________________________________________________________________________
PROBLEM (11.41) A structural steel column with pinned ends has a cross-sectional area of
width b = 3 in. by depth h = 4 in. Determine the shortest length Lmin that the column may have
using Euler’s formula.
Given: σy = 36 ksi, E = 29 x 106 psi (from Table B.4)
SOLUTION
The smallest moment of inertia is
33
min 11
(4)(3) 9 .
12 12 4
I
hb in== =
and
min
min 90.866 .
34
I
ri
A
== =
×n
r
Euler’s formula (11.9) with yc
σ
σ
=
:
22 3
2
min (29 10 )
( ) 7,905.519
36
cr
LE
r
ππ
σ
×
−= = , min 89.2
Lr=
Hence,
min (89.2)(0.866) 77.2 .Li==n
Comment: If this column is 77.2 or more in length, it will be buckle.
Excerpts from this work may be reproduced by instructors for distribution on a not-for-profit basis for testing or
instructional purposes only to students enrolled in courses for which the textbook has been adopted. Any other
reproduction or translation of this work beyond that permitted by Sections 107 or 108 of the 1976 United States
Copyright Act without the permission of the copyright owner is unlawful.
1
/
1
100%