracing .................................................................................... 15 3.2.5 Connection between uprights and plan bracing...................................................................................... 16

3.3 BOUNDARY CONDITIONS ............................................................................................................................... 17 3.4 LOADING CASES............................................................................................................................................. 19

3.4.1 Safety structure load ................................................................................................................................ 19 3.4.2 Pallet loads............................................................................................................................................... 20 3.4.3 Jack load................................................................................................................................................... 20

3.5 SHEAR STIFFNESS OF UPRIGHT FRAMES, SPINE AND PLAN BRACINGS ........................................................... 20 3.5.1 Shear stiffness of upright frames ............................................................................................................. 20 3.5.2 Shear stiffness of spine and plan bracings .............................................................................................. 20

3.6 YOUNG’S MODULUS ...................................................................................................................................... 21 3.7 PALLET MODELLING ...................................................................................................................................... 21

3.7.1 Friction coefficient between pallets and rail beams ............................................................................... 21 3.7.2 Pallet base model ..................................................................................................................................... 22 3.7.3 Pallet top model (dynamic analysis)........................................................................................................ 24

4 COMPARISON BETWEEN FE AND EXPERIMENTAL RESULTS ........................................................ 24 4.1 GENERAL COMPARISON................................................................................................................................. 24 4.2 SPINE AND PLAN BRACING HYSTERESIS BEHAVIOUR..................................................................................... 28

5 EFFECT OF BASE PLATE UPLIFT STIFFNESS ON THE OVERALL RACK BEHAVIOUR ........... 30

6 EFFECT OF THE HORIZONTAL BRACING RESTRAINT OF PALLETS ON THE OVERALL RACK BEHAVIOUR................................................................................................................................................... 31

7 CONCLUSIONS.................................................................................................................................................. 33

8 REFERENCES .................................................................................................................................................... 33 Appendix 1: Structural drawing of the tested rack Appendix 2: Experimental and FE results



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1 INTRODUCTION Storage racks are common structures in industry used for storing goods, mainly on pallets. They are freestanding structures and are often made from cold-formed steel profiles. In the present competitive industry, storage racks are able to carry heavy loads, yet are designed as lightly as possible, and industry often rely on 3-dimensional Finite Element Analysis to achieve this objective. Different types of racks are available in the market and are described in Pekoz and Winter (1973). “Selective racks”, the most common type of rack, are separated by aisles and each pallet is always accessible. On the other hand, “drive-in racks”, require less floor space by storing pallets on rail beams, one after the other, with no space between them. The forklift truck drives into the rack to store the pallets on the first-in, last-out principle. With the increasing price of land, drive-in racks are often a more economical solution than selective racks when storing the same good. An example of a drive-in rack is shown in Figure 1. To allow forklift truck passage, drive-in racks can only be braced at the back (spine bracing) and at the top (plan bracing) in the “down-aisle” direction. Stability in the cross-aisle (down through the bay) direction is provided by upright frames, see Figure 1. Drive-racks can typically be 3 to 7 pallets deep and numerous bays wide resulting in a complex slender structure with poorly understood 3D behaviour and increased risk of collapse. In the literature, very few tests have been performed on drive-in racks and were mainly conducted on parts of the structure (Murray (1995)) or on partial systems (Dunai et al. (1997) and Freitas et al. (2006, 2007)). Few theoretical studies on the behaviour of drive-in racks are available, ((Salmon et al. (1973), Godley (2002) and Hua and Rasmussen (2006)), and the results arising from these studies have not been confirmed experimentally. A detailed literature review of drive-in racks is available in Gilbert and Rasmussen (2009b). The main racking design specifications, RMI (2008) (Rack Manufacturers Institute), FEM (1998) (Fédération Européenne de la Manutention), Section X, recently superseded by EN 15512 (2009) (European Standard), and AS 4084 (1993) (Australian Standard) only deal with selective racks and do not apply to drive-in racks. SEMA (1980) (Storage Equipment Manufacturers’ Association) mentions drive-in racks but is not explicit. A European code for drive-in racks (FEM 10.2.07 (2002)) is currently being developed but is not available yet. Due to the complexity of this type of structure, influenced among other factors by the depth of the rack, the non-linear behaviour of the portal beam to upright connection and base plate to floor connection, the horizontal bracing effect of the pallets (Salmon et al. (1973) and Gilbert and Rasmussen (2009b)) and the not well understood shear behaviour of upright frames (Sajja et al. (2008)), accurate modelling of drive-in racks using FE is challenging. This report presents a FE model of a drive-in rack structure created using the commercial software Abaqus (2005). The model is checked against experimental test results on a full-scale loaded and unloaded drive-in rack (Gilbert and Rasmussen (2009b)) and is found to accurately reproduce the static 3D behaviour of the drive-in rack. The effect of base plate uplift, experimentally observed during the full-scale tests reported in Gilbert and Rasmussen (2009b), on the global behaviour of drive-in racks is studied using the FE model. Results show that the uplift stiffness value of the base plate may significantly influence the overall displacement of the rack, implying that either this effect needs to be considered in the design or the base plate needs to be designed to prevent uplift. Finally, the influence of pallets on the bending moment distribution in the uprights is analysed and reported herein. Acting as flexible horizontal linkages



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between rail beams, the presence of the pallets is found to change the moment distribution in the uprights, and hence considering the pallets in the structural design may lead to more economical solutions.

Figure 1: Example of drive-in rack showing a forklift truck driving in and placing a pallet load

2 FULL-SCALE TESTS PERFORMED ON A DRIVE-IN RACK STRUCTURE This section presents an overview of a series of full-scale static tests performed on a complete drive-in rack. Detailed information about the test set-up and the non-destructive tests performed are reported in Gilbert and Rasmussen (2009b). 2.1 General Non destructive full-scale tests on a complete drive-in rack have been performed in the Structures Laboratory of the School of Civil Engineering at the University of Sydney. The tested rack is 4 pallets deep, 4 bays wide and 4 stories high (i.e. featuring 3 beam rail levels), corresponding to the following overall dimensions: 4.8 meters deep, 5.9 meters wide and 5 meters high (see Figure 2 (a)). The rack is designed following industry practice to carry 2 tons pallet loads. A safety structure, designed to prevent uncontrolled failure propagation, is positioned on top of the rack and is partially supported by the rear of the rack. Structural drawings of the tested rack can be found in Appendix 1.



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(a) (b)

Figure 2: (a) Tested drive-in rack configuration and (b) Fully Loaded drive-in rack configuration During the full scale tests, 2 tons and 1.2 tons concrete blocks placed on wood pallets are used to load the rack in order to reproduce real operating conditions. Only the two middle bays of the rack are loaded during testing (see Figure 2 (b)). A plan view of the tested drive-in rack with associated gridlines is given in Figure 3. Each upright is referenced by the letter and number of the gridlines intersecting at its location. The four bays are referenced as bays AB, BC, CD and DE.

Figure 3: Tested drive-in rack gridlines

2.2 Non destructive static tests In order to gain an understanding of the relative stiffness of the component frames and bracing systems, the rack is subjected to horizontal forces at various positions by means of a servo-controlled hydraulic jack. First, in order to measure the stiffness of the spine bracing, the jack is aligned with the spine bracing plane so as to apply load to the rear portal beam (upright A4) in the down-aisle direction, shown as “position 1” in Figure 4. Specifically, the load was applied at the intersection of the shear centre plane of the upright and the centroidal plane of the portal beam, see insert in Figure 4 (b). Second, to measure the stiffness of the plan bracing, the jack is placed at the front of the rack (rack entry – upright A1), shown as “position 2” in Figure 4.



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Again, the load was applied at the intersection of the shear centre plane of the upright and the centroidal plane of the portal beam. Six different bracing configurations are tested, representing two spine bracing configurations, two plan bracing configurations and no plan or spine bracing. The different bracing configurations are designed to vary the bracing stiffness. Spine bracing configuration 1 covers one bay while spine bracing configuration 2 covers all four bays. Plan bracing configuration 1 covers one bay while spine bracing configuration 2 covers three bays, as shown in Figure 4. Tests are performed on a loaded and an unloaded rack allowing a comparison between the two loading conditions. Tests were performed on two separate nominally identical drive-in racks. Between the two series of tests, the rack was completely dismantled and reassembled using new materials.

(a) (b)

Figure 4: Bracing configurations and jack positions, (a) front view and (b) top view In a separate series of tests, to provide an understanding of the influence of pallets on the global behaviour of the rack, the first tested rack is loaded with a single 2 tons pallet. The pallet is placed at the front of the second rail beam level of bay ‘BC’. The hydraulic jack applies a horizontal load on the fourth front upright (upright B1) at the shear centre plane of the upright and at the loaded beam rail elevation (position 3) as shown in Figure 4. Two pallet stiffness tests are performed, one with Teflon strips inserted between the rail beams and the pallet and one without. The Teflon strips allow the rack to be loaded in an identical configuration while substantially reducing the influence of the pallet on the rack behaviour.

