PSI - Issue 81

Denys Mykhailovskyi et al. / Procedia Structural Integrity 81 (2026) 333–338

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increases their load-bearing capacity and stiffness. Structural analysis of such reinforced elements can be performed using the deformation method (Gomon et al. (2023); Pavluk et al. (2024); Gomon et al. (2024)). Current design standards (DBN B.2.6-161:2017; Eurocode 5: 2004; NDS:2018) used for CLT panel construction do not include provisions for reinforcement. The effect of reinforcement on the performance of timber structures has been presented in various scientific studies (Gomon et al. (2024); Mascia et al. (2018); Mykhailovskyi et al. (2025); Vahedian et al. (2019); Sobczak-Piastka et al. (2020)). Reinforcement enhances the structural stiffness (Mykhailovskyi et al. (2024)), leading to reduced displacements and deflections, and, by redistributing internal forces, lowers the stress levels in the timber as part of the load is transferred to the reinforcing elements. Any timber element subjected to bending or bending with compression demonstrates improved performance when reinforced. Therefore, it was decided to conduct a numerical experiment for CLT panels (Mykhailovskyi (2022)) with varying reinforcement ratios and different bar spacing configurations.

Nomenclature E 0,CLT,mean

modulus of elasticity of wood parallel to the grain; modulus of elasticity of wood perpendicular to the grain;

E 90,CLT,mean G 0,lav,mean

shear modulus of wood;

uniformly distributed load over the area.

q s

2. Numerical model and methods The software package LIRA-SAPR 2024 was selected as the primary tool for analyzing the behaviour of the reinforced CLT panel. This program employs the finite element method (FEM) for structural analysis. Its capabilities include determining displacements and stresses using various types of finite elements. The software environment also allows users to assign material anisotropy, which is essential for timber, an inherently anisotropic material. A number of previous studies have verified the accuracy of results obtained in LIRA-SAPR by comparing them with experimental data and alternative calculation methods. The software consistently demonstrated good agreement, which justified its selection for analyzing the performance of CLT panels. For the numerical simulation, solid finite elements and bar-type finite elements were used. Solid finite element No. 36 from the program’s li brary was adopted. The CLT panels used in the analysis had a thickness of 10 cm and consisted of five layers of boards glued at 90° to one another. The panel length was 3 m and its width 1 m. The outer layers and the central layer were oriented parallel to the longer side of the panel (Fig. 1). The boards used for manufacturing the panel had a cross- section of 2 × 10 cm. To analyze the influence of reinforcement spacing, four spacing values were adopted: 10 cm, 20 cm, 30 cm, and 40 cm. For each case, the diameter of the reinforcing bars was recalculated to achieve a constant reinforcement percentage. Previous studies have indicated that the effective reinforcement ratio for timber beams lies within 1 – 1.5%. Therefore, a reinforcement ratio of 1% was adopted for both the tension and compression zones of the panel. The calculation of diameters and areas for different steps is given in Table 1.

Table 1. The volume of experimental research. Panel name

Step armature, cm Number of rebar

Cross-sectoin area, cm 2

Rebardiameter, cm

Panel - 1 Panel - 2 Panel - 3 Panel - 4

40 30 20 10

3 4 6

3.333 2.500 1.667 0.909

2.061 1.785 1.457 1.076

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For the numerical analysis of the panels, the following physical and mechanical properties of timber were adopted: 1) modulus of elasticity along the grain E 0,CLT,mean =11GPa ; 2) modulus of elasticity perpendicular to the grain E 90,CLT,mean =0.5GPa ; 3) shear modulus G 0,lav,mean =0.5GPa ; and 4) Poisson’s ratios v 90 =0.018 and v 90 =0.48 . The solid finite element used to model the timber had dimensions of 5 cm × 5 cm × 2 cm (width × length × height). The reinforcement was modelled using bar-type finite elements connected between the nodes of the timber elements. The length of each bar element was 5 cm. The cross-sectional areas and diameters of the reinforcing bars adopted for the panels are provided in Table 1, while their layout within the cross-section is illustrated in Fig. 1.