CIVIL ENGINEERING FORMULAS

102 CHAPTER THREE

When tension controls,

(3.47)

When compression governs,

(3.48)

Slender Columns

When the slenderness of a column has to be taken into account, the eccentricity

should be determined from eMc/Pu, where Mcis 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-

ficientKis the ratio of the effective column length to the unbraced length L.

Values of Kdepend on the support conditions of the column to be designed.

The AISC specifications for LRFD and ASD indicate the Kshould be taken as

unity for columns in braced frames unless analysis indicates that a smaller

value is justified. Analysis is required for determination of Kfor unbraced

frames, but Kshould not be less than unity. Design values for Krecommended

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 ris the radius of gyration about the

plane of buckling. For serviceability considerations, AISC recommends that

KL/rnot exceed 200.

LRFD strength for a compression member wf;Pn(kips) is given by

Pn0.85AgFcr (3.49)

whereLRFD resistance factor, less than unity

PnLFRD design strength (kips) of member (also called “maximum load”

for columns, kips):

Pu 

Astfy

3 e/Ds 1



Agfc

12 he/(h0.67Ds)^2 1.18

Pu0.85bhfc

B

e

h

0.5

2

0.67

Ds

h

tm

e

h

0.5



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