Which failure theory provides the most conservative value for shafts made from ductile material subjected to combined bending and twisting moments?

• A. Maximum principal stress theory
• B. Maximum shear stress theory
• C. Maximum strain energy theory
• D. Maximum distortion energy theory

Answer: (B)

The maximum shear stress theory, also known as the Tresca criterion, is appropriate for assessing the failure of ductile materials under complex loading conditions, including combined bending and twisting moments. This theory is particularly focused on shear stress and provides a failure criterion based on the maximum difference between the principal stresses.

When applied to shafts made from ductile materials, the maximum shear stress theory assumes that material failure occurs when the maximum shear stress in the material reaches a critical level. This theory is conservative because it predicts failure at lower stress levels than some of the other criteria, making it safer for design purposes. This is essential in applications like shafts, where the integrity and reliability of the component are crucial under various loading conditions.

In contrast, other failure theories, such as maximum principal stress, may lead to less conservative predictions for ductile materials, as they do not account for the material's ability to withstand more than one type of stress simultaneously. The maximum distortion energy theory is also a viable option but tends to yield less conservative failure predictions compared to the maximum shear stress theory.

By using the maximum shear stress theory, engineers can ensure a safer design, especially in systems where bending and twisting moments coexist. This is why it is the preferred choice for providing a conservative estimate of