sm7 98

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PROBLEM (*7.98) A cantilever beam of length L = 4 ft is subjected to a uniformly
distributed load of intensity w = 3 kip/ft. The cross section of the beam is a hollow box with
wood flanges and aluminum webs, as shown in Fig. P7.98. Determine the required thickness t
of the aluminum plates
Given: Ew = 1.6 x 106 psi, ( w
σ
)all = 1.2 ksi, Ea = 10 x 106 psi, ( a
σ
)all = 20 ksi
*SOLUTION
10 6.25
1.6
a
w
E
nE ===
33
11
{[4 (6.25 2 )](10) } [4(4) ]
12 12
t
It=+× −
3 in.
y
Aluminum
t4 in.
3 in.
Wood
10 in.
z
4
312 1041.7 .tin=+
22
11
(3)(4)
22
MwL==
24 . 288 .kip in kip in=⋅= ⋅
So
anMy
I
σ =;
6.25(288)(5)
20 , 0.132 .
312 1041.7 ti t
==
+n
Likewise
288(5)
; 1.2 , 0.85 .
312 1041.7
wMy ti
It
σ == =
+n
n
Stress in wood governs: 0.85 .ti
=
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