sm7 160

________________________________________________________________________
PROBLEM (7.160) A machine frame has a T-shaped cross section and is subjected to end
moments M (Fig. P7.160). Determine the maximum stress in the member.
Given: M = 600 N⋅m, ri = 80 mm
SOLUTION
C
20
Centroid of the cross section:
80 60 140
o
rm=+= m
=×+×=
2
(40 20) (50 20) 1800Amm
11 22
12
Ar Ar
rAA
+
=+
(40 20)(120) (50 20)(90)
1800
×+×
=
103.3333 mm=
23
12
1800
50 20
rr
rr
A
RdA dr dr
rrr
==
+
∑∫∫ ∫
1800 100.6337
100 140
50ln 20ln
80 100
mm==
+
2.6996erR mm=−=
Now apply Eq.(7.67):
63
() 600(100.6337 80) 31.85
1800(10 )(2.6996 10 )(80)
i
ii
MR r
M
Pa
Aer
σ
−−
−
−
=− =− =−
×
63
600(100.6337 140) 34.96
1800(10 )(2.6996 10 )(140)
o
M
Pa σ
−−
−
=− =
×
20 mm
80 m
m
A
1
A2
40 mm
r
50 mm
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.