sm7 41

PROBLEM (7.41) A hollow aluminum box beam with the rectangular cross section shown in Fig.
P7.41 is subjected to a shear force of V. Determine:
(a) The maximum shear stress max
τ
in the webs of the beam.
(b) The minimum shear stress min
τ
in the webs of the beam.
Given: b = 100 mm, h = 140 mm, t = 10 mm, t1 = 15 mm, V = 200 kN
SOLUTION
33
11
(100)(140) (80)(110)
12 12
I=−
y
a
z
100
15
10
140
15
C10
a
64
14(10 ) mm=
(a) Maximum shear stress (at N.A.):
(100)(70)(35) (80)(55)(27.5)Q=−
33
124(10 ) mm=
36
max 6
200(10 )(124 10 )
14(10 )(0.2)
VQ
Ib
τ
−
−
×
==
8.86
M
Pa=
(b) Minimum shear stress (at section a-a):
33
(100)(15)(70 7.5) 93.75(10 )Qm=−=m
36
min 6
200(10 )(93.75 10 ) 6.7
14(10 )(0.2)
VQ
M
Pa
Ib
τ
−
−
×
== =
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