GEOMETRIC NONLINEAR ANALYSIS OF TWO-LAYER TIMBER COMPOSITE BEAMS WITH ELASTIC CONNECTIONS USING THE γ-METHOD IN MATLAB

Abstract

In sustainable construction, two-layer composite timber beams with elastic shear connections are increasingly adopted due to their efficient use of material and enhanced structural performance. However, existing design procedures, such as the γ-method specified in EN 1995-1-1, are primarily based on linear assumptions and often neglect geometric nonlinearity. This simplification may lead to underestimation of deformation and stiffness reduction in slender composite members subjected to higher load levels. In this study, an enhanced numerical framework is developed in MATLAB to investigate the nonlinear behavior of two-layer composite timber beams. The proposed approach integrates a tangent-stiffness updating scheme with the von Kármán strain formulation, enabling consideration of geometric nonlinearity, including P–Δ effects and membrane forces. The numerical results demonstrate that geometric nonlinearity leads to a significant increase in mid-span deflection, ranging from 22% to 31% compared with linear analysis under advanced loading stages. In addition, the analysis identifies a critical connection stiffness threshold, beyond which the composite system approaches full interaction behavior. The proposed framework provides a practical and reliable computational tool for engineers, allowing more accurate assessment of deformation and stiffness characteristics and contributing to safer and more rational design of slender composite timber beams.