PSI - Issue 78

Tahir Ahmad et al. / Procedia Structural Integrity 78 (2026) 631–638

635

i i h h w

i h   − −  i

(1)

t t

= 

i

i

where: t i is the equivalent thickness (where the holes are located); t is the nominal thickness of the section profile; Δh i is the height between regular perforations; h i represents the maximum dimension, base, or radius of the perforations; w i is the height of the perforation; ξ i is the perforation influence factor. To this aim, the specialized software CARGEO (2025) was used, which is suited for thin-walled steel sections under combined axial and biaxial bending. This software is based on an iterative procedure involving an initial elastic stress-based classification, followed by a three step iterative refinement of the effective section. Step 1 determines an initial effective section by calculating stress based on gross section properties and then applying these stresses to find preliminary effective widths. Step 2 refines this by recalculating the stress state using the effective section from Step 1, which in turn leads to updated effective widths. Finally, Step 3 repeats this refinement using the Step 2 effective section, ensuring good convergence of the final effective section properties. This refinement accounted for local buckling and stress superposition by adjusting slender element widths and effective strain values. Subsequently, effective geometric properties were calculated, and the section's resistance was verified against UNI EN 1993-1-1 (2005) formulae, considering the interaction of axial force and bending moments based on these effective properties and any resulting centroidal shifts, as follows: where: N Ed = Design axial force; A = Cross-sectional area; χ y = Reduction coefficient for flexural compression; M y,Ed , M z,Ed = Bending moment about the y-axis and z-axis; e Ny , e Nz = Shift of centroidal axis due to compression in relevant direction; χ LT = Reduction factor for bending-torsion; W y ,W z = Section modulus for bending about the y-axis and z-axis; k yy, k yz = Interaction factors; f d = Compressive strength . The application of CARGEO software (2025) was extended to capture the PMM interaction domain. Fig. 5 shows the PMM interaction surface for columns. It was observed that the section exhibits higher resistance capacity to bending stresses in the X-direction compared to the Y direction. This enhanced capacity in the X-direction was also evident in the FEM column base analysis, indicating that the inherent geometrical asymmetry of the section is the primary contributing factor. 3. Progressive collapse assessment 3.1. Case Study: Steel Storage Pallet Rack A real-world steel storage rack was selected as a case study. The steel storage rack consisted of a 5 story with a story height of 2.29m, two bays in the Y-direction having a span of 1 m and 19 bays in the X-direction having span of 2.82 m as shown in Fig. 5. All the steel elements are made up of S350 steel with a yield of 350MPa and ultimate strength of 420MPa. The whole rack is composed of thin-walled cold-formed steel elements. The typical section of steel members are synthetized in Fig. 6. The uprights are connected to the base by M10x25 class 8.8 screws. The loading on the rack includes a dead load of 1kN/m and a live load of 5.28 kN/m. The accurate definition of nonlinear hinge properties for various components was paramount for a reliable global analysis of the steel rack structure. This involved combining experimental testing and detailed Finite Element Modelling (FEM) in Abaqus (2024), complemented by specialized software for specific elements. P-M hinge properties for beam-column connections, column base-plate connections, and cold-formed steel columns were defined as illustrated in Section 2. Brace connections were modeled using an axial plastic hinge along the axis of the brace element. As the brace axial capacity was greater than the capacity of brace connections, only the plastic hinge at the brace connection was included in the model of the brace. A global steel storage rack model was developed using SAP2000 software (2025), and the derived nonlinear moment-rotation and axial-moment interaction properties were incorporated as user-defined hinge characteristics. The moment resistance of the beam-to-column connection is lower than the moment resistance of the beam, so only the plastic hinge at the beam-to-column connection was included in the model of the beam. , y Ed M N e k + , z Ed M N e f +  / 1 Ed Ny yz +  Ed yy +  Ed Nz d y  LT y z N k A W W            (2)