Page 166 - Civil Engineering Formulas

COLUMN FORMULAS 103

with 0.85. For c 1.5

F cr 0.658 c 2 F y (3.50)

for c 1.5
0.877
F cr F y (3.51)
2
l c
where c (KL/r
) F y /E
F y minimum specified yield stress of steel, ksi
A g gross area of member, in 2
E elastic modulus of the steel 29,000 ksi
For ASD, the allowable compression stress depends on whether buckling
will be elastic or inelastic, as indicated by the slenderness ratio

2
C c 2 2
E F y (3.52)
When KL/r < C c , the allowable compression stress F a (kips) on the gross sec-
tion should be computed from

2 2
1 (KL r) 2C c
F a 5 3 3 F y (3.53)
3 3(KL r) 8C c (KL r) 8C c
When KL/r > C c , the allowable compression stress is

2
12
E
F a (3.54)
23(KL r) 2
Table of allowable loads for columns are contained in the AISC “Manual of
Steel Construction” for ASD and for LRFD.

Columns Supporting Wind Turbines
With increasing emphasis on renewable energy throughout the world, wind tur-
bines are finding wider use. Today’s wind turbines are growing in generating
capacity, with 5-mW the norm per unit, and 20-mW a near-time goal of turbine
designers.
As the electrical capacity of a wind turbine increases, so too does the direct
load of the nacelle on the supporting column and the wind loads on propeller
blades. Both loads must be considered when designing the support column and
the foundation for the column.