Test label Spine configuration

Plan configuration

Jack position Repeated test

Loading condition

Sp1Un / Sp1Lo 1 1 1 Yes Unloaded / Loaded Sp0Un / Sp0Lo No spine 1 1 Yes Unloaded / Loaded Sp2Un / Sp2Lo 2 1 1 Yes Unloaded / Loaded Pl1Un / Pl1Lo 1 1 2 Yes Unloaded / Loaded Pl0Un / Pl0Lo 1 No plan 2 Yes Unloaded / Loaded Pl2Un / Pl2Lo 1 2 2 Yes Unloaded / Loaded

Op1NoTef 1 1 3 No 1 pallet w/o Teflon Op1Tef 1 1 3 No 1 pallet with Teflon

Table 1: Non destructive test configurations All tests are performed statically at a low jack displacement rate (5 mm/min). A minimum of two load cycles are performed per test for the jack in position 1 and 2. A total of 26 non destructive



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tests (including 12 tests repeated on a nominally identical drive-in rack) have been performed and are summarised in Table 1. 2.3 Transducer locations To accurately capture the 3D drive-in rack behaviour, thirteen LVDTs (Linear Variable Differential Transformers) record displacements in the cross- and down-aisle directions. Five LVDTs record the displacements of the east side uprights (uprights A4 to E4) in the cross-aisle direction at the intersection of the upright and portal beam centrelines. Four LVDTs record the displacements of the uprights on the north side (uprights E1 to E4) in the down-aisle direction at the intersection of the upright shear centre line and the portal beam centreline. Three LVDTs record the displacements of upright C2 at each rail beam elevation in the down-aisle direction at the upright shear centre line. One LVDT measures the jack stroke. The LVDT positions are shown in Figure 5.

Figure 5: General transducer locations

Additionally, when testing with the jack in position 3 (tests ‘Op1Tef’ and ‘Op1NoTef’), a fourteenth LVDT records the down-aisle displacement of the front upright C1 at the second rail beam elevation at the upright shear centre line to measure the opening of bay ‘BC’. The bay opening is defined as the difference between the measured horizontal displacements of the front of the two rail beams where the pallet is located. 20 strain gauges are used to obtain the axial loads and major axis bending moments in five uprights (uprights A1 to D1 and upright C2). Four strain gauges are used per upright as shown in Figure 5. The strain gauges are located 250 mm from the floor. An additional eight strain gauges record the axial loads in four spine and plan bracing members using two diametrically opposed strain gauges on each tubular member, as shown in Figure 5. The strain gauged members are the two bracing members located between the floor and the first rail beam level in spine bracing configurations 1 and 2, and the two plan bracing members located between gridlines 1 and 2 (rack entry) in plan bracing configurations 1 and 2. Determination of the axial forces and bending moments in the strain gauged uprights and determination of the axial forces in the strain gauged bracing members are reported in Gilbert and Rasmussen (2009b).



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3 FINITE ELEMENT MODEL 3.1 General The commercial software Abaqus (2005) is used to model the tested drive-in rack using beam elements. Beams are modelled using elastic material, and second-order geometric non-linear analysis is carried out. The different members composing the rack are modelled as: (a) Made from cold-formed steel lipped open sections and able to wrap, the uprights are modelled at their centroidal axis using type B32OS elements, which consider the shear centre eccentricity and warping torsion. (b) Made from cold-formed steel lipped C-sections, the upright frame bracing members are modelled at their centroidal axis accounting for the eccentricity between the centroidal axis and the bolt holes connecting the bracing members to the uprights (refer to Section 3.2.1). Torsion of the bracing members is not believed to influence the 3D behaviour of the rack, and hence element type B33, which considers the shear centre eccentricity but ignores warping, is used for the bracing members. (c) Made from cold-formed steel lipped open sections, the portal beams are modelled at their centroidal axis. Similarly to the bracing members of the upright frames, torsion of the portal beams is not believed to influence the 3D behaviour of the rack and warping is not considered for these members. Element type B33 is also used to model the portal beams. (d) In operating condition, pallets sit vertically above the shear centre axis of the rail beams, as shown in Figure 6, and hence torsion of the rail beams is not believed to influence the 3D behaviour of the rack and warping is not considered for these members. Rail beams are made from cold-formed steel lipped open-sections and are modelled at their shear centre axis. Element type B33 is also used to model the rail beams. (e) Made from cold-rolled steel circular hollow sections (CHS), the diagonal bracing members of the spine and plan bracings are modelled using type T3D2 truss elements, and are not modelled at their exact centroidal axis as detailed in Sections 3.2.4 and 3.2.5. (f) Made from cold-formed steel open sections, the horizontal spine and plan bracing members (detailed in Sections 3.2.4 and 3.2.5) are modelled at their centroidal axis using type B33 elements. Similarly to the bracing members of the upright frames, portal beams and rail beams, torsion of the horizontal spine and plan bracing members is not believed to influence the 3D behaviour of the rack and warping is not considered for these elements in the Finite Element model.



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Figure 6: Rail beam and pallet loads The section properties used in the Finite Element model are given in Table 2 and in Appendix 1. For simple section shapes, nominal section properties are used and for more complicated shapes, measured or experimentally investigated section properties are used, as indicated in Table 2.

Member Name Gross area

(mm²)

Imajor axis (mm4)

Iminor axis (mm4)

J (mm4)

Warping (mm6)

Upright and Cross-aisle plan bracing RF12519(1) 727.9 1.328×106 6.852×105 780.6 2.510×109

Frame diagonal bracing C7515(2) 283.7 2.662×105 9.928×104 212.8 1.337×108

Portal beam and Horizontal spine bracing SB15019(2) 559.1 1.746×106 1.683×105 672.8 1.011×109

Diagonal spine and plan bracing CHS26.2×2.0(2) 156.5 1.217×104 1.217×104 2433 -- Rail beam DR10019(1) 640.8 1.449×106 6.067×105 771.1 4.638×108

(1): From measured dimensions, (2): From nominal dimensions Table 2: Main section properties

The global axis system is chosen as follows: axis 1 is parallel to the cross-aisle direction and is orientated west-east (see Figure 3), axis 2 is vertical upwards and axis 3 is parallel to the down-aisle direction and is orientated north-south (see Figure 3). 3.2 Constraints between members This section presents detail of the connections between members in the FE model (see Figure 7 for all connections) and the constraints applied to these connections.



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Figure 7: Connections between members

Links are used to model interconnections between members. Contrary to “master-slave” connections, which impose identical displacement or rotation of the constrained nodes and may not be suitable for structures with eccentricities between nodes, links allow the real structural behaviour to be modelled. In defining a rigid link between two selected nodes, displacements and rotations are fully constrained at the first node while selected constraints are applied to the second node as illustrated in Figure 8. Common to all links in the FE model, the fixed node (node 1 in Figure 8) is always associated with the upright node.

(a) (b)

Figure 8: (a) link between two members, (b) deformation example 3.2.1 Connection between uprights and bracing members of the upright frames The bracing members of the upright frames are inserted between the flanges of the uprights and secured in place by two M12 bolts. During installation, the technician had to force the bracing members in place, resulting in the uprights naturally clamping the bracing members. This effect, combined with the standard 20 N.m torque applied to tension the bolts, generated a significant amount of friction between the two members. While testing the full-scale drive-in rack it is not



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expected that the cross-aisle displacements of the upright frames would induce a sufficient moment in the connections to overcome the frictional moment and consequently a “welded” type connection is considered between the bracing members and the uprights in the FE model, i.e. both displacements and rotations are assumed to be coupled at the connection points. In the FE model, a node is created in the upright at the elevation of the bolt connecting the bracing member to the upright and an end node is created in the bracing member at the bolt hole location. The “welded” type link is introduced between the upright and bracing member nodes as shown in Figure 9.

Figure 9: Connection between uprights and upright frame bracing members

3.2.2 Connection between uprights and portal beams The portal beam webs are connected to the upright webs using two M12 bolts per connection, creating bolted-moment connections with possible relative rotation of the connected members about the global axis 1 (see Gilbert and Rasmussen (2009a)). In the FE model, an end node is created in the upright at the elevation of the centroidal axis of the portal beam and an end node is created in the portal beam at the location of the bolted connection between the two members, as shown in Figure 10. A link is created between the two end nodes in which displacements are fully constrained, rotation about the global axis 2 is released to take into account the flexibility of the connection and rotation about the global axis 3 is fully constrained to reflect the greater stiffness about this axis and avoid excessive twisting of the portal beams about their centroidal axis. The moment-rotational behaviour about global axis 1 was investigated experimentally (Gilbert and Rasmussen (2009a)) and is reported in Figure 11. This non-linear relationship is included in the FE model using an “elastic non-linear plastic” moment-rotation curve (see Figure 11 (a)) without cyclic hardening as shown in Figure 11 (b). As detailed in Gilbert and Rasmussen (2009a), the behaviour of the bolted-moment connection can be broken into three distinct phases with the last phase corresponding to the bolts in bearing and associated with a high rotational stiffness. This phase develops after a significant amount of looseness in the connection, and is not expected to be reached while testing the full-scale drive-in rack. Consequently, this phase is considered in the FE model introducing a maximum rotation corresponding to an infinite rotational stiffness (see Figure 11).



