Modal analysis of thin walled timber columns with C shaped and double T core sections using the continuous medium technique

Abstract This study advances the dynamic modeling of timber columns with composite cross-sections by addressing the modal analysis of thin-walled elements in C-shaped and double-T configurations. Unlike traditional approaches based on solid rectangular members spaced by joists, this work incorporates horizontal bracing modeled in the Z and X planes through coupling beams. The methodology involves solving coupled differential equations using generalized coordinates to obtain the transcendental equation and dimensionless parameters (λ) that guide frequency calculation via the Continuous Medium Technique (CMT). Analytical results were validated using the Finite Element Method (FEM) in ANSYS Academic. Two cases - a C-shaped core column and a double-T core column - demonstrated strong agreement, with average convergence of 97.32% for the fundamental frequency and mean errors of 2.33% for the first six modes in the Z-bracing system. In the X-bracing configuration, the average error was 3.64%. The study also proposes correction factors between Euler-Bernoulli and Timoshenko beam models, improving CMT accuracy by accounting for shear deformation in wall panel elements. These results confirm CMT’s robustness as an analytical framework for verifying numerical models in the dynamic analysis of thin-walled timber structures.