A three-bladed wind turbine (Fig. 3.40(a)) has a small unbalanced mass \(m\) located at a radius \(r\) in the plane of the blades. The blades are located from the central vertical \((y)\) axis at a distance \(R\) and rotate at an angular velocity of \(\omega\). If the supporting truss can be modeled as a hollow steel shaft of outer diameter \(0.1 \mathrm{~m}\) and inner diameter \(0.08 \mathrm{~m}\), determine the maximum stresses developed at the base of the support (point \(A\) ). The mass moment of inertia of the turbine system about the vertical ( \(y\) ) axis is \(J_{0}\). Assume \(R=0.5 \mathrm{~m}, m=0.1 \mathrm{~kg}, r=0.1 \mathrm{~m}\), \(J_{0}=100 \mathrm{~kg}-\mathrm{m}^{2}, h=8 \mathrm{~m}\), and \(\omega=31.416 \mathrm{rad} / \mathrm{s}\).

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(a) @ m) L Y a (b) FIGURE 3.39 Aircraft engine with rotating unbalance.