sm10 38

Excerpts from this work may be reproduced by instructors for distribution on a not-for-profit basis for testing or
instructional purposes only to students enrolled in courses for which the textbook has been adopted. Any other
reproduction or translation of this work beyond that permitted by Sections 107 or 108 of the 1976 United States
Copyright Act without the permission of the copyright owner is unlawful.
________________________________________________________________________
PROBLEM (10.38) A structural steel shaft of specific weight
γ
, diameter d, and elastic modulus E,
is supported by roller bearings at its ends A and B (Fig. P10.38). Determine the maximum permissible
length L for this shaft.
Requirement: The deflection of the shaft due to its own weight per unit length w at the midspan is limited
to max
v.
Assumption: Bearings act as simple supports.
Given: max
v=5 mm, d=75 mm, g=9.81 kg/s2,
γ
= 7860 kg/m3 E=200 GPa (from Table B.4)
max
v=5wL4/384EI (from Table B.14)
SOLUTION
4
max 5
384
wL
vEI = (by Table B.14)
or
1
max 4
384
()
5
EIv
Lw =
Where
44 64
(75) 1.55(10 )
64 64
d
I
mm
ππ
== =
2
0.075
( ) (7,860 9.81)( )
4
wgA
π
γ
×
==×
340.65 Nm=
Thus
96
14
384(200 10 )(1.55 10 )(0.005)
[ ] 4.32
5(340.65)
Lm
−
××
==