Análise probabilística de treliças sob regime não linear físico

Abstract

One of the greatest challenges of Engineering is to propose the most efficient solutions with the lowest possible associated cost. In this context, the consideration of the physical nonlinearity of the materials employed and the presence of uncertainties inherent to Engineering projects, through the simulation of the variability of design parameters, becomes an interesting alternative. Thus, alternatively to the use of deterministic values from semi-probabilistic approaches, such as ABNT NBR 8800:2008, the physically non-linear and reliability-based analysis gives more robustness to the analyses and decision making, thus reducing the risks of both excessively conservative and costly projects and the conception of economic but unsafe projects. This work has as main objective the computational implementation of the coupling between mechanical and reliability models, for analysis of the structural behavior of different types of plane and space trusses under material nonlinearity. For this, a mechanical model based on the Direct Stiffness Method is computationally implemented and verified, considering the physical nonlinearity of the material, and a reliability model based on Monte Carlo Simulation, which are later combined, giving rise to a coupled model. All algorithms are implemented in Python language. The random variables considered include the yield strength of the steel, its modulus of elasticity, the dimensions of the cross section of the bars, and the loads involved. The limit states to be evaluated and, consequently, the probabilities of failure to be calculated, refer to the violation of limit values of displacement and stress. The validation and application examples attest to the success of the proposed implementation, while subsidizing reflections regarding the mechanical analysis performed.