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10_ch 07 Mechanical Design budynas_SM_ch07

10_ch 07 Mechanical Design budynas_SM_ch07 - M a = 2178 lbf...

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Chapter 7 187 Shear force, bending moment, and torque diagrams can now be obtained. (c) Potential critical locations occur at each stress concentration (shoulders and keyways). To be thorough, the stress at each potentially critical location should be evaluated. For now, we will choose the most likely critical location, by observation of the loading situation, to be in the keyway for the gear. At this point there is a large stress concentration, a large bending moment, and the torque is present. The other locations either have small bend- ing moments, or no torque. The stress concentration for the keyway is highest at the ends. For simplicity, and to be conservative, we will use the maximum bending moment, even though it will have dropped off a little at the end of the keyway. (d) At the gear keyway, approximately 9 in from the left end of the shaft, the bending is com- pletely reversed and the torque is steady.
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Unformatted text preview: M a = 2178 lbf · in T m = 2500 lbf · in M m = T a = From Table 7-1, estimate stress concentrations for the end-milled keyseat to be K t = 2 . 2 and K ts = 3 . 0. For the relatively low strength steel specified (AISI 1020 CD), estimate notch sensitivities of q = . 75 and q s = . 9, obtained by observation of Figs. 6-20 and 6-21. Assuming a typical radius at the bottom of the keyseat of r / d = . 02 (p. 361), these estimates for notch sensitivity are good for up to about 3 in shaft diameter. Eq. (6-32): K f = 1 + . 75(2 . 2 − 1) = 1 . 9 K f s = 1 + . 9(3 . − 1) = 2 . 8 Eq. (6-19): k a = 2 . 70(68) − . 265 = . 883 For estimating k b , guess d = 2 in. k b = (2 / . 3) − . 107 = . 816 S e = (0 . 883)(0 . 816)(0 . 5)(68) = 24 . 5 kpsi M T R B R A 2500 lbf •in 2178 lbf •in 242 lbf ± 1088 lbf 9 in 2 in 6 in V W Ans....
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