321_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

321_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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SECTION 3.8 Statically Indeterminate Torsional Members 315 N UMERICAL VALUES G s ± 80 GPa G b ± 40 GPa L ± 3.0 m d 1 ± 70 mm d 2 ± 90 mm I Ps I Ps ± 2.357 ² 10 ³ 6 m 4 I Pb I Pb ± 4.084 ² 10 ³ 6 m 4 T 1,allow ± 9.51 kN ´ m (b) A LLOWABLE TORQUE T 2 BASED ON ALLOWABLE SHEAR STRESS IN BRASS , µ b b ± 70 MPa First check hollow segment 1 (brass sleeve only) T 2,allow ± 6.35 kN ´ m controls over T 2 below also check segment 2 with brass sleeve over steel shaft where from stat-indet analysis above T 2, allow ± 2 t b ( G s I PS + G b I Pb ) d 2 G b T b ± T 2 a G b I Pb G s I PS + G b I Pb b t ± T b d 2 2 I Pb ; T 2, allow ± 2 t b I Pb d 2 t ± T 2 d 2 2 I Pb ; ± p 32 A d 2 4 ³ d 1 4 B ± p 32 d 1 4 f a ± 8 a p 180 b rad T 2,allow ± 13.69 kN ´ m so T 2 for hollow segment controls (c) A LLOWABLE TORQUE T 3 BASED ON ALLOWABLE SHEAR STRESS IN STEEL , s s ± 110 MPa First check segment 2 with brass sleeve over steel
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Unformatted text preview: shaft where from stat-indet analysis above T 3,allow 13.83 kN m also check segment 3 with steel shaft alone T 3,allow 7.41 kN m controls over T 3 above (d) T max IF ALL PRECEDING CONDITIONS MUST BE CONSIDERED from (b) above T max 6.35 kN m max. shear stress in hollow brass sleeve in segment 1 controls overall ; ; T 3, allow 2 t s I P s d 1 t T 3 d 1 2 I P s T 3, allow 2 t s ( G s I P s + G b I P b ) d 1 G s T s T 3 a G s I PS G s I PS + G b I Pb b t T s d 1 2 I PS Sec_3.8.qxd 9/27/08 1:13 PM Page 315...
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