Page 301 - Civil Engineering Formulas

BUILDING AND STRUCTURES FORMULAS 235

Pmax (4) Pmax (4)

B X B
t
h
h
X
t
Pmax (4) Pmax (4)
t = web thickness (each web sheet), mm
h = clear distance between flanges, mm

B
2
P max(4) 20,000t 11.1 2.41 (9.89)
B t
Values of P max (4) apply only where the distance x is greater than 1.5h. Other-
wise use P max (3).
The effective length of bearing B for substitution in the above formulas
should not be taken as greater than h.
The column-design formulas recommended by American Iron and Steel
Institute specifications for light-gage cold-formed sections consist of a family
of Johnson parabolas all tangent to a single Euler curve. It can be shown that an
infinite number of such parabolas can be drawn, all having the form

P f y f y 2 2
L
(9.90)
A C D r
and all tangent to a single Euler curve represented by
P D/4C 2
(9.91)
A (L/r) 2
In Eqs. (9.90) and (9.91), C and D are constants that depend on the safety factor
eccentricity allowance, and end fixity, and f is the yield point of the material.
y
Observe that f does not appear in Eq. (9.91). The point of tangency between the
y
equations is always at a P/A value equal to half the initial value (f /2C).
y
If a form factor or bucking factor Q is introduced such that
f cr
Q (9.92)
f y
where f represents the reduced strength of the section due to the presence of wide
cr
thin elements that buckle locally at stresses below the yield point of the material,
then it is a simple matter to transform Eq. (9.90) into a consistent set of column
curves applicable to any value of Q, all tangent to a single curve of Eq. (9.91):
P f y f y 2 2
L
Q Q 2 (9.93)
A C D r