Page 274 - 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 F , ksi
a
(MPa), for main members. The formula to use depends on the relationship
of the largest effective slenderness ratio Kl/r of the cross section of any
unbraced segment to a factor C defined by the following equation and
c
Table 9.1:
2
2
E 756.6
C c (9.4)
B F y F y
where E modulus of elasticity of steel
29,000 ksi (128.99 GPa)
F yield stress of steel, ksi (MPa)
y
When Kl/r is less than C ,
c
2
1 (Kl/r) 2 F y
F a 2C c (9.5)
F.S.

5 3(Kl/r) (Kl/r) 3
where F.S. safety factor .
3 8C c 8C c 3
When Kl/r exceeds C , c

2
12
E 150,000
F a (9.6)
23(Kl/r) 2 (Kl/r) 2
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 K values
for six idealized conditions, in which joint rotation and translation are either
fully realized or nonexistent, are tabulated in Fig. 9.1.

TABLE 9.1 Values of C c
F y C c
36 126.1
50 107.0