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If we rotate a shaft about an axis it is said to be under torsion. It is also said that there will be a deformation. What I'd like to know is will the shaft actually WARP during the process? If not what kind of deformation will take place? If in case the shaft just rotates about an axis without undergoing any kind of deformation (if the two circular ends rotate identically and without any angle of twist) is the torsion still valid?

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This is a question in solid mechanics. Under the action of a constant torque along its length, the shaft experiences a deformation, such that one end of the shaft is rotated slighly relative to the other. But it is not enough to cause the shaft to warp, and the shaft returns elastically to its original shape after the torque is removed. Each cross section of the shaft rotates a little, and the angle of rotation varies linearly with distance along the shaft. This causes the cross sections to shear relative to one another. The accompanying shear stresses results in torque along the entire length. In the limit of infinite shear modulus G, the shaft approaches the behavior of a rigid shaft.

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  • $\begingroup$ thanks a lot. By the way just a last (maybe a stupid) question - does this angular deformation accumulate with each rotation. For example in experiments we apply the torque for n number of rotations, so is the deflection angle actually nXdeflection in 1 rotation? $\endgroup$ – Thomson1 Apr 21 '16 at 17:28
  • $\begingroup$ No. For a given torque, the angle of twist remains constant during rotation. It's the same kind of thing that happens if you hang a weight from a rod. The rod does not continue stretching once the weight equilibrates. In the case of a shaft, the shaft does not continue twisting once the torque equilibrates. $\endgroup$ – Chet Miller Apr 21 '16 at 17:34

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