 In this video, we are quickly going to look at why the formulas we've derived thus far only apply to circular shafts. If you recall, a circular shaft subjected to torsion will deform in a way such that planes perpendicular to the axis of the shaft remain straight, do not warp or distort, and do not extend relative to each other. Furthermore, lines parallel to the axis of the shaft also remain straight, but rotate through an angle. From these observations, we deduced that there is a state of pure shear in a shaft subjected to torsion, and this shear stress varies linearly with radial position. If we take a closer look at this stress state superimposed on the cross-section of a circular shaft, it will appear as shown here at one angular position within the shaft cross-section. Now, in reality, this stress distribution exists at all angular positions. In a way, you can visualize this as a flow of that stress around the axis of the shaft. Applying this fluid flow analogy to a non-circular cross-section, such as the rectangular one shown here, it becomes immediately apparent that the shear stress distribution will be far more complex. As we sweep through various angular positions, the fluid flow or the stress flow around that cross-section will warp and change to maintain the same resultant flow around that cross-section. Thus, for non-circular cross-sections with this variable geometry, you will have a very complex stress state as illustrated here on the rectangular cross-section. We can visualize the impact of this complicated shear stress distribution by observing the deformation of this flexible rectangular shaft. Two lines perpendicular to the axis of the shaft have been drawn on the surface of the shaft. If a cyclic torque has applied to that shaft, you see that the lines actually deform they warp from their initially straight position to a S shape as the torque is applied and removed. This is an indication that the assumptions that we made for circular shafts that those planes remain plain are no longer valid. It is possible to derive formulas for the shear stress and angle of twist for non-circular shafts and many engineering handbooks have tabulated results such as the one shown here for specific geometries. However, for the same cross-sectional area, you will find that the circular cross-section will always provide the most efficient shape. It will have the lowest maximum shear stress and lowest angle of twist. This is why circular shafts are the preferred shaft geometry in many engineering problems and engineering systems. In this course, you will not be required to deal with torsion of solid non-circular shafts. However, there is one case that we can look at and that is the case of the deformation and stresses in thin walled non-circular shafts. The subject of thin walled torsion will be looked at in the next unit.