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Figure 10: Connection between uprights and portal beams

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-0.06 -0.04 -0.02 0 0.02 0.04 0.06

Rotation θH (rad)

Mom

ent (

kN.m

m)

Experimental test result

Abaqus elastic non-linear plasticmoment-rotation curve

Non linear plastic loading

Elastic loading

Sto

p in

Aba

qus

Sto

p in

Aba

qus

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Mom

ent (

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m)

Experimental test result

Abaqus elastic non-linear plasticmoment-rotation curve

Unloading

Elastic loading

Sto

p in

Aba

qus

Sto

p in

Aba

qus

Point of unloading

No cyclic hardening

(a) (b) Figure 11: Portal beam to upright moment-rotation curve in the FE model about global axis 1, (a) Loading example

path and (b) loading and unloading example path 3.2.3 Connection between uprights and rail beams The rail beams are connected to the uprights through cantilever brackets which are bolted to the web of the uprights using two M12 bolts. Each rail beam is bolted to the cantilever brackets using a single M12 bolt, as shown in Figure 12. In the FE model, a node is created in the upright at the elevation of the shear centre plan of the rail beam and a node is created in the rail beam above the location of the bolt connecting the rail beam to the cantilever bracket. A link is created between these two nodes in which displacements are fully constrained, rotation about the global axis 1 is fully constrained to avoid local instability of the rail beam about its longitudinal axis, and due to the single bolt connection, rotations about global axes 2 and 3 are released (see Figure 12).



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Figure 12: Connection between uprights and rail beams

3.2.4 Connection between uprights and spine bracing The narrow spine bracing (configuration 1) is composed of diagonal CHS bolted to the web of the uprights using a single bolt and of horizontal beams, identical to the portal beams, also bolted to the web of the upright and located between each cross-bracing (see Figure 4 (a)). The wide spine bracing (configuration 2) is only composed of diagonal CHS as shown in Figure 4 (a). The ends of the CHS are flattened with the flat sides in line with the external face of the member. In practice two cross-bracing members are connected to the web of the upright to limit initial bending of the bracing members, see Figure 13. The horizontal beams are modelled in the FE model as per Section 3.2.2 for the spine bracing in configuration 1. For each end of a diagonal bracing member, a node is created at the intersection between a vertical plane passing through the centroidal axis of the bracing member and a line parallel to global axis 1 passing through the centroidal axis of the upright at the perpendicular bracing elevation (see Figure 13). A node is also created in the upright, at this bracing elevation, and for spine bracing in configuration 1, this node is common to the horizontal beam and diagonal bracing member connections. Links in the global axis 1 direction are created between the upright nodes and the nodes corresponding to each spine bracing member. As diagonal bracing members are modelled as truss elements (rotations released), only displacements are fully constrained for the corresponding links (see Figure 13). From the positions of the nodes of the diagonal bracing members, one can deduce that the diagonal bracing members are not exactly modelled at their actual positions. However it is unlikely that this simplification in the FE model affects the restraint provided by the spine bracing or the load distribution in the rack.



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Figure 13: Connection between uprights and spine bracing (narrow spine bracing shown – configuration 1)

3.2.5 Connection between uprights and plan bracing The plan bracings (configuration 1 and 2) are composed of two horizontal beams and diagonal CHS. The horizontal beams have the same cross-section as the upright, run north-south and have their webs bolted to the flanges of each intersecting portal beam. Diagonal members are located between the two horizontal beams and are also bolted to the flanges of the portal beams. Nodes are created in each horizontal member vertically above the centroidal axis of each intersecting upright. For each end of the diagonal bracing members, a node is created at the intersection between a horizontal plan passing through the centroidal axis of the bracing member and the centroidal axis of the intersecting upright (see Figure 14). The end nodes at the top of the uprights created in Section 3.2.2 are used to link the plan bracing members to the rack. For the links between the horizontal members and the uprights, displacements are fully constrained, rotation about the global axis 1 is fully constrained to avoid local instability of the beams about their longitudinal axis, and due to the nature of the bolted connection, rotation about global axis 2 is fully constrained and rotation about global axis 3 is released (see Figure 14). Similarly to Section 3.2.4, only displacements are fully constrained for the links associated to the diagonal bracing members. As in Section 3.2.4, one can deduce that the diagonal bracing members are not exactly modelled at their actual positions. However it is unlikely that this simplification in the FE model affects the restraint provided by the plan bracing or the load distribution in the rack.



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Figure 14: Connection between uprights and plan bracing (narrow plan bracing shown – configuration 1)

3.3 Boundary conditions Uprights are bolted to base plate assemblies, which are fastened to the concrete floor by means of anchor bolts. Typically, the rotational stiffness and strength of the base plate to floor connection depend on the axial load in the upright (Davies and Godley (1998)). This relationship, for the base plate assembly and upright type used in the tested drive-in rack, was experimentally investigated for axial loads of 0 kN, 33 kN, 100 kN, 150 kN and 200 kN in Gilbert and Rasmussen (2009a). Yet, for the tested rack, the axial load in the upright is not expected to be greater than 100 kN and hence the moment-rotation curves for the 150 kN and 200 kN axial loads are disregarded in this report. In the FE model, an appropriate multi-linear moment-rotation curve is allocated to each base plate node as “elastic non-linear plastic” boundary conditions for rotation about the global axis 1. The multi-linear curve takes into account the axial load in the upright and is determined by: (i) running a linear analysis of the rack under vertical pallet loads, corresponding to the studied loading pattern, and with the base plate fully fixed, (ii) extracting the vertical reaction for each base plate, (iii) creating multi-linear moment-rotation curves by performing a linear interpolation between the axial loads investigated in Gilbert and Rasmussen (2009a) as illustrated in Figure 15 and (iv) allocating the calculated multi-linear moment-rotation curves to their corresponding base plates. No cyclic hardening is considered.



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0

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5000

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7000

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0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1Base plate rotation θb (rad)

Bas

e pl

ate

mom

ent (

kN.m

m)

0 kN - Multi-linear curve for experimental tests33 kN - Multi-linear curve for experimental tests100 kN - Multi-linear curve for experimental tests50 kN - Multi-linear curve in Abaqus (linear interpolation)

Unloading (example)

Elastic loading

Point of unloading (example)

Figure 15: Base plate to floor boundary condition – example of multi-linear moment-rotational curve for global axis 1 for 50 kN axial load in the upright

As base plate assemblies restrain the torsion of the uprights but do not prevent warping, rotation about the global axis 2 is fully constrained and the upright is free to warp. Rotation about the global axis 3 is released. Being bolted to the concrete floor, translations along global axes 1 and 3 are fully constrained. While performing the full-scale tests, it was observed that the base plates lifted when tension developed in the uprights. The uplift stiffness was experimentally investigated and is reported in Gilbert and Rasmussen (2009a). Therefore, base plate uplift in the global axis 2 direction is modelled using the multi-linear curve given in Gilbert and Rasmussen (2009a) and reproduced in Figure 16. Uplift is modelled using a “non-linear elastic” boundary condition in the FE model, i.e. loading and unloading follow the same path.

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-2 0 2 4 6 8 10 12

Uplift displacement (mm)

Upl

ift a

xial

load

(kN

)

Upright in tension

Upright in compression

Stop

in A

baqu

s

Figure 16: Base plate to floor boundary condition – Multi-linear reaction-displacement curve in the global axis 2

direction – Base plate uplift The modelling of the boundary conditions is shown in Figure 17.



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Figure 17: Base plate to floor boundary condition model

3.4 Loading cases 3.4.1 Safety structure load As detailed in Gilbert and Rasmussen (2009b), part of the safety structure is supported by the rear of the tested drive-in rack. The safety structure is included in the FE model to account for the additional compressive load in the rear uprights produced by the weight of the safety structure, which influences the uplift of the base plates of the uprights. Three horizontal stiff beams running in the east-west direction are modelled with their western ends, corresponding to the part supported by the columns of the safety structure, fully fixed but with the rotation about the global axis 3 released, as shown in Figure 18. “No tension” contact nodes are introduced between the beams and the top of the uprights supporting the structure (see Figure 18). The weight of the safety structure, including the weight of the chains attached to the safety structure, is introduced as uniformly distributed loads on the horizontal beams.

Figure 18: Safety structure in FE model with safety structure loads

The safety structure load is applied first in the structural analysis.



