3. Using Fig. 17.5(c), to find the shaft critical speed
5(32. 2 ft)(12 in. )
5g
nc = s2 ft
4st 4(4. 98 10 in. )
-3
nc 311 rpm ■
17-6
, SOLUTION (17.10)
Known: The dimensions of a steel shaft are given.
Find: Determine the critical speed of rotation for the steel shaft.
Schematic and Given Data:
25 mm dia.
50 kg
600 mm 600 mm
Assumptions:
1. Bearing friction is negligible.
2. The bearings supporting the shafts are accurately aligned.
3. The shaft remains linearly elastic.
4. The shaft is simply supported.
5. The mass of the shaft is negligible.
Analysis:
P
L/2
L
st
P/2 P/2
1. Using Appendix D-2, for a concentrated center load on a simply supported beam
3
we have st = PL where
48EI
E = 207 109 Pa (Appendix C-1) and
I = d (Appendix B-1)
4
64
(0. 025)4
= = 19. 2 10-9 m4
64
17-20
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