Reliability analysis using the main curvatures of limit state surfaces

This work was born from studies conducted by the author since the time he had the first contact with the subject in the year of 2001 during the completion of his master''s degree in mechanical engineering at the Federal University of Espírito Santo (UFES). From that period on he continued his studies through a doctorate carried out at UFOP completed in 2019 and a post-doctorate at UFES finalized in 2021. To date several of his articles have been published in journals book chapters and in the proceedings of national and international conferences.The author is fully convinced that many accidents caused by the rupture of structures could have been avoided if the design as well as the respective maintenance plan were based on a reliability index proposed by the limit state method instead of the safety coefficient provided via the admissible stresses'' method.