sm7 138

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PROBLEM (*7.138 ) A thin-walled half tube is loaded as shown in Pig. P7.138.
(a) Demonstrate that the location of shear center S is given by e
≈
0.27r.
(b) Calculate the shear stress at D for r = 2 in., t = 1/8 in., and Vy = 100 lb.
*SOLUTION
z
QydA 2
0cos sinrtrdrt
θ
=∫
θ
θθ =⋅⋅=
∫
2
3
sin 2 sin
(2)
yz y y
z
VQ Vrt V
I
trtt rt
θ
θ
τππ
== = (1)
(a) 0
2sin 4
0: ( ) ( )
y
oy
Vr
T V e r rdA r rd t V
rt
π
y
θ
τθ
ππ
=+== ⋅=
∑∫
From which
4
(1)0.27
er Q.E.D. r
π
=−=
(b) At D, Eq. (1) becomes
max
2sin90 2
o
yy
VV
rt rt
τ
π
π
==
Substituting the given data:
max 2(100) 255
(2)(0.125)
p
si τπ ==
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