sm7 42

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PROBLEM (7.42) A hollow square steel box beam with the cross section of uniform thickness t
shown in Fig. P7.42 is acted upon a shear force V. Calculate:
(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: a = 8 in., t = ½ in., V = 20 kips
SOLUTION
y
t
z
a
A
A
t
C
a
44
1(2)
12 12
za
I
at=− −
444
81
(7) 141.25 .
12 12 in=− =
(a) Maximum shear stress (at N.A.). 1
()()( 2)( )( )()
24 2 2 2
aa a a
Qa a t t t=−−−−
1
(8)(4)(2) (7)(3.5)(3.5)( )
2
=−
3
21.125 .in=
3
max 20(10 )(21.125) 2.991
1
(141.25)(2 )
2
VQ ksi
Ib
τ == =
×
(b) Minimum shear stress(at section A-A).
3
1
( ) (8)( )(3.75) 15 .
22 2
at
Qat in=−= =
3
max 20(10 )(15) 2.12
1
(141.25)(2 )
2
VQ ksi
Ib
τ == =
×
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