sm11 35

________________________________________________________________________
PROBLEM (*11.35) A 60-in. long, 2 in.-diameter round column is fixed at its base and
pinned at its top. Calculate the axial buckling load Pcr, if the stress-strain diagram for the material
is approximated as depicted in Fig. P11.35.
*SOLUTION
24 20.5 .
464 44
ddId
AIr
A
ππ
======
in
in (see Fig. 11.3c), 0.7 0.7(60) 42 .
e
LL== = 42 84
0.5
e
L
r
=
=
Equation (11.12):
22 6
22
141.7(10 )
( ) (84)
tt
cr t
e
EE E
Lr
ππ
σ
−
=== (1)
From stress-strain diagram, we have
33
66
15 10 (45 15)10
15 10 5 10
0.001 0.007 0.001
tt
EE psi E ps
×−
== =× = =×
−i
ps
Equation (1) gives
(O.K.)
66
141.7(10 )(15 10 ) 2.13 15
cr ksi ksi
σ
−
=×=<
(not valid)
66
141.7(10 )(5 10 ) 0.709 15
cr ksi ksi
σ
−
=×=<
Thus
2
2.13[ (1) ] 6.69
cr cr
PA ki σπ == =
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