This tutorial examines the failure theories of Tresca and von Mises, both of which are crucial for designing metallic structures. Conventionally, Tresca is regarded as more conservative than von Mises from a deterministic perspective. This tutorial, however, introduces a different viewpoint, presenting a scenario where von Mises theory may appear more conservative when variability in the mechanical system parameters is considered. This often overlooked aspect is not extensively addressed in standard textbooks on solid mechanics and the strength of materials. The tutorial aims to shed light on the non-negligible probability where von Mises criterion yields a smaller equivalent stress than Tresca, thus being more conservative. It underscores the importance of integrating probabilistic considerations into stress analyses of solids, offering valuable insights for the education of structural mechanics.

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