Page 165 - Civil Engineering Formulas

102 CHAPTER THREE

When tension controls,

P u 0.85bhf c e 0.5 2 0.67 D s t m e 0.5 (3.47)
B h h h

When compression governs,
A st f y A g f c
P u 3e/D s 1 12he/(h 0.67D s ) 1.18 (3.48)
2

Slender Columns
When the slenderness of a column has to be taken into account, the eccentricity
should be determined from e M c /P u , where M c is the magnified moment.

DESIGN OF AXIALLY LOADED STEEL COLUMNS*

Design of columns that are subjected to compression applied through the cen-
troidal axis (axial compression) is based on the assumption of uniform stress
over the gross area. This concept is applicable to both load and resistance factor
design (LRFD) and allowable stress design (ASD).
Design of an axially loaded compression member or column for both LRFD
and ASD utilizes the concept of effective column length KL. The buckling coef-
ficient K is the ratio of the effective column length to the unbraced length L.
Values of K depend on the support conditions of the column to be designed.
The AISC specifications for LRFD and ASD indicate the K should be taken as
unity for columns in braced frames unless analysis indicates that a smaller
value is justified. Analysis is required for determination of K for unbraced
frames, but K should not be less than unity. Design values for K recommended
by the Structural Stability Research Council for use with six idealized condi-
tions of rotation and translation at column supports are illustrated in Fig. 9.1.
The axially compression strength of a column depends on its stiffness meas-
ured by the slenderness ratio KL/r, where r is the radius of gyration about the
plane of buckling. For serviceability considerations, AISC recommends that
KL/r not exceed 200.
LRFD strength for a compression member wf;P n (kips) is given by

(3.49)
P n 0.85A g F cr
where LRFD resistance factor, less than unity
P n LFRD design strength (kips) of member (also called “maximum load”
for columns, kips):

*Brockenbrough and Merritt—Structural Steel Designer’s Handbook, McGraw-Hill.