Page 302 - Civil Engineering Formulas

236 CHAPTER NINE

(When the effective-width treatment of stiffened elements is used, Q can be
defined as the ratio between effective area and total area of the cross section,
and A in the quantity P/A can mean total area of section.)
Since f can never be greater than f , the value of Q as a form factor or
cr
y
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 4,020/ 2 f for stiffened elements), Q 1.0 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/A shall be
For L/r less than 132/ 2 Q,
L
P 2
17,000 0.485Q 2 (9.94)
A r
For L/r greater than 132/ 2 Q,
P 149,000,000
(9.95)
A (L/r) 2
(AISI) Specification for the Design of Light Gage Steel Structural Members)
where P total allowable load, lb
2
A full, unreduced cross-sectional area of member, sq in (mm )
L unsupported length of member, in (mm)
r radius of gyration of full, unreduced cross section, in (mm)
Q a factor determined as follows:
a. For members composed entirely of stiffened elements, Q is 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-
mining Q is 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, Q is 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 Q is to be the product of a stress factor Q, com-
puted as outlined in b above and an area factor Q computed as
a
outlined in a above. However, the stress on which Q is to be based
a
shall be that value of the unit stress f used in computing Q ; and
c s
the effective area to be used in computing Q shall include the full
a
area of all unstiffened elements.
It is recommended that L/r not exceed 200, except that during
construction a value of 300 may be allowed.