312_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

312_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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Unformatted text preview: Sec_3.8.qxd 9/27/08 306 1:13 PM Page 306 CHAPTER 3 Torsion Combine Eqs. (2) and (5) and solve for T0: SEGMENT AC GOVERNS LBIPA 1 pd3 t a1 + b 16 B allow LAIPB (T0)CB 4 LBdA 1 pd3 t allow a 1 + b 4 16 B LAdB Substitute numerical values: (T0)CB 4597 lb-in. (T0)max ; 3680 lb-in. NOTE: From Eqs. (4) and (6) we find that (6) (T0)AC (T0)CB a LA dB ba b LB dA which can be used as a partial check on the results. 20 mm Problem 3.8-6 A stepped shaft ACB having solid circular cross sections with two different diameters is held against rotation at the ends (see figure). If the allowable shear stress in the shaft is 43 MPa, what is the maximum torque (T0)max that may be applied at section C? (Hint: Use Eqs. 3-45a and b of Example 3-9 to obtain the reactive torques.) 25 mm B C A T0 225 mm 450 mm Solution 3.8-6 Stepped shaft ACB dA 20 mm dB 25 mm LA 225 mm LB 450 mm allow 43 MPa 1 pd 3 t 16 A AC TA 1 pd 3 t 16 A allow (3) Combine Eqs. (1) and (3) and solve for T0: (T0)AC LAIPB 1 3 pdAt allow a 1 + b 16 LBIPA 4 LAdB 1 3 pdAt allow a 1 + b 4 16 LBdA Find (T0)max REACTIVE TORQUES (from Eqs. 3-45a and b) (4) Substitute numerical values: TA LBIPA T0 a b LBIPA + LAIPB (1) (T0)AC TB T0 a (2) IN SEGMENT LAIPB b LBIPA + LAIPB ALLOWABLE TORQUE BASED UPON SHEAR STRESS IN SEGMENT AC tAC 16TA pd3 A 150.0 N m ALLOWABLE TORQUE BASED UPON SHEAR STRESS CB tCB TB 16TB pd3 B 1 pd3 t 16 B CB 1 pd3 t 16 B allow (5) ...
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