CIVIL ENGINEERING FORMULAS

BUILDING AND STRUCTURES FORMULAS 235

(9.89)

Values of Pmax (4) apply only where the distance xis greater than 1.5h.Other-
wise use Pmax (3).
The effective length of bearing Bfor 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

(9.90)

and all tangent to a single Euler curve represented by

(9.91)

In Eqs. (9.90) and (9.91), CandDare constants that depend on the safety factor
eccentricity allowance, and end fixity, and fyis the yield point of the material.
Observe that fydoes not appear in Eq. (9.91). The point of tangency between the
equations is always at a P/Avalue equal to half the initial value (fy/2C).
If a form factor or bucking factor Qis introduced such that

(9.92)

wherefcrrepresents the reduced strength of the section due to the presence of wide
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):

(9.93)

P

A



fy

C

Q

fy^2

D

Q^2 

L

r

2

Q

fcr

fy

P

A



D/4C^2

(L/r)^2

P

A



fy

C



fy^2

D

L

r

2

P max(4)20,000t^2 11.12.41

B

B

t

X

X

t

h

h

t

B B

Pmax (4) Pmax (4)

Pmax (4) Pmax (4)

t = web thickness (each web sheet), mm

h = clear distance between flanges, mm