236 CHAPTER NINE
(When the effective-width treatment of stiffened elements is used, Qcan be
defined as the ratio between effective area and total area of the cross section,
andAin the quantity P/Acan mean total area of section.)
Sincefcrcan never be greater than fy, the value of Qas a form factor or
buckling factor can never exceed 1.0. For any section that does not contain any
element with a flat-width ratio exceeding that for full effectiveness (w/t 10
for unstiffened elements and for stiffened elements), Q1.0 and
disappears from the equation.
Unit Stress for Axially Loaded Cold-formed Members For cold-formed,
axially loaded compression members of Grade C steel, the allowable unit stress
P/Ashall be
ForL/rless than
(9.94)
ForL/rgreater than
(9.95)
(AISI) Specification for the Design of Light Gage Steel Structural Members)
wherePtotal allowable load, lb
Afull, unreduced cross-sectional area of member, sq in (mm^2 )
Lunsupported length of member, in (mm)
rradius of gyration of full, unreduced cross section, in (mm)
Qa factor determined as follows:
a. For members composed entirely of stiffened elements, Qis the
ratio between the effective design area, as determined from the
effective-design widths of such elements, and the full or gross
area of the cross section. The effective design area used in deter-
miningQis to be based on the basic design stress allowed in ten-
sion and bending—20,000 psi for Grade C steel.
b. For members composed entirely of unstiffened elements, Qis the
ratio between the allowable compression stress for the weakest
element of the cross section (the element having the largest flat-
width ratio) and the basic design stress.
c.For members composed of both stiffened and unstiffened ele-
ments, the factor Qis to be the product of a stress factor Q, com-
puted as outlined in babove and an area factor Qacomputed as
outlined in aabove. However, the stress on which Qais to be based
shall be that value of the unit stress fcused in computing Qs; and
the effective area to be used in computing Qashall include the full
area of all unstiffened elements.
It is recommended that L/rnot exceed 200, except that during
construction a value of 300 may be allowed.
P
A
149,000,000
(L/r)^2132/ 2 Q,
P
A
17,0000.485Q^2
L
r2132/ 2 Q,
4,020/ 2 f