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:

(9.96)

and at braced points only

(9.97)

whereFamaximum axial unit stress in compression permitted by this specifi-
cation where axial stress only exists
Fbmaximum bending unit stress in compression permitted by this spec-
ification where bending stress only exists

(9.98)

faaxial unit stress, axial load divided by full cross-sectional area of

memberP/A

fbbending unit stress, bending moment divided by section modulus of

memberM/S, noting that for members having stiffened compression

elements, section modulus shall be based on effective design widths

of such elements

lactual unbraced length in plane of bending

rbradius of gyration about axis of bending

Cm0.85, except as follows:

1.Whenfa/Fais equal to or less than 0.15, the member selected shall

meet the limitation that is equal to or less than unity.

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, Cmmay be taken as 0.6 0.4M 1 /M 2 ,

whereM 1 /M 2 is the ratio of smaller to larger moments at the ends of

the critical unbraced length of the member. M 1 /M 2 is positive when

the unbraced length is bent in single curvature, negative when it is

bent in reverse curvature. (Cmshould not be taken at less than 0.4.)

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 Cm

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.

fa/Fafb/Fb

Fe

149,000,000

(l/rb)^2

fa

0.515Qfy



fb

Fb

 1

fa

Fa



Cmfb

(1fa/Fc)Fb

 1