20

3.4.2 Pallet loads Pallet loads are modelled as uniformly distributed loads on rail beams at the location of the pallets. The load is assumed to be equally distributed along the rail beams. In the structural analysis, the pallet loads are applied after applying the safety structure load. 3.4.3 Jack load The horizontal force applied to the rack by the hydraulic jack is applied at the actual jack location in the FE model. For this purpose, a rigid element is inserted from the centroid to the shear centre of the upright and the load is applied at the shear centre of the upright at the jack elevation. As for the full-scale tests, the jack load is applied cyclically to the rack in the analysis, and is applied after applying the loads from the safety structure and pallet loads. 3.5 Shear stiffness of upright frames, spine and plan bracings 3.5.1 Shear stiffness of upright frames The shear deformation of cold-formed steel upright frames with bolted connections is currently not well understood (Rao et al. (2004), Sajja et al. (2006, 2008)) in so far that the experimentally observed shear deformation of upright frames is typically significantly greater than the shear deformation obtained from either FEA or Timoshenko and Gere’s (1961) shear formulae (see Gilbert and Rasmussen (2009a)). The experimental shear stiffness value of upright frames in the cross-aisle direction is commonly achieved in FEA by reducing either the Young’s modulus or the cross-section area of the bracing members. This reduction of the axial stiffness of the bracing members reduces the FEA sway stiffness of the frame in the cross-aisle direction and can be adjusted to achieve the experimental stiffness value. The combined bending and shear transverse stiffness of a typical upright frame composing the tested drive-in rack was experimentally investigated in Gilbert and Rasmussen (2009a). Results showed that to match the experimental global sway stiffness, the cross-section area of a diagonal bracing member had to be entered in the FE model as 104.5 mm² instead of 283.7 mm² (the nominal cross-section area). This reduced value of the cross-section area is used in the present FE model. 3.5.2 Shear stiffness of spine and plan bracings Being also made from cold-formed steel profiles with bolted connections, there is no reason to believe that the actual shear stiffness of the spine and plan bracings can be accurately modelled in FEA without reducing either the Young’s modulus or the cross-section area of the diagonal bracing members. In the absence of experimental test results for the spine and plan bracing shear stiffness, a trial-and-error procedure was used to find an appropriate value for the Young’s modulus of the diagonal bracing members to be entered in the FE model. Numerical results for the complete drive-in rack system, presented in Section 4, show that dividing the Young’s modulus of the diagonal spine and plan bracing members by a factor 9 allows the global stiffness of the rack to be accurately modelled, and this reduction factor is therefore included in the present FE model.



21

3.6 Young’s modulus The average value of the Young’s modulus of the uprights has been measured experimentally and found to be equal to 218325 MPa (Gilbert and Rasmussen (2009a)). In the absence of experimental data for the Young’s modulus of the remaining members composing the rack, which are also made from cold-formed steel profiles from the same manufacturer, the same value of Young’s modulus is used for these members in the FE model. 3.7 Pallet modelling Theoretical and experimental studies (Pekoz and Winter (1973), Gilbert and Rasmussen (2009b)) showed that the horizontal bracing restraint of the pallets influences the behaviour of the rack and consequently, this effect needs to be considered in the present FE model to accurately capture the 3D behaviour of the drive-in rack. It should be noticed that current industry practice does not allow the horizontal bracing restraint of the pallets to be considered in structural design. The influence of pallets on the structural design is investigated in Section 6. 3.7.1 Friction coefficient between pallets and rail beams The friction force F between two surfaces in contact is defined as,

NF μ= (1)

where μ is the friction coefficient and N is the normal force acting between the two surfaces. More specifically, a static and kinetic coefficient of friction can be defined. The static coefficient of friction μs corresponds to the force Fs required to initiate motion between two surfaces and the kinetic coefficient of friction μk corresponds to the force Fk required to maintain motion between the two surfaces as illustrated in Figure 19 (a) (Blau (2009)).

Applied force F

Fric

tion

forc

e F F

Normal N

Applied force F

Friction force FF

FF = μsN

FF = μkN

Stick Slide

1

1

Applied force F

Fric

tion

forc

e F F

Normal N

Applied force F

Friction force FF

FF = μsN

Stick Slide

1

1

(a) (b)

Figure 19: (a) Static and kinetic frictional behaviour, (b) Approximate frictional behaviour used in FEA The static coefficient of friction μs between the wood pallets and the rail beams was evaluated by the “sliding angle” method. A piece of wood, cut from a pallet and with a weight attached to it, is placed on a rail beam. The rail beam is then slowly inclined by an angle θ until sliding of the wood piece occurs, and the maximum angle θmax of the rail beam is measured. The static coefficient of friction is calculated as,

maxtanθμ =S (2)

and is found to be equal to 0.3. The test set-up is illustrated in Figure 20.



22

Figure 20: Test set-up to determine the static coefficient of friction μs

The approximate “perfect stick-slide” behaviour, shown in Figure 19 (b), is used in the present FE model with the measured coefficient of friction μs of 0.3. 3.7.2 Pallet base model The base of the pallet is modelled using a mesh of four cross-aisle beams and four down-aisle beams, as shown in Figure 21. Type B33 elements are used to model the pallet base.

Figure 21: Pallet base model in the FE model

When subjected to a horizontal force in the down-aisle direction, a drive-in rack essentially deforms linearly in the down-aisle direction (Gilbert and Rasmussen (2009b)), resulting in each pallet undergoing shear deformation as shown in Figure 22 (a). Similarly, the action of the plan bracing may force one row of upright frame to deform in the cross-aisle direction (Gilbert and Rasmussen (2009b)), also resulting in each pallet undergoing shear deformation as shown in Figure 22 (b).



23

(a) (b)

Figure 22: shear deformation of a row of pallet when (a) rack is subjected to a down-aisle force, (b) rack is subjected to a cross-aisle force

The shear stiffness of wood pallets was investigated by CASE (1996) and found to be equal to 13.04 N/mm. However, this shear stiffness is related to the pallet alone and it is likely that the concrete blocks used to load the rack considerately restrain the shear deformation of the pallets. A trial-and-error procedure was used to find an appropriate value for the shear stiffness of the pallet, to be used in the FE model. Numerical results on the complete drive-in rack system, presented in Section 4, show that using 44 mm diameter circular rods for the pallet base elements in Figure 21, with an associated value of the Young’s modulus of wood of 11000 MPa and a Poisson’s ratio of 0.3, allows the global behaviour of the rack to be accurately modelled. This pallet base characteristic corresponds to a pallet shear stiffness of 325 N/mm, as shown in Figure 23.

0

2

4

6

8

10

12

0 5 10 15 20 25 30 35

Pallet shear deformation u (mm)

App

lied

forc

e F

(kN

)

Shear stiffness = 0.3253 kN/mm

(a) (b)

Figure 23: (a) pallet shear deformation FE model and (b) FE element results with 44 mm circular rod, E = 11000 MPa and μ = 0.3

To complete the model of the pallet base, the frictional behaviour introduced in Figure 19 (b) is used between the rail beams and the pallet in the cross- and down-aisle directions at the eight common nodes, see Figure 21. The vertical reaction at the four corner nodes (nodes 1 to 4) is assumed to be 1/12 of the pallet weight while the reaction at the remaining four nodes (nodes 5



24

to 8) is assumed to be 1/6 of the pallet weight. The “stick-slide” characteristic is entered in the FE model using these coefficients as shown in Figure 21. Moreover, the relative vertical displacement between the pallet base and the rail beams is fully constrained at the four corner nodes. All rotations are released. 3.7.3 Pallet top model (dynamic analysis) The model of the base of the pallet presented in Section 3.7.2 is sufficient for static analyses. However for dynamic analysis purposes only, a top part is added to the pallet base. This part models the pallet mass at the centre of gravity of the load. Vertical type T3D2 truss elements are inserted from the four corners of the pallet base to the elevation of the centre of gravity of the pallet load, and T3D2 truss elements brace each top of the vertical members to the two nearest corners of the pallet base (see Figure 24). A fourth of the pallet mass is added to the top of each four vertical element. This arrangement ensures that the truss elements do not add stiffness to the structure. The added masses do not represent a loading case in the structural analysis.

Figure 24: Pallet top model in the FE model (for dynamic analysis)

4 COMPARISON BETWEEN FE AND EXPERIMENTAL RESULTS 4.1 General comparison Figure 25, Figure 26 and Figure 27 plot the experimental and numerical cross-aisle (LVDTs 1 to 5, see Figure 5), down-aisle (LVDTs 6 to 9, see Figure 5) and upright C2 (LVDTs 10 to 12, see Figure 5) displacements, respectively, against the horizontal jack load for test ‘Pl1Lo’, which corresponds to spine and plan bracing in configuration 1, jack aligned with the plan bracing and a loaded rack. It is observed that the FE model accurately reproduces the experimental 3D behaviour of the rack. The experimental hysteresis behaviour of the rack is also captured by the elastic non-linear plastic behaviour of the portal beam to upright connections and base plate to floor boundary conditions. However, it may be noted that the “amplitude” of the FE hysteresis loop (i.e. difference between the loading and unloading responses) is less than for the experimental hysteresis loop. The difference is likely due to the not well understood shear stiffness of the spine and plan bracings as discussed in Section 4.2. Figure 28, Figure 29 and Figure 30 plot the experimental and numerical upright axial forces, spine and plan bracing members axial forces and upright bending moment about the major axis



25

of bending, respectively, against the horizontal jack load for test ‘Pl1Lo’. The internal forces plotted in Figure 28 to Figure 30 only arise from the horizontal load contribution and do not include the pallet loads. The FE model is also found to accurately reproduce the experimental internal forces in the rack. Similar good agreement between experimental and FE results is generally found for all tests included in Table 1. All experimental and FE results are given in Appendix 2. As mentioned in Gilbert and Rasmussen (2009b), due to the uprights sliding on the portal beams under shear loading, the experimental displacement at the jack location (row A) is greater than the displacement of the opposite upright in row E. This effect is not modelled in the FE model and is only related to the horizontal force applied to the structure by the hydraulic jack. As this horizontal force is only an approach to capturing the 3D behaviour of the rack and does not represent an actual force applied to the drive-in rack in operating conditions, this sliding effect can be disregarded. Hence, the experimental jack displacement is not compared to the FE results. However, it is still reported in Appendix 2. To summarise, the proposed FE model has been shown to accurately reproduce the 3D behaviour of the tested drive-in rack.

