Page 303 - Civil Engineering Formulas

BUILDING AND STRUCTURES FORMULAS 237

Members subject to both axial compression and bending stresses shall be pro-
portioned to meet the requirements of both of the following formulas, as applicable:

f a C m f b
1 (9.96)
F a (1 f a /F c )F b
and at braced points only
f a f b
1 (9.97)
0.515Qf y F b
where F maximum axial unit stress in compression permitted by this specifi-
a
cation where axial stress only exists
F maximum bending unit stress in compression permitted by this spec-
b
ification where bending stress only exists
149,000,000
F e (9.98)
(l/r b ) 2
f axial unit stress, axial load divided by full cross-sectional area of
a
member P/A
f bending unit stress, bending moment divided by section modulus of
b
member M/S, noting that for members having stiffened compression
elements, section modulus shall be based on effective design widths
of such elements
l actual unbraced length in plane of bending
r radius of gyration about axis of bending
b
C 0.85, except as follows:
m
1. When f /F is equal to or less than 0.15, the member selected shall
a a
is equal to or less than unity.
meet the limitation that f a /F a f b /F b
2. For restrained compression members in frames braced against joint
translation but not subject to transverse loading between their sup-
ports in the plane of loading, C may be taken as 0.6 0.4 M /M ,
m 1 2
where M /M is the ratio of smaller to larger moments at the ends of
1 2
the critical unbraced length of the member. M /M is positive when
1 2
the unbraced length is bent in single curvature, negative when it is
bent in reverse curvature. (C should not be taken at less than 0.4.)
m
3. For restrained compression members in frames braced against joint
translation in the plane of loading and subject to transverse loading
between their supports (joints) in the plane of loading, a value of C
m
may be taken as 0.85 or may be determined by rational analysis.
Braced Wall Studs A fairly common application of cold-formed shapes—
and one that requires special treatment—is as load-bearing wall studs in small
light-occupancy buildings. Cold-formed steel studs are usually I, channel, or
zee sections, to both flanges of which collateral materials are fastened. The
American Iron and Steel Institute Specification for the Design of Light-gage Cold-
formed Steel Structural Members permits the strength of studs to be computed
on the assumption that they are laterally supported in the plane of the wall.