sm7 86

________________________________________________________________________
PROBLEM (7.86) Design a cantilever beam of uniform strength and width b subjected to to
a linearly varying loading of intensity zero at the free end and w0 at the fixed end (Fig. P7.86).
Assumption: Only the normal stresses owing to the bending need be considered; the allowable
stress is all
σ
.
SOLUTION
3
0
1
6w
M
x
L
=
6
2
0Lw
x
/3
L
2
0Lw
y
2
0
2
1x
L
w
w0
x
1
Equation (7.31), at a distance x is
3
0
21
6
6all
w
x
bh L
σ
= (1)
At
,L
x
=
3
0
2
0
1
6
6all
wL
bh L
σ
= (2)
Divide Eq. (1) by Eq. (2):
23
23
0
hx
hL
=
or
32
0()
x
hh
L
=
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