________________________________________________________________________
PROBLEM (11.17) A round steel column of length L is fixed at its base and pinned at its
top end supports a maximum permissible load P (Fig. P11.17). Calculate the diameter d of the
member based on a safety factor of ns with respect to buckling.
Given: L = 50 in., P = 4.5 kips, ns = 3, E = 30 x 106 psi. σy = 55 ksi
SOLUTION
, 3(4.5) 13.5
cr s
PnP kN== = 0.7 0.7(50) 35 .
e
LL in
=
==
2
4
64 4 4
dd
IdA r
ππ
===
Equation (11.5) gives
232
4336
64 64(13.5 10 )(35) , 1.033 .
(30 10 )
cr e
PL
dd
E
ππ
×
== =
×in
Hence
35 135.5
1.033 4
e
L
r==
Equation (11.10):
3
30 10
( ) 73.4 135.5
55
ecy
LE
r
ππ
σ
×
== =<
Euler formula applies, Hence
1.033 .di=n
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