________________________________________________________________________
PROBLEM (7.159) A steel bar of square (b = h) cross section, curved to a radius r along the
centroidal axis, is acted upon by end moments M, as shown in Fig. P7.159. Calculate the maximum
permissible value of the bending moment M, if the allowable stress is all
.
Given: ri = 250 mm, ro = 300 mm, b = h = 50 mm, σall = 140 MPa
SOLUTION
50 274.2407
300
ln
ln 250
o
i
h
mm
r
r
== =
11
( ) (250 300) 275
22
io
rrr m=+= += m
m
2
(50)(50) 2500Am==
275 274.2407 0.7593erR mm=−= − =
Using Eq.(7.67):
36
() (274.20407 250)
; 140(10 ) 2500(10 )(250)
i
ii
MR r M
Aer
σ
−
−
=− − =− 3.62
kN m
⋅
Similarly,
36
() (274.20407 300)
; 140(10 ) 2500(10 )(300)
o
oo
MR r M
Aer
σ
−
−
=− =− , 4.07
kN m=⋅
Therefore
3.62
all
kN m=⋅
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