-6

-4

-2

0

2

4

6

-6 -4 -2 0 2 4 6

Cross aisle displacement (mm)

Jack

load

(kN

)

A4 - CA - Test 1B4 - CA - Test 1C4 - CA - Test 1D4 - CA - Test 1E4 - CA - Test 1A4 - CA - Test 2 (repeat)B4 - CA - Test 2 (repeat)C4 - CA - Test 2 (repeat)D4 - CA - Test 2 (repeat)E4 - CA - Test 2 (repeat)Abaqus - A4 - CAAbaqus - B4 - CAAbaqus - C4 - CAAbaqus - D4 - CAAbaqus - E4 - CA

(West)(East)

Figure 25: Test ‘Pl1Lo’, cross-aisle displacements (LVDTs 1 to 5)



26

-6

-4

-2

0

2

4

6

-40 -30 -20 -10 0 10 20 30 40

Down aisle displacement (mm)

Jack

load

(kN

)

E4 - DA - Test 1E3 - DA - Test 1E2 - DA - Test 1E1 - DA - Test 1E4 - DA - Test 2 (repeat)E3 - DA - Test 2 (repeat)E2 - DA - Test 2 (repeat)E1 - DA - Test 2 (repeat)Abaqus - E4 - DAAbaqus - E3 - DAAbaqus - E2 - DAAbaqus - E1 - DA

(North)(South)

Figure 26: Test ‘Pl1Lo’, down-aisle displacements (LVDTs 6 to 9)

-6

-4

-2

0

2

4

6

-20 -15 -10 -5 0 5 10 15 20

C2 - Down aisle displacement (mm)

Jack

load

(kN

)

C2 - DA - El1 - Test 1C2 - DA - El2 - Test 1C2 - DA - El3 - Test 1C2 - DA - El1 - Test 2 (repeat)C2 - DA - El2 - Test 2 (repeat)C2 - DA - El3 - Test 2 (repeat)Abaqus - C2 - DA - El1Abaqus - C2 - DA - El2Abaqus - C2 - DA - El3

(North)(South)

Figure 27: Test ‘Pl1Lo’, upright C2 displacements (LVDTs 10 to 12)



27

-6

-4

-2

0

2

4

6

-15 -10 -5 0 5 10 15

Upright axial load (kN)

Jack

load

(kN

)

A1 - Test 1B1 - Test 1C1 - Test 1D1 - Test 1C2 - Test 1A1 - Test 2 (repeat)B1 - Test 2 (repeat)C1 - Test 2 (repeat)D1 - Test 2 (repeat)C2 - Test 2 (repeat)Abaqus - A1Abaqus - B1Abaqus - C1Abaqus - D1Abaqus - C1

(Tension)(Compression)

Figure 28: Test ‘Pl1Lo’, upright axial forces

-6

-4

-2

0

2

4

6

-3 -2 -1 0 1 2 3

Bracing members axial load (kN)

Jack

load

(kN

)

Spine n°1 - Test 1Spine n°2 - Test 1Plan n°1 - Test 1Plan n°2 - Test 1Spine n°1 - Test 2 (repeat)Spine n°2 - Test 2 (repeat)Plan n°1 - Test 2 (repeat)Plan n°2 - Test 2 (repeat)Abaqus - Spine n°1Abaqus - Spine n°2Abaqus - Plan n°1Abaqus - Plan n°2


Figure 29: Test ‘Pl1Lo’, spine and plan bracing member axial forces



28

-6

-4

-2

0

2

4

6

-1500 -1000 -500 0 500 1000 1500

Upright bending moment (kN.mm)

Jack

load

(kN

)


Figure 30: Test ‘Pl1Lo’, upright bending moment about major axis of bending Specific case - Spine bracing in

configuration 2 4.2 Spine and plan bracing hysteresis behaviour It may be noticed that for the specific case of test ‘Sp2Un’ and ‘Sp2Lo’ associated with the spine bracing in configuration 2 (wide spine bracing), the FE model is not able to capture the hysteresis behaviour of the rack, as shown in Figure 31, which plots the down-aisle displacements of test ‘Sp2Un’, and in Appendix 2. As the spine bracing in configuration 2 runs over the full width of the rack, it most likely effectively reduces the rotations of the portal beams and base plates, which therefore stay in their elastic ranges. Consequently, the experimentally observed hysteresis behaviour of the rack has to come from another source than the portal beam to upright or base plate to floor connections and is likely attributed to the spine bracing and the not well understood shear behaviour of cold-formed steel bolted frames, see Gilbert and Rasmussen (2009a). This effect is unclear and needs more investigation. However, the FE model is still able to fairly accurately capture the maximum displacements of the rack as shown in Figure 31 and in Appendix 2.



29

-8

-6

-4

-2

0

2

4

6

8

-20 -15 -10 -5 0 5 10 15 20


Jack

load

(kN

)


(North)(South)

Figure 31: Test ‘Sp2Un’, down-aisle displacements (LVDTs 6 to 9)

To further illustrate and validate the FE model, when tests are conducted on a rack with no spine or plan bracing, the FE is able to accurately capture the hysteresis loop of the rack as illustrated in Figure 32, which plots the down-aisle displacements of test ‘Sp0Un’, and in Appendix 2.

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

-40 -30 -20 -10 0 10 20 30 40


Jack

load

(kN

)


(North)(South)

Figure 32: Test ‘Sp0Un’, down-aisle displacements (LVDTs 6 to 9)



30

5 EFFECT OF BASE PLATE UPLIFT STIFFNESS ON THE OVERALL RACK BEHAVIOUR

The effect of the base plate uplift stiffness on the overall behaviour of the rack is investigated using the FE model of the tested drive-in rack. As the base plate uplift was particularly predominant in tests ‘Sp1Un’ and ‘Sp1Lo’ (spine and plan bracings in configuration 1, jack aligned with the spine bracing and unloaded or loaded rack), FE analyses of test ‘Sp1Lo’ are run with: (i) the base plates not able to lift off the support (fixed), (ii) the experimentally observed base plate stiffness (Figure 16, i.e. actual rack behaviour) and (iii) the base plates able to freely lift off the support (released). The horizontal force is applied cyclically to the rack. Figure 33 plots the down-aisle displacements of upright E4 (aligned with the jack) and the front upright E1 against the applied load for the three base plate uplift cases. When the jack displaces the structure to the north, the transfer of the horizontal force down through the narrow spine bracing results in tension in upright D4 and compression in upright E4. However, as upright D4 is already loaded in compression under vertical pallet loads, the additional tension induced by the horizontal load does not overcome the initial compression in the upright, and base plate D4 does not lift. Consequently, the rack behaves similarly for the three base plate uplift cases, as shown in Figure 33. When the jack displaces the structure to the south, because upright E4 is not initially loaded by pallet loads, base plate E4 can lift, and the rack behaves differently for the three base plate uplift cases. Figure 33 shows that the down-aisle stiffness of the rack for upright E4 is about 2.5 greater when the base plate is fixed to the ground than when the actual base plate uplift stiffness is considered. When the base plate is free to lift, the rack becomes unstable and starts to buckle for an applied load of about 5 kN. From Figure 33, one can deduce that the base plate uplift stiffness may considerably affect the behaviour of the rack under horizontal loads, such as impact, placement or loads arising from out-of-plumb. By increasing the overall displacement of the rack, the base plat uplift may become an issue for the serviceability limit state. The increased lateral displacement of the upright may also increase the second order P-Δ effect, resulting in lower structural capacity.

-8

-6

-4

-2

0

2

4

6

8

-40 -30 -20 -10 0 10 20


Jack

load

(kN

)

(North)(South)

E1 - (i) No base plate uplift

E1 - (ii) Actual base plate uplift stiffness

E1 - (iii) Free base plate uplift

E4 - (i) No base plate uplift

E4 - (ii) Actual base plate uplift stiffness

E4 - (iii) Free base plate uplift

Figure 33: Down-aisle displacements from various base plate uplift cases



31

It is therefore recommended to include the effect of base plate uplift in the design of storage racks or ensure that the design of the base plate does not permit uplift.

6 EFFECT OF THE HORIZONTAL BRACING RESTRAINT OF PALLETS ON THE OVERALL RACK BEHAVIOUR

It is current industry practice to design storage racks ignoring the horizontal bracing restraint of the pallets because of the uncertainty associated with the friction between pallets and rail beams. However, previous studies (Salmon et al. (1973), Gilbert and Rasmussen (2009b)) showed that the pallets influence the structural behaviour and buckling loads of drive-in racks. It is therefore important to evaluate the impact of this horizontal restraint on the load distribution in the uprights. The load case shown in Figure 34 generally represents the governing design combination of axial force and bending moment in the bottom part of the upright of the middle row second from the front (FEM 10.2.07 (2002)). Consequently, this load case has been analysed for the tested drive-in rack with 2 tons pallet loads and with the spine and plan bracings as per configuration 1. The bending moment in upright C2, under vertical pallet loads, is plotted in Figure 35 with the pallets modelled (accurate solution) or not (current industry practice) in the FEA.

