sm7 137

________________________________________________________________________
PROBLEM (7.137) Verify that the distance e that locates the shear center, point S, of a thin-walled
member having I an cross as section shown in Fig. P7.137 may be expressed in the form:
3
11
33
11 22
htb
eht ht =+ (P7.137)
Calculate the value of e for h1 = h2 = 120 mm, t1 = 20 mm, t2 = 40 mm, and b = 150 mm.
SOLUTION
(See: Table B.6)
At the neutral axis(z):
2
1111
11
11
()
248
yy y
zz z
VQ V V
ht h h
1
I
tIt I
τ == =
In a similar manner, we have
2
2
28
y
z
Vh
I
τ =
We write
12 1
0: 0:
yy By
FVFF M Ve==+ = =
∑∑
Fb
1
12
Fb
e (1)
FF
=+
And 3
1112 2
2
312
y
z
V
2
t ht
I
τ ==
Fh (2)
Likewise
3
2
12y
Z
V
F
I
=22
ht (3)
Substitute Eqs. (2) & (3) into Eq. (1):
3
11
33
11 22
ht
e Q.E.D. b
ht ht
=+
Introducing the given data, we obtain
3
33
(120) (20)(150) 50
(120) (20) (120) (40)
em m==
+
y
F
2
S
t3e
t1
F
1
h2
h1
b
1
2
111
3
Ah
τ
τ
=
Vyt2
2
2
222
3
A
h
τ
z
=
τ
Excerpts from this work may be reproduced by instructors for distribution on a not-for-profit basis for testing or
instructional purposes only to students enrolled in courses for which the textbook has been adopted. Any other
reproduction or translation of this work beyond that permitted by Sections 107 or 108 of the 1976 United States
Copyright Act without the permission of the copyright owner is unlawful.