sm11 46

________________________________________________________________________
PROBLEM (11.46) Redo Prob. 11.45 for the case in which the tube fixed at its base and
free at its top, and has a factor of safety of ns = 2 (Fig. P11.43).
SOLUTION
Refer to Solution of Prob. 11.45. Here
(See Fig. 11.3a) 22(2.5)5
e
LL== =m
3
510 217 108.5
23.05 2
ee
LL
rr
×
== =
(a) Equation (1) yields
3
max 3
10 10
(9.794) 1 (2.141)sec 108.5 (1021)(210 10 )
σ
⎡⎤
⎛⎞
×
⎢⎥
=+ ⎜⎟
⎜⎟
×
⎢⎥
⎝⎠
⎣⎦
38.2 kN=
(b) Equation (2) gives
616 3
250(10 ) 1 (2.141)sec 108.5
1021(10 ) (1021)(210 10 )
yy
PP
−
⎡
⎤
⎛⎞
⎢
⎥
=+
⎜⎟
⎜⎟
×
⎢
⎥
⎝⎠
⎣
⎦
Solving numerically, 29.94P=. Equation (11.22):
y
29.94 14.79
2
y
all s
P
Pk
n
== = N
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