Keywords: steel racks, upright, cold formed, elasto-plastic analysis, finite element, nonlinear, buckling.

This research describes the numerical modeling to obtain the buckling load of cold-formed column profiles with rear flanges and additional lip stiffeners used in storage rack systems for unperforated and perforated sections. Pallet racking is one of the most widely used systems, where the racking consists of thin walled compression members and beams with hook-on connectors. Columns of individual steel storage racks are generally made of cold-formed steel lipped channels. The columns are braced into upright frames by connecting inclined bracing between the channel lips of opposing channels using either welded or bolted connections. If welding is used, the braces are welded directly to the flange stiffening lips. If bolting is used, additional elements parallel to the channel flanges are located at the ends of the flange stiffening lips, and are often used to permit the braces to be bolted to the channel column. These additional elements, called "Rear Flanges", are often wide and may require additional lip stiffeners. Perforations in these special lipped channel sections are not a result of punched holes in the cross-section. However, the perforations are formed by displacing the material of the cross-section by 6 mm.

Two kinds of sections are used: Unperforated and perforated sections, having two thicknesses of 2mm and 3mm. The analysis has been carried out for two end conditions : pinned-pinned and fixed-pinned. The ranges of the slenderness ratio are between 31.55 and 200. The sections considered in the study are the commercial sections produced by an Egyptian Company. The columns are covered by end plates with thickness equal 20mm at both ends. The load is assuned to be acting at the centroid of the section . The steel used is steel (37/2) with = 2400 Kgm/cm, the modulus of elasticity = 2100 t /cm and the tangent modulus = 20 t/cm.

A nonlinear 3-D finite element model is developed to investigate the buckling modes and ultimate strength of uprights of steel racks shaped as channel sections with multiple perforations and rear flanges. The model utilizes a 4-node shell element with membrane, bending, and shears deformation capabilities. Geometric nonlinearity is considered by using large displacement analysis, while material nonlinearity is considered by using a bi-linear stress-strain relationship for the steel material.

The main conclusions from the current study can be summarized as follows:

1. For the case of pinned-pinned end condition, local buckling occurs at a half-wavelength equal to the maximum width of the column specimen (86 mm), while it occurs at a half-wavelength equal to (1.5) times the maximum width of the column specimens for the case of fixed-pinned end condition for the column specimen with thickness 3.0mm.
2. Concerning the section under analysis, The governing failure mode for column specimens with length 1.0m or less is the local buckling mode as the distortional buckling mode has no significant effect on the failure mode behavior.
3. For columns with length ranging between 1.0m to 2.0m, the mode of failure is the distortional flexural buckling mode, while for columns with length greater than 2.0m, the mode of failure is flexural buckling mode about X-axis.
4. For the case of pinned-pinned end condition, it is noted that the use of perforated sections results in a 24% to 40% strength reduction compared to the strength of the unperforated section.
5. For the case of fixed-pined end condition, the perforated sections strength has 16% to 35% strength reduction compared to the strength of the unperforated sections.
6. The percentage of reduction in the strength of the perforated sections relative to the unperforated sections has inverse relationship with the length of the column specimen. This means that the taller the column is , the less the strength reduction due to the perforation.
7. For the perforated sections the stress in the middle of the web is almost equal to percentage ranges between 20two cases of end conditions , which means that the perforation affect the section so as not to be fully utilized.
8. Dealing with the working stresses induced in the E.C.P. [1], two equations are proposed for calculating the stress for perforated section at the working state as follows:

   For				(53)
   For				(54)

   
   

1

ECP, Egyptian Code of Practice for Steel Construction and Bridges, code No.(205), 2001.

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