The rod has a circular cross section with a polar moment of inertia (J) and moment of
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The rod has a circular cross section with a polar moment of inertia \(J\) and moment of inertia \(I\). If a vertical force \(\mathbf{P}\) is applied at \(A\), determine the vertical displcement at this point. Consider the strain energy due to bending and torsion. The material constants are \(E\) and \(G\).
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