sm9 65

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PROBLEM (9.65) A metal beam ABC with a wide flange cross section is simply supported at
A and B and has an overhang AB as shown in Fig. P9.65. The beam supports a concentrated load
P at its free end . Determine the value of the maximum permissible load P based on an
allowable shear stress of all
τ
.
Given: z
I
= 5.464 in.4, A = 1.911 in.2 , all
τ
= 14 ksi
SOLUTION
Reactions, as obtained from equations of equilibrium, are indicated in Fig. (a).
We observe that the critical point is at D of a section just to the left of support B:
VP= and (4 12) 48
M
PP=× =
Stress at point D:
3
2(10 ) 48 (2 0.23)
1.911 5.464
xP
σ
−
=+
1046.6 15.549P=+
0.23
[(3 0.23)(2 )]
2
5.464(0.15)
xy
P
VQ
Ib
τ
×−
=− =−
1.5869P=−
Therefore, with
max all
τ
τ =; we have
22
()
2x
all xy
σ
τ
τ =+
or
32 2 2
1
(14 10 ) (1,095,376.6 32,547.2 241.77 ) ( 1.5869 )
4PP P×= + + +−
from which
2129,2349 3,108,674 0PP+−=
Solving this quadratic equation:
3.399 3.4 .
all
Plbkips==
D
x
y
x
y
τ
x
σ
F
i
g
ure
(
a
)
y
2 kips
B
R
=3P/2
A
P
Cy
R
B
Cx
R
C