## 1 Introduction  
In scientific endeavors, significant emphasis has been placed on ecological and economic matters, consequently necessitating the rational management of limited resources. Consequently, the quantity of necessary experimental investigations has been reduced to the bare minimum and the bare minimum was based on the premise of achieving repeatable results. The repeatability of outcomes has typically been understood through the attainment of pertinent statistical indices regarding the measures of dispersion of the results. Greater emphasis has instead been placed on the ability to anticipate the behavior of actual entities. These predictions are conducted via theoretical and numerical investigations. This methodology appears to be justified and has been utilized to examine non-strengthened and strengthened timber components. A common method for evaluating the bending behavior of complex sections composed of constituents with different mechanical characteristics is the employment of the transformed cross-section method. The main assumptions of this method were described in the study carried out in [1] regarding the analysis of solid beams reinforced with steel sections. [PERSON] et al. [2] utilized this approach to assess the mechanical performance of glued laminated timber beams made from varied wood species amalgamations and a Carbon Fiber-Reinforced Polymer (CFRP). The maximal mean value of resulting coefficient of variation was 15%. [PERSON] et al. [3] used it to analyze the possibility of repairing solid timber beams using reinforcements inserted into near surface grooves. They deduced, among other things, that the most effective reinforcement is a steel profile or CFRP and that the most optimal configuration proposes reinforcing both the compressed and tensile zones. [PERSON] [4] characterized the transformed cross-section method as a simplified methodology for the design of reinforced timber beams employing composite laminates and honeycomb-structured sandwich panels. The study comprised both experimental outcomes and a case study regarding employing an analytical method for predicting the load-bearing capacity of the reinforced element. According to the author's assessment, the depicted reinforcement technique will lead to a 300% enhancement in load-bearing capacity. [PERSON] et al. [5] examined the mechanical characteristics of glued laminated timber beams reinforced with steel rods. This research used the transformed cross-section methodology to assess the bending stiffness of a composite cross-section. Upon conducting a parametric analysis, the significance of the proportionality ratio between the elasticity moduli of both wood and reinforcement was emphasized. Specifically, the higher the ratio, the higher the reinforcement efficiency. [PERSON] et al. [6] employed a transformed cross-section method to estimate the bending stiffness of glued laminated timber beams reinforced with glass and carbon fiber sheets. The experimental data validated the theoretical findings. [PERSON] et al. [7] studied the potential of reinforcing glued laminated timber beams using smooth and ribbed steel and basalt rods. Similar to other authors, they derived comparable theoretical stiffness values using a transformed section and an experimental one. [PERSON] et al. [8] introduced an analytical model employing transformed section attributes to evaluate the performance of glued laminated timber beams reinforced with cords and composite rods. They assumed a linear stress distribution over the depth of the cross-section, and considered the potential for lamellae with various mechanical characteristics within the cross-section of the timber. They achieved high accuracy between experimental and theoretical outcomes. In their research, [PERSON] et al. [9] conducted a comparative analysis between a linear and a non-linear model relative to the performance of beams strengthened with CFRP laminates.