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Problem 3.9-6 Obtain a formula for the strain energy U of the statically indeterminate circular bar shown in the figure. The bar has fixed supports at ends A and B and is loaded by torques 2 T 0 and T 0 at points C and D , respectively. Hint: Use Eqs. 3-46a and b of Example 3-9, Section 3.8, to obtain the reactive torques. Solution 3.9-6 Statically indeterminate bar SECTION 3.9 Strain Energy in Torsion 239 (a) L OAD T ACTS ALONE (Eq. 3-51a) (b) L OAD t ACTS ALONE From Eq. (3-56) of Example 3-11: U 2 5 t 2 L 3 6 GI P U 1 5 T 2 L 2 GI P (c) B OTH LOADS ACT SIMULTANEOUSLY At distance x from the free end: T ( x ) 5 T 1 tx N OTE : U 3 is not the sum of U 1 and U 2 . 1 t 2 L 3 6 GI P 5 T 2 L 2 GI P 1 TtL 2 2 GI P U 3 5 # L 0 [ T ( x )] 2 2 GI P dx 5 1 2 GI P # L 0 ( T 1 tx ) 2 dx t dx x T 2 T 0 T 0 AB D C L 4 L 4 L 2 R EACTIVE TORQUES From Eq. (3-46a):
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This note was uploaded on 09/20/2009 for the course COE 3001 taught by Professor Armanios during the Spring '08 term at Georgia Institute of Technology.

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