Equation: Tao = (T*C)/J
i know the equation but it just seems counter-intuitive that the maximum shear stress is at the biggest radius for 3 reasons that I have(thought of).
1- imagine/assume that the applied force propagates (like water waves) in an equidistant manner, or in a circular manner for a cross-sectional view which is in 2D. As the force propagates further away from the center (assuming the torsion is applied at the center), the stress should decrease because the surface area increases as the radius increases (stress is N/M^2)
2- the axle-wheel friction analogy: it is a well known fact that as the axle diameter decreases the axle-wheel friction decreases because the friction's leverage is smaller at smaller axle diameters (thus static & dynamic friction are lesser in magnitude for smaller axle diameters). Thinking of it Intuitively, a smaller axle will try to push the wheel closer to its center which is harder. Similarly, the reaction friction force of the wheel will be less effective on a smaller diameter axle since it is pushing the axle from its edges which are close to the center as well. I don't know whether I can say there is friction/connection between the particles of a solid circular shaft in the same way but I think that the concept of leverage applies here just as it applies for the axle-wheel analogy since torsion is essential bending moment(s). If so, then in a circular cross-section, it should be easier for smaller diameters to shear relative to each other (rather than move with each other; lesser friction/connection force at smaller diameters due to reduced leverage). For the same reasons, larger diameters should feel the opposite. Consequently, this should cause earlier yielding at smaller diameters than at larger diameters for the same applied force(s). (Stress increases as strain increases. So again stress should be greater at smaller diameters) *** (the main contradiction of this part to the literature is that: if this was true, a material at smaller diameters will need SLIGHTLY lesser stress to strain for all points on the curve(since it is easier to strain at smaller leverage) than needed at the larger diameters. This would contradict (only a little bit) the notion that each material has a constant, defined stress-strain curve/behavior.) )
3- based on (2-): as smaller diameters are more prone to elastically deform than larger diameters. There should be some force that goes into motion-deformation at smaller diameters more than at larger diameters (some force is translated into motion-deformation (relieved) instead of stress, thus the force(s) propagating towards later, bigger radii is/are less than the initial force(s), which should further decrease the shear stress at larger diameters than at smaller diameters)
I am not sure whether these reasons are valid/true that's why I was skeptical about mentioning them at first. So can these reasons be valid ?? If so, then are there any other missing factors that make stress maximum at the biggest radii regardless of the 3 factors I mentioned ??
Thanks in advance.