Figure 34: Loading case generally governing the design

Figure 35 shows that, acting essentially as horizontal elastic restraints, the pallets significantly change the distribution of the bending moment in upright C2, yet have only a minor impact on the maximum bending moment. The observation appears to be general for the type of loading pattern shown in Figure 34. However, as pallets influence the upright buckling load (Salmon et al. (1973)), even if the value of maximum bending moment is essentially unchanged, pallets may still influence the design of the upright section.



32

(a) (b) Figure 35: Bending moment in Upright C2 under vertical loads for loading case shown in Figure 34 for (a) pallets

modelled in the FEA (accurate solution) and (b) pallet not modelled in the FEA (current industry practice) The FEM 10.2.07 (2002) also proposes several loading cases which, for some rack configurations, may be more critical than the loading case introduced in Figure 34. The loading case shown in Figure 36 induces the maximum bending moment in one row of uprights and has been analysed using FEA for the tested rack, with and without the pallets modelled. The rack is loaded with 2 tons pallets and the plan and spine bracings are as per configuration 1.

Figure 36: Critical loading case inducing maximum bending moment in a row of uprights

The bending moment in upright C2, under vertical pallet loads, is plotted in Figure 37. It is observed that the horizontal bracing restraint of the pallets significantly affects the distribution of the bending moment and, contrary to the previous loading case, the presence of pallets reduces the maximum bending moment by almost 50%, consequently impacting on the design of the upright section.



33

(a) (b)

Figure 37: Bending moment in Upright C2 under vertical loads for loading case shown in Figure 36 for (a) pallet modelled in the FEA (accurate solution) and (b) pallet not modelled in the FEA (industry design practice)

To summarise, considering the horizontal bracing restraint of pallets in FEA allows the correct bending moment distribution in the uprights to be obtained and, depending of the governing load case, may lead to a more economical design. It is emphasised that the horizontal restraint of the pallets should only be considered when the friction forces developing between the rail beams and the pallets are sufficient to restrain the movement of the pallet on the rail beam.

7 CONCLUSIONS This report presents the development of an FE model for a cold-formed steel drive-in rack. The FE model includes non-linear behaviour for the portal beam to upright and base plate to floor connections as well as stiffness contributions from pallets. The FE results are compared to experimental results from tests of a full-scale drive-in rack structure. The FE model is shown to accurately capture the 3D behaviour of the tested unloaded and loaded rack. Using the FE model, the influence of base plate uplift on the rack behaviour is investigated and found to influence the overall displacement of the rack. It is recommended to either consider the base plate uplift stiffness in design or to prevent uplift by a suitable design of the base plate. The influence of the horizontal restraint provided by pallets is also reported herein. Results show that not considering the pallets in FEA, as is current industry practice, provides the incorrect bending moment distribution and may lead to conservative design.

8 REFERENCES Abaqus (2005), Abaqus ver. 6.5-4 - User manual, ABAQUS, Inc., Providence, USA

AS 4084 (1993), Steel storage racking, Standards Australia, Sydney, Australia

Baldassino, N. & Bernuzzi, C. (2000), Analysis and behaviour of steel storage pallet racks, Thin-Walled Structures, vol. 37, pp. 277-304



34

Blau, P. J. (2009), Friction science and techonlogy from concepts to applications, 2nd edition, CRC Press Inc., Boca Raton, Florida, USA

CASE (1996), Investigation Report S1046, Shear stifness of pallets, School of Civil Engineering, The University of Sydney, Australia

Davies, J. M. & Godley, M. H. R. (1998), A European design code for pallet racking, 14th International Specialty Conference on Cold-Formed Steel Structure In Yu, W.W. & LaBoule, R.A. (Eds.), pp. 289-310, St Louis, Missouri, U.S.A.

Dunai, L., Hegedus, T., Kaltenbach, L. & Adany, S. (1997), Experimental and numerical studies on the stability of racking frames, 5th International Colloquium on the Stability and Ductility of Steel Structures In Usami, T. & Itoh, Y. (Eds.), pp. 647-652, Nagoya, Japan

EN 15512 (2009), Steel static storage systems - Adjustable pallet racking systems - Principles for structural design, European Committee for Standardization (CEN), Brussels, Belgium

FEM 10.2.07 (2002), Version 0.02 - Draft - The Design of 'Drive in' and 'Drive through' pallet racking, Federation Europeenne de la Manutention, Brussels, Belgium

FEM (1998), Section X - Recommendations for the design of steel static pallet racking and shelving, Federation Europeenne de la Manutention, Brussels, Belgium

Freitas, A. M. S., Souza, F. T. & Freitas, M. S. R. (2006), Theoritical-experimental analysis of industrial storage racks - Drive-in in cold formed steel members, International Colloquium on Stability and Ductility of Steel Structures, In Camotim, D. , Silvestre, N. & Dinis, P.B. (Eds.), pp. 373-380, Lisbon, Portugal

Freitas, A. M. S., Souza, F. T. & Freitas, M. S. R. (2007), Analysis and behaviour of drive-in storage structures, 6th International Conference on Steel and Aluminium Structures, In Beale, R. G. (Ed.), pp. 955-962, Oxford, UK

Gilbert, B. P. & Rasmussen, K. J. R. (2009a), Research Report R899, Experimental test on steel storage rack components, School of Civil Engineering, The University of Sydney, Australia

Gilbert, B. P. & Rasmussen, K. J. R. (2009b), Research Report R900, Stiffness tests, failure tests and load transfer in steel drive-in storage racks, School of Civil Engineering, The University of Sydney, Australia

Godley, M. H. R. (2002), The behaviour of drive-in storage structures, 16th International Specialty Conference on Cold-Formed Steel Structures, In LaBoule, R.A. & Yu, W.W. (Eds.), pp. 340-352, Orlando, Florida, U.S.A.

Hua, V. & Rasmussen, K. J. R. (2006), Research Report R871, The behaviour of drive-in racks under horizontal impact load, School of Civil Engineering, The University of Sydney, Australia



35

Murray, N. W. (1995), Stability analysis of drive-in racking storage systems, International Conference on Structural Stability and Design In Kitipornchai, S., Hancock, G. J. & Bradford, M. A. (Eds.), pp. 189-195, Sydney, Australia

Pekoz, T. & Winter, G. (1973), Cold-formed steel rack structures, 2nd Specialty Conference on Cold-Formed Steel Structures, In Yu, W.W. (Ed.), pp. 603-615, St louis, Missouri, USA

Rao, S. S., Beale, R. G. & Godley, M. H. R. (2004), Shear stiffness of pallet rack upright frames, 7th International Speciality Conference on Cold-Formed Steel Structures, pp. 295-311, Orlando, Florida, U.S.A.

RMI (2008), Specification for the design, testing and utilization of industrial steel storage racks, Rack Manufacturers Institute, Charlotte, U.S.A.

Sajja, S. R., Beale, R. G. & Godley, M. H. R. (2006), Factors affecting the shear stiffness of pallet rack uprights, Stability and Ductility of Steel Structures, In Camotim, D. et al. (Ed.), pp. 365-372, Lisbon, Portugal

Sajja, S. R., Beale, R. G. & Godley, M. H. R. (2008), Shear stiffness of pallet rack upright frames, Journal of Constructional Steel Research, vol. 64, pp. 867-874

Salmon, M. A., Welch, R. E. & Longinow, A. (1973), Analysis of drive-in and drive-thru storage racks, 2nd Specialty Conference on Cold-Formed Steel Structures, In Yu, W.W. (Ed.), pp. 617-639, St Louis, Missouri, U.S.A.

SEMA (1980), Code of practice for the design of static rack, Storage Equipment Manufacturers' Association, London, UK

Timoshenko, S. P. & Gere, J. M. (1961), Theory of elastic stability, 2nd edition, McGraw-Hill Book Company, Inc, New York, U.S.A.

