Timothy A. Philpot - Mechanics of materials _ an integrated learning system-John Wiley (2017)

698
COLuMNS
For short and intermediate-length columns, the AISC formula for the critical compression
stress is
σ
cr
⎡ σ Y ⎤
kL E
= ⎢0.658 σ e ⎥σY
when ≤ 4.71
⎣⎢
⎦⎥
r σ
(16.22)
Y
where
σ
e
2
π E
=
⎛ KL
⎝ ⎜ ⎞
⎟
r ⎠
2
(16.23)
is the elastic buckling stress (i.e., Euler stress).
For long columns with effective-slenderness ratios greater than 4.71 E/ σ Y,
the
AISC formula simply multiplies the Euler buckling stress by a factor of 0.877 to account
for initial column crookedness. This reduction accounts for the fact that no real
column is perfectly straight. The AISC formula for the critical compression stress of
long columns is
σcr
KL E
= 0.877σe
when > 4.71
(16.24)
r σ
Y
The AISC recommends that the effective-slenderness ratios of columns not exceed 200.
The allowable compression stress for either short to intermediate-length or long columns
is equal to the critical compression stress [given by either Equation (16.22) or (16.24)]
divided by a factor of safety of 1.67:
σ
allow
σ cr
= (16.25)
1.67
Aluminum-Alloy columns
The Aluminum Association publishes specifications for the design of aluminum-alloy
structures. Euler’s formula is the basis of the design equation for long columns, and straight
lines are prescribed for short and intermediate-length columns. Design formulas are specified
for each particular aluminum alloy and temper. 2 One of the most common alloys used
in structural applications is 6061-T6, and the column design formulas for this alloy are
given next. Each of these design formulas includes an appropriate safety factor.
For short columns with effective-slenderness ratios less than or equal to 9.5,
σ allow = 19 ksi
KL
= 131 MPa where ≤ 9.5
r
(16.26)
2
Specifications for Aluminum Structures, Aluminum Association, Inc., Washington, DC, 1986.