Thanks for the explanation. It seems to make more sense that way. Question: You have a table or statue or any other object that stands on legs. One leg is made of steel the other is made of paper. It falls over into the leg of paper. Why the paper leg and not the steel leg? I am smart enough to know this is too simple to apply to shafts, so await the dressing down. Is this not similar to the two sides of a shaft? As Dave referred to, it seems intuitively that it would bend in one direction more easily than the other, though in reality it doesn't. I may get out of 9th grade physics yet.
Al
At 05:18 PM 12/28/2002, you wrote:
In an attempt to understand where the 'weak and strong' sides of a shaft concept came from it occurs to me that one of the problems with understanding this concept is that it is easy to visualize a shaft that is stronger on one side than the other; a thicker wall on one side in a steel shaft, or more fibers on one side in a composite shaft. This will, indeed, result in a shaft that is 'stronger' on that side - to a tensile (or compressive) load applied parallel to the axis of the shaft! Assuming the shaft remains straight the strain and stresses in the shaft material will be the same through a cross section but, because of the greater cross sectional area on the 'thick' side of the shaft more of the reaction force to the axial shaft load will be carried on that side of the shaft, so, in a sense, it is 'stronger'. In a bending situation, however, because of the redistribution of stresses that occurs in the shaft to balance the forces on either side of the neutral axis, this does not result in a shaft being stiffer in one direction than in the opposite direction. In a given bending plane the shaft has the same stiffness in both directions. The 'neutral axis' is defined, by the way, as the line of zero stress through the cross section of a shaft under bending load and is not always at the geometric center of the shaft. The stresses in the material on one side of the neutral axis are compressive and tensile on the other for bending in one direction and then reverse for bending in the other, but the neutral axis remains in the same location, hence the resistance to bending (stiffness) is the same. I hope this helps.
Regards,
Alan
At 04:58 PM 12/26/02 -0500, you wrote:
At 04:32 PM 12/26/02 -0500, Al Taylor wrote:I'm impressed. I have no clue if you answered my question, but I was impressed. John, you still there? ;-)OK, John and Alan and I all said, counterintuitive as it may seem, yes it bends exactly the same TOWARD and AWAY FROM the spine, as long as it's in the same plane.
Al
You could weld a small steel rod to the shaft, to give it as stiff a spine as you want. It will still have exactly the same stiffness in BOTH DIRECTIONS in the same plane.
Twirling it in a spine finder might or might not say that. But measuring the REAL stiffness will. I have posted here how to measure true stiffness, several times over the past week.
Hope this answers it.
DaveT
