Consider a long cylinder of circular cross-section with radius R, as shown in Fig. 3. The cross section is subjected to torque T on its ends. As you can see from the special case of a = b in the solution for the warping function of an elliptical cross-section under torsion, the warping function or out-of-plane displacement of a circular cross-section vanishes.
(a) What is the maximum shear stress in the cross-section and where does it occur?
(b) What is the shear stress, σθz, as a function of radius, r? (Hint: you should have a linear
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2. f(σij,σy0)=max(|σ1 −σ2|,|σ2 −σ3|,|σ3 −σ1|)−σy0 ≤0
relation between σθz and r).
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Consider a long cylinder of circular cross-section with radius R, as shown in Fig. 3. The cross section is subjected to torque T on its ends. As you can see from the special case of a = b in the solution for the warping function of an elliptical cross-sec