Impacto do fogo em estruturas de madeira: aplicação de otimização para treliças submetidas a incêndio

Abstract

This work investigates the optimal design of Howe-type timber trusses under normal and fire conditions, with the objective of understanding the effects of fire on structural efficiency and on the selection of cross sections. The research is based on a gap in the literature regarding integrated methodologies that combine thermal analysis, structural modeling, and optimization applied to timber truss systems. A procedure is proposed that is capable of quantifying the influence of thermal degradation on the resistant and geometric behavior of the members, in addition to providing parameters for preliminary design under fire conditions. The methodology employs a deterministic formulation coupled with the Firefly Algorithm, which is responsible for searching for configurations with minimum structural weight, with simultaneous verification of ultimate and serviceability limit states, geometric constraints, slenderness, and minimum admissible areas. Four spans (6, 9, 12, and 15 meters) and three fire exposure times (10, 20, and 30 minutes) are analyzed, considering the thermal and mechanical properties of five timber species (Cambará-rosa, Cupiúba, Angelim-pedra, Garapa, and Jatobá). Each combination is evaluated through thirty independent runs, allowing the statistical characterization of the obtained solutions. The effects of fire are quantified by means of the Gross Area Correction Index (ICAB) and the Gross Weight Increase (IPB), used as measures of the increase in cross sections and the increase in structural mass required to compensate for the loss of resistance caused by charring. For 10 minutes of exposure, a maximum ICAB equal to 3.48 was observed, indicating localized increases greater than 240% of the initial gross area, while the maximum IPB reached 57.68%. At 20 minutes, the maximum ICAB was 2.78, associated with a maximum IPB of 97.13%, indicating the possibility of an almost doubling of the structural mass. For 30 minutes, the maximum ICAB remained at 2.78, suggesting stabilization of the geometric requirements imposed by normative constraints, while the maximum IPB reached 155.30%, indicating that the total mass of the truss may more than double. In all scenarios, the solutions remained within normative limits, with negative values of the constraint function g. The results confirm that fire exposure time exerts a decisive influence on the design of timber trusses, with IPB being highly sensitive to thermal severity, while ICAB provides an objective measure of the geometric requirements imposed by charring, offering consistent quantitative support for preliminary structural design under fire conditions.