CIVIL ENGINEERING FORMULAS

208 CHAPTER NINE

ALLOWABLE-STRESS DESIGN FOR
BUILDING COLUMNS

The AISC specification for allowable-stress design(ASD) for buildings pro-
vides two formulas for computing allowable compressive stress Fa, ksi
(MPa), for main members. The formula to use depends on the relationship
of the largest effective slenderness ratio Kl/rof the cross section of any
unbraced segment to a factor Ccdefined by the following equation and
Table 9.1:

(9.4)

where Emodulus of elasticity of steel
29,000 ksi (128.99 GPa)
Fyyield stress of steel, ksi (MPa)

WhenKl/ris less than Cc,

(9.5)

where F.S.safety factor.

WhenKl/rexceedsCc,

(9.6)

The effective-length factor K, equal to the ratio of effective-column length
to actual unbraced length, may be greater or less than 1.0. Theoretical Kvalues
for six idealized conditions, in which joint rotation and translation are either
fully realized or nonexistent, are tabulated in Fig. 9.1.

Fa

12

2 E

23(Kl/r)^2



150,000

(Kl/r)^2

5

3



3(Kl/r)

8 Cc



(Kl/r)^3

8 C^3 c

Fa

^1 

(Kl/r)^2

2 C^2 c 

Fy

F.S.

Cc

B

2

2 E

Fy



756.6

Fy

TABLE 9.1 Values of Cc

Fy Cc

36 126.1

50 107.0