The pipe lies in the horizontal plane. If it is subjected to a vertical force (mathbf{P}) at
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The pipe lies in the horizontal plane. If it is subjected to a vertical force \(\mathbf{P}\) at its end, determine the strain energy due to bending and torsion. Express the results in terms of the cross-sectional properties \(I\) and \(J\), and the material properties \(E\) and \(G\).
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