If a shaft made from ductile material is subjected to combined bending and twisting moment, calculations based on which one of the following failure theories will give the most conservative value?

Correct Answer: Maximum distortion energy theory

When a shaft made from ductile material is subjected to combined bending and twisting moments, the failure criteria need to account for both normal and shear stresses. Among the given options, the Maximum distortion energy theory, also known as the Von Mises stress theory or Tresca-Maxwell theory, provides the most conservative value for failure prediction.

This theory combines the normal and shear stresses into a single equivalent stress value and compares it to the material's yield strength. It is widely used for designing components subjected to complex stress states, such as combined bending and twisting.

The other theories listed are:
Option A: Maximum principal stress theory (Rankine's theory) focuses on the maximum normal stress and may not be as conservative in combined loading cases.
Option B: Maximum shear stress theory (Guest's theory or Tresca's theory) considers only shear stress and may not be conservative in cases where normal stresses dominate.
Option C: Maximum strain energy theory (Beltrami-Michell's theory) relates to the strain energy stored in the material and is not typically used for ductile materials in combined loading situations.

So, in the case of a ductile material shaft under combined bending and twisting moments, the Maximum distortion energy theory provides the most conservative failure prediction.