319_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

319_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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Unformatted text preview: Sec_3.8.qxd 9/27/08 1:13 PM Page 313 SECTION 3.8 Statically Indeterminate Torsional Members Solution 3.8-13 Composite shaft shrink fit TORQUES Total torque: T Eq. (3-44 a): TB TB TS Ta GBIPB b GBIPB + GSIPS 0.237918 T d1 1.6 in. d2 2.0 in. GB 5,400 psi Eq. (3-44 b): TS GS 12,000 psi B 4500 psi 7500 psi S GSIPS b GBIPB + GSIPS 0.762082 T T Allowable stresses: Ta TB TS (CHECK) ALLOWABLE TORQUE T BASED UPON BRASS CORE TB(d1/2) 2tBIPB TB IPB d1 Substitute numerical values: BRASS CORE (ONLY) tB TB 0.237918 T 2(4500 psi)(0.643398 in.4) 1.6 in. IPB GBIPB p4 d1 32 0.643398 in.4 3.47435 106 lb-in.2 T 15.21 k-in. ALLOWABLE TORQUE T BASED UPON STEEL SLEEVE TS(d2/2) 2tSIPS TS IPS d2 Substitute numerical values: tS STEEL SLEEVE (ONLY) tS T 0.762082 T 2(7500 psi)(0.927398 in.4) 2.0 in. 9.13 k-in. STEEL SLEEVE GOVERNS IPS GSIPS p (d 4 32 2 11.1288 d14) Tmax 9.13 k-in. ; 0.927398 in.4 106 lb-in.2 Problem 3.8-14 A steel shaft (Gs 80 GPa) of total length L 3.0 m is encased for one-third of its length by a brass sleeve (Gb 40 GPa) that is securely bonded to the steel (see figure). The outer diameters of the shaft and sleeve are d1 70 mm and d2 90 mm. respectively. 313 ...
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This note was uploaded on 12/22/2011 for the course MEEG 310 taught by Professor Staff during the Fall '11 term at University of Delaware.

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