sm7 44

________________________________________________________________________
PROBLEM (7.44) Calculate the ratio of the largest vertical shear force V1 to the maximum vertical
shear force V2 that can be carried by the I beam for the cases of web positioned vertical and horizontal
as shown in Figs. P7.44a and P7.44 b, respectively.
Assumption: The vertical shear force V2 acts through a point (S) so that only bending of the beam
occurs as is discussed in Sec. 7.16.
SOLUTION
Area properties, from solution of Prob. 7.18, are:
77.5
y
mm
=
46
1022.41 mIz− ×=
y
Also
3
20 40 (120)
12
y
I
+
=
3
120 (20)
12
+
46
1072.8 mm×=
We have
max z
yz
I
b
VQ
τ
=, where for lower half of section:
33
101.29025.41205.825.9220120 mmQz×=××+××=
So,
63
max max
6
(41.22 10 )(20 10 ) 0.00284
290.01 10
y
V
τ
τ
−−
−
××
==
×
Similarly,
max y
zy
I
b
VQ
τ
=, where for the upper shaded area:
33
1070355040 mmQy×=××=
Thus,
63
max max
6
(8.7210)(4010) 0.00498
70 10
z
V
τ
τ
−−
−
××
==
×
Hence,
max
max
0.00284 0.57
0.00498
y
z
V
V
τ
τ
==
20 mm
20 mm
z
C
40 mm
20 50 mm
120 mm
120 m
m
102.5 mm
y
=77.5 m
m
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