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30_ch 05 Mechanical Design budynas_SM_ch05

# 30_ch 05 Mechanical Design budynas_SM_ch05 - 0707 The...

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144 Solutions Manual Instructor’s Solution Manual to Accompany Mechanical Engineering Design 5-44 (a) First convert the data to radial dimensions to agree with the formulations of Fig. 3-33. Thus r o = 0 . 5625 ± 0 . 001in r i = 0 . 1875 ± 0 . 001in R o = 0 . 375 ± 0 . 0002in R i = 0 . 376 ± 0 . 0002in The stochastic nature of the dimensions affects the δ = | R i | − | R o | relation in Eq. (3-57) but not the others. Set R = (1 / 2)( R i + R o ) = 0 . 3755 . From Eq. (3-57) p = E δ R ( r 2 o R 2 )( R 2 r 2 i ) 2 R 2 ( r 2 o r 2 i ) Substituting and solving with E = 30 Mpsi gives p = 18 . 70(10 6 ) δ Since δ = R i R o ¯ δ = ¯ R i ¯ R o = 0 . 376 0 . 375 = 0 . 001 in and ˆ σ δ = 0 . 0002 4 2 + 0 . 0002 4 2 1 / 2 = 0 . 000 070 7 in Then C δ = ˆ σ δ ¯ δ = 0 . 000 070 7 0 . 001 = 0 . 0707
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Unformatted text preview: . 0707 The tangential inner-cylinder stress at the shrink-ﬁt surface is given by σ it = − p ¯ R 2 + ¯ r 2 i ¯ R 2 − ¯ r 2 i = − 18 . 70(10 6 ) δ ³ . 3755 2 + . 1875 2 . 3755 2 − . 1875 2 ´ = − 31 . 1(10 6 ) δ ¯ σ it = − 31 . 1(10 6 ) ¯ δ = − 31 . 1(10 6 )(0 . 001) = − 31 . 1(10 3 ) psi Also ˆ σ σ it = | C δ ¯ σ it | = . 0707( − 31 . 1)10 3 = 2899 psi σ it = N ( − 31 100, 2899) psi Ans....
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