sm7 84

________________________________________________________________________
PROBLEM (*7.84) Design a simple rectangular beam of constant strength and width b,
acted upon a downward triangular loading as depicted in Fig. P7.84.
Assumption: Only normal stresses due to bending need be considered; the allowable stress is
all
σ
.
*SOLUTION
Referring to Fig. P7.84, we write
0
1
4
AB
R
RwL== , 2
0
1
024
CC
wL==VM
The magnitude of moment at x :
23
00
0
11
()()()() (8
24 2 2 3 24
wx w
x3
)
M
wL x L x
LL
=− =−
33
202
(8
64
all wL x
bh M
SSLbh
σ
−
===
)
or
12
33
0(8)
4all
wL x
hbL
σ
⎡⎤
−
=⎢⎥
⎣⎦
12
23
03
8
(1 )
4all
wL x
bL
σ
⎡
⎤
=−
⎢
⎥
⎣
⎦
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