Appendix 1 - 1 -

APPENDIX 1

Characteristics of the tested drive-in rack

Appendix 1 - 2 -

Appendix 1 - 3 -

Appendix 1 - 4 -

Appendix 1 - 5 -

Appendix 1 - 6 -

Appendix 1 - 7 -

Appendix 1 - 8 -

Upright section properties – RF12519 – 450 MPa

Appendix 1 - 9 -

Frame bracing section properties – C7515 – 450 MPa

Appendix 1 - 10 -

Beam rail section properties – DR10019 – 450 MPa

Appendix 1 - 11 -

Portal beam section properties – SB15019 – 450 MPa

Appendix 2 - 1 -

APPENDIX 2

Full-scale drive-in rack experimental test and FE results

Appendix 2 - 2 -

Test ‘Sp0Un’

No spine bracing Plan bracing in configuration 1

Jack in position 1 (aligned with the spine bracing) Unloaded rack

Appendix 2 - 3 -

Cross-aisle displacements (LVDTs 1 to 5)

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

-6 -4 -2 0 2 4 6


Jack

load

(kN

)


(West)(East)

Appendix 2 - 4 -

Down-aisle displacements (LVDTs 6 to 9)

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

-40 -30 -20 -10 0 10 20 30 40


Jack

load

(kN

)


(North)(South)

Appendix 2 - 5 -

Upright C2 displacements (LVDTs 10 to 12)

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

-20 -15 -10 -5 0 5 10 15 20


Jack

load

(kN

)


(North)(South)

Appendix 2 - 6 -

Jack displacement (LVDT 13)

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

-50 -40 -30 -20 -10 0 10 20 30 40 50


Jack

load

(kN

)

Jack - Test 1Jack - Test 2 (repeat)

(North)(South)

Appendix 2 - 7 -

Upright axial forces

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

-15 -10 -5 0 5 10 15


Jack

load

(kN

)



Appendix 2 - 8 -

Bracing member axial forces

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

-0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4


Jack

load

(kN

)

Plan n°1 - Test 1

Plan n°2 - Test 1

Plan n°1 - Test 2 (repeat)

Plan n°2 - Test 2 (repeat)

Abaqus - Plan n°1

Abaqus - Plan n°2


Appendix 2 - 9 -

Upright bending moment about major axis of bending

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

-500 -400 -300 -200 -100 0 100 200 300 400 500


Jack

load

(kN

)


Appendix 2 - 10 -

Test ‘Sp1Un’

Spine bracing in configuration 1 Plan bracing in configuration 1


Appendix 2 - 11 -


-7

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

7

-20 -15 -10 -5 0 5 10 15 20


Jack

load

(kN

)


(West)(East)

Appendix 2 - 12 -


-7

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

7

-40 -30 -20 -10 0 10 20 30 40


Jack

load

(kN

)


(North)(South)

Appendix 2 - 13 -


-7

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

7

-15 -10 -5 0 5 10 15


Jack

load

(kN

)


(North)(South)

Appendix 2 - 14 -


-7

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

7

-50 -40 -30 -20 -10 0 10 20 30 40 50


Jack

load

(kN

)


(North)(South)

Appendix 2 - 15 -


-7

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

7

-25 -20 -15 -10 -5 0 5 10 15 20 25


Jack

load

(kN

)



Appendix 2 - 16 -


-7

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

7

-4 -3 -2 -1 0 1 2 3 4


Jack

load

(kN

)



Appendix 2 - 17 -


-7

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

7

-400 -300 -200 -100 0 100 200 300 400


Jack

load

(kN

)


Appendix 2 - 18 -

Test ‘Sp2Un’



Appendix 2 - 19 -


-8

-6

-4

-2

0

2

4

6

8

-7 -5 -3 -1 1 3 5 7


Jack

load

(kN

)


(West)(East)

Appendix 2 - 20 -


-8

-6

-4

-2

0

2

4

6

8

-20 -15 -10 -5 0 5 10 15 20


Jack

load

(kN

)


(North)(South)

Appendix 2 - 21 -


-8

-6

-4

-2

0

2

4

6

8

-7 -5 -3 -1 1 3 5 7


Jack

load

(kN

)


(North)(South)

Appendix 2 - 22 -


-8

-6

-4

-2

0

2

4

6

8

-30 -20 -10 0 10 20 30


Jack

load

(kN

)


(North)(South)

Appendix 2 - 23 -


-8

-6

-4

-2

0

2

4

6

8

-7 -5 -3 -1 1 3 5 7


Jack

load

(kN

)



Appendix 2 - 24 -


-8

-6

-4

-2

0

2

4

6

8

-6 -4 -2 0 2 4 6


Jack

load

(kN

)



Appendix 2 - 25 -


-8

-6

-4

-2

0

2

4

6

8

-350 -250 -150 -50 50 150 250 350


Jack

load

(kN

)


Appendix 2 - 26 -

Test ‘Pl0Un’

Spine bracing in configuration 1 No plan bracing

Jack in position 2 (aligned with the plan bracing)

Unloaded rack

Appendix 2 - 27 -


-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

-1.5 -1 -0.5 0 0.5 1 1.5


Jack

load

(kN

)


(West)(East)

Appendix 2 - 28 -


-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

-45 -35 -25 -15 -5 5 15 25 35 45


Jack

load

(kN

)


(North)(South)

Appendix 2 - 29 -


-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

-20 -15 -10 -5 0 5 10 15 20


Jack

load

(kN

)


(North)(South)

Appendix 2 - 30 -


-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

-50 -40 -30 -20 -10 0 10 20 30 40 50


Jack

load

(kN

)


(North)(South)

Appendix 2 - 31 -


-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

-2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5


Jack

load

(kN

)



Appendix 2 - 32 -


-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

-0.3 -0.2 -0.1 0 0.1 0.2 0.3


Jack

load

(kN

)

Spine n°1 - Test 1

Spine n°2 - Test 1

Spine n°1 - Test 2 (repeat)


Abaqus - Spine n°1

Abaqus - Spine n°2


Appendix 2 - 33 -


-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

-450 -350 -250 -150 -50 50 150 250 350 450


Jack

load

(kN

)


Appendix 2 - 34 -

Test ‘Pl1Un’



Unloaded rack

Appendix 2 - 35 -


-3

-2

-1

0

1

2

3

-6 -4 -2 0 2 4 6


Jack

load

(kN

)


(West)

(East)

Appendix 2 - 36 -


-3

-2

-1

0

1

2

3

-45 -35 -25 -15 -5 5 15 25 35 45


Jack

load

(kN

)


(North)(South)

Appendix 2 - 37 -


-3

-2

-1

0

1

2

3

-25 -20 -15 -10 -5 0 5 10 15 20 25


Jack

load

(kN

)


(North)(South)

Appendix 2 - 38 -


-3

-2

-1

0

1

2

3

-50 -40 -30 -20 -10 0 10 20 30 40 50


Jack

load

(kN

)


(North)(South)

Appendix 2 - 39 -


-3

-2

-1

0

1

2

3

-15 -10 -5 0 5 10 15


Jack

load

(kN

)



Appendix 2 - 40 -


-3

-2

-1

0

1

2

3

-2 -1.5 -1 -0.5 0 0.5 1 1.5 2


Jack

load

(kN

)



Appendix 2 - 41 -


-3

-2

-1

0

1

2

3

-600 -400 -200 0 200 400 600


Jack

load

(kN

)


Appendix 2 - 42 -

Test ‘Pl2Un’



Unloaded rack

Appendix 2 - 43 -


-6

-4

-2

0

2

4

6

-10 -8 -6 -4 -2 0 2 4 6 8 10


Jack

load

(kN

)


(West)

(East)

Appendix 2 - 44 -


-6

-4

-2

0

2

4

6

-40 -30 -20 -10 0 10 20 30 40


Jack

load

(kN

)


(North)(South)

Appendix 2 - 45 -


-6

-4

-2

0

2

4

6

-30 -20 -10 0 10 20 30


Jack

load

(kN

)


(North)(South)

Appendix 2 - 46 -


-6

-4

-2

0

2

4

6

-50 -40 -30 -20 -10 0 10 20 30 40 50


Jack

load

(kN

)


(North)(South)

Appendix 2 - 47 -


-6

-4

-2

0

2

4

6

-25 -20 -15 -10 -5 0 5 10 15 20 25


Jack

load

(kN

)



Appendix 2 - 48 -


-6

-4

-2

0

2

4

6

-5 -4 -3 -2 -1 0 1 2 3 4 5


Jack

load

(kN

)



Appendix 2 - 49 -


-6

-4

-2

0

2

4

6

-600 -400 -200 0 200 400 600


Jack

load

(kN

)


Appendix 2 - 50 -

Test ‘Sp0Lo’

No spine bracing Plan bracing in configuration 1

Jack in position 1 (aligned with the spine bracing) Loaded rack

Appendix 2 - 51 -


-5

-4

-3

-2

-1

0

1

2

3

4

5

-4 -3 -2 -1 0 1 2 3 4


Jack

load

(kN

)


(West)(East)

Appendix 2 - 52 -


-5

-4

-3

-2

-1

0

1

2

3

4

5

-45 -35 -25 -15 -5 5 15 25 35 45


Jack

load

(kN

)


(North)(South)

Appendix 2 - 53 -


-5

-4

-3

-2

-1

0

1

2

3

4

5

-25 -20 -15 -10 -5 0 5 10 15 20 25


Jack

load

(kN

)


(North)(South)

Appendix 2 - 54 -


-5

-4

-3

-2

-1

0

1

2

3

4

5

-50 -40 -30 -20 -10 0 10 20 30 40 50


Jack

load

(kN

)


(North)(South)

Appendix 2 - 55 -


-5

-4

-3

-2

-1

0

1

2

3

4

5

-8 -6 -4 -2 0 2 4 6 8


Jack

load

(kN

)



Appendix 2 - 56 -


-5

-4

-3

-2

-1

0

1

2

3

4

5

-0.6 -0.4 -0.2 0 0.2 0.4 0.6


Jack

load

(kN

)

