Building Design and Construction Handbook - Merritt - Ventech!

7.52 SECTION SEVEN
Constructions that inhibit sidesway in building frames include substantial masonry
walls, interior shear walls; braced towers and shafts; floors and roofs providing
diaphragm action—that is, stiff enough to brace the columns to shear walls or
bracing systems; frames designed primarily to resist large side loadings or to limit
horizontal deflection; and diagonal X bracing in the planes of the frames. Compression
members in trusses are considered to be restrained against translation at
connections. Generally, for all these constructions, K may be taken as unity, but a
value less than one is permitted if proven by analysis.
When resistance to sidesway depends solely on the stiffness of the frames; for
example, in tier buildings with light curtain walls or with wide column spacing,
and with no diagonal bracing systems or shear walls, the designer may use any of
several proposed rational methods for determining K. A quick estimate, however,
can be made by using the alignment chart in an AISC ‘‘Manual of Steel Construction.’’
The effective length Kl of compression members, in such cases, should not
be less than the actual unbraced length.
7.19.2 ASD of Compression Members
The allowable compressive stress on the gross section of axially loaded members
is given by formulas determined by the effective slenderness ratios Kl/r of the
members. A critical value, designated C c, occurs at the slenderness ratio corresponding
to the maximum stress for elastic buckling failure (Table 7.12). This is
illustrated in Fig. 7.28. An important fact to note: when Kl/r exceeds C c � 126.1,
the allowable compressive stress is the same for A36 and all higher-strength steels.
C � �2�;s2E/F (7.4)
c y
where E � modulus of elasticity of the steel � 29,000 ksi and F y � specified
minimum yield stress, ksi.
When Kl/r for any unbraced segments is less than C c, the allowable compressive
stress, ksi is
2 2
[1 � (Kl/r) /2C c]Fy Fa � (7.5)
FS
where FS is the safety factor, which varies from 1.67 when Kl/r � 0 to 1.92 when
Kl/r � C c.
TABLE 7.12 Slenderness Ratio at
Maximum Stress for Elastic Buckling
Failure
F y, ksi C c F y, ksi C c
36.0 126.1 60.0 97.7
42.0 166.7 65.0 93.8
45.0 112.8 90.0 79.8
50.0 107.0 100.0 75.7
55.0 102.0