Lateral Torsional Buckling of Built-Up Beams

Abstract

Built-up timber beams are composed of multiple thin plies of equal depth, mechanically connected along their vertical interfaces using discrete fasteners to provide partial composite action. These beams are increasingly used in modern timber structures because thin plies are more economical and more readily available than wide solid sections. However, when such members are employed in long-span applications without adequate lateral bracing, their strength is often governed by lateral-torsional buckling (LTB). The LTB behaviour of these systems is further complicated by the presence of discrete mechanical fasteners, which provide only partial interaction between plies, rather than full composite action. Accurately quantifying this partial interaction and its influence on the critical moment remains a challenge in timber engineering and is not addressed in current American or European timber design standards. The former Canadian standard permitted the use of the LTB capacity of an equivalent monolithic section, provided that the plies were "securely connected." However, ambiguity surrounding what constitutes a secure connection prompted a shift to a more conservative approach in the most recent version of the standard, where the LTB capacity is taken as the sum of the individual capacities of the plies. Within this context, the present thesis investigates the elastic lateral-torsional buckling behaviour of built-up timber beams while accounting for partial interaction between plies. The first part of the study develops a three-dimensional finite element model to simulate the elastic LTB behaviour of two-ply built-up beams. The model captures relative slip between plies and idealizes fasteners as discrete springs at the ply interfaces by assigning shear stiffness in both longitudinal and transverse directions. This approach enables an investigation of the effect of fastener stiffness and spacing on the elastic LTB resistance and corresponding mode shapes of two-ply built-up beams.

Building on this, the second part of the study introduces a variational principle and a beam finite element formulation for the LTB analysis of two-ply built-up timber beams. The formulation accounts for relative transverse and longitudinal slip between plies and characterizes fastener shear stiffness at their interface as linearly elastic springs, leading to an eigenvalue-type solution. The proposed solution yields results that are comparable to 3D finite element models but requires only a one-dimensional discretization along the member span, significantly reducing modeling, computational, and post-processing efforts. This finite element is then used for a parametric investigation of the effects of fastener stiffness, beam geometry, moment gradient, and load height on the elastic LTB capacity of two-ply built-up beams. The study also explores the potential of non-uniform fastener spacing, as opposed to conventional uniform spacing, as a means of optimizing beam capacity.

The third part of the research extends the variational principle and finite element formulation to built-up timber beams composed of multiple plies. Predictions from the developed finite element model are verified against a 3D finite element model and full-scale experimental results reported by other researchers. The verified model is then used to conduct a comprehensive parametric study of 733 cases, investigating the effects of the number of plies, normalized fastener stiffness, longitudinal and transverse spacing, normalized span, ply aspect ratio, common load configurations, and load height on LTB resistance. The resulting database is used to develop dimensionless design equations through symbolic regression, characterizing elastic critical moments relative to the case of no interaction and deriving moment-gradient factors for common loading conditions and load-height coefficients. These proposed equations are integrated into a simplified design procedure, and their practical application is illustrated through design examples.

In summary, the present study advances the understanding of LTB behaviour in built-up timber beams and provides practical tools for characterizing their elastic LTB resistance. The proposed solutions enable engineers to achieve more accurate and economical designs and lay the groundwork for future revisions of timber design standards regarding the LTB of built-up beams.