Span–Thickness Limits Based on three-Dimensional Elasticity for Using Classical Plate Theory in Orthotropic Rectangular Plates

Classical plate theory (CPT)¹ is the default model for the bending of thin orthotropic plates, yet the span–thickness ratio beyond which it can be trusted is typically taken from isotropic experience. This study determines this ratio from three-dimensional (3D) elasticity for the 21 distinct orthotropic rectangular plates with clamped, simply supported, and at most one free edge, under uniformly distributed loading. A Ritz solution of 3D elasticity, validated against exact and finite-element solutions, was compared with CPT over 3,360 cases (E₁/E₂ = 5–40, aspect ratios 0.5–3, span–thickness ratios 4–100). The ratio needed for CPT to be within 5% of the 3D deflection ranges from 10 to 90, and the common threshold of 20 fails in 76% of the 420 combinations. For aspect ratios of 1.5 or more and the 15 plates whose fibres end on supported edges, the limit depends only on those two edges and scales with the square root of E₁/G₁₃. These limits follow a Timoshenko beam strip spanning the fibres, which is first-order shear deformation theory in cylindrical bending: the group averages agree within 0.3% and individual plates within 4.5% (9% in one case). This yields a closed-form rule: the square of the limit equals 0.96, 2.65, or 4.80 times E₁/(εG₁₃) for simply supported, propped, and clamped strips, where ε is the tolerance. The rule holds within 1.2% for graphite–epoxy, glass–epoxy, and glulam plates, and soft simple supports increase the limits by at most 3%. Plates with a free edge across the fibres and no clamped edge opposite it carry the load across the fibres and follow √(E₂/G₂₃) instead. Deflection governs the limit in 88% of cases; moments govern mainly when a free edge crosses the fibres.