________________________________________________________________________
PROBLEM (7.161) The curved frame with a T-shaped cross section is in pure bending as shown in
Fig. P7.160. If the member is made of a material having an allowable stress of all
σ
, determine the largest
moment M that can be applied.
Given: ri = 80 mm, σall = 150 MPa
SOLUTION
From the solution of Prob. 7.160, we have
2
140 1800
o
rmmAm==m
103.3333 100.6337rmmR==mm
m=
em 2.6996
Assume tension failure:
663
() (100.6337 140)
; 150(10 ) 1800(10 )(2.6996 10 )(140)
o
oo
MR r M
Aer
σ
−−
−
−
=− =− ×
or
2.592
M
Nm=⋅
Assume compression failure:
663
() (100.6337 80)
; 150(10 ) 1800(10 )(2.6996 10 )(80)
i
ii
MR r M
Aer
σ
−−
−
−
=− − =− ×
or 2.826
M
Nm=⋅
Thus, tension controls,
2.592
all
M
Nm=⋅
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