24_ch 05 Mechanical Design budynas_SM_ch05

24_ch 05 Mechanical Design budynas_SM_ch05 - 5 2 ³ = −...

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138 Solutions Manual • Instructor’s Solution Manual to Accompany Mechanical Engineering Design 5-33 The moment about the center caused by force F is Fr e where r e is the effective radius. This is balanced by the moment about the center caused by the tangential (hoop) stress. Fr e = ± r o r i r σ t w dr = w p i r 2 i r 2 o r 2 i ± r o r i ² r + r 2 o r ³ dr r e = w p i r 2 i F ( r 2 o r 2 i ) ´ r 2 o r 2 i 2 + r 2 o ln r o r i µ From Prob. 5-31, F = w r i p i . Therefore, r e = r i r 2 o r 2 i ´ r 2 o r 2 i 2 + r 2 o ln r o r i µ For the conditions of Prob. 5-31, r i = 0 . 5 and r o = 1in r e = 0 . 5 1 2 0 . 5 2 ² 1 2 0 . 5 2 2 + 1 2 ln 1 0 . 5 ³ = 0 . 712 in 5-34 δ nom = 0 . 0005 in (a) From Eq. (3-57) p = 30(10 6 )(0 . 0005) (1 3 ) (1 . 5 2 1 2 )(1 2 0 . 5 2 ) 2(1 . 5 2 0 . 5 2 ) · = 3516 psi Ans. Inner member: Eq. (3-58) ( σ t ) i =− p R 2 + r 2 i R 2 r 2 i =− 3516 ² 1 2 + 0 . 5 2 1 2
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Unformatted text preview: . 5 2 ³ = − 5860 psi ( σ r ) i = − p = − 3516 psi Eq. (5-13) σ ± i = ( σ 2 A − σ A σ B + σ 2 B ) 1 / 2 = [( − 5860) 2 − ( − 5860)( − 3516) + ( − 3516) 2 ] 1 / 2 = 5110 psi Ans. Outer member: Eq. (3-59) ( σ t ) o = 3516 ² 1 . 5 2 + 1 2 1 . 5 2 − 1 2 ³ = 9142 psi ( σ r ) o = − p = − 3516 psi Eq. (5-13) σ ± o = [9142 2 − 9142( − 3516) + ( − 3516) 2 ] 1 / 2 = 11 320 psi Ans. R ± t 1 2 " 1" R r e r...
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