sm7 60

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PROBLEM (7.60) A beam is composed of two 20 x 100-mm steel plates welded together as shown
in Fig. P7.60. Determine:
(a) The largest permissible vertical shear force in the beam.
(b) The corresponding maximum shearing stress in the beam.
Given: An allowable shear force per unit length in each weld of 200 kN/m.
SOLUTION
(a) 25 100 75 100 25 12.5 43.75
100 25 100 25
y
mm
××+××
==
×+ ×
25 mm
y
z C
z
’ 25 mm
100 mm
100 m
m
81.25 mm
y
=43.75 m
m
33
22
25(100) 100(25)
100 25(31.25) 100 25(31.25)
12 12
I=+× ++×
64
7.096 10 mm=×
At welds
Q
33
1013.7825.3125100 mm×=××=
63
6
(78.13 10 ) 2(200 10 )
7.096 10
VQ V
qI
−
−
×
== = ×
×
from which
kNV 33.36=
(b) 3
max 3
2(200 10 ) 16
25(10 )
VQ
M
Pa
Ib
τ
−
×
== =
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