291_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

291_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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SECTION 3.4 Nonuniform Torsion 285 Problem 3.4-20 Two hollow tubes are connected by a pin at B which is inserted into a hole drilled through both tubes at B (see cross-section view at B ). Tube BC fits snugly into tube AB but neglect any friction on the interface. Tube inner and outer diameters d i ( i ± 1, 2, 3) and pin diameter d p are labeled in the figure. Torque T 0 is applied at joint C . The shear modulus of elasticity of the material is G . Find expressions for the maximum torque T 0,max which can be applied at C for each of the following conditions. (a) The shear in the connecting pin is less than some allowable value ( ² pin ³ p , allow ). (b) The shear in tube AB or BC is less than some allowable value ( tube ³ t , allow ). (c) What is the maximum rotation ´ C for each of cases (a) and (b) above? Cross-section at B d 3 L A Pin d p T 0 , F c T A L B C A B d 2 d 2 d 1 Solution 3.4-20 (a) T 0,max BASED ON ALLOWABLE SHEAR IN PIN AT
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Unformatted text preview: B Pin at B is in shear at interface between the two tubes; force couple V d 2 T (b) T 0,max BASED ON ALLOWABLE SHEAR IN TUBES AB & BC t tube AB T a d 3 2 b I PAB I PAC p 32 a d 2 4 d 1 4 b I PAB p 32 a d 3 4 d 2 4 b ; T 0,max t p,allow a p d 2 d p 2 4 b t pin T d 2 a p d p 2 4 b t pin 4 T p d 2 d p 2 V T d 2 t pin V A S # so based on tube AB : and based on tube BC : ; T 0,max t t,allow J p ( d 2 4 d 1 4 ) 16 d 2 K t tube BC 16 T d 2 p ( d 2 4 d 1 4 ) t tube BC T a d 2 2 b p 32 ( d 2 4 d 1 4 ) ; T 0,max t t,allow c p ( d 3 4 d 2 4 ) 16 d 3 d t tube AB 16 T d 3 p ( d 3 4 d 2 4 ) t tube AB T a d 3 2 b p 32 ( d 3 4 d 2 4 ) Sec_3.4.qxd 9/27/08 1:09 PM Page 285...
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