Reduced Stiffness Modeling of Perforated Thin-Walled C- and Z-Sections with Warping Effects

Web openings in cold-formed steel members modify not only individual stiffness components but also the interactions between bending, shear, torsion, and warping. Capturing these effects in a compact structural model is essential for repeated assessment of deflections and twist as opening geometry changes. This study develops a reduced stiffness formulation for perforated C- and Z-sections by combining shell finite element analysis, static condensation, and interface kinematics enriched with sectorial warping. The resulting 14 × 14 element matrix transfers the local influence of an opening into a beam-type representation suitable for assembling members with repeated or non-uniform perforations. Geometry-dependent stiffness variations are approximated using proper orthogonal decomposition and Gaussian process regression in an energy-scaled logarithmic matrix space, preserving rigid-body modes and positive deformational stiffness. Verification combines comparisons against continuous shell models with independent analytical torsion benchmarks for unperforated sections. For the investigated members, direct reduction decreases the number of degrees of freedom by factors of 662-794, with displacement and twist profile errors below 1.33%. A surrogate using three coefficients per section family reproduces the tested member responses for opening geometries excluded from training with errors below 0.47%. The framework provides a compact basis for preliminary stiffness assessment and opening-geometry studies within the small-displacement, pre-buckling elastic regime.