sm7 17

________________________________________________________________________
PROBLEM (7.17) A rectangular beam of width b and depth h is to be cut from a circular
bar of diameter D, as shown in Fig. P7.17. Determine the ratio of h/b so that the beam will
carry a maximum moment M in pure bending.
SOLUTION
2
6
all
M
cM
I
bh
σ ==
or 2
1
6all
M
bh σ = (1)
We have
2222
()bh b D b bD b
y
D
C
D
h
z
3
=
−= −
b
In order bh be maximum:
2
223 2 2 22 2 2 2
() ()3 3 2 dbh d bD b D b b h b h b
db db
=−=−=+−=−
0=
or 2hb =
Hence, Eq. (1):
2
max 1(2
)
6all bb
σ =× 3
1
3all
b
σ
=
M
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