17_ch 05 Mechanical Design budynas_SM_ch05

17_ch 05 Mechanical Design budynas_SM_ch05 -...

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Chapter 5 131 Using the Distortion-Energy theory σ ± = ( σ 2 t σ r σ t + σ 2 r ) 1 / 2 = 0 . 011 61 ω 2 Solving ω = ± 30 000 0 . 011 61 ² 1 / 2 = 1607 rad/s So the inner radius governs and n = 13 000 rev/min Ans. 5-20 For a thin-walled pressure vessel, d i = 3 . 5 2(0 . 065) = 3 . 37 in σ t = p ( d i + t ) 2 t σ t = 500(3 . 37 + 0 . 065) 2(0 . 065) = 13 212 psi σ l = pd i 4 t = 500(3 . 37) 4(0 . 065) = 6481 psi σ r =− p i =− 500 psi These are all principal stresses, thus, σ ± = 1 2 { (13 212 6481) 2 + [6481 ( 500)] 2 + ( 500 13 212) 2 } 1 / 2 σ ± = 11 876 psi n = S y σ ± = 46 000 σ ± = 46 000 11 876 = 3 . 87 Ans. 5-21 Table A-20 gives S y as 320 MPa. The maximum significant stress condition occurs at r i where σ 1 = σ
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