sm7 164

________________________________________________________________________
PROBLEM (*7.164) The curved frame shown in Fig. P7.163 with a circular cross section of
diameter d has the allowable tensile stress σall. Calculate the largest permissible distance a from the line
of action of the load P to the center of curvature O of the frame.
Given: b = 5/8 in., d = 1 in., P = 40 lb, σall = 5 ksi
*SOLUTION
58 .
A
rb in==
10.5 . 0.625 0.5 1.125 .
2
cd inr i== = += n
22
1[
2]
R
rrc=+− (from Table 7.1)
22
1[1.125 1.125 0.5 ] 1.0664 .
2in
=+ −=
0.0586 .erR in=−=
,
22
(0.5) 0.7854 .Ac in ππ == = 2()
M
Pa r−+
=
Largest tensile stress occurs at point A; all A
σ
σ
=
Applying Eq.(7.70), we have
() ()()
1
AA
AAA
M
Rr arRr
PP
AAer A er
σ
⎡
⎤
−+
−
=− = +
⎢
⎥
⎦
kP
A
=
⎣
where
()(
1A
A
arRr)
er
+−
=+
k (1)
This gives
3
(5 10 )(0.7856) 98.2
40
AA
k
P
σ
×
== =
From Eq.(1), we obtain
(1) (97.2)(0.0586)(0.62) 8.001
1.0664 0.625
A
A
ker
ar
Rr
−
+= = =
−−
n=−=
Hence ai 8.001 1.125 6.876 .
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.