sm7 157

________________________________________________________________________
PROBLEM (7.157) A curved bar with a rectangular cross section is subjected to the bending
moment as shown in Fig. P7.157. Calculate:
(a) The stresses i
σ
and o
σ
of the inside and outside fibers, respectively, using the curved beam formula.
(b) Resolve item (a) using the flexure formula.
Given: M = 1.2 kN m, b = 25 mm, h = 50 mm, r
⋅i = 60 mm
SOLUTION
60 50 110
oi
rrh mm=+= + =
2
(50)(25) 1,250Abh mm== =
We have
50 82.4898
110
ln
ln 60
o
i
h
Rr
r
== =
1()85
2i
rrr m
θ
=+=m
2.5102erR mm=−=
(a) Using Eq.(7.67):
6
1200(82.4898 60) 143.3
1250(10 )(0.06)(85 82.4898)
i
M
Pa σ
−
−
=− =−
−
6
1200(82.4898 110) 98.6
1250(10 )(0.11)(85 82.4898)
o
M
Pa σ
−
−
=− =
−
(b) 3
3
1.2 10 (0.025) 66.7
1(0.025)(0.06)
12
oi
Mc
M
Pa
I
σσ
×
=− = = =
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.