________________________________________________________________________
PROBLEM (11.33) A 6-ft-long column of 4-in. by 2-in. rectangular cross section fits
between a rigid ceiling and a rigid floor. Calculate the change in temperature that-will cause the
column to buckle.
Given: E = 30 x 106 psi, α = 6.7 x 10-6 /°F, σy = 34 ksi
Assumption: The ends are taken to be rounded.
SOLUTION
Assume that
ycr
σ
σ
=. So
26
3
(30 10 )
( ) 93.3
34 10
c
L
r
π
×
==
×, 34
min 4(2) 12 2.667 .
I
in==
,
2
248 .Ai=×= nmin 0.578 .rI A in==
and
6 12 0.578 124.6Lr
=
×=
Thus,
22
22
() ,
() ()
E
ET T
Lr Lr
ππ
σα α
=Δ= Δ=
Substituting the given data:
2
62
6.7 10 (124.6)
T
π
−
Δ= ×94.9oF=
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%