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When equal and opposite torque act on the two ends of a circular shaft,how do we know that deformations occur in a uniform fashion throughout the length of shaft?Is it because that all cross section of shaft have same torque acting on them and hence the stress distribution on the cross section is same which further results in same strain throughout the cross section?If not,then how?

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    $\begingroup$ We don't. It is assumed that the material property is uniform. And from that and small displacements theory and materialsampling we conclude that the material behaves linearily. Its only true if all these assumptioms that we make are true. $\endgroup$ – joojaa Dec 4 '18 at 10:33
  • $\begingroup$ But if it is stressed over the yield and becomes plastic , the plasticity is limited to a small zone ( based on research done on solid round bars). $\endgroup$ – blacksmith37 Dec 4 '18 at 22:00
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Yes you are right:

Is it because that all cross section of shaft have same torque acting on them and hence the stress distribution on the cross section is same which further results in same strain throughout the cross section?

Let's cut the shaft into 100 short pieces. Each will experience the same torque and each will twist exactly 1/100 of the total shaft's deformation.

Why? because it is the same material and its crystals have identical structural properties, including identical shear modulus, G.

Although in metal forging impurities are bound to enter into the alloy, by the time the quality control lets a batch through they are within the tolerance of the standards!

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