323_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

323_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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SECTION 3.8 Statically Indeterminate Torsional Members 317 (a) R EACTIVE TORQUES , T A & T B , FOR CASE OF CONSTANT THICKNESS OF HOLLOW SECTION OF TUBE compatibility equation: ± 1 ² 2 ³ 0 T B ³ redundant T 0 ³ 40000 in.-lb T B ³ 24708 in-lb T A ³ T 0 ² T B T A ³ 15292 in-1b T A ´ T B ³ 40,000 in.-lb (check) ; ; T B ³ 1.94056 T 0 p T B ³ a 608 T 0 L 81 G p d A 4 ba Gd A 4 3.86804 L b (b) R EACTIVE TORQUES , T A & T B , FOR CASE OF CONSTANT DIAMETER OF HOLE T B ³ 31266 in.-lb T A ³ T 0 ² T B T A ³ 8734 in.-lb T A ´ T B ³ 40,000 in.-1b (check) ; ; T B ³ 2.45560 T 0 p T B ³ a 608 T 0 L 81 G p d A 4 ba Gd A 4 3.05676 L b Problem 3.8-16 A hollow circular tube A (outer diameter d A , wall thickness t A ) fits over the end of a circular tube B ( d B , t B ), as shown in the figure. The far ends of both tubes are fixed. Initially, a hole through tube B makes an angle µ with a line through two holes in tube A . Then tube B is twisted until the holes are aligned, and a pin (diameter d p ) is placed through the holes. When tube B is released, the system returns to equilibrium. Assume that G is constant. (a) Use superposition to find the reactive torques T A and T B at the supports. (b) Find an expression for the maximum value of if the shear stress in the pin, p , cannot exceed p ,allow. (c) Find an expression for the maximum value of
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Unformatted text preview: if the shear stress in the tubes, t , cannot exceed t ,allow. (d) Find an expression for the maximum value of if the bearing stress in the pin at C cannot exceed b ,allow. Solution 3.8-16 (a) S UPERPOSITION TO FIND TORQUE REACTIONS- USE T B AS THE REDUNDANT compatibility: B 1 B 2 B 1 joint tubes by pin then release end B T A T B statics ; T B G b L a I PA I PB I PA I PB b ; f B 2 T B L G a I PB + I PA I PA I PB b f B 2 T B L G a 1 I PA + 1 I PB b (b) A LLOWABLE SHEAR IN PIN RESTRICTS MAGNITUDE OF TORQUE T B FORCE COUPLE Vd B WITH V SHEAR IN PIN AT C ; ca I PB + I PA I PA I PB b d B p d P 2 d b max t p, allow L 4 G t p, allow G b L a I PA I PB I PA I PB b d B p 4 d p 2 t p, allow T B d B p 4 d P 2 t p V A s V T B d B Pin at C Tube A Tube B b Cross-section at C C L Tube B Tube A L I PA I PB T A T B A B Sec_3.8.qxd 9/27/08 1:13 PM Page 317...
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