The fillet welds are conventionally calculated to shear stress in the weakest section: the throat area of the weld. This consideration is a simplification for any fillet weld. Nevertheless, this procedure is internationally accepted as a justified procedure, mainly, for the simplification that makes the calculation of the welded joints of an engineering construction an easy procedure. This premise has motivated that different authors try to obtain calculation expressions for different cases that are presented in the practice, looking to facilitate the work of the industry technicians and engineers in charge of carrying out the calculation of these unions, however, in this pawn they don’t always use the most appropriate methods settled down by the Mechanics of the Materials introducing inaccuracies in these expressions. The Fracture Mechanics has outlined a new necessity: the development of methods of predicting defects that could exist in the welding cords. In order to do that, it is required to determine the stresses that arise in the welding with a superior accuracy. In this paper, the Theory of the Torsion of Thin Walls Profiles is applied to the calculation of the torsion shear stresses of the fillet weld joints. New calculation expressions are obtained that belong together better than the classic expressions with relationship to the values obtained by the Finite Elements Method.

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