313_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

313_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 307 SECTION 3.8 Statically Indeterminate Torsional Members Combine Eqs. (2) and (5) and solve for T0: (T0)CB SEGMENT AC GOVERNS LBIPA 1 pd 3 t a1 + b 16 B allow LAIPB (T0)max (T0)AC (T0)CB (6) Substitute numerical values: (T0)CB 240.0 N m a LA dB ba b LB dA which can be used as a partial check on the results. Problem 3.8-7 A stepped shaft ACB is held against rotation at ends dA A and B and subjected to a torque T0 acting at section C (see figure). The two segments of the shaft (AC and CB) have diameters dA and dB, respectively, and polar moments of inertia IPA and IPB, respectively. The shaft has length L and segment AC has length a. A a T0 a LBIPA b ; TB LBIPA + LAIPB (a) EQUAL SHEAR STRESSES TA(dA/2) tCB tAC IPA CB or TAdA IPA T0 a LAIPBdB IPB LBdA LAdB dA dA + dB a L a)IPA Solve for a/L: (Eq. 1) adB (b) EQUAL TORQUES TA TB or LBIPA or (L TB(dB/2) IPB TBdB IPB or a)dA Solve for a/L: LAIPB b LBIPA + LAIPB Substitute TA and TB into Eq. (1): LBIPAdA IPA L or (L SEGMENT CB: dB, IPB LB L a REACTIVE TORQUES (from Eqs. 3-45a and b) AC C Stepped shaft SEGMENT AC: dA, IPA LA T0 a dB IPA (a) For what ratio a/L will the maximum shear stresses be the same in both segments of the shaft? (b) For what ratio a/L will the internal torques be the same in both segments of the shaft? (Hint: Use Eqs. 3-45a and b of Example 3-9 to obtain the reactive torques.) TA ; 150 N m NOTE: From Eqs. (4) and (6) we find that 4 LBdA 1 3 pdBt allow a 1 + b 4 16 LAdB Solution 3.8-7 307 or a L LAIPB aIPB a L 4 dA 4 4 dA + dB IPA IPA + IPB ; ; IPB B ...
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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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