308_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

308_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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Unformatted text preview: Sec_3.8.qxd 302 9/27/08 1:13 PM Page 302 CHAPTER 3 Torsion Statically Indeterminate Torsional Members T0 Problem 3.8-1 A solid circular bar ABCD with fixed supports is TA acted upon by torques T0 and 2T0 at the locations shown in the figure. Obtain a formula for the maximum angle of twist max of the bar. (Hint: Use Eqs. 3-46a and b of Example 3-9 to obtain the reactive torques.) B A 2T0 C 3L — 10 D 3L — 10 TD D TD 4L — 10 L Solution 3.8-1 Circular bar with fixed ends ANGLE OF TWIST AT SECTION B From Eqs. (3-46a and b): TA T0 LB L TB T0 LA L fB TA(3L/10) GIP fAB 9T0 L 20GIP ANGLE OF TWIST AT SECTION C APPLY THE ABOVE FORMULAS TO THE GIVEN BAR: TA T0 a 7 4 b + 2T0 a b 10 10 15T0 10 TD 3 6 T0 a b + 2T0 a b 10 10 15T0 10 fC TD(4L/10) GIP fCD MAXIMUM ANGLE OF TWIST fmax 3T0 L 5GIP fC (a) For what distance x will the angle of twist at points B and C be a maximum? (b) What is the corresponding angle of twist max? (Hint: Use Eqs. 3-46a and b of Example 3-9 to obtain the reactive torques.) ; T0 TA A T0 B Problem 3.8-2 A solid circular bar ABCD with fixed supports at ends A and D is acted upon by two equal and oppositely directed torques T0, as shown in the figure. The torques are applied at points B and C, each of which is located at distance x from one end of the bar. (The distance x may vary from zero to L/2.) 3T0 L 5GIP C x x L ...
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