Plan n°1 - Test 1Plan n°2 - Test 1Plan n°1 - Test 2 (repeat)Plan n°2 - Test 2 (repeat)Abaqus - Plan n°1Abaqus - Plan n°2


Appendix 2 - 57 -


-5

-4

-3

-2

-1

0

1

2

3

4

5

-1500 -1000 -500 0 500 1000 1500


Jack

load

(kN

)


Appendix 2 - 58 -

Test ‘Sp1Lo’



Appendix 2 - 59 -


-8

-6

-4

-2

0

2

4

6

8

-12 -7 -2 3 8


Jack

load

(kN

)


(West)(East)

Appendix 2 - 60 -


-8

-6

-4

-2

0

2

4

6

8

-30 -20 -10 0 10 20 30


Jack

load

(kN

)


(North)(South)

Appendix 2 - 61 -


-8

-6

-4

-2

0

2

4

6

8

-15 -10 -5 0 5 10 15


Jack

load

(kN

)


(North)(South)

Appendix 2 - 62 -


-8

-6

-4

-2

0

2

4

6

8

-40 -30 -20 -10 0 10 20 30 40


Jack

load

(kN

)


(North)(South)

Appendix 2 - 63 -


-8

-6

-4

-2

0

2

4

6

8

-8 -6 -4 -2 0 2 4 6 8


Jack

load

(kN

)



Appendix 2 - 64 -


-8

-6

-4

-2

0

2

4

6

8

-6 -4 -2 0 2 4 6


Jack

load

(kN

)



Appendix 2 - 65 -


-8

-6

-4

-2

0

2

4

6

8

-1000 -800 -600 -400 -200 0 200 400 600 800 1000


Jack

load

(kN

)


Appendix 2 - 66 -

Test ‘Sp2Lo’



Appendix 2 - 67 -


-9-8-7-6-5-4-3-2-10123456789

-7 -5 -3 -1 1 3 5 7


Jack

load

(kN

)


(West)(East)

Appendix 2 - 68 -


-9-8-7-6-5-4-3-2-10123456789

-15 -10 -5 0 5 10 15


Jack

load

(kN

)


(North)(South)

Appendix 2 - 69 -


-9-8-7-6-5-4-3-2-10123456789

-8 -6 -4 -2 0 2 4 6 8


Jack

load

(kN

)


(North)(South)

Appendix 2 - 70 -


-9-8-7-6-5-4-3-2-10123456789

-30 -20 -10 0 10 20 30


Jack

load

(kN

)


(North)(South)

Appendix 2 - 71 -


-9-8-7-6-5-4-3-2-10123456789

-7 -5 -3 -1 1 3 5 7


Jack

load

(kN

)



Appendix 2 - 72 -


-9-8-7-6-5-4-3-2-10123456789

-5 -4 -3 -2 -1 0 1 2 3 4 5


Jack

load

(kN

)



Appendix 2 - 73 -


-9

-8

-7

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

7

8

9

-800 -600 -400 -200 0 200 400 600 800


Jack

load

(kN

)


Appendix 2 - 74 -

Test ‘Pl0Lo’

Spine bracing in configuration 1 No plan bracing

Jack in position 2 (aligned with the plan bracing) Loaded rack

Appendix 2 - 75 -


-4

-3

-2

-1

0

1

2

3

4

-2 -1.5 -1 -0.5 0 0.5 1 1.5 2


Jack

load

(kN

)


(West)

(East)

Appendix 2 - 76 -


-4

-3

-2

-1

0

1

2

3

4

-40 -30 -20 -10 0 10 20 30 40


Jack

load

(kN

)


(North)(South)

Appendix 2 - 77 -


-4

-3

-2

-1

0

1

2

3

4

-20 -15 -10 -5 0 5 10 15 20


Jack

load

(kN

)


(North)(South)

Appendix 2 - 78 -


-4

-3

-2

-1

0

1

2

3

4

-50 -40 -30 -20 -10 0 10 20 30 40 50


Jack

load

(kN

)


(North)(South)

Appendix 2 - 79 -


-4

-3

-2

-1

0

1

2

3

4

-8 -6 -4 -2 0 2 4 6 8


Jack

load

(kN

)



Appendix 2 - 80 -


-4

-3

-2

-1

0

1

2

3

4

-1.5 -1 -0.5 0 0.5 1 1.5


Jack

load

(kN

)

Spine n°1 - Test 1

Spine n°2 - Test 1



Abaqus - Spine n°1

Abaqus - Spine n°2


Appendix 2 - 81 -


-4

-3

-2

-1

0

1

2

3

4

-1500 -1000 -500 0 500 1000 1500


Jack

load

(kN

)


Appendix 2 - 82 -

Test ‘Pl1Lo’



Appendix 2 - 83 -


-6

-4

-2

0

2

4

6

-6 -4 -2 0 2 4 6


Jack

load

(kN

)


(West)(East)

Appendix 2 - 84 -


-6

-4

-2

0

2

4

6

-40 -30 -20 -10 0 10 20 30 40


Jack

load

(kN

)


(North)(South)

Appendix 2 - 85 -


-6

-4

-2

0

2

4

6

-20 -15 -10 -5 0 5 10 15 20


Jack

load

(kN

)


(North)(South)

Appendix 2 - 86 -


-6

-4

-2

0

2

4

6

-50 -40 -30 -20 -10 0 10 20 30 40 50


Jack

load

(kN

)


(North)(South)

Appendix 2 - 87 -


-6

-4

-2

0

2

4

6

-15 -10 -5 0 5 10 15


Jack

load

(kN

)



Appendix 2 - 88 -


-6

-4

-2

0

2

4

6

-3 -2 -1 0 1 2 3


Jack

load

(kN

)



Appendix 2 - 89 -


-6

-4

-2

0

2

4

6

-1500 -1000 -500 0 500 1000 1500


Jack

load

(kN

)


Appendix 2 - 90 -

Test ‘Pl2Lo’



Appendix 2 - 91 -


-8

-6

-4

-2

0

2

4

6

8

-9 -7 -5 -3 -1 1 3 5 7 9


Jack

load

(kN

)


(West)(East)

Appendix 2 - 92 -


-8

-6

-4

-2

0

2

4

6

8

-45 -35 -25 -15 -5 5 15 25 35 45


Jack

load

(kN

)


(North)(South)

Appendix 2 - 93 -


-8

-6

-4

-2

0

2

4

6

8

-25 -20 -15 -10 -5 0 5 10 15 20 25


Jack

load

(kN

)


(North)(South)

Appendix 2 - 94 -


-8

-6

-4

-2

0

2

4

6

8

-40 -30 -20 -10 0 10 20 30 40


Jack

load

(kN

)


(North)(South)

Appendix 2 - 95 -


-8

-6

-4

-2

0

2

4

6

8

-15 -10 -5 0 5 10 15


Jack

load

(kN

)



Appendix 2 - 96 -


-8

-6

-4

-2

0

2

4

6

8

-5 -4 -3 -2 -1 0 1 2 3 4 5


Jack

load

(kN

)



Appendix 2 - 97 -


-8

-6

-4

-2

0

2

4

6

8

-1500 -1000 -500 0 500 1000 1500


Jack

load

(kN

)


Appendix 2 - 98 -

Test ‘OpNoTef’


Jack in position 3 1 pallet loaded rack

Appendix 2 - 99 -


-4

-3.5

-3

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

-4 -3 -2 -1 0 1 2 3 4


Jack

load

(kN

)

A4 - CA - Test 1B4 - CA - Test 1C4 - CA - Test 1D4 - CA - Test 1E4 - CA - Test 1Abaqus - A4 - CAAbaqus - B4 - CAAbaqus - C4 - CAAbaqus - D4 - CAAbaqus - E4 - CA

(West)(East)

Appendix 2 - 100 -


-4

-3.5

-3

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

-25 -20 -15 -10 -5 0 5


Jack

load

(kN

)

E4 - DA - Test 1E3 - DA - Test 1E2 - DA - Test 1E1 - DA - Test 1Abaqus - E4 - DAAbaqus - E3 - DAAbaqus - E2 - DAAbaqus - E1 - DA

(North)(South)

Appendix 2 - 101 -


-4

-3.5

-3

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

-20 -15 -10 -5 0 5


Jack

load

(kN

)

C2 - DA - El1 - Test 1C2 - DA - El2 - Test 1C2 - DA - El3 - Test 1Abaqus - C2 - DA - El1Abaqus - C2 - DA - El2Abaqus - C2 - DA - El3

(North)(South)

Appendix 2 - 102 -


-4

-3.5

-3

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

-25 -20 -15 -10 -5 0 5


Jack

load

(kN

)

Jack - Test 1

Abaqus - Jack - DA(North)(South)

Appendix 2 - 103 -

Bay opening

-4

-3.5

-3

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

-1 0 1 2 3 4 5 6


Jack

load

(kN

)

Bay opening - Test 1

Abaqus - Bay opening - DA

(North)(South)

r901

Documents

drivein racks

steel storage racks

selective racks

fe modelling

r901 benoit

order finite element

freestanding structures

slender structures