sm9 79

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PROBLEM (9.79) A thin-walled, closed-ended metal tube having ultimate strengths in
tension u
σ
and compression '
u
σ
, outer and inner diameters D and d, respectively, is subjected
to an internal pressure of p and a torque of T. Determine the factor of safety
s
naccording
to the maximum principal stress theory.
Given: u
σ
= 36 ksi, '
u
σ
= 74 ksi, D = 8 in., d = 7 ½ in , p = 800 psi, T = 400 kip
⋅
in.
SOLUTION
3
2Jrt
π
≈
800(3.875)
0.25
tpr
t
σ ==
12ksi
=
6
2
apr ksi
t
σ ==
3
3
400 10 (4) 19.32
2 (3.75) (0.25)
Tc ksi
J
τπ
×
=− =− =−
22
1,2 612 612
( ) (19.32)
22
σ
+−
=± +
9 19.55=±
12
28.6 10.6ksi ksi
σ
σ ==−
Thus,
136
; 28.6 , 1.3
us
ss
n
nn
σ
σ ===
and
2'74
; 10.6 , 6.98
us
ss
n
nn
σ
σ
−
=−= =
t
σ
a
σ
τ