Keywords: pallet rack, collapse, three-dimensional analysis, cold-formed steel, steel structures, semi-rigid connections.

Steel racking structures are commonly used for storage. A standard pallet racking system is made up of columns, beams, bracing members and connections. These lightweight, cold-formed steel slender structures normally fail due to elastic instability with plasticity occurring after the maximum loads have been achieved [1]. Collapse is often sudden and without warning [2].

Following research codes of practice have been published for the design of such structures. However, research has targeted the static performance of the structure and very few studies have been conducted to investigate the collapse behaviour of these structures, for example [3,4]. The first research on dynamic collapse of steel rack structures was undertaken by Kelly in 1982. Kelly explained the behaviour and the mechanisms involved during a collapse, which include bottom leg sway and successive leg failures. He found that joint 'pull-out' strength played a vital role in determining the type of collapse that will occur [5]. His analysis was a two-dimensional analysis and thus Kelly was not able to consider the interaction between the front and rear frames connected by cross-aisle bracing. Collapse was assumed to progress down the front legs only.

Kelly's study was further developed by Bajoria in 1986. A 3-dimensional computer program was developed to predict the behaviour of rack structures. The interaction between the beams and cross-aisle bracing was studied. Bajoria recommended that the design of pallet racks should include a strong bracing system in conjunction with low pull-out strength beam end joints to arrest the collapse [6]. However, this is not feasible as the longitudinal stability of the structure depends on the stiffness of the beam column joints, low pull-out strength leads to a low stiffness which would cause premature elastic failure. Current pallet racks usually have high beam column stiffness which implies high pull-out strengths.

The current study develops a numerical model which can predict the types of collapse that can occur and produce cost effective methods of reducing their occurrence. A three-dimensional model was built using the LUSAS finite element software. The model consisted of 5 levels and 5 bays; 1.5m each with a total width and height of 7.5m. Front and rear frames were connected by K-shaped cross-aisle bracing. Beam elements using the Kirchoff formulation were used to model the vertical and horizontal members with 5 elements per member, joint elements for the semi-rigid connections between the beam and columns and bar elements for cross-aisle bracing. Typical geometric and material data related to the member properties were used and joints were considered to be semi-rigid with reference to the moment-rotation curves. Geometrical and material non-linearity was handled using the Total Lagrangian formulation.

For the frame considered, it was found that at buckling, the structure experienced a sway in opposite directions for the front and rear frames instead of the predicted sway mode in the direction of the side loads. The frame's behaviour was affected by the applied out-of-plane side loads. Besides affecting the sway mode, side loads also affect the buckling load factor and the maximum load carrying capacity of the frame at collapse. To study the effects of structural damage on the collapse behaviour of the frame, individual bottom legs were removed. It was found that the removal of the second rear leg created the most critical condition on the frame. It reduced the buckling load factor by 33.6% and increased the axial stress in adjacent legs. The maximum increase was 104% in the first rear column. Plan bracing was then added at either the top or the first beam level and it was found that the collapse loads were increased by about 10%, the most effective position being plan bracing at the first beam level.

This is a continuing study and research is now underway to model the cross-bracing with beam elements rather than bar elements in order to get more accurate results and to enable the bracing to buckle during the structural collapse. The ultimate objective of this study is to provide a method of preventing total collapse that is simple to apply and cost effective.

1

R.G. Beale, "The Influence of Semi-Rigid Connections on the Non-Linear Behaviour of Pallet Rack and Scaffold Structures". PhD Thesis: Oxford Brookes University, UK, 2004.

2

N.W. Murray, "Introduction to the Theory of Thin-Walled Structure", Clarendon Press, Oxford, 1984.

3

M.S. Abdel-Jaber, "The Influence of Semi-Rigid Connections on the Behaviour of Beam and Column Structural System", PhD Thesis: Oxford Brookes University, UK, 2002.

4

A.T. Sarawit, "Cold-Formed Steel Frame and Beam-Column Design", PhD Thesis: Cornell University, US, 2003.

5

S.J. Kelly, "Structural Aspects of the Progressive Collapse of Warehouse Racking", PhD Thesis: University of Cambridge, UK, 1982

6

K.M. Bajoria, "Three Dimensional Progressive Collapse of Warehouse Racking", PhD Thesis: University of Cambridge, UK, 1986.

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