03-02ChapGere.0020

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Statically Indeterminate Torsional Members Problem 3.8-1 A solid circular bar ABCD with fixed supports is acted upon by torques T 0 and 2 T 0 at the locations shown in the figure. Obtain a formula for the maximum angle of twist f max of the bar. ( Hint: Use Eqs. 3-46a and b of Example 3-9 to obtain the reactive torques.) Solution 3.8-1 Circular bar with fixed ends SECTION 3.8 Statically Indeterminate Torsional Members 223 AB C D T D 2 T 0 T 0 T A 3 L 10 3 L 10 4 L 10 L From Eqs. (3-46a and b): A PPLY THE ABOVE FORMULAS TO THE GIVEN BAR : T D 5 T 0 ¢ 3 10 1 2 T 0 ¢ 6 10 5 15 T 0 10 T A 5 T 0 ¢ 7 10 1 2 T 0 ¢ 4 10 5 15 T 0 10 T B 5 T 0 L A L T A 5 T 0 L B L A NGLE OF TWIST AT SECTION B A NGLE OF TWIST AT SECTION C M AXIMUM ANGLE OF TWIST f max 5 f C 5 3 T 0 L 5 GI P f C 5 f CD 5 T D (4 L / 10) GI P 5 3 T 0 L 5 GI P f B 5 f AB 5 T A (3 L / 10) GI P 5 9 T 0 L 20 GI P A B T B T 0 T A L A L L B C D T D 2 T 0 T 0 T A 3 L 10 3 L 10 4 L 10 Problem 3.8-2 A solid circular bar ABCD with fixed supports at
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