The shaft is subjected to a distributed torque along its length of where x is in meters

Chapter 5, Problem 5-30

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The shaft is subjected to a distributed torque along its length of \(t=\left(10 x^{2}\right) \mathrm{N} \cdot \mathrm{m} / \mathrm{m}\), where x is in meters. If the maximum stress in the shaft is to remain constant at 80 MPa, determine the required variation of the radius c of the shaft for \(0 \leq x \leq 3\) m.

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