A cantilever beam of length \(1 \mathrm{~m}\) is subjected to a uniformly distributed load \(p(x)=p_{0}=\) \(12,000 \mathrm{~N} / \mathrm{m}\) and a clockwise couple \(5,000 \mathrm{~N} \cdot \mathrm{m}\) at the tip. The load factors for the distributed load and couple are, respectively, 1.5 and 2.0. When the cross section is circular, calculate the minimum diameter. Use Young's modulus 80 GPa and yield strength \(250 \mathrm{MPa}\).

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Po = 120 N/m C=-50 N-m