NUMERICAL MODELING OF THE BEHAVIOR OF A HYBRID-REINFORCED TIMBER BEAM USING PLANE FINITE ELEMENTS

Abstract

The study is devoted to the numerical modeling of reinforced wooden beams using 
the  LIRA-SAPR  software  package.  One  of  the  main  disadvantages  of  wooden  beams  is  their excessive flexibility, which leads to large deflections and displacements. Reinforcing wooden beams with stiffening elements is an effective method for increasing their rigidity and reducing internal stresses. However, in current engineering practice, there is a lack of design guidelines and examples for modeling such reinforced wooden structures using modern software tools. Therefore, the aim of this work is to investigate different methods for modeling reinforcement in wooden beams using finite element analysis. The paper presents an analysis of recent publications where different reinforcement types—such as basalt, carbon, and glass fiber—were used in wooden structures. Special attention is given to the challenge of numerically modeling such reinforcements, particularly when using planar finite  elements  instead  of  volumetric  ones,  as  this  approach  significantly  reduces computational complexity. Three reinforcement modeling methods are proposed and tested: 1) placing reinforcing bars between planar finite element nodes; 2) adjusting the modulus of elasticity of the elements to reflect the combined stiffness of wood and reinforcement; 3) modeling reinforcement as a separate layer with equivalent cross-sectional area. Each method was implemented and analyzed for accuracy and practicality. Experimental data from full-scale beam tests were used for comparison. Results indicate  that  all  three methods  provide  acceptable  accuracy,  with  deviations  from  experimental deflection values averaging around 11%, which is considered satisfactory for wood materials. Stress 
distributions obtained through numerical analysis showed good agreement across methods, though each has specific advantages. For instance, modeling reinforcement as individual bars allows precise evaluation of stresses in wood, whereas layer-based modeling offers direct assessment of stresses in reinforcement  elements.  The  study  demonstrates  that  numerical  modeling  of  reinforced  wooden beams using planar finite elements in LIRA-SAPR is a reliable and efficient alternative to volumetric modeling. Each proposed method can be effectively applied depending on the design goal, offering engineers flexibility in structural analysis and optimization.