03-03ChapGere.0008 - Tube A Tube A L I PA I PB b T UBE A T...

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Problem 3.9-10 A hollow circular tube A fits over the end of a solid circular bar B , as shown in the figure. The far ends of both bars are fixed. Initially, a hole through bar B makes an angle b with a line through two holes in tube A . Then bar B is twisted until the holes are aligned, and a pin is placed through the holes. When bar B is released and the system returns to equilibrium, what is the total strain energy U of the two bars? (Let I PA and I PB represent the polar moments of inertia of bars A and B , respectively. The length L and shear modulus of elasticity G are the same for both bars.) Solution 3.9-10 Circular tube and bar SECTION 3.9 Strain Energy in Torsion 243 L Bar B Bar B
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Unformatted text preview: Tube A Tube A L I PA I PB b T UBE A T 5 torque acting on the tube f A 5 angle of twist B AR B T 5 torque acting on the bar f B 5 angle of twist C OMPATIBILITY f A 1 f B 5 b F ORCE-DISPLACEMENT RELATIONS Substitute into the equation of compatibility and solve for T : S TRAIN ENERGY Substitute for T and simplify: U 5 b 2 G 2 L I PA I PB I PA 1 I PB 5 T 2 L 2 G 1 I PA 1 1 I PB U 5 a T 2 L 2 GI P 5 T 2 L 2 GI PA 1 T 2 L 2 GI PB T 5 b G L I PA I PB I PA 1 I PB f A 5 TL GI PA f B 5 TL GI PB L Bar B Bar B Tube A Tube A L I PA I PB b T f A T f B A-PDF Split DEMO : Purchase from www.A-PDF.com to remove the watermark...
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