Análise de confiabilidade em projetos de elementos de treliças planas de madeira considerando a variabilidade da inclinação das fibras

Abstract

Wood, widely used in civil construction in various regions of the world, stands out for its sustainability, low energy consumption, and remarkable mechanical properties. In Brazil, although its application in structural systems is less predominant compared to countries in the Northern Hemisphere, wood plays a significant role, especially in roofing structures. The country preserves some historical roofing structures that remain in use, demonstrating the material’s durability when properly treated. In this context, three scenarios deserve attention: the restoration of historical structures, the transition to prefabricated systems, and the uncertainties in design and service conditions throughout the lifespan of the structures. The difficulty in accurately establishing the properties of materials, actions, and inherent defects often leads engineers to adopt deterministic approaches, despite many of these variables being random. Thus, reliability analysis becomes essential for decision-making regarding the structure’s fate. Given the above, this study emphasized reliability analysis in the design of flat timber truss elements, considering grain orientation as the main random variable, which, under certain conditions, significantly impacts the material’s mechanical properties. Models were developed that incorporate this variability, considering different species of hardwood, comparing the reliability indices (β) obtained with normative standards and the ideal condition of perfect fiber parallelism. The methodology employed included Monte Carlo Simulation (MCS), using random variables representing wood properties, grain inclination, actions, and loads. The physical and mechanical properties of three types of wood were characterized: Cambará, Angelim-pedra, and Angelim-vermelho. Regression models were developed to estimate these properties at different fiber inclinations, demonstrating statistical significance and satisfactory determination coefficients (R2). The results indicated that the instability of axially compressed members is crucial in the design and reliability of flat wooden trusses, with a concerning reduction in β values in larger spans, compromising reliability and suggesting the need for adjustments. New simulations revealed that thicker profiles improve reliability indices (β), even while maintaining the cross-sectional area. The wood species had little influence on β values, while variability, represented by Coefficients of Variation (CV), and the proximity of limit state equations to the null value play a crucial role. The p-values of the t-test evidenced the statistical significance of failure probabilities from a 2° inclination, challenging the Hankinson model, which suggests limited impact for inclinations up to 6°. The research reinforces the importance of grain inclination variability in the reliability of elements, highlighting the need for adjustments in the modification factor, although this requires a comprehensive study of the probabilistic modeling of fiber inclination. Therefore, this research represents an initial advance in integrating this variability into wooden structural designs, with the potential for significant improvements in structural reliability and the adoption of safer and more effective design practices.