sm11 44

________________________________________________________________________
PROBLEM (11.44) An aluminum alloy 2014-T6 pipe of outside diameter do , inner
diameter di, and length L, both ends pinned, carries a compressive load P with eccentricity e
(Fig. P11.43). What is the maximum stress in the pipe?
Given: do = 3 in., di = 2.9 in., L = 35 in., e = 0.2 in., P = 1.5 kips
E = 10.6 x 106 ksi, σy = 60 ksi (from Table B.4)
SOLUTION
22 2 2
( ) (3 2.9 ) 0.463 .
44
oi
Add in
4
π
π
=−=−=
44 4 4
( ) (3 2.9 ) 0.504 .
64 64
oi 4
I
dd in
π
π
=−=−= , 0.504 1.043 .
0.463
I
ri n
A
== =
ksi
(from Table B.4)
6
10.6 10 60
y
Epsi σ =× =
We have
1.5 35
3.24 32.14
0.463 1.089
PL
ksi
Ar
== ==
22
(0.2)(1.5) 0.276
(1.043)
ec
r==
Equation (11.15b) is thus
max 2
1sec
2
Pec LP
Ar rAE
σ
⎡⎤
⎛⎞
=+
⎢⎥
⎜⎟
⎜⎟
⎢⎥
⎝⎠
⎣⎦
3
3.5
(3.24) 1 0.276sec 16.07 (0.463)(10.6 10 )
⎡⎤
⎛⎞
=+
⎢⎥
⎜⎟
⎜⎟
×
⎢⎥
⎝⎠
⎣⎦
4.22 ksi=
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