sm7 170

________________________________________________________________________
PROBLEM (7.170) The triangular cross section of a curved bar is shown in Fig. P7.170. Derive the
expression for the radius R along the neutral axis. Compare the result with that given for Fig. C in Table
7.1.
SOLUTION
1
2
Ab
=h
r
The section width w varies linearly with r. Thus
(1)
01
wc cr=+
Since
(2)
()
0( )
i
o
wb atrr
watr
==
==
Substituting Eq.(1) into Eq.(2);
10
o
br
b
cc
hh
=− =
Then
01
o
i
r
Ar
ccr
dA wdr dr
rr r
+
==
∫∫
w
O
dr
b
ri
r
ο
h
r
Inserting c and into this, after integrating and rearranging,
1 0
c
we have
(ln 1)
oo
i
rr
dA b
rhr
=−
∫
Therefore
12
ln 1
oo
i
Ah
RdA r r
rhr
==
−
∫
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