(Solution) - A statically indeterminate stepped shaft ACB is fixed at ends -(2025 Original AI-Free Solution)

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A statically indeterminate stepped shaft ACB is fixed at ends A and B and loaded by a torque T0 at point C (see figure). The two segments of the bar are made of the same material, have lengths LA and LB, and have polar moments of inertia IPA and IPB.
Determine the angle of rotation ( of the cross section at C by using strain energy.
Use Eq. 3-51b to determine the strain energy U in terms of the angle (. Then equate the strain energy to the work done by the torque T0.
Compare your result with Eq. 3-48 of Example 3-9, Section 3.8.