200Solutions Manual• Instructor’s Solution Manual to Accompany Mechanical Engineering DesignModeling the shaft separately using 2 elements gives approximatelyThe spreadsheet can be easily modiﬁed to giveδ11=9.605(10−7),δ12=δ21=5.718(10−7δ22=5.472(10−7)y1=1.716(10−5y2=1.249(10−5y21=2.946(10−10y22=1.561(10−10±wy=3.316(10−4±wy2=5.052(10−9)ω1=²386³3.316(10−4)5.052(10−9)´=5034 rad/sAns.A ﬁnite element model of the exact shaft gives ω1=5340 rad/s. The simple model is5.7% low.CombinationUsing Dunkerley’s equation, Eq. (7-32):1ω21=158602+150342⇒3819 rad/sAns.7-19We must not let the basis of the stress concentration factor, as presented, impose a view-point on the designer. Table A-16 shows
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