identify any limitation of the formula used and explain the reason for such limimatation to arise?

Question

many technological application involve the twisting of circular elastic shafts .one such application is the drive shaft of an automobile in which the power from the engine is transmitted to the wheels .all of these application that involve rotational movements , are subjected to torsion or twisting ,and to a certain extent ,breakage might occur.develop the basic knowledge that determine the angle of twist and stress distribution in solid and hollow circular shaft .theories should include shear stress and strain , shear modulus , theory of torsion and its assumption , distribution of shear stress ,angle of twist

Answer 1

It's been decades since I took strength of materials in college. However, I recall all materials have a breaking point, where the strain placed on them by a stress exceeds the elastic limit.

Strain vs. stress equations, like your twisting/torque ones, are valid only up to the break point for the most part. And some materials change elasticity even before the break point, which means the stress vs. strain equations for these may fail even before the break point.

As you may know, many strength of materials equation involve a math called tensors. Fundamentally, these are vectors and vector differentials to account for the fact that strains and stresses act in all directions throughout material. And, clearly, the shape of the material and the directions of the forces on it need to be accounted for.