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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

Consider a long cylinder of circular cross-section with radius R, as shown in Fig. 3. The cross section is subjected to torque on its ends. As you can see from the special case of 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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222

2. f(σijy0)=max(|σσ2|,|σσ3|,|σσ1|)σy0

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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
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