Optimization of roof slope, design and wood strength classes in timber Fink type truss

Wood is widely used in structural systems worldwide due to its mechanical properties and sustainability. In Brazil, its application is relative modest compared to Northern Hemisphere countries yet remains prevalent in roof structures, some of which date back to the twentieth century. Over time, empirical assumptions have influenced the design of timber roof structures has been observed, such as those related to roof slope. Many builders assume that lower slopes reduce material consumption since shorter elements are required. However, the magnitude of forces on the members is inversely proportional to the slope, potentially resulting in oversized structures. To assess the validity of these assumptions, this study investigates the optimal slope and appropriate strength class for a Fink truss with a 10-m span, employing the Firefly Algorithm for optimization. The results indicate that the D20 strength class, which has a characteristic compressive strength of 20 MPa, was optimal, reducing timber volume by up to 32.4% compared to higher strength classes, which significantly decreases structural mass and column loads. Specifically, optimal slopes ranged between 10° and 15°, achieving a total timber volume below 0.20 m3. It was observed that lower slopes (e.g., 5°) increased material volume by up to 324%, compared to the optimal slope configuration (typically between 10° and 15°), primarily due to strength and stability requirements. Similarly, very high slopes (above 36°) led to an average volume increase of approximately 250%. Furthermore, adopting a cross-sectional dimensions of 75 × 75 mm provided an effective solution to control slenderness within regulatory limits, ensuring both structural efficiency and economical usage of timber.